.









                                      L  E  N  A

                          Linear Electronic Network Analysis

                                    program manual

                           

                                            

                             Release of 31 January 1994

                    ==============================================

                       Programs, Documentation and Instructions

                                         by

                                 Leonard H. Anderson


                        Copyright (c) 1994, all rights reserved

                    ==============================================



             Linear frequency analysis of electronic circuits having up to
             56 nodes and 204 branches, solving single node voltage or
             impedance at DC or swept-frequency.  Branch types include
             single components, series and parallel passive components in
             one branch, macromodels of transmission line, two-winding
             variable coupling transformer, bipolar hybrid-pi transistors,
             operational amplifier with one internal breakpoint.  Requires
             8086 or later CPU, 142 KB free RAM, any ASCII-character-set
             display and printer.  Numeric co-processor version included.
             
             LENA is a smaller version of LINEA (released August 1993) and
             compatible in every way except repetitive waveform analysis.
        



















                                 TABLE OF CONTENTS

          GENERAL............................................................1
                Consent and Disclaimer.......................................1
                Conventions in this Document.................................2
          DESCRIPTION/OPERATION OF LENA......................................4
                Introduction.................................................4
                Program Command Organization.................................4
             INPUT...........................................................6
                General Keyboard Input in LENA...............................6
                Numeric Value Entry..........................................6
                Y/N Queries..................................................7
                Main Commands (Listing)......................................7
                Output Command Combinations.................................10
                Printer Margins and Pagination..............................10
                ASCII-Character Plot Equivalents............................11
                Output Plot Scale Choices...................................11
                Rotating Twiddle Characters.................................12
                Off-Line Use of Solution Files..............................12
             GENERAL INPUT-OUTPUT SOLUTION COMMANDS.........................13
                Setting Frequency Limits....................................13
                Node of Solution............................................13
                Zero-Decibel Reference Voltage..............................14
                Opening or Closing a Branch.................................14
             CIRCUIT LIST COMMANDS..........................................15
                Starting or Continuing a Circuit List.......................15
                Branch Description and Designation..........................15
                Modifying a Branch Value....................................15
                Deleting a Branch...........................................16
                Inserting a New Branch......................................16
                General Branch-Node Circuit Building in LENA................16
             CIRCUIT COMPONENTS AVAILABLE IN LENA...........................18
                Type Descriptions...........................................18
                Passive Single Branches.....................................18
                Independent Current Sources.................................19
                Current Direction in Sources................................19
                Dependent Current Sources...................................19
                Macromodels.................................................21
                Transformer Macromodel Details..............................22
                Unbalanced Transmission Line Macromodel Details.............22
                Bipolar Transistor Macromodel Details.......................23
                Operational Amplifier Macromodel Details....................24
             ENTERING CIRCUIT COMPONENTS....................................25
                Branch Entry, Single-Value Branches.........................25
                Branch Entry, Double-Value Branches.........................26
                Quicker Entry, Single-Value and Double-Value Branches.......26
                Dependent Current Source Value Entry........................27
                Signal (Generator) Value Entry..............................27
                Macromodel Entries..........................................28
                Required-Listed Macromodel Values...........................28
                Seeing the Full Circuit List................................29
                Circuit List Hardcopy.......................................30
             CIRCUIT LIST EDITING...........................................30
                Special Note on Insert Command..............................30
                Special Notes on All Macromodels............................31
   
     
                                
                                LENA - Contents Page i




             
             DISK DATA FILES................................................31
                Setting the Data Storage Drive:\Directory Path..............31
                Reading/Writing Circuit Files...............................32
                Circuit Creation Dates and Remarks..........................32
                Solution Storage and Retrieval..............................33
                Compatibility with LINEA Data Files.........................33
             SOLUTIONS AND OUTPUT...........................................34
                General Solution Organization of LENA.......................34
                Scale Limit Selection on Plot...............................34
                Two Forms of Impedance Plot.................................34
                Syntax on Solution Type and Form............................35
                Generating Plot Artwork.....................................35
                Single DC Output............................................35
             CONVERTING FROM SCHEMATIC TO LISTING...........................36
                In the Beginning............................................36
                Node Numbers Must be Contiguous.............................36
                Commons, "Ground" and Supply Lines..........................36
                Parasitic Reactance, Resistance.............................37
                Current Through Dependent Branches..........................37
                Voltage Across Dependent Branches...........................38
                Creating "Stiff" Voltage Sources............................38
                Negative Resistance or Reactance............................38
                Operational Amplifier Circuits..............................38
                Field-Effect Transistor Models..............................39
                Bandwidth-Alterable Networks with Transformer Macromodel....39
                Creating "Black Box" Sub-Circuits...........................39
          INSTALLING LENA...................................................40
                LENA Program Set Files......................................40
                Appendices..................................................40
                Registry....................................................41
                CPU Versions and Copies.....................................41
          FIRST-USE LENA PRIMER/TUTORIAL....................................42
                On-Line Help................................................42
                Getting Acquainted With Circuit Listings....................42
                Trying Out a Macromodel.....................................43
                Trying Out Circuit Edit Functions...........................44
                Saving a Circuit File, Trying out DOS Functions.............45

         APPENDICES are contained in text files LE_APX_*.TXT; titles and file
         names are given here for reference.

         Appendix A, LENA Data file structures....................LE_APX_A.TXT

         Appendix B, Example circuit PHASER.......................LE_APX_B.TXT

         Appendix C, LENA Configuration...........................LE_APX_C.TXT

         Appendix D, General history of CAE, LINEA, LENA..........LE_APX_D.TXT

         Appendix E, Comparison of current "BBS" programs.........LE_APX_E.TXT



                       =============================================
                       Important:  See page 40 (Installing LENA) for
                        files and necessary procedures to make your
                              personal working copy of LENA.
                       =============================================


                                LENA - Contents Page ii




.
     GENERAL
     =======

     LENA is a Linear Electronic Network Analysis program set for determining
     the frequency response of an electronic circuit having a maximum of 204
     component (branches) and 56 connection points (nodes).  Components may be
     resistors, capacitors, inductors, series and parallel resistor-reactances,
     reactances with specified Q, stimuli, and dependent current sources.
     Macromodels of transformers, transmission lines, transistors and
     operational amplifiers are included.  Frequency range may be anything from
     DC to Terahertz in linear or logarithmic increments.  Numerical input is
     free-form, scaling letter suffixes from femto to Tera at user's option.
     Analysis solutions may be printed or plotted on any ASCII character-set
     printer.  Circuit lists and solutions may be stored on or retrieved from
     disk.  

     LENA works in any MS-DOS computer, 80x86 CPU or later, having a minimum of
     142 kilobyte contiguous free RAM.  There is no restriction or requirement
     on special display devices, but ANSI.SYS should be present as a DEVICE
     stated in DOS CONFIG.SYS file to see color.  Any ASCII character printer
     may be used for hard copy output.  The Standard version is for any 8086,
     80186, 80286, 80386, or 80486 CPU computer, with or without a numerical
     coprocessor.  The Numerical coprocessor version is for any 80386DX or
     80486DX CPU or those with 80x87 numeric coprocessors.  A Numeric co-    
     processor version can decrease analysis-solution times by a factor of
     three to seven.

     LENA is an analysis _tool_, useful to engineers, technicians, educators,
     and advanced electronics hobbyists alike.  It is not intended as a
     teaching aid but it is very useful in lending insight into frequency-
     domain properties of complex circuits.

     The LENA program set is Shareware.  Anyone may try out the LENA set on
     one computer for a period of 21 days; beyond that time every user is
     obligated to obtain a registration for continued use, including
     commercial, educational, or governmental associations.


     CONSENT AND DISCLAIMER

     LENA, associated LENA files and documentation are the exclusive property
     of Leonard H. Anderson and are copyrighted 1994.  No part of the LENA
     program set (programs plus documentation) may be reproduced, transmitted,
     transcribed, stored in a retrieval system, or translated into any other
     language or computer language in whole or in part, in any form or by any
     means, except for distribution without fee as a program collection or for
     individual single-user archive purposes, without prior written consent of
     the author.

     The author disclaims all warranties as to this software, whether express
     or implied, including, without limitation, any implied warranties of
     merchantability, fitness for a particular purpose, functionality,
     accuracy, data integrity or protection.

     The included CPUID.EXE file was written and assembled by Intel Corporation
     and was declared public domain by Intel Corporation.




                                LENA - Page 1 of 46





     Distribution of the LENA program collection by Bulletin Board Systems is
     encouraged.  Companies and organizations engaged in the collection and
     sale of shareware shall require permission from the author before
     distributing all or part of the LENA program set.


     CONVENTIONS IN THIS DOCUMENT

     This Manual is an explanation of the LENA program operation and
     application.  Users are expected to know the basics of electronics and be
     familiar with electronic terms.  There is very little of esoteric material
     found in comprehensive textbooks for college courses, yet the program
     operates with such esoterica and solves node-branch circuit arrangements
     accurately and quickly for frequency-domain analysis.  The LENA program
     set is useful to working electronics engineers, electronic technicians,
     hobbyists, students and educators alike.  The author is an electronics
     engineer who is also an electronics hobbyist and a writer published in
     BYTE, Ham Radio, ELECTRONICS, and Popular Electronics magazines.

     LENA and its documentation files were written with a prime rule that the
     American Standard Code for Information Interchange (ASCII) characters are
     to be used for ALL input-output.  This makes it possible to display
     everything, regardless of display type, and to be printed on nearly
     every page-size printer used in North America.

     As a result of restrictions to ASCII characters, the few "schematics" in
     here are somewhat lacking in quality and appearance.  Given those
     limitations, diagrams are as simple and understandable as possible.  Also,
     many of the terms common to electronics notations use subscripts and
     superscripts and italics, features missing in ASCII.  To bridge the gap
     between common use and LENA, the following is a short list of not-quite-
     standard notation:

          Hfe = Hybrid forward current gain, common-emitter transistor;
                   common term is all-lower-case italics.
          Hoe = Hybrid output conductance, common-emitter transistor;
                   common term is all-lower-case italics.
          Ic  = Transistor DC collector current, commonly written
                   "I-sub-c."
          Ft  = Transistor cut-off frequency; commonly written
                   "f-sub-t."
          Zo  = Characteristic impedance, as applied to transmission
                   lines; commonly written all-caps as "Z-sub-O."
          Fc  = "Corner frequency" in operational amplifiers, point of
                   frequency intersection between open-loop gain and
                   slope of gain falling at a rate of 20 db per decade.
          Av  = Voltage gain, commonly written "A-sub-V", used in here
                   denoting open-loop gain of operational amplifiers.
          gm  = transconductance, values in mhos.
      <units> = Any number not having a specific value name, as
                opposed to Ohms, Farads, Henries, Hertz, etc.
        <xyz> = General designation for entry, "<xyz>" explained in
                text.

     Main Commands and Branch Type Designations have no rule regarding case. 
     They can be entered as capitals, 'small' letters, or mixed-case...the only
     requirement is that the letters be correct and contiguous as shown.  All-
     capitals notation in text here is an emphasis device.


                                LENA - Page 2 of 46





     Where keyboard inputs are described within text, they are shown
     capitalized within single- or double-quotes.  Single- or double-quotes
     themselves are NOT keyboard entries.

     All documents in the LENA program set are formatted for 8.5 x 11 inch page
     sizes, 85 characters maximum line width, 66 lines maximum per page. 
     Printer Form-Feed control characters are not used.  Documents are limited
     to 75 characters per line and include a 5-character left margin; printing
     is continuous and automatically paginated.

     For better illustration of single-branch components and their formulae,
     the user is directed to Byte Books' publication "Simulation; Programming
     Techniques Volume 2," edited by Blaise W. Liffick, pp 87-97, article
     entitled "Linear Circuit Analysis" by Leonard H. Anderson.  Byte
     Publications is now owned by McGraw-Hill and the "Simulation" book,
     copyrighted 1979, was out of print a few years ago.  Among several texts
     on computer-aided design/engineering, the author has found the following
     to be useful:

       "IBM Electronic Circuit Analysis Program," by Randall W. Jensen and Mark
       D. Lieberman (Prentice-Hall, 1968).  ECAP is the grand-daddy of all CAE
       programs and the frequency-domain modelling techniques are applicable to
       LENA. 

       "Computer Methods for Circuit Analysis and Design," by Jiri Vlach and
       Kishore Singhal (Van Nostrand Reinhold, 1983).  A very detailed overview
       and theory of all CAE programs, although a bit "academic" for working
       circuit designers.

       "Basic Circuit Theory with Digital Computations," by Lawrence P.
       Huelsman (Prentice-Hall, 1972).  Gets down to basics on individual
       components and presents many FORTRAN routines to analyze components and
       networks.



























                                LENA - Page 3 of 46




.
     DESCRIPTION/OPERATION OF LENA
     =============================

     INTRODUCTION

     LENA analyzes the response of an electronic circuit modelled from passive
     and active component branches connected to contiguous nodes.  Complex
     voltage (from specified stimuli) or complex impedance may be measured at
     any node at any frequency for up to 200 frequencies in a sweep, linear or
     logarithmic-increment.  Each circuit may have a maximum of 204 branches
     and 56 nodes.  Branches may be single R, C, or L; series or parallel R-C,
     R-L combinations; L or C with frequency-independent Q; dependent current
     sources specified by transconductance or current gain; independent current
     sources.  Macromodels of an isolated two-winding transformer, unbalanced
     transmission line, bipolar transistor, and operational amplifier are
     included.  Circuit models and analysis-solutions may be stored on disk.
     All values are named and have scaling letters.

