EE2003 Circuit Theory

Chapter 19 Two-Port Networks

1 Two Port Networks Chapter 19 19.1 Introduction 19.2 Impedance parameters z 19.3 Admittance parameters y 19.4 Hybrid parameters h 19.5 Transmission parameters T 19.6 Relationship between parameters 19.7 Interconnection of networks

19.9 Applications 2 19.1 Introduction (1)

What is a port?

It is a pair of terminals through which a current may enter or leave a network or an electrical circuit.

3 19.1 Introduction (2)

One port or two terminal circuit

Two port or four terminal circuit

• It is an electrical network with two separate ports for input and output.

• We assume No independent sources. 4 Why we study Two port Networks For two reasons: • First, such networks are useful in communications, control systems, power systems, and electronics. For example, they are used in electronics to model transistors and to facilitate cascaded design. • Second, knowing the parameters of a two- port network enables us to treat it as a “black box” when embedded within a larger network. 5 19.2 Impedance parameters (1)

Assume no independent source in the network

V1  z11I1  z12I2 V1  z11 z12  I1  I1          z   V2  z21I1  z22I2 V2  z21 z22  I2  I2 

where the z terms are called the impedance parameters, or simply z parameters, and have units of ohms. 6 19.2 Impedance parameters (2)

V1 V2 z11  and z21  I1 I1 I2 0 I2 0

z11 = Open-circuit input impedance

z21 = Open-circuit transfer impedance from port 1 to port 2

V1 V2 z12  and z22  I2 I2 I1 0 I1 0

z12 = Open-circuit transfer impedance from port 2 to port 1

z22 = Open-circuit output impedance 7 19.2 Impedance parameters (2a)

V1 V2 z11  and z21  I1 I1 I2 0 I2 0

V1 V2 z12  and z22  I2 I2 I1 0 I1 0

When z11 = z22, the two-port network is said to be symmetrical. This implies that the network has mirrorlike symmetry about some center line; that is, a line can be found that divides the network into two similar halves.

When the two-port network is linear and has no dependent sources, the transfer impedances are equal (z12 = z21), and the two-port is said to be reciprocal. This means that if the points of excitation and response are interchanged, the transfer8 impedances remain the same.

19.2 Impedance parameters (3)

Example 1

Determine the Z-parameters of the following circuit.

I1 I 2 V1 V2 z11  and z21  I1 I1 I2 0 I2 0

V1 V2 V1 V2 z12  and z22  I2 I2 I1 0 I1 0

z z  60 40 z  11 12  Answer: z    z z  40 70  21 22  11

19.3 Admittance parameters (1)

Assume no independent source in the network

I1  y11V1  y12V2 I1  y11 y12  V1  V1          y   I2  y21V1  y22V2 I2  y21 y22  V2  V2 

where the y terms are called the admittance parameters, or simply y parameters, and they have units of Siemens. 15 19.3 Admittance parameters (2)

I1 I2 y11  and y21  V1 V1 V2 0 V2 0

y11 = Short-circuit input admittance

y21 = Short-circuit transfer admittance from port 1 to port 2

I1 I2 y12  and y22  V2 V2 V1 0 V1 0

y12 = Short-circuit transfer admittance from port 2 to port 1

y22 = Short-circuit output admittance 16

19.3 Admittance parameters (3)

I1 I2 I1 I2 y11  and y21  V1 V1 V2 0 V2 0 V 1 V2

I1 I2 y12  and y22  V2 V2 V1 0 V1 0

0.75  0.5 y y  Answer:   11 12 y    S y    S  0.5 0.625 y21 y22  18

19.4 Hybrid parameters (1)

Assume no independent source in the network

V1  h11I1  h12V2 V1  h11 h12  I1  I1          h   I2  h21I1  h22V2 I2  h 21 h 22  V2  V2 

where the h terms are called the hybird parameters, or simply h parameters, and each parameter has different units, refer above. 23 19.4 Hybrid parameters (2)

Assume no independent source in the network

V h = short-circuit V1 h = open-circuit h  1 11 h  12 11 input impedance () 12 reverse voltage-gain I1 V2 V2 0 I1 0

I2 I2 h  h21 = short-circuit h  h22 = open-circuit 21 22 V I1 forward current gain 2 I 0 output admittance (S) V2 0 1