0195136047.pdf

164 TIME-DEPENDENT CIRCUIT ANALYSIS

V 2 =z 21 I 1 +z 22 I 2 =zfI 1 +zoI 2 (3.4.14)

where

z 11 =zi=

V 1

I 1

∣

∣∣

∣

∣

I 2 = 0

=open-circuit input impedance

z 12 =zr=

V 1

I 2

∣

∣

∣

∣

∣

I 1 = 0

=open-circuit reverse transfer impedance

z 21 =zf=

V 2

I 1

∣

∣

∣

∣

∣

I 2 = 0

=open-circuit forward transfer impedance

z 22 =zo=

V 2

I 2

∣

∣

∣

∣

∣

I 1 = 0

=open-circuit output impedance

3. Two-port hybrid orhparameters,

V 1 =h 11 I 1 +h 12 V 2 =hiI 1 +hrV 2 (3.4.15)

I 2 =h 21 I 1 +h 22 V 2 =hfI 1 +hoV 2 (3.4.16)

where

h 11 =hi=

V 1

I 1

∣

∣

∣

∣

∣

V 2 = 0

=short-circuit input impedance (ohms)

h 12 =hr=

V 1

V 2

∣

∣

∣

∣

∣

I 1 = 0

=open-circuit reverse voltage gain (dimensionless)

h 21 =hf=

I 2

I 1

∣

∣∣

∣

∣

V 2 = 0

=short-circuit forward current gain (dimensionless)

h 22 =ho=

I 2

V 2

∣

∣

∣

∣

∣

I 1 = 0

=open-circuit output admittance (siemens)

EXAMPLE 3.4.3

Consider Equations (3.4.11) through (3.4.16). Develop they-parameter,z-parameter, andh-

parameter equivalent circuits. Also express thez-parameters in terms ofy-parameters.

Solution

Equations (3.4.11) and (3.4.12) can be expressed as

−I 1 +(y 11 +y 12 )V 1 −y 12 (V 1 −V 2 )= 0

−I 2 +(y 22 +y 12 )V 2 −y 12 (V 2 −V 1 )+(y 21 −y 12 )V 1 = 0