     All non-integer numeric entries may use mantissa/decimal-point/fraction
     format, 'E format' common to BASIC or FORTRAN languages, or Scaling Letter
     suffixes ranging from femto to Tera, or any mixture thereof.  Except for
     Scaling Letters and circuit list Remarks, there is NO distinction on entry
     case.  No PC function keys, Control or Alternate key combinations are used
     at any time.  All LENA program commands are done at a Main Command level
     using clear English words or accepted abbreviations.  Circuit model lists
     are just lists of components; all frequency limit settings and output type
     selection is done at the Main Command level.  Circuit lists and solution
     outputs may be directed to a printer port or screen; printer may be any
     ASCII character set type and pagination is automatic for a 66-line
     standard print page.  "Line-printer" style graph equivalents, using ASCII
     characters, may be selected in lieu of tabulated values.  Scale range of
     every graph plot output is selectable to default minimum-maximum or to
     user-specified limits.

     Each circuit model list is editable from Main Command level.  Branches and
     macromodels may be added, inserted, deleted, have values modified, or
     switched open or closed.  Open branches remain in a circuit list but are
     not analyzed.  Circuit lists may be named and have remarks; all are time-
     date-stamped for later reference.  Branch type descriptions may include
     reference designations.  Output is selectable to any circuit node.  Each
     circuit list is checked for errors after entry with extensive description
     to permit easy correction.

     On computer systems with color displays, functions are color-coded.  If
     data entry is required but not entered as part of a Main Command, LENA
     will prompt for the data.  Extensive checking is done to guard against
     impossible solution conditions, error messages explaining the nature of
     error for correction.  LENA should not crash under any condition.


     PROGRAM COMMAND ORGANIZATION

     All LENA program commands are done at a 'Main Command' level, using clear
     English words or accepted abbreviations.   Most commands are one word. 
     Command words may be abbreviated to the first 3 letters, first 2 letters,
     or, sometimes, as a single letter or symbol.  A few commands use two words
     separated by a space.  Where some numeric value should be entered
     following the first command word, a "data word," that numeric value may be


                                LENA - Page 4 of 46





     entered following a space separator as a 'second word.'  If a first
     command word requiring data input is given, but data inadvertently
     omitted, LENA displays a prompt for the type and kind of data.  If that
     data should consist of two or three numerics and only one is entered, LENA
     will re-prompt for all of them.

     Command word entry may be the following, depending on command:

          <WORD>

          <WORD>  <DATAWord>             <-- space separator

          <1stWORD>  <2ndWORD>           <-- space separator


     Data words have contiguous characters, individual data items separated by
     a comma, semicolon, or forward-slant delimiter.
     Data words may be entered as:

          <DATAWord>  (single item)

          <ITEM1>,<ITEM2>  or  <ITEM1>;<ITEM2>  or  <ITEM1>/<ITEM2>
                 ^                    ^                    ^
              (any of the three delimiter characters accepted)

          <ITEM1>,<ITEM2>,<ITEM3>


     Circuit entry is handled much the same as Main Commands.  Component type
     descriptions recognize, in order, first letter, first two letters, or
     first three letters of a component name.  All other letters or numbers,
     including a few symbols, may be added for reference designation.  The Node
     number entries (integer) describe the location of the branch in the
     circuit.  Entering type but no node numbers results in a prompt for node
     numbers.  Numeric value entry for a branch is prompted next, some branches
     requiring two values; omitting one value of a two-value entry will result
     in a "re-entry" prompt.  It is possible to enter everything for a single
     branch on one line.

     Throughout LENA, the organization is aimed at being interactive, clear-
     language, communicating with the user.  There is a minimum of 'programese'
     spoken, no "command line shorthand," no screen cluttering with pull-down
     menus or small screen displays.  The only jargon is that of electronics.

















                                LENA - Page 5 of 46




.
     INPUT
     -----

     GENERAL KEYBOARD INPUT IN LENA

     All keyboard input is free-form in nature.  No PC Function keys or Ctrl-
     <key> or Alt-<key> combinations are used for any purpose.  The program is
     controlled from a 'Main Command' level having the following screen prompt:

               MAIN*>       (printer port inactive) (yellow, black background)
                       -or-
               Main->       (printer port active) (white on blue background)

     Main Command expects an all-alphabetic 'command word' to be entered.  The
     'word' itself may be an abbreviation of, in order, the first three
     letters, the first two letters, or the first letter or a symbol.  Some
     commands may require two words; two words must be separated by at least
     one space. 

     Command words may be entered in all-capitals, all-lower-case, or even
     mixed-case; only the letters themselves matter.  Exception to this overall
     rule occurs only with Scaling Letters or textual input for Circuit List
     Remarks.


     NUMERIC VALUE ENTRY

     Some commands require data as the second word.  A 'data word' in LENA
     consists of alphanumeric data of one to five items.  Each data item is
     separated (delimited) from the following data item by a comma, semicolon,
     or forward-slant ('/').  No entry for an item is considered a space for
     alphabetic data or zero for numeric data.

     ALL numeric data items in LENA have flexible input format.  Each data item
     may have any one or a mixture of any of the following formats:

          *  Mantissa-decimal-point-fraction.

          *  'E-format' style common to BASIC and FORTRAN

          *  Scaling letter suffixes from femto to Tera.

     Scaling letter multipliers are as follows:

          T  =  Tera  =  1E+12                 f  =  femto  =  1E-15
          G  =  Giga  =  1E+9                  p  =  pico   =  1E-12
          M  =  Mega  =  1E+6                  n  =  nano   =  1E-9 
          K  =  Kilo  =  1E+3                  u  =  micro  =  1E-6
          <none>      =  1                     m  =  milli  =  1E-3
                        
     Scaling letter case MUST be observed.  All below unity require lower-case,
     all above unity require upper-case.  The lower-case 'u' has been
     substituted for the Greek 'mu' to permit direct compatibility with ASCII-
     character printers.






                                LENA - Page 6 of 46





     The following keyboard-entry combinations all denote the same numerical
     quantity:

                     12345.67             12.34567E+3       12.34567K

                     0.01234567E+6       .01234567e+6       1234567m

                     12.34567KE-6        .01234567M


     Scaling letter suffixes take precedence over any 'E-format' power of ten;
     in the 7th example (12.34567KE-6), the "E-6" would be ignored.  E-format
     allows either case for the "E."  

     The maximum number of digits in the mantissa is limited to 7.  The
     exponent ranges are limited to E+29 and E-28.  Polarity is considered
     positive by default (plus signs are ignored) and a minus sign must precede
     a number to indicate it is negative.  Except for Scaling Letters and the
     "E", all other characters are ignored.  Where data required is expected to
     be integer-only, any fractional part of an entry is ignored.

     Data item delimiters within a numeric data word are a comma, semicolon, or
     forward-slant.  Two contiguous separators indicate a zero value between
     the delimiters.  In the case of a delimiter character being the first
     character in a data word, the first data item would be zero (null entry).
     Depressing an <Enter> key without entering anything else in response to a
     prompt will make ALL requested data items zero.


     Y/N QUERIES

     In several LENA functions there are Yes-No queries having "[Y/n]" or
     "[y/N]" entry prompts, each having only one letter capitalized.  Pressing
     <Enter> key without entering anything else is the same as entering the
     capitalized key.  


     MAIN COMMANDS

     All of LENA's Main Command words are listed following.  All-capitals form
     is used here to emphasize required _letters_; user may enter either case
     or even mixed-case.  These are all "first words"; if a second word is
     required, LENA will prompt for it if not entered.  This list, in
     abbreviated form, is duplicated in the HELP display on-line and in text
     file MAINCMND.LST.


     QUIt  QUI  QU  Q
           -or-           Quit LENA and return to DOS level.
     EXIt  EXI  EX  X

     HELp  HEL  HE  ?     Display 1 to 6 screens of on-line Help
                          information.

           DOS  DO  \     Temporary drop to DOS level.  One DOS
                          request will return to LENA afterwards
                          unless word 'COMMAND' is entered...will not
                          leave DOS level until 'EXIT' is entered.


                                LENA - Page 7 of 46





           NEW  NE        Begin entry of a new circuit list.  Old
                          circuit data is discarded.

           ADD  AD  A     Add to an existing circuit list.

     LISt  LIS  LI  L     List entire circuit to screen or printer.

                ON  (     Enable printer port to accept outputs or circuit
                          listing.  Main Command prompt changes to "Main->"
                          when printer port is on/enabled.  All PRInts, PLOts,
                          or LISts are directed to the printer when ON.  Active
                          printer port is that set by Operating System.
                          Printer port remains on until turned off.

           OFF  OF  )     Disable printer port.  All outputs are directed back
                          to screen and Main Command prompt returns to "MAIN*>"
                          to show printer port is off.  Default state when LENA
                          is first run.

     DRIve  DRI DR  &     Select another Drive:\Directory path for reading or
           -or-           writing Circuit, Solution, or Waveform data files.
     DIRectory DIR DI     Default on LENA start is same Drive:\Directory as
                          LENA program drive and directory.

     REAd  REA  RE  R     Read a Circuit file from disk.  Requires only the
                          8-character-maximum filename.  File extension of .LIN
                          is automatically appended.  'LIN' file extension is
                          LENA's identification for Circuit list files.

     WRIte WRI  WR  W     Write an existing Ciruit file to disk.  Same
                          filename and extension conditions as REAd.

     SAVe  SAV  SA  /     Save a solution to disk, including frequency limits
                          and circuit filename (but not circuit itself). 
                          Requires only the 8-character-maximum filename.  File
                          extension of .LNA is automatically appended.  'LNA'
                          is LENA's identification for Solution data files.

     BRIng BRI  BR  B     Bring (back) a previously-SAVed solution.  Same file-
                          name and extension conditions as SAVe.  Displays
                          filename of circuit that was solved but does not read
                          it in.  Used for viewing previous solutions. 

     OPEn  OPE  OP  O     Open the connection of a designated circuit branch.
                          Branch remains in circuit list but is not part of
                          circuit solution.  Opening a previously-opened branch
                          has no effect.  If an OPEn designates any branch in a
                          macromodel, the entire macromodel is Opened.

     CLOse  CLO CL  C     Close, or reconnect a designated circuit branch.
                          Opposite of OPEn.  Closing an already-closed branch
                          has no effect.  If a CLOse command designates any
                          branch in an opened macromodel, the entire macromodel
                          is closed.

     MODify MOD MO  M     Modify only the values of a designated circuit
                          branch.  Type and nodes remain intact.  Inoperative
                          with macromodels.


                                LENA - Page 8 of 46




.
     DELete DEL DE  |     Delete a designated circuit branch from a circuit
                          list.  All higher-listed branches move down to fill in
                          list.  If a DELete command designates one branch of a
                          macromodel, the entire macromodel is Deleted.

     INSert INS IN  ^     Insert a new branch at the designated branch position
                          in a list.  Branch type, nodes, value prompts and
                          entries are the same as for one component under NEW or
                          ADD.  Designated branch and all higher branches move
                          move up to make room for INSertion.

     NAMe  NAM  NA  $     Change existing circuit list filename.  Circuit file
                          REAds and WRItes assume the existing filename or allow
                          choice of another filename; this command is primarily
                          for hardcopy outputs so as to show the new filename
                          prior to any WRIte to disk.

     REMark REM RE  *     Change 47-character Remark line accompanying each
                          circuit list or output title.  Remark line is written
                          to or read from disk with other circuit list data.

     NODe  NOD  NO  N     Select NODe of solution.  Every NEW circuit or
                          ADDition to a circuit, MODification of branch value,
                          INSert of a new branch, DELetion of an old branch,
                          REAd-in of a circuit from disk will always make the
                          highest node in a circuit as the node of solution.

     DBRef DBR  DB  D     Change reference voltage for 0 db on all outputs.
                          Default at LENA start is 1 Volt.  Does not affect
                          solution voltage, only decibel value equivalent to
                          solution voltage.

     FREquency   -or-     First Command Word to select frequency limits, first
           FRE  FR  F     or second word to select frequency-voltage output
                          type.  At LENA start there are no frequency limits.

     IMPedance   -or-     First or second word to select frequency-impedance
           IMP  IM  Z     output.

     PRInt PRI  PR  P     First or second word of an output to select printed,
                          tabulated solution values.

     PLOt  PLO  PL  =     First or second word of an output to select ASCII-
                          character plot equivalents.

     MARgin    MAR        Select margins for hardcopy; 1 to 7 characters left
                          margin (5 is default), 1 to 6 lines top and bottom
                          equally (3 is default).  Margins do not appear on
                          screen displays.

     SETtings  SET  SE    Convenience screen display to show user the current
                          circuit filename, circuit creation time/date,
                          circuit Remarks, current time, node of solution,
                          open circuit branches (if any), frequency limits, 0 db
                          reference voltage, and Data file directory path.

     DATe  DAT            Current computer time and date.  Convenience only;
                          computer time and date are resettable only from DOS
                          level.

                                LENA - Page 9 of 46





     OUTPUT COMMAND COMBINATIONS

     A solution output is obtained by a two-word combination of <type> <format>
     or <format> <type>.  FREquency and IMPedance are <type> words, PRInt and
     PLOt are <format> words.  Either order is fine but each word must be
     separated by at least one space, no other character.  To obtain an
     IMPedance PLOt, any of the following two-word combinations can be used:

                    PLOT IMPEDANCE           IMPEDANCE PLOT

                    PLO  IMP                 IMP  PLO

                    PL  Z                    Z  =   

     For user convenience, the following single-word, three-letter acronyms may 
     be used as an alternate for output:

          PRF   -  Print tabulation of complex node voltage over frequency.
          PRZ   -  Print tabulation of complex node impedance over frequency.
          PLF   -  Plot node voltage over frequency, ASCII-character plot.
          PLZ   -  Plot node impedance over frequency, ASCII-character plot.



