10 CLS 20 PRINT " PARLIN11" 30 PRINT "Solution to the Parallel Line Transmission Line Transformer" 45 PRINT " by" 50 PRINT " Albert E Weller, WD8KBW" 60 PRINT : PRINT 70 GOTO 160 80 'FOR TEST CASES DISABLE LINE 70 and choose one of lines 90-145 '90 GL = 1: BL = 1: GG = 3.01118: BG = 3.37518: YO1=1: YO2=1.5 '100 GL = 1: BL = 1: GG = 6: BG = -6: YO1 = 1: YO2 = 1.5 '110 GL = 1: BL = 1: GG = .6: BG = 1: YO1 = 1: YO2 = 1 '120 GL=.6: BL=.8: GG=1: BG=0: YO1=1: YO2=.6667 '130 GL = 4: BL = 0: GG = 1: BG = 0: YO1 = 1: YO2 = .6667 '140 GL=1.47058802:BL=.7843137:GG=1:BG=0:YO1=1:YO2=2/3 '145 GL=.9008:BL=-.26987:GG=1:BG=0:YO1=1:YO2=1.5 150 GOTO 260 160 PRINT "Enter admittance of load.": PRINT 170 INPUT " Conductance of load? ", GL 180 INPUT " Susceptance of load? ", BL: PRINT 190 PRINT "Enter admittance at input of parallel lines": PRINT 200 INPUT " Conductance at input? ", GG 210 INPUT " Susceptance at input? ", BG: PRINT 220 PRINT "Enter the characteristic admittances of the two transmission lines" 230 PRINT "used in the parallel line transformer.": PRINT 240 INPUT " Characteristic admittance of line 1? ", YO1 250 INPUT " Characteristic admittance of line 2? ", YO2 260 PI = 3.1415927# 270 'VERSION OF 12/11/97 280 CLS 290 PRINT "For the case YO1 ="; YO1; " :YO2 ="; YO2; " :YL ="; GL; "+j"; BL; " :and YG="; GG; "+j"; BG 300 PRINT 310 GOSUB 400 320 END ' Calculating the network parameters to accomplish the desired ' transformation. 400 YLSQ = GL ^ 2 + BL ^ 2 'magnitude squared of load admittance 410 YGSQ = GG ^ 2 + BG ^ 2 'magnitude squared of admittance at input 420 YOPSQ = (GG * YLSQ - GL * YGSQ) / (GL - GG) 'YOP squared 430 YOP = SQR(ABS(YOPSQ)) 440 AA = (YOPSQ - YO1 ^ 2 - YO2 ^ 2) / (YO1 * YO2) 450 IF ABS(AA) < 2 THEN GOTO 1600 460 IF (GG * BL + GL * BG) ^ 2 < .00000001 THEN GOTO 570 465 IF ABS((GL-GG)/(GG*BL+GL*BG))>10E6 THEN GOTO 570 470 TANHPSQ = -YOPSQ * (GL - GG) ^ 2 / (GG * BL + GL * BG) ^ 2'hyperbolic tangent of propagation constant 475 IF YOPSQ<0 THEN RR=-1 ELSE RR=1 480 TANHP = (SQR(ABS(TANHPSQ)))*RR*SGN((GL-GG)/(GG*BL+GL*BG)) 490 IF TANHPSQ < 0 THEN GOTO 535 500 GAMMAP = .5 * LOG((1 + TANHP) / (1 - TANHP))'ARC HYPERBOLIC TANGENT 510 GAMMAPH = .5 * GAMMAP 520 TANHPH = (EXP(GAMMAPH) - EXP(-GAMMAPH)) / (EXP(GAMMAPH) + EXP(-GAMMAPH))'HYPERBOLIC TANGENT 530 GOTO 580 535 TANHP=-TANHP 540 GAMMAP = ATN(TANHP) 550 GAMMAPH = .5 * GAMMAP 560 TANHPH = TAN(GAMMAPH): GOTO 580 570 TANHPH = 1: JJ = 3: TANHPSQ = 1E+12 * SGN(GL - GG): GOTO 630 580 IF YOPSQ < 0 THEN JJ = 2 590 IF YOPSQ > 0 THEN JJ = 1 630 MM = (SQR(ABS(YOPSQ))) * TANHPH 640 LL = AA + SQR(AA ^ 2 - 4) 700 GOSUB 800 710 GOSUB 1400 720 LL = AA - SQR(AA ^ 2 - 4) 730 GOSUB 800 740 GOSUB 1400 750 PRINT "Phase shift is "; PHI; "degrees" 760 GOTO 1610 ' Calculating the two line lengths. 