0195136047.pdf

3.4 FREQUENCY RESPONSE 163

ω 0 =

1

√

LC

; Q=

ω 0 L

R

; Zm=

L

RC

=RQ^2

The universal resonance curve and the conclusions obtained from it apply to this circuit, provided

ωL >> R,orQ≥10.

Two-Port Network Parameters

A pair of terminals at which a signal may enter or leave a network is called aport, and a network
having two such pairs of terminals, labeled generally input and output terminals, is known as atwo-
port network. A two-port network forms a very important building block in electronic systems,
communication systems, automatic control systems, transmission and distribution systems, or in
other systems in which an electric signal or electric energy enters the input terminals, is acted
upon by the network, and leaves via the output terminals.
Thetwo-port network(or two-terminal-pair network) shown in Figure 3.4.10 is described
by port currents and voltages (i.e., four variables) related by a set of linear equations in terms of
two-port parameters. Of the six possible parameter sets, the three used extensively in electronic
circuit analysis are given next in thefrequency domain.

1. Two-port admittance oryparameters (in siemens),

I 1 =y 11 V 1 +y 12 V 2 =yiV 1 +yrV 2 (3.4.11)

I 2 =y 21 V 1 +y 22 V 2 =yfV 1 +yoV 2 (3.4.12)

where

y 11 =yi=

I 1

V 1

∣

∣

∣

∣

∣

V 2 = 0

=short-circuit input admittance

y 12 =yr=

I 1

V 2

∣

∣

∣

∣

∣

V 1 = 0

=short-circuit reverse transfer admittance

y 21 =yf=

I 2

V 1

∣

∣

∣

∣∣

V 2 = 0

=short-circuit forward transfer admittance

y 22 =yo=

I 2

V 2

∣

∣

∣

∣

∣

V 1 = 0

=short-circuit output admittance

2. Two-port impedance orzparameters (in ohms),

V 1 =z 11 I 1 +z 12 I 2 =ziI 1 +zrI 2 (3.4.13)

V 1 (s) V 2 (s)

I 1 (s) I 2 (s)

1

1 ′

2

2 ′

+

−

−

Figure 3.4.10Two-port network (or

two-terminal-pair network).