     PRINTER MARGINS AND PAGINATION

     Printer-directed output is formatted for the 8.5 x 11 inch North American
     standard page size, expecting 85 columns per page horizontal ("10 Pitch" or
     ten characters per inch) and 66 lines per page vertical (6 lines per inch).

     Top and bottom page margins, left margin are selected via the "MAR" main
     command.  Top and bottom margins (equal) are selectable from 1 to 6 lines,
     3 line margin (half inch) being default at LENA start.  Left margin is
     selectable 1 to 7 characters/columns, 5 characters (half inch) being
     default at LENA start.

     Pagination of "Page nn of mm" is done at the bottom right of each page and
     "...continued from Page nn" at the top left of each page after the first
     page.  The first page always begins with a title bearing circuit filename,
     when circuit was created (or last changed), remarks, current time and date,
     any circuit branches which are set open.

     Margins and the "...continued" identification are omitted from screen
     displays and "Page nn of mm" only appears on screen if an output or circuit
     list goes beyond a single page.  Top and bottom margins (always equal)
     allow the following number of solution data lines per page:

          Margin Lines  1st Page Data Lines   2nd, subsequent Pages' Lines
               1             52                     55
               2             50                     53
               3             48                     51   <- default
               4             46                     49
               5             44                     47
               6             42                     45






                                LENA - Page 10 of 46





     ASCII-CHARACTER PLOT EQUIVALENTS

     The "character plot" technique is an old method of making a coarse graph
     plot equivalent using only printer characters as data and graph marks.  It
     is also the fastest and most equipment-versatile, requiring only that a
     printer support ASCII characters.

     LENA outputs plot graphs having 6 major divisions, 60 minor divisions,
     'rotated' a quarter turn so that the lowest frequency is at page top,
     amplitude increasing from left to right.  Every line is identified by
     frequency.

     Major graph divisions are identified by a plus sign.  Any data plot
     character will override a graph division character.  The prime data
     character is an asterisk, secondary a colon, tertiary an up-arrow.

     If, for one plot point, characters are at the same plot location, the prime
     character predominates.  If the prime character location is calculated to
     be beyond the scale extremes, a left or right arrow mark at appropriate
     left or right limit lines indicates overscale.

     Data location is very close to the physical center of a character.  The
     center of a colon character is mid-way between the two marks.  Group Delay 
     is shown by an up-arrow and the _point_ of the up-arrow is significant.
     Group Delay is the derivative of phase divided by derivative of radian
     frequency; the point of the arrow is approximately mid-way between each
     frequency, thus corresponding to approximate frequency of delay.


     OUTPUT PLOT SCALE CHOICES

     Every solution's plot output is scanned for minimum and maximum, those
     minima and maxima shown as a screen prompt.  Users have a choice to accept
     those extremes as the scale limits or to enter desired limits.  Pressing
     _only_ the <Enter> key after the prompt accepts the solution's extremes as
     scale limits.  There is no auto-scaling by decades or octaves.

     Phase-angle scale limits are fixed for frequency-voltage solutions, default
     value at +/- 180 degrees.  Phase-angle limits may be set to any other
     values and will remain at those settings until changed.

     Impedance plots are selectable polar (default) or rectangular.  Polar form
     impedance plot has the prime data mark signifying impedance magnitude,
     secondary data mark signifying impedance phase-angle.  Entered impedance
     phase-angle plot limits remain only for that particular impedance plot. 
     Rectangular form impedance plot has prime mark indicating Real/Resistive
     part, secondary mark indicating Imaginary/Reactive part.

     All plot outputs have the scale limit values at the header of each page.
     Limits can be reversed left-for-right by reversing the order of limit
     entry.

     If a re-plot of the same solution is desired with different scale limits of
     some parameter, it may be done without delay.  Solutions are stored
     internally and re-plotting/re-printing may be done immediately without
     waiting for a new solution.




                                LENA - Page 11 of 46





     ROTATING TWIDDLE CHARACTERS

     Every circuit solution requires all circuit branches to be mathematically
     analyzed at each solution frequency.  With large circuits, this may take
     many seconds.  To indicate this is in process, "Working!" is displayed on
     the screen, preceded by a 'rotating twiddle character' that appears to turn
     in 45-degree increments for every frequency.  Every 8th frequency is marked
     by the "equal symbol" composed of three stacked horizontal dashes.  Both
     indicators disappear after the last frequency's analysis is completed.


     OFF-LINE USE OF SOLUTION FILES

     All solutions may be stored on disk.  All files generated by LENA are the
     functional equivalent of ASCII files.  Other programs may be used to parse 
     the characters for any other tabulation or plot format.  A full description
     of disk file data fields is given in Appendix file LE_APX_A.TXT.











































                                LENA - Page 12 of 46





     GENERAL INPUT-OUTPUT SOLUTION COMMANDS
     --------------------------------------

     SETTING FREQUENCY LIMITS

     Entering F, FR, or FRE at the Main Command prompt without a second word
     will invoke a prompt of:

               Frequency Limits [Hz] (min,max,delta):

     "min" and "max" are self-explanatory, but "delta" has two possibilities:  A
     positive delta entry is the linear frequency increment while a negative
     delta entry refers to the _total_ number of logarithmic-increment
     frequencies.

     Entering "99K,101K,-17" would mean a log-sweep of 17 total frequencies
     starting at 99 KHz and ending at 101 KHz.

     An entry of "99K,101K,100" would mean a total of 21 linear-increment
     frequencies starting at 99 KHz and ending at 101 KHz.

     Maximum number of frequencies is 200, regardless of linear or logarithmic
     increment.  LENA checks for that and prompts if entry is incorrect.  LENA
     will accept a 0 minimum frequency (DC) if the delta is positive/linear, but
     will not accept a 0 minimum frequency if the delta is negative/logarithmic.

     If the delta entry is 0, regardless of whatever else is entered for minimum
     and maximum, the "frequency" is DC.  For all other conditions of delta,
     minimum and maximum frequencies must be positive.

     Frequency limits may be set at the Main Command level by entering "F 
     <limits>" where <limits> is the min-max-delta.  This single-line short form
     of command requires only that one or more spaces are between the "F" and
     the first character of "<limits>;" also, the three data items of <limits>
     are separated by commas, semicolons, or forward-slants, not spaces.  It is
     also possible to select a DC solution from the Main Command prompt by
     entering "FREquency DC" or just "F DC".


     NODE OF SOLUTION

     Any node in a circuit may be selected as the "measuring point" for a
     solution.  Selection of a new node of solution will cause it to remain;
     however, after every ADD or NEW circuit completion, INSert new branch,
     DELete old branch, or REAd in of another circuit, the node of solution is
     reset to the highest node in the circuit.  If in doubt of the node of
     solution, a user can use the SET command to see which node is the current
     node of solution.

     Node of solution may be set as a single-line command at Main Command level
     by entering "N  <node-number>".









                                LENA - Page 13 of 46





     ZERO-DECIBEL REFERENCE VOLTAGE

     Frequency-voltage outputs give both node voltage directly and in decibels
     relative to a zero-db reference voltage.  At LENA start, this reference
     voltage is 1.  It may be reset at any time and will remain at that voltage
     reference until changed again.  A zero or negative reference voltage is not
     allowed.

     Zero-db reference voltage may be given at Main Command by the single entry
     of "D  <voltage>".


     OPENING OR CLOSING A BRANCH

     Every single branch or an entire macromodel may be "switched" open or
     closed, functionally the same as disconnecting and reconnecting a physical
     component.  An OPEned branch remains in the circuit list but is not solved.

     CLOsing an open branch will restore it to solution with the rest of the
     circuit.

     As an example, consider a circuit having a load resistor.  It may be
     desireable to solve for the impedance looking into the load end, without
     the load resistor.  An easy way to do that is to OPEn the load resistor
     branch, then request an impedance solution at that node.  The load resistor
     may be reconnected with a simple CLOse command for that branch.  OPEns and 
     CLOses do not affect the circuit list order, type, nodes, or values.

     Single-line Main Commands may be "O  <branch>" for OPEn, or
     "C  <branch>" for CLOse.  "<branch>" is either the branch order number or
     the full type description (see circuit entry for differentiation,
     explanation).

     OPEning an open branch or CLOsing a closed branch has no effect.

     A reminder:  'Open' and 'close' of a branch component refers to the
     hardware connection; it has NO relation to computer _file_ terminology.























                                LENA - Page 14 of 46





     CIRCUIT LIST COMMANDS
     ---------------------

     STARTING OR CONTINUING A CIRCUIT LIST

     The single command word, "NEW," at Main Command will begin a new circuit
     list, starting at branch 1.  All old circuit list data (if any) will be
     lost.

     The single command word, "ADD," or "AD," or just "A" at Main Command will
     allow new branches to be added to an existing circuit list, beginning with
     the next higher branch order following the last branch.

     If there is no circuit data, the command ADD will also begin a new circuit
     list, starting at branch 1.

     Every branch entry begins with a type description.  This is followed by
     node connection data, finally by branch component values.  Once branch data
     has been fully entered, branch entry begins again with the next branch. 
     Branch entry continues until "END," "EN," "E," "ND," or "N" is entered for
     a branch type, signifying completion of a circuit list.


     BRANCH DESCRIPTION AND DESIGNATION

     Branch type descriptions allow up to 8 characters per branch.  The minimum
     _first_ letters for electrical type identification are shown in the
     comprehensive branch descriptions following.  Those minimums are from 1 to
     3 alphabetic characters.  The remaining characters may be used for
     reference designations or whatever the user wishes.  As an example, a
     single resistor branch will be identified as to type by just the single
     first letter "R."  Entering "RESISTOR," "R-123," "R_LOAD," or just "R"
     would all signify a single resistor branch for the purposes of completing a
     branch entry.  The _entire_ type description may be used for designating a
     branch for some action.

     Main Commands OPEn, CLOse, MODify, DELete, and INSert require designation
     of a particular branch.  Designator <branch> for those commands may be
     either the branch number or the full type description.

     LENA parses the first character of a <branch> designator entry.  If that
     character is alphabetic, the entire circuit list is searched for a match
     between <branch> and any type description; if there is a match, then the
     circuit branch number has been reached.  If that character is numeric, the
     designator is assumed to call out the circuit branch number directly.

     Since most circuit analyses concentrate on only a few components of a
     circuit, it is probably easier to enter "OPEN R_LOAD" to open that branch
     rather than entering "OPEN 109" (assuming R_LOAD was branch number 109).


     MODIFY A BRANCH VALUE

     A single-line Main Command "MOD <branch>" allows changing just the values
     of that branch.  Type description and nodes remain intact.  MODify command
     will not work with macromodels.  The finish of a MODify will reset the
     circuit creation time and date to that when the MODify took place.



                                LENA - Page 15 of 46





     DELETING A BRANCH

     A single-line Main Command "DEL <branch>" will remove the branch at
     designator <branch>. 

     This may present some slight difficulty if the DELeted branch is the
     dependent branch of a dependent current source.  LENA does a circuit check
     of each circuit after an Edit command.  If LENA finds an improper
     dependent branch relation, the dependent branch is automatically switched
     open, and a warning message to that effect displayed on the screen.  Such
     an automatic Open cannot be CLOsed until the dependent branch exists in
     proper form.

     If a DELeted branch is the only link between two parts of circuit, one part
     having a stimulus and the node of solution being in the other part,
     solution analysis will stop and a warning message shown, citing that
     probability.

     DELeting any branch number within a macromodel will cause the _entire_
     macromodel to be deleted.

     After a DELetion, all higher-order branches will move down to fill in the
     empty branch space.  If any of the moved-down branches contain a dependent
     branch, the dependent branch number of a dependent current source will be
     automatically changed to the new number.  The finish of a DELetion will
     also reset the node of solution to the highest node in the remaining
     circuit and reset the circuit creation time to the time of DELetion.


     INSERTING A NEW BRANCH

     The Main Command single-line command is "INS <branch>".  The designated
     branch and all higher branches will be moved up in the circuit list to make
     room for the INSertion.  LENA will issue a prompt for the inserted branch
     type and nodes.  Once the branch type is known (it may be a macromodel with
     many branches), the list movement will take place.

     If one of the moved branches is the dependent branch of a dependent current
     source, the dependent branch number of that dependent source will be
     automatically adjusted to be the new branch number.  The finish of an
     INSertion will reset the node of solution to the highest node in the new
     circuit and reset the circuit creation time to the time of INSertion.


     GENERAL BRANCH-NODE CIRCUIT BUILDING IN LENA

     Every single component is called a "branch."  Every connection point is
     called a "node."  Every branch is connected between two nodes.  Node zero
     is common-ground-earth to the entire circuit.  Non-zero nodes must be
     contiguous.  A branch may not have each end connected to the same node. 
     There is no limit to the number of branches connected between the same two
     nodes.  There is no restriction to the ordering of branches in any circuit;
     branches may be located anywhere in a listing. 

     Node location makes no difference to the final solution although it may
     have some effect on speed of solution execution; more of that in
     explanation of the sample circuits distributed with the LENA program set. 



                                LENA - Page 16 of 46





     As a practical matter, node ordering is best when following the general
     flow of a schematic diagram; that makes for easier interpretation of a
     circuit list at a later date.

     Branch and node arrangement follows conventional theoretical analysis
     techniques.  LENA expands single component per branch theoretical concept
     to include parallel R-L and parallel R-C, series R-L and series R-C
     branches.  While this is more for user convenience, in the physical world
     every component contains combinations of resistance, capacitance, and
     inductance.  In LENA, each resistance is a pure resistance, each
     capacitance is a pure capacitance, and each inductance is a pure
     inductance.

     Current flow in LENA is provided by current sources.  Every current source
     is assumed to be the theoretical type having an infinite source impedance. 