800 THETA2 = 2 * ATN(MM / (YO1 * LL/2 + YO2)) 810 THETA1 = 2 * ATN(MM / (YO1 + YO2 * 2/LL)) ' Calculating how the two lines divide the load. 900 A = YO1 * SIN(THETA2) + YO2 * SIN(THETA1) 910 GL1 = YO1 * SIN(THETA2) * GL / A 'conductance of load presented to line 1 920 GL2 = YO2 * SIN(THETA1) * GL / A 930 BB = (YO1 * YO2 * (COS(THETA2) - COS(THETA1))) / A 'a constant 940 BL1 = (BL * GL1 / GL) - BB 'susceptance of load presented to line 1 950 BL2 = (BL * GL2 / GL) + BB ' Calculating phase shift of the network and the SWR on each line. 960 PHI = -57.2958 * ATN((GL1 * TAN(THETA1)) / (YO1 - BL1 * TAN(THETA1))) 970 PHI = (CINT(PHI * 100)) / 100 'phase shift of the parallel line network 980 H = (GL1 ^ 2 + BL1 ^ 2 + YO1 ^ 2) 990 SWR1 = (H + SQR(H ^ 2 - 4 * GL1 ^ 2 * YO1 ^ 2)) / (2 * ABS(GL1) * YO1) 1000 H = (GL - GL1) ^ 2 + (BL - BL1) ^ 2 + YO2 ^ 2 1010 SWR2 = (H + SQR(H ^ 2 - 4 * GL2 ^ 2 * YO2 ^ 2)) / (2 * ABS(GL - GL1) * YO2) ' Calculating the sensitivity of the solution to errors in the line ' lengths--change in achieved YG for 1 percent error in lenghts. 1100 PP = 1.01: QQ = 1 1110 GOSUB 1170 1120 REERR1 = REERR: IMERR1 = IMERR 1130 PP = 1: QQ = 1.01 1140 GOSUB 1170 1150 REERR2 = REERR: IMERR2 = IMERR 1160 GOTO 1340 1170 T1 = TAN(PP * THETA1) 1180 DEN1 = (YO1 - BL1 * T1) ^ 2 + GL1 ^ 2 * T1 ^ 2 1190 REYG1 = YO1 ^ 2 * GL1 * (1 + T1 ^ 2) / DEN1 1200 IMYG1 = (-YO1 * T1 * (GL1 ^ 2 + BL1 ^ 2 - YO1 ^ 2) + BL1 * YO1 ^ 2 * (1 - T1 ^ 2)) / DEN1 1210 T2 = TAN(QQ * THETA2) 1220 DEN2 = (YO2 - BL2 * T2) ^ 2 + GL2 ^ 2 * T2 ^ 2 1230 REYG2 = YO2 ^ 2 * GL2 * (1 + T2 ^ 2) / DEN2 1240 IMYG2 = (-YO2 * T2 * (GL2 ^ 2 + BL2 ^ 2 - YO2 ^ 2) + BL2 * YO2 ^ 2 * (1 - T2 ^ 2)) / DEN2 1250 REYG = REYG1 + REYG2: IMYG = IMYG1 + IMYG2 1260 YGESQ = (REYG1 + REYG2) ^ 2 + (IMYG1 + IMYG2) ^ 2 '1270 REERR = (GG*REYG + BG*IMYG)/YGESQ 'multiplicative/divisive sensitivity 1280 REERR = REYG - GG 'Additive/subtractive sensitivity '1290 IMERR = (BG*REYG - IMYG*GG)/YGESQ 'multiplicative/divisive sensitivity 1300 IMERR = IMYG - BG 'Additive/subtractive sensitivity 1310 REERR = (CINT(REERR * 100)) / 100 1320 IMERR = (CINT(IMERR * 100)) / 100 1330 RETURN 1340 RETURN 1400 PRINT " THETA1"; " THETA2"; " SWR1"; " SWR2" '1410 IF THETA1 < 0 THEN THETA1 = THETA1 + 2 * PI '1420 IF THETA2 < 0 THEN THETA2 = THETA2 + 2 * PI 1430 PRINT USING "####.## "; THETA1 * 180 / PI; THETA2 * 180 / PI; SWR1; SWR2 1440 PRINT "Fraction of power in lines 1 and 2:" 1450 PRINT USING " ##.