{ This code was written for the microwave lab at the University Of Central Florida by Robert Middelveen. March 11, 1986 } Program Double_Stub_Impedance_Matching; Const Conv = 1.7453292e-2; { CONVERT FROM DEGREES TO RADIANS } C = 2.998e8; { SPEED OF LIGHT IN FREE SPACE (Meters/Sec) } VAR Z0, { CHARACTERISTIC IMPEDANCE OF THE LINE } ZST1, { '' '' '' '' 1st STUB } ZST2, { '' '' '' '' 2nd STUB } F, { FREQUENCY (Hz) } D,DD, { DISTANCE FROM THE LOAD D, Wavelengths } { DD, Degrees } DBS, { DISTANCE BETWEEN THE STUBS, Wavelengths } ZZR, { LOAD IMPEDANCE, REAL PART } ZZI, { '' '' , IMAGINARY PART } ZLR, { NORMALIZED LOAD IMPEDANCE, REAL PART } ZLI, { '' '' '' , IMAGINARY PART } YLR, YLM, LAM_LM, { Y's ARE NORMALIZED LOAD ADMITTANCES } { R's ARE REAL, I'S ARE IMAGINARY, } { M's ARE THE MAGNITUDES, P'S ARE THE PHASE. } YLI, YLP, LAM_LP, { LAM's ARE THE REFLECTION COEFFICIENT } { AT THIS POINT } YD1R, { THE NORMALIZED ADMITTANCE LOOKING AT THE LOAD } YD1I, { FROM DISTANCE D } A,B, { 2 PARAMETERS USED BY PROCEDURE CIRCLE } Y11R_1, LAM_11_1R, LAM_11_1M, Y11I_1, LAM_11_1I, LAM_11_1P, Y11R_2, LAM_11_2R, LAM_11_2M, Y11I_2, LAM_11_2I, LAM_11_2P, { THE ABOVE: THE NORMALIZED ADMITTANCE AND THE REFLECTION COEFFICIENT } { LOOKING AT THE PARALLEL COMBINATION OF YD1 AND THE FIRST STUB. } { THERE ARE 2 POSSIBLE SOLUTIONS AT THIS POINT. } { R, I, M, P: REAL, IMAGINARY, MAGNITUDE, PHASE } YS1_1, LAM_S1_1P, { THE NORMALIZED ADMITTANCE OF THE FIRST STUB } YS1_2, LAM_S1_2P, { 2 SOLUTIONS. LAM's ARE REFLECTION } DUMMY, { DUMMY REAL VARIABLE } L1_1, { LENGTH OF THE FIRST STUB IN WAVELENGTHS } L1_2, { THERE ARE 2 SOLUTIONS. } LGTH1_1, LGTH1_2, { SAME LENGTHS BUT IN METERS. } Y22R_1, Y22I_1, LAM_22_1M, LAM_22_1P, Y22R_2, Y22I_2, LAM_22_2M, LAM_22_2P, { THE ABOVE: THE NORMALIZED ADMITTANCE AND THE REFLECTION COEFFICIENT } { LOCATED AT POINT 22 ON THE CHART. LOCATED DOWN THE LINE DISTANCE D } { + THE DISTANCE BETWEEN THE STUBS. REPRESENTS THE PARALLEL } { COMBINATION OF THE LINE AT 22 AND THE SECOND STUB. } YS2_1, LAM_S2_1P, { THE NORMALIZED ADMITTANCE OF THE SECOND STUB. } YS2_2, LAM_S2_2P, { THE LAM's ARE REFLECTION } L2_1, { THE LENGTH OF THE SECOND STUB IN WAVELENGTHS } L2_2, LGTH2_1, { AND IN METERS. } LGTH2_2, SWR_1, SWR_2: REAL; { THE STANDING WAVE RATIO BETWEEN THE TWO } { SECTIONS OF STUBS. 