     There are no voltage sources in LENA.  A theoretical voltage source has
     zero source impedance.  A voltage source may be approximated by a current
     source in parallel with a very low resistance.  This is no problem with the
     large magnitude range of LENA's numeric calculation...a MegaAmpere current
     source in parallel with a microOhm resistor would create a very 'stiff'
     one-volt source...such would be numerically and theoretically correct
     despite the impractical-seeming combination.

     Current sources come in two varieties, "independent" and "dependent." 
     Independent current sources are the stimuli or the fixed sources.  Note:
     ALL stimuli are _always_ at phase-frequency coherence in LENA.

     Dependent current sources are dependent on the voltage across a branch or
     the current through a branch.  More on those in the later section on
     dependent current sources.

     In this version of LENA, there are four macromodels.  These are always
     made up of contiguous branches, are always handled by commands as if they
     were a single branch.   

























                                LENA - Page 17 of 46





     CIRCUIT COMPONENTS AVAILABLE IN LENA
     -------------------------------------

     TYPE DESCRIPTIONS

     All of the following branch type descriptions may be found in short form in
     the Appendix and included in the HELP display within LENA.  All TYPE
     letter combinations are shown in all-capitals to emphasize the _letters_
     required; users may enter letters of either case or even mixed case,
     provided they are the correct letters.  Circuit Lists will always show
     branch types in all-capitals.


     PASSIVE SINGLE BRANCHES

           TYPE                    Description
        ----------     --------------------------------------------
        R  RE  RES  =  Single pure resistance

        C  CA  CAP  =  Single pure capacitance

        L  IN  IND  =  Single pure inductance

           LQ       =  Single inductance with specified Q; Q is constant over
                       frequency.  Q is modelled as a loss resistance in series
                       with inductance.  Loss resistance is magnitude of
                       inductive reactance divided by Q.

           CQ       =  Single capacitance with specified Q; Q is constant over
                       frequency.  Q is modelled as a loss resistance in
                       parallel with capacitance.  Loss resistance is the
                       magnitude of capacitive reactance divided by Q.

               SRL  =  Series R and L.

               SRC  =  Series R and C.

               PRC  =  Parallel R and C.

               PRL  =  Parallel R and L.


        E  EN  END  =  Non-branch.  Entered by itself (no nodes), causes a
           -or-        termination of the circuit list entry and return to
        N  ND          Main Command level.

        B  BA  BAK  =  Non-branch.  Entered by itself (no nodes), causes listing
                       to back up to the previous branch for re-entry.  Used for
                       correcting errors made in previous branch entry.

        ?  HE  HEL  =  On-line Help screen listing circuit branch types.

     At DC all inductors assume a resistance of 1 microOhm and all capacitors
     assume an infinite resistance.

     All passive branch values are normally entered as _positive_ quantities.  A
     negative value may be entered at the user's discretion.  Negative entries
     of inductance or capacitance will result in the same magnitude of reactance


                                 LENA - Page 18 of 46





     over frequency but the signs of those reactances are reversed.  This is
     useful in modelling certain theoretical circuit equivalents.


     INDEPENDENT CURRENT SOURCES

           TYPE                       Description
         ---------     -----------------------------------------------
        S  SI  SIG  =  "Signal generator" stimulus, specified by current in
                       Amperes and phase-angle in degrees (optional) for
                       frequency solutions.  For time solutions with repetitive
                       waveforms, phase-angle is ignored and the entered current
                       is the peak value of the described waveform.

        D  DC  IDC  =  Direct current source.  Active _only_ when the frequency
                       is zero (DC).

     Independent current sources are automatically ignored during an impedance
     solution.

     All current sources have infinite source impedance.  Voltage across the
     nodes of any current source depends on the voltage drop through all other
     branches connected across the current source nodes.  A "stiff" voltage
     source may be created by a high-current source in parallel with a low-value
     resistance; source impedance of this "stiff" voltage source is that of the
     low-value resistance.


     CURRENT DIRECTION IN SOURCES

     Current flow in LENA is assumed equal to _electron_flow_.  Current flow
     _within_ all current sources is from "plus node" to "minus node" if the
     entered current value is positive.  Entering a negative value of current or
     current gain reverses the current flow.

     Node entry order of all passive branches is irrelevant...except for those
     which are dependent branches of a dependent current sources.


     DEPENDENT CURRENT SOURCES

     LENA has two types:  GMS or transconductance-specified ('gm') dependent
     current source, and HFS or current-gain-specified ('hfe') dependent current
     source.  Current is dependent on the voltage across a dependent branch
     (type GMS) or the current through a dependent branch (type HFS).  Dependent
     branches may be any passive branch type located anywhere in the circuit;
     dependent branches may not be another current source.


           TYPE                      Description
        ----------     -----------------------------------------------
        G  GM  GMS  =  Transconductance-specified current source.  Current
                       depends on the specified transconductance ('gm') times
                       the voltage across the nodes of a specified dependent
                       branch.  Transconductance is specified in mhos,
                       transconductance being the derivative of current divided
                       by derivative of voltage.  Current is then proportional
                       to the voltage across a dependent branch.


                                LENA - Page 19 of 46





        H  HF  HFS  =  Current-gain-specified ('hfe') current source.  Current
                       depends on the specified current gain times the current
                       through the dependent branch.

                          Note: "hfe" is not conventional notation for
                          current gain, being the hybrid parameter of
                          collector current versus base current gain of a
                          common-emitter transistor; it is used due to
                          limitations of ASCII not allowing subscripts.
                          "hfe" to most circuit designers is fairly well
                          synonymous with current gain.


     Current flow in circuits with dependent current sources is illustrated
     following:


           Plus node                    Plus nodes
               o    +e            o ------------------o
               |                  |                   |  /|\
               |                  |    |  Current     |   |
               Rd       ->       GMS   |  Within     Rm   |
               |                  |   \|/  GMS        |  Current
               |                  |                   |  through
               o    -e            o ------------------o  Rm
           Minus node                   Minus nodes

            Dependent          Type GMS Dependent Current Source
             Branch               with connected resistor Rm

     Voltage drop across Rm is in-phase with voltage across Rd.  Exchanging Plus
     and Minus nodes of the GMS or dependent branch Rd will reverse current
     through the GMS and through Rm.  Exchanging Plus and Minus nodes of _both_
     GMS and the dependent branch, Rd, will make current through the GMS and
     through Rm as shown.  Entering a negative transconductance value for the
     GMS will also reverse current flow of the GMS.

     If there are several branches connected to the same nodes as the dependent
     branch, GMS current magnitude is dependent on the total impedance magnitude
     across the dependent branch nodes...but GMS current direction is still
     dependent on the Plus and Minus node entry of the dependent branch. 


           Plus node                    Plus nodes
               o                  o-------------------o
               |                  |                   |  /|\
               |  /|\             |    |   Current    |   |
               Rd  |     ->      HFS   |   Within    Rm   |
               |   |              |   \|/   HFS       |  Current
               | Current thru     |                   |  through
               o   dependent      o-------------------o  Rm
             Minus   branch            Minus nodes      
              node

            Dependent          Type HFS Dependent Current Source
             Branch               with connected resistor Rm




                                LENA - Page 20 of 46





     Current through Rm is in-phase with current through Rd.  Exchanging Plus
     and Minus nodes of the HFS or dependent branch Rd will reverse current
     through the GMS and through Rm.  Exchanging Plus and Minus nodes of _both_
     HFS and the dependent branch, Rd, will make the current through HFS and Rm
     as shown.  Current flow in the HFS may also be reversed by entering a
     negative value of current gain.

     If several branches are connected to the same nodes of the dependent
     branch, HFS current magnitude is dependent _only_ on the current through
     the dependent branch...but HFS current direction is dependent on the node
     entry order for the dependent branch.


     MACROMODELS

     Macromodels use 3 to 5 branches, branches _always_ being contiguous in any
     list.

           TYPE                       Description
        ----------     ---------------------------------------------
        Z  ZL  ZLN  =  Unbalanced transmission line equivalent macromodel;
                       uses 3 branch spaces, requires 3 nodes (input, output,
                       common).  Specified by characteristic impedance,
                       velocity of propagation, length in inches, and
                       decibels of loss per 100 feet.

        T  TR  TRF  =  Two-winding ideal transformer having specified
                       coefficient of coupling between 0.01 and 0.99, DC
                       isolation between windings.  Uses 4 branch spaces,
                       requires 4 nodes maximum (2 each for primary, secondary).
                       Specified by primary winding inductance, turns ratio of
                       primary winding to secondary winding, and coefficient of
                       coupling.

                          One node of primary, one node of secondary may be
                          common, if desired.

        Q  QT  QTR  =  Bipolar transistor, hybrid-pi model.  Creates 4
                       branches, requires 3 nodes (base, emitter, collector).
                       Specified by:  Hfe or base-to-collector current gain;
                       Ft, cutoff frequency; Ic, average value of collector
                       current; Hoe, collector conductance in mhos.

                          Model does not include base spreading resistance, Rbb.
                          Model makes no distinction between PNP or NPN.

        O  OP  OPA  =  Operational Amplifier.  Creates 5 branches, requires 
                       4 nodes (non-inverting input, inverting input, output,
                       common).  Specified by:  DC open-loop voltage gain in db;
                       Fc, or "corner frequency", the break-point of open-loop
                       gain where gain begins to decrease at a rate of 20 db per
                       decade; R-input, equivalent resistance of each input,
                       both assumed to have equal resistance; R-output, source
                       resistance of output.

                          Common node is common to both inputs as well as
                          output.



                                LENA - Page 21 of 46





     TRANSFORMER MACROMODEL DETAILS

     Two-winding isolated transformer macromodel is modelled as:



          Primary  o----o-----o           o----o-----o  Secondary 
           + node       |     |           |    |        - node
                       Lp   HFSp  < - -  Ls   HFSs
                        |     |           |    |
          Primary  o----o-----o           o----o-----o  Seconday  
           - node       \                               + node
                          - - - - > - - - - - -^

          where:

              Lp' = Calculated primary inductance.
              Ls' = Calculated secondary inductance.
             HFSp = Current-gain dependent current source dependent on
                    current through Ls.
             HFSs = Current-gain dependent current source dependent on
                    current through Lp. 
          
          with internal values:

                    Lp = Entered primary inductance.
               N  = Entered turns ratio, primary to secondary.
               Ls = Secondary inductance calculated from primary inductance
                    divided by square of N.
               K  = Coefficient of coupling (entered)

              Lp' = Lp x (1 - (K x K))
              Ls' = Ls x (1 - (K x K))
      Hfe of HFSp = -(K / N)                <- [dependent branch is Ls]
      Hfe of HFSs = -(K x N)                <- [dependent branch is Lp]
        

     DC isolation is a relative term here.  Inductors have a 1 microOhm
     resistance at DC to avoid an error-crash in the analysis-solution routine. 
     While that is a very low impedance, it will show up as a small, small
     "leakage" of signal from primary to secondary and vice versa at DC.

     One primary node may be common to one secondary node in the circuit list.
     The orientation of secondary nodes is purposely chosen to yield a voltage
     polarity of the same sign as voltage across the primary.


     UNBALANCED TRANSMISSION LINE MACROMODEL DETAILS

     Unbalanced transmission line macromodel is a pi-form having the same
     attenuation at every frequency.  Macromodel attenuation is internally
     computed from the ratio of specified length to the loss per 100 feet.  Loss
     per 100 feet is a common specification for transmission lines and may be
     taken directly from manufacturer's data.  User must compensate for loss
     varying over frequency.  Lengths in meters must be converted to inches;
     legal USA conversion is 2.54 centimeters = 1.0 inch.




                                LENA - Page 22 of 46





     Open-line sections ('half-wave' resonant lines) may be created by having
     the "output" node isolated from all other branches; in effect, that would
     create the equivalent of an open end.  'Quarter-wave shorted stubs' are
     simulated by connecting a very low resistance branch to the output node.


     BIPOLAR TRANSISTOR MACROMODEL DETAILS

     The created bipolar transistor hybrid-pi model is as follows:
 
          Base node                              Collector node
              o------*-------           --------*------o
                     |      |           |       |
                     |      |           |       |
                    Cb'e   Rb'e   ->   HFS   (1/Hoe)
                     |      |           |       |
                     |      |           |       |
                     -------*-----*-----*--------
                                  |
                                  o  Emitter node

        where:
               Hfe = base-to-collector current gain at Ic
               Ft = cutoff frequency
               Ic = average collector current
               Hoe = collector-emitter output conductance
               HFS is dependent on Rb'e branch current with current
                    gain equal to Hfe such that collector voltage is
                    at opposite phase relative to base voltage.

        then:
               Rb'e = (Hfe x 0.027) / Ic
               Cb'e = 1 / (Ft x 2pi x Rb'e)

     Hybrid-pi models have an additional resistance, Rbb, "base spreading
     resistance," in series with the Rb'e-Cb'e junction and external base node.
     Rbb is not readily calculated since it is subject to variations in design
     and type of the base junction rather than operating parameters.  If no Rbb
     value is known, a suggestion is to use a value equal to or slightly larger
     than Rb'e.

     An added Rbb external to the macromodel can also include an independent DC
     current source (IDC) to create the Vbe diode junction voltage.  However,
     the IDC current must be chosen to fit a PNP or NPN transistor; the bipolar
     transistor macromodel is neither PNP nor NPN type.  An IDC branch is active
     _only_ at DC, ignored otherwise.

     Important note:  Those acquainted with SPICE programs may be used to SPICE
     calculating the quiescent condition of transistors.  LENA does not do that,
     presuming the transistor model already represents that quiescent bias
     condition.









