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S-, H-, Y-, Z-, ABCD- Parameter Conversions

 

This table of conversion between various forms of 2-port electrical parameters is difficult to find, so once I finally located some papers that included them, I felt it was my duty to publish it for public access.

 

Note: Complex values must be used for conversions (do not use magnitude only)

S11 = (Z11-1)*(Z22+1)-Z12*Z21
  = (1-Y11)*(1+Y22)+Y12*Y21
  = (h11-1)*(1+h22)-h12*h21
  = A+B-C-D
  = T21
(Z11+1)*(Z22+1)-Z12*Z21(1+Y11)*(1+Y22)-Y12*Y21(1+h11)*(1+h22)-h12*h21A+B+C+DT11
          
S12 = 2*Z12
  = -2*Y12
  = 2*h12
  = 2*(A*D-B*C)
  = T11*T22-T12*T21
(Z11+1)*(Z22+1)-Z12*Z21(1+Y11)*(1+Y22)-Y12*Y21(1+h11)*(1+h22)-h12*h21A+B+C+DT11
          
S21 = 2*Z21
 = -2*Y21
 = -2*h21
 = 2
 = 1
(Z11+1)*(Z22+1)-Z12*Z21(1+Y11)*(1+Y22)-Y12*Y21(1+h11)*(1+h22)-h12*h21A+B+C+DT11
          
S22 = (Z11+1)*(Z22-1)-Z12*Z21
  = (1+Y11)*(1-Y22)+Y12*Y21
  = (1+h11)*(1-h22)+h12*h21
  = -A+B-C+D
  = -T12
(Z11+1)*(Z22+1)-Z12*Z21(1+Y11)*(1+Y22)-Y12*Y21(1+h11)*(1+h22)-h12*h21A+B+C+DT11

 

A = (1+S11)*(1-S22)+S12*S21
 = Z11
 = -Y22
 = h12*h21-h11*h22
 = T11+T12+T21+T22
2*S21Z21Y21h212
          
B = (1+S11)*(1+S22)-S12*S21
 = Z11*Z22-Z12*Z21
 = -1
 = -h11
 = T11+T21-T12-T22
2*S21Z21Y21h212
          
C = (1-S11)*(1-S22)-S12*S21
 = 1
 = Y12*Y21-Y11*Y22
 = -h22
 = T11+T12-T21-T22
2*S21Z21Y21h212
          
D = (1-S11)*(1+S22)+S12*S21
 = Z22
 = -Y11
 = -1
 = T11-T21-T12+T22
2*S21Z21Y21h212

 

Z11 = (1+S11)*(1-S22)+S12*S21
  = Y22
  = h11*h22-h12*h21
  = A
  = T11+T12+T21+T22
(1-S11)*(1-S22)-S12*S21Y11*Y22-Y12*Y21h22CT11+T12-T21-T22
          
Z12 = 2*S12
  = -Y12
  = h12
  = A*D-B*C
  = 2*(T11*T22-T12*T21)
(1-S11)*(1-S22)-S12*S21Y11*Y22-Y12*Y21h22CT11+T12-T21-T22
          
Z21 = 2*S21
  = -Y21
  = -h21
  = 1
  = 2
(1-S11)*(1-S22)-S12*S21Y11*Y22-Y12*Y21h22CT11+T12-T21-T22
          
Z22 = (1-S11)(1+S22)+S12*S21  = Y11  = 1  = D  = T11-T21-T12+T22
(1-S11)*(1-S22)-S12*S21Y11*Y22-Y12*Y21h22CT11+T12-T21-T22

 

Y11 =  (1-S11)*(1+S22)+S12*S21
  =  Z22
  =  1
  =  D
  =  T11-T21-T12+T22
(1+S11)*(1+S22)-S12*S21Z11*Z22-Z12*Z21h11BT11-T12+T21-T22
    
Y12 =  -2*S12
  =  -Z12
  =  -h12
  =  B*C-A*D
  =  -2*(T11T22-T12T21)
(1+S11)*(1+S22)-S12*S21Z11*Z22-Z12*Z21h11BT11-T12+T21-T22
    
Y21 =  -2*S21
  =  -Z21
  =  h21
  =  -1
  =  -2
(1+S11)*(1+S22)-S12*S21Z11*Z22-Z12*Z21h11BT11-T12+T21-T22
    
Y22 =  (1+S11)*(1-S22)+S12*S21
  =  Z11
  =  h11*h22-h12*h21
  =  A
  =  T11+T12+T21+T22
(1+S11)*(1+S22)-S12*S21Z11*Z22-Z12*Z21h11BT11-T12+T21-T22

 

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