2 SOLUTIONS. } Q1,Q2: CHAR; { ANSWERS TO QUESTIONS. } (*$I B:ATAN2.PAS *) (* A TWO ARGUMENT ARCTANGENT FUNCTION NOT PRESENT IN STANDARD PASCAL *) (* CALCULATES ANGLES IN DEGREES FOR ALL 4 QUADRENTS *) PROCEDURE R_P(VAR MAG,PHASE:REAL; RE,IM:REAL); { RECTANGULAR TO POLAR CONVERSION } BEGIN MAG:=SQRT(SQR(RE)+SQR(IM)); PHASE:=ATAN(RE,IM); IF PHASE<0.0 THEN PHASE:=PHASE+360.0 END; PROCEDURE P_R(VAR RE,IM:REAL; MAG,PHASE:REAL); { POLAR TO RECTANGULAR CONVERSION } BEGIN RE:=MAG*COS(PHASE*CONV); IM:=MAG*SIN(PHASE*CONV) END; PROCEDURE ADM_REF(VAR LAMBDA_M,LAMBDA_P:REAL; Y_R,Y_I:REAL); { NORMALIZED ADMISSION TO REFLECTION CONVERSION } VAR NR,NI,DR,DI,NM,NP,DM,DP:REAL; BEGIN NR:=Y_R-1.0; NI:=Y_I; R_P(NM,NP,NR,NI); DR:=Y_R+1.0; DI:=Y_I; R_P(DM,DP,DR,DI); LAMBDA_M:=NM/DM; LAMBDA_P:=NP-DP; IF LAMBDA_P<0.0 THEN LAMBDA_P:=LAMBDA_P+360.0 END; PROCEDURE REF_ADM(VAR Y_R,Y_I:REAL; LAMBDA_M,LAMBDA_P:REAL); { REFECTION TO NORMALIZED ADMISSION CONVERSION } VAR LAMBDA_R,LAMBDA_I,Y_M,Y_P,NR,NI,NM,NP,DR,DI,DM,DP:REAL; BEGIN P_R(LAMBDA_R,LAMBDA_I,LAMBDA_M,LAMBDA_P); NR:=1.0+LAMBDA_R; NI:=LAMBDA_I; R_P(NM,NP,NR,NI); DR:=1.0-LAMBDA_R; DI:=-LAMBDA_I; R_P(DM,DP,DR,DI); Y_M:=NM/DM; Y_P:=NP-DP; P_R(Y_R,Y_I,Y_M,Y_P) END; PROCEDURE CIRCLE(VAR X1,Y1,X2,Y2:REAL; A,B,C,D,E:REAL); { THIS PROCEDURE CALCULATES THE INTERSECTION OF THE SPACING CIRCLE AND A } { CIRCLE OF CONSTANT CONDUCTANCE ON THE SMITH CHART. THE INPUTS ARE THE } { PARAMETERS OF THE TWO CIRCLES AND THE OUTPUTS ARE THE X AND Y COORDINATES } { OF THE TWO SOLUTIONS. THESE TWO SOLUTIONS DENOTE THE REFLECTION } { COEFFICIENT AT THE POINT Y11 ON THE CHART. } CONST TOLERANCE=0.001; VAR F,G,H,I,J,YSQ:REAL; BEGIN F:=C*C-B*B+D*D-E*E-A*A; G:=2.0*A-2.0*D; H:=4.0*B*B*(E*E-D*D)-F*F; I:=8.0*B*B*D-2.0*G*F; J:=-(4.0*B*B+G*G); X1:=(-I+SQRT(I*I-4.0*J*H))/(2.0*J); X2:=(-I-SQRT(I*I-4.0*J*H))/(2.0*J); YSQ:=E*E-SQR(X1-D); IF ABS(SQR(X1-A)+SQR(SQRT(YSQ)-B)-C*C)>TOLERANCE THEN Y1:=-SQRT(YSQ) ELSE Y1:=SQRT(YSQ); YSQ:=E*E-SQR(X2-D); IF ABS(SQR(X2-A)+SQR(SQRT(YSQ)-B)-C*C)>TOLERANCE THEN Y2:=-SQRT(YSQ) ELSE Y2:=SQRT(YSQ); END; PROCEDURE GET_DATA; { THIS PROCEDURE PROMPTS THE USER AND INPUTS THE VARIABLES NEEDED TO SOLVE } { THE DOUBLE STUB PROBLEM. } BEGIN