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PARAMETER  CONVERSIONS

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S-, H-, Y-, Z-, ABCD- PARAMETER CONVERSIONS

 
S11 (Z11-1)(Z22+1)-Z12Z21   =  (1-Y11)(1+Y22)+Y12Y21   =  (h11-1)(1+h22)-h12h21   =  A+B-C-D   =  T21
(Z11+1)(Z22+1)-Z12Z21 (1+Y11)(1+Y22)-Y12Y21 (1+h11)(1+h22)-h12h21 A+B+C+D T11
                   
S12 2Z12   =  -2Y12   =  2h12   =  2(AD-BC)   =  T11T22-T12T21
(Z11+1)(Z22+1)-Z12Z21 (1+Y11)(1+Y22)-Y12Y21 (1+h11)(1+h22)-h12h21 A+B+C+D T11
                   
S21 2Z21   =  -2Y21   =  -2h21   =  2   =  1
(Z11+1)(Z22+1)-Z12Z21 (1+Y11)(1+Y22)-Y12Y21 (1+h11)(1+h22)-h12h21 A+B+C+D T11
                   
S22 (Z11+1)(Z22-1)-Z12Z21   =  (1+Y11)(1-Y22)+Y12Y21   =  (1+h11)(1-h22)+h12h21   =  -A+B-C+D   =  -T12
(Z11+1)(Z22+1)-Z12Z21 (1+Y11)(1+Y22)-Y12Y21 (1+h11)(1+h22)-h12h21 A+B+C+D T11
A =  (1+S11)(1-S22)+S12S21  =  Z11  =  -Y22  =  h12h21-h11h22  =  T11+T12+T21+T22
2S21 Z21 Y21 h21 2
                   
B =  (1+S11)(1+S22)-S12S21  =  Z11Z22-Z12Z21  =  -1  =  -h11  =  T11+T21-T12-T22
2S21 Z21 Y21 h21 2
                   
C =  (1-S11)(1-S22)-S12S21  =  1  =  Y12Y21-Y11Y22  =  -h22  =  T11+T12-T21-T22
2S21 Z21 Y21 h21 2
                   
D =  (1-S11)(1+S22)+S12S21  =  Z22  =  -Y11  =  -1  =  T11-T21-T12+T22
2S21 Z21 Y21 h21 2
Z11 (1+S11)(1-S22)+S12S21   =  Y22   =  h11h22-h12h21   =  A   =  T11+T12+T21+T22
(1-S11)(1-S22)-S12S21 Y11Y22-Y12Y21 h22 C T11+T12-T21-T22
                   
Z12 2S12   =  -Y12   =  h12   =  AD-BC   =  2(T11T22-T12T21)
(1-S11)(1-S22)-S12S21 Y11Y22-Y12Y21 h22 C T11+T12-T21-T22
                   
Z21 2S21   =  -Y21   =  -h21   =  1   =  2
(1-S11)(1-S22)-S12S21 Y11Y22-Y12Y21 h22 C T11+T12-T21-T22
                   
Z22 (1-S11)(1+S22)+S12S21   =  Y11   =  1   =  D   =  T11-T21-T12+T22
(1-S11)(1-S22)-S12S21 Y11Y22-Y12Y21 h22 C T11+T12-T21-T22
Y11 (1-S11)(1+S22)+S12S21   =  Z22   =  1   =  D   =  T11-T21-T12+T22
(1+S11)(1+S22)-S12S21 Z11Z22-Z12Z21 h11 B T11-T12+T21-T22
       
Y12 -2S12   =  -Z12   =  -h12   =  BC-AD   =  -2(T11T22-T12T21)
(1+S11)(1+S22)-S12S21 Z11Z22-Z12Z21 h11 B T11-T12+T21-T22
       
Y21 -2S21   =  -Z21   =  h21   =  -1   =  -2
(1+S11)(1+S22)-S12S21 Z11Z22-Z12Z21 h11 B T11-T12+T21-T22
       
Y22 (1+S11)(1-S22)+S12S21   =  Z11   =  h11h22-h12h21   =  A   =  T11+T12+T21+T22
(1+S11)(1+S22)-S12S21 Z11Z22-Z12Z21 h11 B T11-T12+T21-T22