0195136047.pdf

3.4 FREQUENCY RESPONSE 165

They-parameter equivalent circuit that satisfies these equations is shown in Figure E3.4.3(a).

V 1 V 2

−y 12

y 11 + y 12 y 22 + y 12 (y 21 − y 12 )V 1

I 1 I 2

1

1 ′
(a)

2

2 ′

+

−

+

−

Figure E3.4.3(a)y-para-

meter equivalent circuit.

(b)z-parameter equivalent

circuit.(c)h-parameter

equivalent circuit.

V 1 z 12 V 2

z 11 − z 12 z 22 − z 12

(z 21 − z 12 )I 1

I 1 I 2

1

1 ′
(b)

2

2 ′

+

− +

−

+

−

V 1 h 12 V 2 h 21 I 1 h 22 V 2

I 1 h 11 I 2

1

1 ′
(c)

2

2 ′

+

+

−

−

+

−

Equations (3.4.13) and (3.4.14) can be arranged as

V 1 =(z 11 −z 12 )I 1 +z 12 (I 1 +I 2 )

V 2 =(z 21 −z 12 )I 1 +(z 22 −z 12 )I 2 +z 12 (I 1 +I 2 )

Thez-parameter equivalent circuit that satisfies these equations is shown in Figure E3.4.3(b).
Theh-parameter equivalent circuit satisfying Equations (3.4.15) and (3.4.16) is shown in Figure
E3.4.3(c).
Equations (3.4.11) and (3.4.12) can be solved simultaneously to yield

V 1 =

y 22

y 11 y 22 −y 12 y 21

I 1 +

−y 12

y 11 y 22 −y 12 y 21

I 2

V 2 =

−y 21

y 11 y 22 −y 12 y 21

I 1 +

y 11

y 11 y 22 −y 12 y 21

I 2

By comparing these with Equations (3.4.13) and (3.4.14), one gets

z 11 =

y 22

y 11 y 22 −y 12 y 21

; z 12 =

−y 12

y 11 y 22 −y 12 y 21

z 21 =

−y 21

y 11 y 22 −y 12 y 21

; z 22 =

y 11

y 11 y 22 −y 12 y 21