                                LENA - Page 23 of 46




.
     OPERATIONAL AMPLIFIER MACROMODEL DETAILS

     The equivalent operational amplifier macromodel is as follows:

          +Input node                                   Output node
              o---        ------*-----*-----        -----*----o
                 |        |     |     |    |        |    |
                 |        |     |     |    |        |    |
                Rin  ->  GMS+  GMS-  Cfc  Rfc  ->  GMSo  Rout
                 |        |     |     |    |        |    |
                 |        |     |     |    |        |    |
                 *--------*-----*-----*----*--------*----*
                 |           _                      |
                 |           /|                     |
                Rin     ->                          o
                 |                           Common node
                 |
              o---         GMS+ dependent on Rin at +Input;
          -Input node      GMS- dependent on Rin at -Input with
                                gm negative;
                           GMSo dependent on Rfc

        Where:
               Av = open-loop voltage gain
               Fc = 'corner frequency' or 'breakpoint' where Av
                    magnitude begins to decrease 20 db per decade.
               Rfc = 1 Ohm
               gm+ = transconductance of GMS+ = 1
               gm- = transconductance of GMS- = -1
               gmo = transconductance of GMSo = Av / Rout
        Then:
               Cfc = 1 / (Fc x 2pi)

     The center of this op-amp macromodel is a summing point for the current
     analogue to the non-inverting and inverting voltage inputs.  It also
     modifies the DC open-loop gain over frequency.  Output is a current
     analogue of the voltage at this center, summing 'node', multiplied by Av
     and divided by output source resistance.

     LENA simplifies this model by reducing 8 branches to only 5, using 
     mathematical equivalents to the center summing node and output GMS.  Each
     input node still 'sees' only R-input and the output node still has Rout.

     The break-point frequency is found in manufacturer's data sheets.  Most op-
     amp ICs have more than one breakpoint frequency, the first somewhere around
     or below 1 KHz, others about a decade or two higher.  Any higher than the
     first can be simulated by creating an external GMS-R-C cluster.  Modelling
     additional breakpoints are explained in Model Tips and Hints later in this
     manual.

     "Input resistances" are seldom specified for op-amp ICs.  Their existance
     in the macromodel is required for internal mathematical analysis-solution
     of dependent current sources.  An approximation can be done by entering a
     very high resistance value.  Since the exponent range of non-integer
     numbers in LENA is very large, a high, seemingly-impractical value will
     not disturb analysis-solution calculation.




                                LENA - Page 24 of 46




.
     ENTERING CIRCUIT COMPONENTS
     ---------------------------

     This is a step-by-step procedure on entering circuit components in LENA. 
     The process begins after entering "NEW" at the Main Command level.  Note
     that ALL input to any one prompt is considered a "data word;" that is, one
     or more data items within the word must be separated by commas, semicolons,
     or forward-slants, no spaces.  There is no need to memorize any special
     order of data entry; prompts for all items are self-explanatory.


     BRANCH ENTRY, SINGLE-VALUE BRANCHES

     The first prompt will be:

               Branch  1, Type, Plus-node, Minus-node:

     The user has a choice on input, Type description alone or Type description
     with the Plus and Minus nodes.  Assume that RESISTOR was entered by itself,
     no node numbers.  This results in another prompt:

               Branch  1, Type "RESISTOR" Plus-node, Minus-node:

     With the second prompt, the user gets verification that RESISTOR was indeed
     the Type description (LENA supplies the double quotes around RESISTOR). 
     LENA requires _some_ kind of numerical data in response and will keep
     requesting until it gets something.  Let's say that the Plus node was 2 and
     the Minus node was 3.  Response to the prompt would be simply "2,3".

     Supplying all three data items would have an entry to the first prompt of
     "RESISTOR,2,3".

     If a mistake was made in entry and it became "RESISTOR,2,2", then LENA
     would recognize that both nodes were equal and the screen would show:

               Nodes may not be equal, please re-enter.

               Branch 1, Type, Plus-node, Minus-node:

     Let's assume that entry was good, that the Type description is RESISTOR,
     the Plus node is 2, and the Minus node is 3.  The next prompt would be for
     the Value:

               Resistor value [Ohms]:

     Let's say the value is 4700 Ohms.  Scaling letters can be used and an entry
     can be "4.7K".  Or, E-format can be used for an entry of "47E2" or "4.7E3".

     Or simply "4700".  Whichever format is easiest for the user is fine with
     LENA.  

     Completion of Value entry results in a prompt for the next branch:

               Branch  2, Type, Plus-node, Minus-node:

     Note that the branch number has been incremented in the prompt.  This
     incrementation will repeat until the list is terminated or after it has



                                LENA - Page 25 of 46





     completed Branch 204, the maximum number of branches in LENA.

     To end the circuit list entry at any time, just enter END or EN or E or ND
     or N for the Type description, no node numbers.  List entry will terminate 
     with a prompt showing the total number of branches and the node of solution
     being the highest node in the circuit list...then return to Main Command
     level.

     Suppose that the resistor value should have been 47 KOhms instead of 4.7
     KOhms and this mistake is seen.  To correct it quickly, just enter "BAK" or
     "BA" or "B" and the list entry 'backs up' to the previous branch's prompt
     for Type and Nodes.  Re-entering everything is required.

     A mistake in Value entry could be corrected later by the MODify command...
     but that requires a note to oneself to do so.  Going back one branch is
     easy enough to do now and corrects the entry immediately, allowing
     concentration on entering all the other branches in the list.


     BRANCH ENTRY, DOUBLE-VALUE BRANCHES

     The same Type and Nodes prompt is issued for every branch; LENA doesn't
     know what Values are required until the Type Description is entered.  For
     example, suppose the branch was type LQ, a single inductor with specified
     Quality factor.  After completion of Type and Nodes entry, the Value prompt
     would be:

               Inductance value [Henries], Q [Units]:

     Suppose the inductance was 56 microhenries with a Q of 70.  The data word
     entry would be "56u,70".

     Note the _lower_case_ "u" for 'micro'.  Scaling Letters in entry must use
     lower case for multipliers less than unity, upper case for greater than
     unity.  Letter "u" replaces Greek letter "mu" for ASCII compatibility.

     If there was a mistake made and one Value was not entered, LENA would
     detect that and issue the error message:

               Caution:  One or both values zero, please re-enter

     ...and then return to the Value entry prompt for that branch.  That same
     "zero" caution would appear with single-value branches if the single Value
     entry was zero.  LENA expects _something_ in the Value and keeps prompting
     until it is entered.


     QUICKER ENTRY, SINGLE-VALUE AND DOUBLE-VALUE BRANCHES

     LENA has a built-in 'shortcut' to allow entry of everything about simple
     branches on one line.  Once the user becomes acquainted with Value entry
     order, Values can be entered as part of the data word following the Type 
     and Nodes data items.  For illustration, suppose the two previous examples
     were connected to the same nodes; the screen display would look like:

               Branch  1, Type, Plus-node, Minus-node: RESISTOR,2,3,4700
                                        -and-



                                LENA - Page 26 of 46





               Branch  2, Type, Plus-node, Minus-node: LQ,2,3,56u,70


     It should be emphasized that users should not try this until they are
     familiar with the Value entry order.  It is easy to mix up two values...but
     the Type description and Value entry order match...L is first, Q is second
     in an LQ.  In both kinds of R-L and R-C combinations, Resistance Value is
     always first.


     DEPENDENT CURRENT SOURCE VALUE ENTRY

     Whether the Type description is GMS or HFS, the second Value data item is
     _always_ the dependent branch identification.  This identification can be
     done either by dependent branch's Branch Number or by its entered Type
     Description.

     If the Type Description is used for identification, then it is required
     that the dependent branch should have additional characters to make it
     distinctive; the minimum Type Description entry might be repeated the same
     way in several circuit list locations.  For example, suppose an HFS has a
     current gain of 2 and it is dependent on a resistor in Branch 6 which has
     the Type Description of "R-78".  The screen display of Value prompt and
     subsequent keyboard entry would like:

               Current Gain [Units], Dependent Branch No.: 2,R-78
                                   -or-
               Current Gain [Units], Dependent Branch No.: 2,6

     Either form of entry is correct.

     LENA checks the data of every branch after Circuit Entry termination. 
     Dependent branches must be passive types and they must exist in the circuit
     list; if incorrect, an error message is made and the dependent current
     source is switched open.  Should that error happen, the MODify command can
     be used to correct the dependent branch identification.


     SIGNAL (GENERATOR) VALUE ENTRY

     Value prompt for a SIG Branch Type is:

               Signal-source cur.[Amps], phase-angle [Deg]:

     Phase angle does not have to be entered.  Omitting it will make the phase
     angle zero.  A circuit list may have more than one SIG and each one may
     have a different current magnitude and phase angle; all stimuli are
     "locked" frequency-phase, so phase angles are relative to one another.

     Current magnitude _and_ phase angle applies only to frequency-voltage
     solutions.  For time solutions, current magnitude entry is equal to the
     peak current of a waveform.  Any phase angle entry is ignored for time
     solutions.

     On output of a circuit list, the display will be as if the circuit had a
     frequency-voltage solution; i.e., magnitude and phase-angle.  A zero phase-
     angle will not be displayed, only assumed.



                                LENA - Page 27 of 46




.
     MACROMODEL ENTRIES

     Only the Type Description of a macromodel is required at the Type and Nodes
     prompt.  Once the Type Description is entered, a second prompt for specific
     nodes for that macromodel is given.  For illustration, let's assume a
     Bipolar Transistor called "Q67" is to be entered beginning at Branch number
     5 with Base node at 8, Emitter node at 9, and Collector node at 10.  The
     screen display of prompts and entries might look like:

               Branch  5, Type, Plus-node, Minus-node: Q67
               Base, Emitter, Collector nodes: 8,9,10

     If the LENA user is familiar with node entry order, the one-line
     'shortcut' method can be used.  The screen display of prompt and entry
     might look like:

               Branch  5, Type, Plus-node, Minus-node: Q67,8,9,10

     Either form is correct for LENA.  Once all the nodes have been entered,
     the first set of Values is prompted.  There is no further 'shortcut' entry
     method for Values of macromodels.  Users have to follow the prompts.

     Node entry order for other macromodels is as follows:

     Transformer >   Primary, Secondary, Primary Return, Sec. Return nodes

     Transmission Line >   Input, Output, Common nodes

     Op-Amp >   Non-inverting Input, Inverting Input, Output, Common nodes


     Note that while the transformer macromodel is designed for DC isolation,
     one node of the primary and one node of the secondary may be the same node.

     The Transmission Line macromodel is entirely passive.  "Input" and "Output"
     labels only serve as identification.


     REQUIRED-LISTED MACROMODEL VALUES

     Individual macromodel branch data is not immediately available. 
     Macromodels are described and listed in parameters which apply to the
     entire macromodel.  These parameters are:

     Transmission Line

          *  Characteristic Impedance in Ohms.
          *  Velocity of Propagation (if entered zero, defaults to
                    0.75)
          *  Length in inches (If length is Metric, users must convert
                    prior to entry, using legal conversion of one
                    inch equals 2.54 centimeters)
          *  Attenuation per 100 foot length (obtained from cable
                    tables or handbooks)

          If the attenuation of the entered line length is known, user
          should enter Attenuation-per-100-feet as known-attenuation



                                LENA - Page 28 of 46





          multiplied by 1200.  There is no compensation of attenuation
          variation with frequency; users must limit frequency-sweep
          range for accurate attenuation effects.


     Ideal Transformer

          *  Primary Inductance
          *  Turns ratio, primary to secondary
          *  Coefficient of coupling

          Coefficient of coupling is limited to a range of 0.001 to 0.999.


     Bipolar Transistor

          *  Hfe, forward current gain, common-emitter (at Ic)
          *  Ft, cutoff frequency (at Ic)
          *  Ic, average DC collector current
          *  Hoe, collector conductance, mhos, common-emitter (at Ic)

          Collector current DC value must be entered even if the Base
          bias network is described in the circuit.  LENA does not
          "set" the DC collector current from any DC bias network. 


     Operational Amplifier

          *  Open-loop Voltage Gain in Decibels
          *  "Corner" frequency where 20 db slope per decade voltage
                      reduction intersects open-loop voltage gain.
          *  Input resistance, assumed identical for both inputs.
          *  Output source resistance.



     SEEING THE FULL CIRCUIT LIST

     Enter "LIS" or "LI" or "L" at the Main Command level.  The Circuit List
     will appear headed by a title display.  For long lists, the Pause key may
     have to be pressed to stop scrolling.  Branch information is reasonably 
     easy to understand without further explanation.

     Note:  Although all non-integers are stored internally to the equivalent of
     15 decimal digits, Value display is rounded-off to no more than 6 decimal
     digits.

     Any OPEned branches will be indicated by the * asterisks * in the spaces
     between that branch's data.  The last line of the title block also displays
     branch numbers of opened branches; if none are switched open, the last line
     indicates so.

     Dependent branches in a dependent current source List-line are identified
     by both list branch number and Type Description, in that order.






                                LENA - Page 29 of 46





     CIRCUIT LIST HARDCOPY

     Make sure the printer is powered on, then enter ON at the Main Command. 
     The Main prompt changes from "MAIN*>" to "Main->" indicating the output is
     directed to the printer.  If your display has color, the "Main->" will be
     white letters on a screen-wide blue bar.  When output is directed to the
     printer, there is no screen display for that output but the word "Printing"
     in flashing white letters on a blue background will indicate data going to
     the printer.  All prompts, messages, entries will still appear on the
     screen but circuit lists, print tabulations and plot graphics are directed
     to the printer port.

     A reminder:  LENA takes care of full printer page formatting.  Before
     sending anything to the printer, position the paper so that it begins on
     the top edge of the paper.  The end of a printout will stop at the bottom
     of the last page, ready for the next page.