## "; GL1 / GL; GL2 / GL 1460 PRINT "Sensitivity is "; REERR1; "+ j"; IMERR1; "for one percent error in" 1470 PRINT " theta1 and "; REERR2; "+j"; IMERR2; "for one percent error in theta2" 1480 PRINT 1490 RETURN 1600 PRINT "No solution is possible": PRINT 1610 IF JJ = 1 THEN GOTO 1650 1620 IF JJ = 2 THEN GOTO 1660 1630 IF JJ = 3 THEN GOTO 1640 1640 PRINT "Network parameters are YOP="; YOP; " TANHP=jTAN(90 DEGREES)": GOTO 1670 1650 PRINT "Network parameters are YOP="; YOP; " TANHP=j"; TANHP: GOTO 1670 1660 PRINT "Network parameters are YOP=j"; YOP; " TANHP="; TANHP: GOTO 1670 1670 RETURN Solutions for the test cases. Line THETA1 THETA2 SWR1 SWR2 PWR1 PWR2 PHI YOP TANHP 90 60 30 3.60 3.22 .28 .72 -24.69 2.68 j.844 100 139.87 51.66 3.62 6.58 .45 .55 45 3.46 jtan90 110 6.67 -12.40 4.97 3.26 2.18 -1.18 18.43 j.632 -.158 120 -24.26 71.83 5.33 8.16 1.41 -.41 12.09 j1.0 0.5 130 118.59 50.73 2.44 2.88 .57 .43 -90 2.0 jtan90 140 -45.01 -44.98 1.67 1.67 .60 .40 30.96 1.67 -j1.0 145 356.11 -4.92 5.21 4.13 5.36 6.36 20.18 0.408 -j.150 _____________________________________________________________________ 0 CLS 5 PRINT " PARSOVL1":PRINT 10 PRINT " SOLVES PARALLEL LINES GIVEN THETA1 AND THETA2, OUTPUTS INPUT ADMITTANCE" 15 PRINT " by A. E. Weller, WD8KBW": PRINT 30 INPUT "ENTER LOAD ADMITTANCE, G AND B. ", GL, BL 40 INPUT "ENTER YO1, YO2. " ,YO1, YO2 50 INPUT "ENTER THETA1, THETA2 IN DEGREES. ",THETA1, THETA2: PRINT 60 'VERSION OF 12/11/97 90 PI = 3.141593 110 THETA1 = THETA1 * PI / 180: THETA2 = THETA2 * PI / 180 120 A = YO1 * SIN(theta2) + YO2 * SIN(THETA1) '125 PRINT A 130 GL1 = YO1 * SIN(theta2) * GL / A 140 GL2 = YO2 * SIN(THETA1) * GL / A 150 B = (YO1 * YO2 * (COS(theta2) - COS(THETA1))) / A '155 PRINT B 160 BL1 = (BL * GL1 / GL) - B 170 bl2 = (BL * GL2 / GL) + B 180 C = (YO1 - BL1 * TAN(THETA1)) ^ 2 + GL1 ^ 2 * (TAN(THETA1)) ^ 2 190 GG1 = (YO1 ^ 2 * GL1 * (1 + (TAN(THETA1)) ^ 2)) / C 200 BG1 = (YO1 * (-(GL1 ^ 2 + BL1 ^ 2 - YO1 ^ 2)) * TAN(THETA1) + BL1 * YO1 ^ 2 * (1 - (TAN(THETA1)) ^ 2)) / C 210 C = (YO2 - bl2 * TAN(theta2)) ^ 2 + GL2 ^ 2 * (TAN(theta2)) ^ 2 220 GG2 = (YO2 ^ 2 * GL2 * (1 + (TAN(theta2)) ^ 2)) / C 230 BG2 = (YO2 * (-(GL2 ^ 2 + bl2 ^ 2 - YO2 ^ 2)) * TAN(theta2) + bl2 * YO2 ^ 2 * (1 - (TAN(theta2)) ^ 2)) / C 240 GG = GG1 + GG2: BG = BG1 + BG2 250 PHI = -57.2958 * ATN((GL1 * TAN(THETA1)) / (YO1 - BL1 * TAN(THETA1))) 260 PHI = (CINT(PHI * 100)) / 100 'phase shift of the parallel line network 270 H = (GL1 ^ 2 + BL1 ^ 2 + YO1 ^ 2) 'version of 11/20/97 280 SWR1 = (H + SQR(H ^ 2 - 4 * GL1 ^ 2 * YO1 ^ 2)) / (2 * ABS(GL1) * YO1) 290 H = (GL - GL1) ^ 2 + (BL - BL1) ^ 2 + YO2 ^ 2 300 SWR2 = (H + SQR(H ^ 2 - 4 * GL2 ^ 2 * YO2 ^ 2)) / (2 * ABS(GL - GL1) * YO2) 310 CLS 320 PRINT "For theta1=";THETA1*180/PI;",theta2=";theta2*180/PI;",YO1=";YO1; ",YO2=";YO2;",GL=";GL;",BL=";BL 330 PRINT " GG"; " BG";" SWR1";" SWR2" 340 PRINT GG, BG, SWR1, SWR2 350 PRINT "POWER DIVIDISION BETWEEN LINES 1 AND 2 IS"; GL1/GL;"/";GL2/GL 360 PRINT "PHASE SHIFT IS"; PHI; "DEGREES" 370 END