EE2003 Circuit Theory Chapter 19 Two-Port Networks Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 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 24 .