     If a printout has been completed and output is to be directed back to the
     screen, enter OFF at the "Main->" command prompt.  The prompt changes back
     to "MAIN*>" (yellow letters on black background) and the printer 'pops' one
     line feed, positioning itself at the top of the next print page.  That
     'pop' is a peculiarity in I/O handling of the MS-FORTRAN runtime package;
     the last character, usually a line-feed, is stored internally and will not
     be sent out until another output is started, the printer port is closed
     (OFF command), or exiting LENA. 


     CIRCUIT LIST EDITING
     --------------------

     The Edit commands are ADD, MODify, DELete, INSert, OPEn, and CLOse.  They
     are all done from Main Command level.  Except for ADD, which re-starts
     Circuit Entry immediately after the highest branch in the current list, all
     will return to Main Command level when completed.

     All Edit commands have been described prior to this section.  Except for
     ADD, they will require a branch identification.  That identification may be
     either Branch Number or full Type Description.  If the identification is
     incorrect, a warning message will be displayed and no further action taken
     except a return to Main Command level.

     A reminder:  Except for OPEns and CLOsures, alterations in the Circuit List
     are _final_.  Old values and deleted branches cannot be restored.  If 
     versions of a circuit are desired to be kept for comparison, they can be
     sent to disk.  See Disk Operations for storage and retrieval.


     SPECIAL NOTE ON INSERT COMMAND

     On the "INS  <branch>", the <branch> refers to where the new, INSerted
     branch will be located.  The existing <branch> will be moved up in the
     circuit list to INSert the new branch.  From there, everything is as it was
     with Circuit Entry, except that completion of a single branch or macromodel
     INSert will return to Main Command level.






                                LENA - Page 30 of 46




.
     SPECIAL NOTES ON ALL MACROMODELS

     When an Edit command identifies a macromodel by Branch Number, it is
     possible to call out _any_ of the 3 to 5 branch numbers of that macromodel
     or just the Type Designation of the macromodel.  LENA takes care of
     identification/ordering of a macromodel.

     A MODify will not operate with macromodels.  INSert, DELete, OPEn, CLOse
     will all operate on the _entire_ macromodel.

     It may not be desireable to OPEn and CLOse an _entire_ macro-model; it may
     be preferred to disconnect/connect just one node.  In that case, sacrifice
     a branch and node such that a single branch connects that macromodel node
     to the rest of the circuit.  The single branch could be switched OPEn or
     CLOsed to achieve the disconnect/connect of one node.


     DISK DATA FILES
     ---------------

     LENA has two types of data files, identified by file extension:

                    .LIN  =  Circuit Lists
                    .LNA  =  Solutions

     The file extensions are appended automatically for both reads and writes.
     Users need only specify the filename.  Filename follows DOS syntax:  8
     characters maximum, first letter alphabetic, underline and dash allowed as
     symbols, no spaces within filename.  DOS itself does error-checking on
     filenames; LENA interprets some DOS error codes to present clear-language
     error messages.

     All data files have values written in ASCII characters, and are otherwise
     indistinguishable from text files.  For data field specifications on all
     data files, see the Appendix file LE_APX_A.TXT.


     SETTING THE DATA STORAGE DRIVE:\DIRECTORY PATH

     At LENA start, the Drive and Directory for all data files is, by default,
     the same Drive and Directory where LENA itself is located.  The user may
     specify another location from the Main Command level by entering DRI or
     DIR.  LENA will display a prompt for the Drive:\Directory entry showing
     the entry length for the Drive:\Directory string between vertical bars. 
     Use conventional DOS syntax with the Drive:\Directory string; i.e.,
     alphanumeric characters, no punctuation, limiting symbols to dashes and
     underlines, 8 characters per directory name.  The following entry would be
     acceptible:

               C:\IN1492\COLUMBUS\SAILED\OCEAN\BLUE\
                                                   ^
     The trailing back-slant delimiter symbol need not be entered...LENA will
     include it if missing.  Drive C: and all five directories should already 
     exist.  LENA will reject all read/write commands to non-existant drives or
     directories.

        Note:  To check the disk(s) or to inspect the available directories,
        enter "DOS" from Main Command level, then enter "COMMAND" (7 letters)


                                LENA - Page 31 of 46





        to stay in the DOS shell.  Conventional DOS commands can be used for
        inspection or directory creation.  When DOS operations are completed,
        enter "EXIT" (4 letters) at DOS level to return to LENA.  LENA has
        remained in memory, all data intact.

     For short Drive:\Directory strings, it is possible to enter everything in
     one line at the Main Command level.  The preceding example could have been
     entered as:

               DIR  C:\IN1492\COLUMBUS\sailed\ocean\BLUE

     Alphabetic character case is not important on entry.  Each Drive:\Directory
     entry completion has a confirmation prompt repeating the entry in all-
     capitals.


     READING/WRITING CIRCUIT FILES

     To read in a Circuit file, enter "R  <filename>" at Main Command.  If no
     filename is entered and no circuit list exists, LENA will prompt for the
     filename, the prompt including an 8-character space for the filename.

     If a circuit list exists, or did exist, the circuit _filename_ is in
     storage and LENA will display the name, then query whether or not to use
     it.  The prompt ends with "[Y/n]" and the capitalized "Y" indicates that
     depressing the <Enter> key alone will signify a Y for yes.  Entering N (no)
     to the query displays a prompt for a new filename entry.

     When the <filename> entry is completed, the Circuit read is done and a
     prompt is shown, indicating "New circuit read in, old circuit discarded." 
     This is followed by a display of the node of solution, the highest node
     number in the circuit.

     To write an existing Circuit to a disk file, enter "W <filename>" at the
     Main Command level.  If the filename is omitted, LENA will prompt for one
     in the same manner as a Read.

        Caution:  Using the same filename as an existing file will cause the
        existing file to be over-written.  The only way to save an existing
        file is to vary the filename of the Circuit to be written.

     When a Circuit Write is completed, control returns to Main Command level
     without further reminders or prompts.


     CIRCUIT CREATION DATES AND REMARKS

     Any time a Circuit Value is MODified, or any time a branch is DELeted or
     INSerted, that time will be set into the "creation date" of the Circuit.  
     Creation Date is Read from, and Written to, disk.  That is separate from
     DOS' own file Write time-stamp; alteration may take place some time before
     a new file is written.  Creation Date is a convenience for keeping track of
     several Circuit versions.

     It is also useful to include short notes about a Circuit.  The "REM" (also
     "*") entry at Main Command level allows writing a 47-character Remarks
     string for such notes.  The Remarks string can be entered between vertical
     bar symbols or directly, using "REM <remarkline>".  Depressing the <Enter>


                                LENA - Page 32 of 46





     key without entering anything will result in a blank Remarks string.

     A Remarks string will remain as-is until changed manually or a new Circuit
     is read in from disk.  A Circuit Read will displace any old Remarks string
     with that stored in the file, including any file-stored string which is
     all-blanks.


     SOLUTION STORAGE AND RETRIEVAL

     Any completed Solution may be SAVed by entering "SAV <filename>" at the
     Main Command level.  If <filename> is omitted, its entry will be prompted. 
     Data stored consists of the magnitudes and phase angles over all
     frequencies of solution, frequency limits, type of solution (frequency-
     voltage, impedance, etc.), time-and-date of solution, and the filename of
     the Circuit solved.  Solution filenames may be the same as Circuit
     filenames; file extensions identify which is which.

     A Solution may be retrieved by entering "BRI <filename>" at the Main
     Command level.  ('BRI' for BRIng back)  This restores the solution data and
     displays the filename of the Circuit solved (stored by a SAVe).  Solutions
     may be viewed directly but _conditions_ of analysis-solution may not be
     changed; i.e., if a frequency-amplitude solution is brought back, you
     cannot request an impedance solution since the circuit itself may be
     missing or the circuit does not have the same node maximum.  Similarly, you
     cannot change the Node of Solution other than what was originally SAVed.

     Some care should be exercised with BRIng.  You may BRIng back a PLOtted
     solution, change scale limits to whatever you want, print out a new PLOt, 
     even do a PRInt-tabulation.  This can be very useful in recording analysis
     data or visually comparing solutions, but there is no greater capability of
     that function.

     Note:  A great number of combinations of conditions were tried for
     deliberately setting up a program crash situation.  None were found but it
     might happen if BRIng is used improperly.

     The principal reason for Solution storage is to permit external program
     data formatting/presentation.  Viewing or hardcopying previous solutions is
     only the secondary reason.


     COMPATIBILITY WITH LINEA DATA FILES

     LENA's circuit-list and solution files have an identical structure to 
     those of LINEA.  LINEA-generated circuit and solution files are compatible
     with LENA.  LINEA has a third type of data file containing repetitive
     waveform coefficients (.LWC).  Since LENA has no waveform reconstruction
     routines, that file type cannot be used with LENA.











                                LENA - Page 33 of 46





     SOLUTIONS AND OUTPUT
     --------------------

     GENERAL SOLUTION ORGANIZATION OF LENA

     LENA has two major solution forms:  Frequency-voltage ('Frequency'), and
     Impedance.  Frequency-voltage solutions yield voltage magnitude and phase
     angle at one selected Circuit node at each frequency of a specified
     frequency sweep.  Impedance solutions find the impedance at one selected
     node at each frequency of a specified frequency sweep.  Frequency sweep is
     selectable up to a maximum of 200 discrete frequencies.
 
     Two forms/format of output are selectable:  Tabulation ('Print') of written
     values or Graphical ('Plot') equivalent using characters in a simulated
     plot.  Either output form is available from one solution.

     LENA compares all requested solution-output combinations requested with
     previous solution-output combinations, calling the time-consuming
     mathematical analysis-solution calculation routine only when required. 
     Users need only request output and form.


     SCALE LIMIT SELECTION ON PLOT

     Every parameter kind in a PLOt is scanned for minimum and maximum value,
     then displayed with a query as to whether those extremes are to be used as
     scale limits.  Pressing the <Enter> key without entering anything else will
     set solution extremes as scale limits.  Entering specific numerical values
     will make those values the scale limits.

     If desired, all PLOt scales can be 'flopped' left-for-right by specifying
     scale limits in reverse order.

     Specific scale value entries follow the 'data word' rules of LENA. 
     Omitting a data item, entering only the separator character (comma,
     semicolon, forward-slant), will make that data item zero.

     Degree limits for phase angles in Voltage PLOts are fixed, _not_ set by the
     solution.  At LENA start, those degree limits are -180 and +180 degrees.
     Degree limits may be set to anything else and will remain at those settings
     until changed again.


     TWO FORMS OF IMPEDANCE PLOT

     Either Polar or Rectangular complex form may be selected for Impedance
     PLOts (both forms are tabulated together in PRInts).  At the query,
     pressing <Enter> key without entering anything else will select Polar form;
     an "N" for 'no' must be entered to select Rectangular form.

     Polar form _phase_angle_ scale limits are default-set by solution values or
     reset by user entry, unlike the Frequency-Voltage PLOt degree setting
     rule.







                                LENA - Page 34 of 46





     SYNTAX ON SOLUTION TYPE AND FORM

     Only two Main Command words are required, one to select Type, the other to
     select Format.  They may be in either order.  "PRInt FREquency" will yield
     the same solution and tabulation as "FREquency PRInt."  Or, to simplify
     entry, "P F" or "F P."  Or a three-letter acronym can substitute for either
     double word.  "PRF" would be equal to "P F" or "F P", itself
     being an acronym for PRint Frequency.


     GENERATING PLOT ARTWORK

     ASCII-character "plotting" is rather coarse.  Quick, yes, but still too
     coarse for smooth graphic output.  The character plot outputs can made in
     sections so that a 2X to 10X larger master can be generated for tracing
     finished art.  The only requirement is that frequency spacing is continuous
     and the scale extremes set to allow amplitude-phase-delay to be continuous.
     All scale extremes may be set manually, including reverse, left-for-right
     direction.

     Solution files may be read by an auxilliary program (not included) which
     can format data to whatever output device is available.  Solution file data
     is composed of ASCII characters in generally-decimal format.  Records and
     data fields are described in Appendix file LE_APX_A.TXT.


     SINGLE DC OUTPUT

     It is possible to PRInt and PLOt zero-frequency (DC) output but hardly
     necessary to send such output to the printer.  A DC-only PRInt or PLOt will
     have only one line; manual notation at each node will be as easy as 
     printing one page for each node.

     To set DC-only from Main Command, enter "F DC" or "F 0,0,0".

     There are no provisions to analyze-solve all nodes at one output command.

     It is possible to examine the DC stability of transistor bias networks and
     the like, but somewhat cumbersome to perform with LENA.  A branch(s) for 
     base-emitter diode voltage drop must be added and, possibly, an IDC branch
     to simulate varying supply voltage to the bias network.  MODify edit
     functions can vary those values, plus the bias network values to see the
     effect of change.  It may be that conventional, manual techniques, using a
     pocket calculator are quicker and easier.
















                                LENA - Page 35 of 46




.
     CONVERTING FROM SCHEMATIC TO LISTING
     ------------------------------------

     LENA doesn't have any way to convert from a symbolic schematic drawing to
     a Circuit List.  To fully analyze and solve frequency response of a
     circuit, you need to convert the components into the nodes and branches
     which LENA will recognize.  Most of those branches are simply duplicates
     of schematic symbols.


     IN THE BEGINNING...

     ...there was scratch paper.  As a suggestion based on others' experiences,
     enough paper should be available so that you can redraw schematics, make
     notes, and tabulate all the branches before keying a circuit into LENA>
     A few things will not appear the same as either schematic or actual
     actual circuit or may require different components.  Redrawing the
     schematic saves the original diagram.

     Node numbering can follow signal flow, low node numbers toward input, high
     numbers toward output.  That also results, generally, in quicker solution
     execution times.  LENA produces the same solution results regardless of
     node ordering.  One method is to mark redrawn schematics with node numbers
     enclosed in a circle, a distinctive marking not usually used as a symbol
     except in "Sams Photofact" (tm) schematics.