ClrScr; WRITELN; WRITELN; WRITE('Z0=? '); READLN(Z0); WRITE('ZST1=? '); READLN(ZST1); WRITE('ZST2=? '); READLN(ZST2); WRITELN; WRITELN('Will distances be in wavelengths or meters?'); WRITELN('from the load and between the stubs ( 1=WAVELENGTHS 2=METERS ) '); READLN(Q1); WRITELN; WRITE('Distance from the load? '); READLN(D); WRITE('Distance between the stubs? '); READLN(DBS); WRITELN; WRITE('ZLR=? '); READLN(ZZR); WRITE('ZLI=? '); READLN(ZZI); WRITELN; WRITE('F=? (GHz) '); READLN(F); F:=F*1E9; END; PROCEDURE CALCULATIONS; { THIS PROCEDURE SOLVES THE PROBLEM. } BEGIN ZLR:=ZZR/Z0; { NORMALIZE THE LOAD RESISTANCE } ZLI:=ZZI/Z0; R_P(YLM,YLP,ZLR,ZLI); { FIND THE NORMALIZED ADMITTANCE AT THE LOAD. } YLM:=1.0/YLM; YLP:=-YLP; P_R(YLR,YLI,YLM,YLP); ADM_REF(LAM_LM,LAM_LP,YLR,YLI); { FIND THE REFLECTION COEFFICIENT } { AT THE LOAD. } IF Q1='2' THEN { ADJUST DISTANCES TO WAVELENGTHS IF NEEDED. } BEGIN D:=D*F/C; DBS:=DBS*F/C END; DD:=D*720.0; LAM_LP:=LAM_LP-DD; { MOVE DISTANCE D AWAY FROM THE LOAD. } REF_ADM(YD1R,YD1I,LAM_LM,LAM_LP); { FIND THE NORMALIZED ADMITTANCE AT THIS } { POINT. } P_R(A,B,0.5,720*DBS); { CALCULATE CIRCLE PARAMETERS A AND B. } CIRCLE(LAM_11_1R,LAM_11_1I,LAM_11_2R,LAM_11_2I, A,B,0.5,YD1R/(1.0+YD1R),1.0/(1.0+YD1R)); { CIRCLE FINDS THE REFLECTION COEFFICIENT AT POINT 11 ON THE CHART. THERE } { ARE 2 POSSIBLE SOLUTIONS. SOLUTIONS ARE IN RETANGULAR COORDINATES. } R_P(LAM_11_1M,LAM_11_1P,LAM_11_1R,LAM_11_1I); R_P(LAM_11_2M,LAM_11_2P,LAM_11_2R,LAM_11_2I); { CONVERT THESE TO POLAR COORDINATES. } SWR_1:=(1.0+LAM_11_1M)/(1.0-LAM_11_1M); SWR_2:=(1.0+LAM_11_2M)/(1.0-LAM_11_2M); { THE STANDING WAVE RATIO ON THE SECTION OF LINE BTWEEN THE STUBS CAN NOW } { BE CALCULATED. } REF_ADM(Y11R_1,Y11I_1,LAM_11_1M,LAM_11_1P); REF_ADM(Y11R_2,Y11I_2,LAM_11_2M,LAM_11_2P); { FIND THE ADMITTANCE AT 11. } YS1_1:=(Y11I_1-YD1I)*ZST1/Z0; YS1_2:=(Y11I_2-YD1I)*ZST1/Z0; { THE NORMALIZED SUSCEPTANCE OF THE FIRST STUB CAN NOW BE FOUND. } ADM_REF(DUMMY,LAM_S1_1P,0.0,YS1_1); ADM_REF(DUMMY,LAM_S1_2P,0.0,YS1_2); { THE PHASE OF THE REFLECTION COEFFICIENT CORRESPONDING TO A CONDUCTANCE OF } { ZERO AND A SUCEPTANCE OF THE STUB IS CALCULATED. } L1_1:=0.5-LAM_S1_1P/720.0; L1_2:=0.5-LAM_S1_2P/720.0; { CALCULATE THE LENGTH OF THE FIRST STUB IN WAVELENGTHS. } LGTH1_1:=C*L1_1/F; LGTH1_2:=C*L1_2/F; { AND IN METERS. } LAM_22_1M:=LAM_11_1M; LAM_22_1P:=LAM_11_1P-DBS*720.0; REF_ADM(Y22R_1,Y22I_1,LAM_22_1M,LAM_22_1P); LAM_22_2M:=LAM_11_2M; LAM_22_2P:=LAM_11_2P-DBS*720.0; REF_ADM(Y22R_2,Y22I_2,LAM_22_2M,LAM_22_2P); { MOVE TO POSITION 22 ON THE CHART. } YS2_1:=-Y22I_1; YS2_2:=-Y22I_2; { CALCULATE THE NORMALIZED SUSCEPTANCE OF THE SECOND STUB. } ADM_REF(DUMMY,LAM_S2_1P,0.0,YS2_1); ADM_REF(DUMMY,LAM_S2_2P,0.0,YS2_2); { SAME PROCEDURE USED WITH THE FIRST STUB. } L2_1:=0.50-LAM_S2_1P/720.0; L2_2:=0.50-LAM_S2_2P/720.0; { CALCULATE THE LENGTH OF THE SECOND STUB IN WAVELENGTHS. } LGTH2_1:=C*L2_1/F; LGTH2_2:=C*L2_2/F; { AND IN METERS. } END; PROCEDURE ANSWER; { THIS PROCEDURE OUTPUTS THE LENGTHS OF THE STUBS NEEDED AND INFORMATION } { CONCERNING THE PROBLEM. } BEGIN ClrScr; WRITELN; WRITELN('Z0= ',Z0:10:5); WRITELN('ZST1= ',ZST1:10:5); WRITELN('ZST2= ',ZST2:10:5); WRITELN('ZL= ',ZZR:10:5,' +j ',ZZI:10:5); WRITELN('zl= ',ZLR:10:5,' +j ',ZLI:10:5); WRITELN('yl= ',YLR:10:5,' +j ',YLI:10:5); WRITELN('yd1= ',YD1R:10:5,' +j ',YD1I:10:5); WRITELN('y11_1= ',Y11R_1:10:5,' +j ',Y11I_1:10:5); WRITELN('y11_2= ',Y11R_2:10:5,' +j ',Y11I_2:10:5); WRITELN('ys1_1= +j ',YS1_1:10:5); WRITELN('ys1_2= +j ',YS1_2:10:5); WRITELN('l1_1= ',L1_1:10:5,' Wavelengths'); WRITELN('l1_2= ',L1_2:10:5,' Wavelengths'); IF LGTH1_1>1.0 THEN WRITELN('LGHT1_1=',LGTH1_1:10:5,' Meters') ELSE WRITELN('LGHT1_1=',(LGTH1_1*100):10:5,' Cm'); IF LGTH1_2>1.0 THEN WRITELN('LGTH1_2=',LGTH1_2:10:5,' Meters') ELSE WRITELN('LGHT1_2=',(LGTH1_2*100):10:2,' Cm'); WRITELN; WRITELN('TYPE TO CONTINUE'); READLN(Q2); ClrScr; WRITELN; WRITELN('y22_1= ',Y22R_1:10:5,' +j ',Y22I_1:10:5); WRITELN('y22_2= ',Y22R_2:10:5,' +j ',Y22I_2:10:5); WRITELN('ys2_1= +j ',YS2_1:10:5); WRITELN('ys2_2= +j ',YS2_2:10:5); WRITELN('l2_1 = ',L2_1:10:5,' Wavelengths'); WRITELN('l2_2 = ',L2_2:10:5,' Wavelengths'); IF LGTH2_1>1.0 THEN WRITELN('LGHT2_1=',LGTH2_1:10:5,' Meters') ELSE WRITELN('LGTH2_1=',(LGTH2_1*100):10:5,' Cm'); IF LGTH2_2>1.0 THEN WRITELN('LGTH2_2=',LGTH2_2:10:5,' Meters') ELSE WRITELN('LGHT2_2=',(LGTH2_2*100):10:5,' Cm'); WRITELN('SWR_1= ',SWR_1:10:5,' v/v'); WRITELN('SWR_2= ',SWR_2:10:5,' v/v'); WRITELN('F= ',(F/1E9):10:5,' GHz') END; { MAIN PROGRAM } BEGIN GET_DATA; CALCULATIONS; ANSWER; END.