     Passive components can convert readily to single branches.  Since LENA
     allows up to 8 characters for type descriptions, you can use conventional
     reference designations such as "R-12," "C-5A," and so forth.  Follow the
     signal flow again, branches beginning at signal input, generally ending at
     signal output.


     NODE NUMBERS MUST BE CONTIGUOUS

     LENA will check for missing node numbers and display a prompt indicating
     each one.  LENA won't "crash" but it will stop analysis of the circuit 
     (error message shown) or result in zero node voltage or impedance.  It is
     better to organize the node ordering in the beginning to avoid missing node
     numbers.

     During the course of analyzing-solving a circuit, a connecting branch may
     be manually OPEned.  If such an OPEn results in the equivalent of a missing
     branch number, analysis may stop with an error message or produce a zero
     solution.  Again, non-fatal, but it can cause some confusion until the user
     understands what was done.  It is better to plan ahead and anticipate which
     branch openings might result in breaking signal flow.


     COMMONS, "GROUND" AND SUPPLY LINES

     Overall circuit 'ground' (or 'earth' common) is ALWAYS node 0.  Always.

     Power supply lines can _also_ be node 0...provided they are well bypassed 
     to ground in the actual circuit.  This is a startling departure from usual
     circuit thinking but, considering LENA does the equivalent of "small-
     signal" analysis-solution in frequency domain _only_, quite acceptible.



                                LENA - Page 36 of 46





     LENA doesn't normally set bias, enabling DC control of collector current,
     or the like.  In "small-signal," frequency-domain analysis, all voltages 
     are presumed to be linear.  There are no provisions for simulating
     transistor or diode saturation or cut-off.  As far as AC and RF are
     concerned, power supply lines are just another common; if well bypassed to
     ground, they can BE ground to LENA.

     If there is some doubt as to a supply line's bypassing, use a separate node
     or nodes for that line and simulate the bypassing, using series R-C
     branches for electrolytics (resistance approximately calculated from an
     electrolytic's ESR), possibly even small inductances in series with
     capacitors.

     It is possible to model a very-high-gain amplifier circuit in LENA.  [over
     200 db gain is possible]  High-gain amplifiers might have destructive
     feedback via inadequate supply line decoupling.  LENA can show such
     feedback without simulating the oscillation that would happen with a real-
     world circuit.


     PARASITIC REACTANCE, RESISTANCE

     LENA branch types LQ and CQ are good for simulating lossy reactances at
     RF.  For practical programming and memory reasons, Q is the same at every
     frequency except DC.  A quick look at Q tables from manufacturer's data
     sheets indicates Q does vary at least 2:1 over a wide frequency range. 
     Accurate simulation might require limiting analysis bandwidth, modifying Q
     for the next limited analysis bandwidth, and so on.

     LQ branches are simulated internally by a series R-L equivalent, resistive
     part equal to inductive reactance magnitude divided by Q.  CQ branches are
     simulated internally by a parallel R-C equivalent, conductive part equal to
     capacitive susceptance magnitude divided by Q.  Together, an LQ branch and
     a CQ branch can accurately portray a real L-C resonant circuit.

     Resistors have some parasitic capacity in parallel with resistance, varying
     from 100 femtofarads (SMTs) to 1 picofarad (axial-lead types).  At
     frequencies where that capacity becomes significant, a PRC branch should be
     used.  If a circuit has very long leads on a resistor, lead inductance can
     have an effect on total component impedance but can be simulated with an
     SRL branch.  A capacitor with lead inductance or an inductor with lots of
     winding capacity must each use two branches.

     The most difficult part about modelling parasitics is _knowing_ what the
     parasitics are.  LENA can't help you there, but, once known, LENA can
     simulate parasitics exactly.


     CURRENT THROUGH DEPENDENT BRANCHES

     Using a type HFS dependent current source to monitor current through a
     branch is an excellent _non-intrusive_ technique of analysis.  There is
     absolutely no 'probe capacity' or change in any measured branch due to the
     real-world measuring equipment.  However, some of us 'schematic oriented'
     analysts may fall into a trap with certain branches.





                                LENA - Page 37 of 46





     LENA's double-component branches LQ, CQ, SRL, SRC, PRL, and PRC are
     analyzed as complex quantities at each frequency.  If you want to measure
     the current through an LQ, you will get the current through the _entire_
     series R-L equivalent branch, not just the inductor.  With a type CQ,
     current is the total to the parallel R-C, not just the capacitor.  

     Measuring separate resistive or reactive currents requires a circuit having
     only resistance or reactance.


     VOLTAGE ACROSS DEPENDENT BRANCHES

     The voltage across a dependent branch for a type GMS dependent current
     source is straightforward.  It should be kept in mind that voltage polarity
     depends on the ordering of Plus and Minus nodes for a dependent branch.

     You can visualize a GMS's dependent branch as having a differential
     voltmeter connection to the GMS...reversing the 'voltmeter' leads will
     reverse the 'reading' polarity.


     CREATING "STIFF" VOLTAGE SOURCES

     Ideal current sources have infinite source resistance.  Voltage across such
     a source is the voltage drop across _everything_ connected to that source. 
     While that will correctly model a transistor collector or drain, or a
     vacuum tube plate, you may want a very _low_ impedance voltage source or
     one with a specified source impedance.

     LENA allows real-world-impractical voltage sources.  A 1000 Ampere current
     source across a 1 milliohm resistance will produce a 1 Volt voltage source
     having a source impedance of 1 milliohm.  Add a series resistance of, say,
     50 Ohms, and you have a voltage source with a 50 Ohm source resistance.
     A Mega-Ampere current source across a micro-Ohm resistance makes an even
     'stiffer' voltage source.  Such is quite within the magnitude range of
     LENA.


     NEGATIVE RESISTANCE OR REACTANCE

     There are a few _theoretical_ equivalents to real-world circuits that
     require 'negative' value components.  LENA allows this; just enter a
     negative resistance, capacitance, or inductance.

     Negative values do not change the magnitude of single-component branches,
     only the phase-angle/polarity.  A negative inductor has inductive reactance
     magnitude proportional to frequency, a negative capacitor has capacitive
     reactance magnitude inversely proportional to frequency.


     OPERATIONAL AMPLIFIER CIRCUITS

     All 'Op-Amp' Integrated Circuits have a built-in "breakpoint" frequency
     where the open-loop gain begins to fall at a rate of 20 db per decade of
     frequency...and also produces a definite phase-shift at higher frequencies.

     This _will_ affect overall response of ideal voltage-frequency-selective
     circuits which don't have compensation for that Op-Amp phase shift.


                                LENA - Page 38 of 46





     If you are analyzing a circuit which is questionable as to such phase-shift
     compensation, try setting all Op-Amp macromodels to high Megahertz
     breakpoint frequencies at first.  Get a hardcopy response printout, then
     replace all the Op-Amp macromodels with those having a lower breakpoint
     frequency, re-analyze, finally comparing the responses.

        Note:  At least two hardcover textbooks have circuit examples and tables
        of values, all of which assume _ideal_, no-breakpoint Op-Amps.  Such
        circuits will only work as advertised over a frequency range _below_
        real-world Op-Amp breakpoint frequencies.


     FIELD-EFFECT TRANSISTOR MODELS

     These were not included in LENA because they are simple enough to model
     with four conventional branches:  Three single capacitors representing the
     three junction capacities and a GMS across the Source-Drain junction
     dependent on Source-Gate capacitance voltage.


     BANDWIDTH-ALTERABLE NETWORKS WITH THE TRANSFORMER MACROMODEL

     Double-tuned transformers with specific coupling coefficients are a simple
     way to set the passband of an amplifier.  Coupling coefficient k is one of
     the critical items.  The transformer macromodel can be used quite
     effectively in the analysis-solution of such circuits since coupling
     coefficient is one of the parameters of the macromodel.  There is one word
     of caution on such use:  The macromodel does not include quality factor Q
     and Q is often the other critical parameter.

     Q of a tuned transformer can be modelled with parallel resistances across
     each winding.  Resistance value is Q times the resonance-frequency
     inductive reactance.  An alternate can be a series resistance with each
     winding, resistance equal to resonance-frequency inductive reactance
     divided by Q.  The alternate requires at least one extra circuit node,
     which may not be practical in large circuits.

     Another possibility is to not use the macromodel at all and to manually
     calculate the four branch values illustrated under TRANSFORMER MACROMODEL
     DETAILS.  The difference here is that each winding can use an LQ branch
     type instead of a pure inductance.


     CREATING "BLACK BOX" SUB-CIRCUITS

     If you have a component with _known_ characteristics over frequency, some
     creativity will allow a combination of branches to simulate that component.

     LENA will allow tailoring that "black box" simulation to fit the known
     characteristics.  That may take several nodes.

     To apply such a simulation to the entire circuit, it can be re-created
     there...but the nodes needed _within_ the simulation cannot be connected to
     other parts of the entire circuit.






                                LENA - Page 39 of 46




.
     INSTALLING LENA
     ===============

     LENA PROGRAM SET FILES

          README.1ST   - Short text description of LENA Program Set.
          LENAMANL.TXT - Text file, description/instruction for LENA program.
          LENACFG.EXE  - Configuration program, LENA.CFG file generator.
          LENAS.EXE    - Standard/non-coprocessor version executable.
          LENAN.EXE    - Numeric coprocessor version executable.
          LENAMAIN.HLP - On-line Help file for LENA Main commands.
          LENACKT.HLP  - On-line Help file for LENA circuit model types.
          LENAREG.TXT  - Text file for LENA Registry
          SINGSHOW.LIN - Circuit file example, all single branches.
          TRANSFRM.LIN - Circuit file for transformer macromodel circuit.
          TLINE.LIN    - Circuit file for transmission-line macromodel.
          BIPOLAR.LIN  - Circuit file for transistor macromodel circuit.
          OPAMP.LIN    - Circuit file for operational amplifier macromodel in a
                         Sallen-Key low-pass filter.
          PHASER.LIN   - Circuit file, audio phase-shift network for a
                         phasing-method SSB generator.
          PHASER7.LNA  - Solution file for PHASER circuit, node 7.
          RES100K.LIN  - Circuit file, simple 100 KHz resonant circuit.
          FILE_ID.DIZ  - Short text file description preferred in some BBSs.
          LE_APX_A.TXT - Appendix text on LENA data file structure.
          LE_APX_B.TXT - Appendix text on use of example circuit PHASER.
          LE_APX_C.TXT - Appendix text on Configuring LENA, use of LENACFG file.
          LE_APX_D.TXT - Appendix text, history of LINEA - LENA, other CAE.
          LE_APX_E.TXT - Appendix text, comparison of LENA with other programs;
                         transferring circuits to/from SPICE net-lists.
          LENACMND.LST - One-page list of main command words for optional user
                         reference.
          CIRCTYPE.LST - One-page list of circuit model Type words for optional
                         user reference.
          CPUID.EXE    - CPU/numeric coprocessor identifying program; public
                         domain from Intel Corporation.

     LENA.CFG is required to run either LENAS or LENAN (or their renamed equals)
     and that file is generated by LENACFG.EXE.  LENACFG must be run first.
     Answering the few questions in that program will set up constants for
     incorporation into the created LENA.CFG file.  LENACFG does not alter any
     other computer system data.

     LENACFG will ask for your computer system's CPU (Central Processor Unit)
     type and whether or not you have a numeric coprocessor.  If you answer
     "don't know" to that question, it will prompt you to run CPUID from within
     LENACFG.  CPUID will produce a one-line statement indicating the detected
     CPU and coprocessor.  All .EXE files are compiled to run with an 8086 or
     higher CPU (every PC except the very first).  If you have an 80386DX or
     80486DX CPU, the numeric coprocessor is built in.

     The last action of LENACFG is a request to rename/copy either LENAS or 
     LENAN to LENA.  LENAS is compiled to include software mathematics routines 
     and will run whether or not a numeric coprocessor is present.  LENAN is 
     compiled with in-line calls to a numeric coprocessor and is smaller in
     code size and much faster in execution.  Trying to run LENAN on a computer
     without a numeric coprocessor will result in a system "hang." 



                                LENA - Page 40 of 46





     Once LENA.CFG is created and LENA.EXE copied/renamed, copy/move those two
     files and the two .HLP files to a more-permanent directory.  All four
     should reside in the _same_ directory.  Data files (.LIN and .LNA
     extensions) may be in a different directory.  Note: LENA allows for Data
     files in other drives:\directories but, when first run, assumes the same
     drive:\directory as LENA.EXE and LENA.CFG.  The Help files (.HLP extension)
     are optional.  As an alternate to the Help files, the enclosed .LST files
     are each one page, containing Main Command words and circuit model Type
     words.

     It is recommended that LENAMANL.TXT be printed out first.  This text file
     (the document now being read) is formatted for 8 1/2 by 11 paper size, 75
     character maximum line width (5-character left margin provided), 66 lines
     per page and is directly printable by DOS command "COPY LENAMANL.TXT PRN".


     APPENDICES

     All LE_APX_x.TXT files are appendices for this manual.  Users can append
     them to LENAMANL with any text editor, print them out separately, or leave
     them as they are.  Those references were split from the manual text so as
     to make the manual more manageable.

     CPUID.EXE is a public-domain executable file that may be used elsewhere or
     on another computer to identify CPU type.  It was written and assembled by
     Intel Corporation.  It is included as an aid to running LENACFG.


     REGISTRY

     The LENA Program Set is _not_ free.  It is Shareware.  You are free to use
     it on a trial basis for 21 days.  After the trial period, continued use
     obligates the individual user to Register the LENA Program Set with the
     author.  Full details on Registry are found in text file LENAREG.TXT and
     are briefly noted following:

     Individual user Registry is $30 U.S., payable by check or money order.
     This also applies to any business, organization, or educational institution
     after the trial period.  Upon registration, each registrant is sent a disk
     containing the LENA Program Set without the registration message on-screen.


     CPU VERSIONS AND PROGRAM SET COPIES

     Installation of a numeric co-processor is highly recommended.  LENA does
     extensive floating-point numeric calculation; a numeric coprocessor can
     greatly reduce execution times.  

     Additional copies of the LENA Program Set (with choice of disk size, on
     high-density media) is available from the author for $10 U.S., postpaid,
     surface mail only.  Additional copies may be ordered only by registrants.









                                LENA - Page 41 of 46





     FIRST-USE LENA PRIMER/TUTORIAL
     -------------------------------

     This assumes that the entire LENA program set is on disk and that LENACFG
     has been run and completed.  The following short primer assumes the user
     has some knowledge of circuit theory but is unacquainted with computer-
     aided design/engineering programs.
  


     ON-LINE HELP

     A short, 6-screen display of commands and circuit elements is available at
     the Main Command by entering HELp, HEL, HE, or ?.

     Help screens are always in the same order and all but the last have a 
     "More [Y/n] ?" prompt.  To get the next screen, just depress the <Enter>
     key or enter "Y".  To exit the Help display, enter "N" and it will return
     to Main Command level.

     Help screens are stored on disk as a Text file, approximately 10K in size. 
     Users familiar with LENA may delete that .HLP file, if desired.  If the
     .HLP is deleted, a Help request will only result in an error message
     indicating that the Help file cannot be read.  Help file presence or
     absence does not affect LENA operations.


     GETTING ACQUAINTED WITH CIRCUIT LISTINGS

     At the Main Command, enter "READ SINGSHOW".  This reads example data file
     SINGSHOW.LIN from disk into LENA, a non-working listing showing all
     available single-branch circuit components.  A prompt will appear
     indicating a new circuit read in, old circuit (if any) discarded, and the
     node of solution, then return to Main Command.

     Enter "LIST" at Main Command.  The circuit list will scroll up, headed by
     the title display showing circuit filename, when it was created, remarks
     for that circuit, node of solution, current time and date, and any branches
     opened.

     To get a printed copy, check that printer paper is positioned at the top of
     a page, enter "ON" at Main Command, then enter "LIS" again.  The screen
     only shows the Main prompt which has changed from "MAIN*>" to "Main->"
     indicating output is directed to printer.  Enter "OFF" at Main; Command
     prompt becomes "MAIN*>" again indicating output is to screen.  [printer
     will do one line-feed on the OFF command, quite normal] 

     List data is fairly self-explanatory.  Branch type descriptions allow up to
     8 characters maximum but only the first one, two, or three letters matter. 
     The first branch is designated RESISTOR but it could also have been "R-1"
     or just "R" or even "R_FIRST."

       Note:  Branch type descriptions will always be displayed as all-capitals,
       regardless of entry case.

     'Plus' nodes and 'Minus' nodes have specific meanings only for current
     _sources_ and for dependent branches of a dependent current source.  If
     this is confusing, please review the description of independent and


                                LENA - Page 42 of 46





     dependent current sources given earlier.  'Plus' and 'Minus' nodes would be
     arbitrary for a circuit composed entirely of passive branches.

     In the value columns, two-value branches will always have the same ordering
     as the minimum branch type description; i.e., an LQ branch would show
     inductance first, Quality factor second.  The number of significant digits
     is rounded-off to five.

     There is a bit of shorthand in the 3-letter type description of series and
     parallel R-L and R-C branches.  The first letter for a Series branch is
     "S."  The first letter of a Parallel branch is "P."

     Dependent current sources GMS or HFS will always indicate their dependent
     branches by both branch number and type description. 


     TRYING OUT A MACROMODEL

     Read in circuit file TLINE ("R TLINE" at Main Command), then List it.  Note
     that SIG ('signal generator') and the two resistors (R-SOURCE, R-LOAD) are
     in the same format as with SINGSHOW...all three are single branches.  Type
     "Z" is a minimum type description for a transmission line macromodel and
     occupies three contiguous branch positions in a List, corresponding to the
     three branches created and analyzed within LENA.

     Where single branches had node numbers under both Plus and Minus columns, a
     macromodel has only one node (under Plus column) with an identification of
     that node of the model (under Minus column).  [A transmission line doesn't
     really have an "input" and "output" but that arbitrary identification is
     better than saying "one end" and "other end."]  Values are shown for the
     entire model, not individual model branches.

     Enter "F  1M,50M,-15" at Main Command.  This tells LENA to set a frequency
     sweep from 1 MHz to 50 MHz in 15 logarithmic steps.  ["1M" and "50M" must
     use upper-case M for Mega]  You can confirm this by entering "SET" at
     Main...resulting in a circuit title describing TLINE followed by frequency
     range.  A SETtings display is screen-only and useful for checking current
     settings.

     Enter "PRI  FRE" at Main...requesting a Print (tabulation) of voltage
     solutions over Frequency.  Tabulation will scroll up on the screen.  The
     node of solution is 2 and the voltage across R-LOAD is 22.800 Volts.  LENA
     has a default zero-decibel reference of one volt so the DB column shows
     27.15 decibels.  TLINE has no reactive branches so the voltage remains
     constant over frequency.  Phase angle at node 2 varies over frequency
     (expected) but Group Delay is constant at 13.556 nanoseconds.

     Group Delay follows actual time delay from a signal source to node of
     solution...provided that frequency increments are small enough and phase
     angle changes are smooth enough...it is a calculated value of differential
     phase angle divided by differential frequency.  TLINE has a transmission 
     line length of 120 inches and a velocity of propagation of 0.75, equivalent
     to a free-space path of 160 inches.  Signal propagation at the speed of
     light (299,792.5 KM/Sec) over a 160 inch distance is 13.556 nanoseconds.

     Enter "DBR  25" at Main Command.  This tells LENA to set the zero-db
     reference at 25 Volts.  Enter "P  F" at Main to repeat the tabulation of 



                                LENA - Page 43 of 46





     voltage at node 2.  Everything is the same as before except the decibels
     column shows "-0.80 db" instead of the previous 27.15 db.

     Enter "PLOT  F" at Main.  Three prompts will appear in sequence, each one
     indicating minimum and maximum solution values of voltage, phase angle, and
     group delay.  To use solution extremes as scale limits, just use the
     <Enter> key at each query.  A simulation of a graph plot will appear
     following a circuit title header.  Scale limits are shown on the graph top.

     Relative voltage in db [* mark] and Group Delay [^ mark] is fairly
     constant; phase angle [: mark] changes over the entire scale range.

     You can experiment with different scale limits by entering "PLF" (alternate
     single-word command for "PLOt FREquency") and then entering your own values
     at each limit prompt.  Note: If there is no change in frequency limits, no
     node of solution change, no circuit change, LENA retains the first
     solution; repeated PLOts use the same solution data, changing only the
     simulated plot mark positions.

     Enter "NOD  1" at Main to tell LENA to solve for voltage at node one
     (signal generator or transmission line 'input').  Enter "PRF" at Main
     (shorthand for "PRInt FREquency").  Tabulation of voltage at node one shows
     a constant 25 Volt, 0 db, 0 degree phase-angle over frequency.  Considering
     the 50 ohm characteristic impedance line is matched at both ends with
     perfect 50 Ohm resistors, this is expected at the signal source end of the
     line.

     To check the "input" impedance of the line, enter the following at each
     Main Command prompt:  "O  2" (OPEn branch 2); "PR  Z" (Print-tabulate
     Impedance).  R-SOURCE has been temporarily disconnected and LENA will
     tabulate impedance "looking into" node 1.  Impedance will be a constant,
     resistive 50 Ohms.  [All signal sources are automatically disconnected
     during impedance solutions.]

     Perfect transmission lines with perfect resistive terminations tend a bit
     towards boredom.  For variety, Open and Close the terminations and check
     voltage at each end, or use the Modify command to change the termination
     resistance values.  This is quick way to see the effects of "open" and
     "shorted" transmission line sections over frequency.


     TRYING OUT CIRCUIT EDIT FUNCTIONS

     Read in SINGSHOW and note branch number four's list line.  Enter
     "OPEN 4" at Main Command, then "LIST" again.  Branch 4 will show asterisks
     between the fourth branch's data, indicating that, while it is still in the
     list, it is "struck out" of any analysis.  Displays in color show an open
     branch in grey rather than cyan.  Branch 4 is now disconnected but it
     remains in the listing.  Note the bottom line in the circuit header display
     indicating number 4 branch open.

     At Main Command, enter "CLOSE 4," then "LIS."  Branch 4 has no asterisks,
     indicating its connections have been closed to the rest of the circuit. 
     The bottom line of the title display indicates that no branches are open.

     Note branches 5 and 6, then enter "DELETE 5" at Main Command.  Enter "LI" 
     to see the list again.  Old branch 5 is gone and the former branch 6 now
     occupies that list position.  All higher branches have moved down one.


                                LENA - Page 44 of 46





     Enter "INSERT 5" at Main Command.  A new prompt for Type-Nodes will appear,
     indicating that INSert has jumped into the Circuit Entry.  Enter "CQ,1,5"
     at the Type-Nodes prompt.  Enter "5u,50" at the prompt for Branch 5 values.
     The Main Command will return.  Enter "L" to see the list again.

     Branch 5 has been restored, and all higher branches have returned to their
     original branch order numbers.  However, a 5 microfarad capacitor with a Q
     of 50 is unlikely while a 5 nanofarad capacitor is more realistic.  Enter
     "MODIFY CQ" at Main Command.  This results in a request for values of
     branch 5 (type "CQ").  Enter "5n,50" at the values prompt (being careful to
     enter a lower-case 'n') then List the circuit.  Branch 5 has been changed
     to 5 nanofarads with a Q of 50.  Note that the creation time and date is
     now the same as the current time and date.  

     Enter "OPE 1" at Main Command.  A prompt will appear indicating that branch
     13 is dependent on an open branch and, as a result, branch 13 has been made
     open also.  List the circuit to show both branches indicated as open. 
     LENA has checked for this possibility after the OPEn command was
     completed.  Had this check not been done, LENA would not have crashed or
     hung, merely stopped trying to analyze the circuit (and indicating it
     stopped) and returned to Main Command.  LENA lets you know what caused
     most of the common errors.

     Enter "CLO 1" at Main Command, then List the circuit.  Branch 1 is back to
     closed connection but branch 13 is still open.  Notice also that 13 must
     have a separate CLose command to restore it.  The extra CLOse command is
     necessary since one passive branch can be the dependent branch for several
     dependent current sources.

     Note the dependent branch description of branch 13.  Enter "DE 1" at Main. 
     A notice will appear that branch 12 is now open and dependent on a "<none>"
     branch.   Branch 1, "RESISTOR," will be gone from a Listing, all higher
     branches have moved down one list position, and the "HFS" branch is
     dependent on branch "0, <none>."  LENA automatically opened the HFS
     dependent current source since it no longer has a dependent branch.  The
     HFS cannot be CLOsed...but you can MODify that branch to be dependent on
     another branch that does exist in the circuit.  Once the dependent branch
     exists, a dependent current source can be CLOsed and OPEned at will.

     You have the choice of entering a branch number or a branch's type
     description for any edit function.  This is also true for entry of
     dependent branch of a dependent current source.  LENA is quite flexible...
     and forgiving.

     An "ADD" at Main Command drops into Circuit Entry, beginning at the next
     highest branch number...operation is otherwise identical to "NEW."  This is
     a good time to try out adding in your own circuit components, to get the
     "feel" of building a circuit.


     SAVING A CIRCUIT FILE, TRYING OUT DOS FUNCTIONS

     With SINGSHOW circuit edited to something else, enter "WRITE" at Main
     Command.  A prompt will tell you that "SINGSHOW" filename exists and
     queries if you want to use that name.  Enter "N" for no.  Another prompt
     requests the new filename, cursor stopping at left-most position within two
     vertical bars.  Enter something like "TEST1."  The edited file will be



                                LENA - Page 45 of 46





     written to disk in the same directory containing LENA.

     Enter "L" at Main Command.  The List header now shows "TEST1" as the
     filename, not "SINGSHOW."  LENA always uses the last circuit filename
     entered as the filename of the circuit title.  Using the "NAMe" command,
     just the circuit filename can be changed.  Circuit title Remarks will
     remain the same as for SINGSHOW and that can be changed any time with the
     "REMarks" Main Command. 

     Enter "DOS" at Main Command.  This goes into a 'DOS Shell' with LENA held
     in memory.  A prompt reminds you to enter "COMMAND" if you want to stay in
     DOS; the Shell is good for only one DOS command unless that "COMMAND" word
     is entered.  Request DOS to show the directory.  TEST1.LIN will appear in
     the directory list, indicating you really did write the circuit file.

     If you entered "COMMAND" once in DOS, you can stay in that environment
     until you enter "EXIT."  You can change directories, delete or rename old
     files, do any DOS command.  LENA remains patiently in the background, all
     data intact.  [Note: This assumes your computer has a minimum of 142K free
     RAM]  Entering "EXIT" takes you out of the DOS Shell and returns to
     LENA...the Main Command prompt will appear, indicating you returned
     safely.  Enter an "L" for List and the TEST1 circuit will scroll up.

     Except for the DRIve and DIRectory commands, LENA has no other DOS
     functions within program.  The "DATe" command at Main is a user-
     convenience, display-only function; resetting the computer time and date
     must be done at DOS level.

     To change the DRIve:\DIRectory for LENA data files, drive and directory
     must _already_ exist; LENA doesn't create them.  If a non-existant drive
     or directory is specified, a prompt is issued to that effect, no read or
     write is done, and there is a return to Main Command level.




























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