# Two Port Networks. Definition of 2-Port Network A two-port network is an electrical network with two separate ports for input and output

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1 Two Port Networks Definition of 2-Port Network A two-port network is an electrical network with two separate ports for input and output What is a Port? It is a pair of terminals through which a current may enter or leave a network Basic building block Figure 5-1. Basic building block Several Restrictions of 2-port network dealt in this class 1. There can be no energy stored within the circuit 2. There can be no independent sources (Dependent sources are OK) 3. Currents: i 1 = i 1 and i 2 = i 2 4. All external connections must be made to either Input or Output port Why study two-port networks? Cal Poly State University, SLO 1

2 Importance of 2-port network Enables us to treat any circuit as a black box (subsystem) when embedded within a larger network Used in communications, control systems, power systems, and electronics Two-port Network Parameters Impedance Parameters Admittance Parameters Hybrid Parameters Transmission Parameters Two-port Network Input/Output may be: Voltage Driven Current Driven Figure 5-2. Voltage-driven 2-port network Figure 5-3. Current-driven 2-port network Cal Poly State University, SLO 2

3 Two-Port Network Using Impedance Parameters Terminal voltages are related to terminal currents by the following equations: How do we determine the Z or impedance parameters? o First, let input port be open circuited such that I 1 = 0, hence: o Secondly, now let output port be open circuited such that I 2 = 0, hence: So to summarie, the Z parameters of a given two-port network are found by using the following equations: Cal Poly State University, SLO 3

4 That s why these parameters are called the Impedance parameters, since each one of them is obtained from V/I Unit of each Z parameter is Ohms Ω Two special cases: o Symmetrical 2-port network, when 11 = 22 o Reciprocal 2-port network, when 12 = 21 May be obtained in any two-port network made entirely of resistors, capacitors and inductors When reciprocity is encountered in two-port network, the following T-equivalent may be used for its analysis Figure 5-4. T-equivalent circuit of reciprocal 2-port network Cal Poly State University, SLO 4

5 Example: Find the Z parameters of the following 2-port network Figure port network example Cal Poly State University, SLO 5

6 Two-Port Network Using Admittance Parameters Figure port network example for Admittance parameters Terminal voltages are related to terminal currents by the following equations: Admittance parameters are then found using: How do you make V 1 = 0 in above solutions? By shortcircuiting port 1 V 2 = 0 obtained by short circuiting port 2 Cal Poly State University, SLO 6

7 Why do we call these parameters Admittance? The SI unit of each admittance or Y parameter is Siemens [S] Other unit used for Y is mhos or Reciprocal Admittance 2-port network, when y 12 = y 21 May be modeled by the following Π-equivalent for its analysis Figure 5-7. Pi-equivalent circuit for Admittance parameters Two-Port Network Using Hybrid Parameters Input voltage and Output current are in terms of Input Current and Output Voltage Or in matrix form: Cal Poly State University, SLO 7

8 Where: Two-Port Network Using Inverse-Hybrid Parameters Input current and Output voltage are in terms of Input Voltage and Output Current Or in matrix form: Where: Cal Poly State University, SLO 8

9 Example: Determine the Y-parameters of the following circuit Figure 5-8. Example of 2-port network Cal Poly State University, SLO 9

10 Two-Port Network Using Transmission Parameters For transmission parameters, the basic building block of 2-port network is now redrawn Figure port network for Transmission Parameters In transmission parameters, Input Parameters are described in terms of Output Parameters Cal Poly State University, SLO 10

11 Or in matrix form: The transmission parameters are obtained from: Two-Port Network Using Inverse-Transmission In inverse-transmission parameters, Output Parameters are described in terms of Input Parameters Or in matrix form: The inverse transmission parameters are then obtained from: Cal Poly State University, SLO 11

12 Example: Determine the h-parameters of the following circuit Answer: Figure port network example To find h 11 and h 21, we need V 1, I 1 and I 2 while V 2 = 0 or shorted. One way to do this is to apply current source I 1 for input port: Cal Poly State University, SLO 12

13 To find h 22 and h 12, we need V 1 open-circuited and apply voltage source V 2 for output port: Cal Poly State University, SLO 13

14 Example: Find I 1 and I 2 Cal Poly State University, SLO 14

15 Interconnection of 2-Port Networks It is a useful tool in analying a large complex network consisting of many sub-networks All six parameters may be used when analying connection of networks, but the use of certain parameters may be easier (have a definite advantage) o Series Connection Use Impedance Parameters o Parallel Connection Use Admittance Parameters o Cascaded Connection Use Transmission Parameter o Series-Parallel Connection Use Hybrid Parameters o Parallel-Series Connection Use Inverse Hybrid Parameters Solving interconnection of networks usually involves converting from one parameter to another parameter Series Connection Figure Series connection of 2-port networks Cal Poly State University, SLO 15

16 Individual Z add up to give the Z of overall series network Cal Poly State University, SLO 16

17 Parallel Connection Figure Parallel connection of 2-port networks Individual Y add up to give the Y of overall parallel network Cascaded Connection Figure Cascaded connection of 2-port networks Individual T s are multiplied to give the T of overall cascaded network Cal Poly State University, SLO 17

18 Series-Parallel Connection Figure Series-Parallel connection of 2-port networks Individual h adds up to give the h of overall seriesparallel network Parallel-Series Connection Figure Parallel-Series connection of 2-port networks Cal Poly State University, SLO 18

19 Individual g adds up to give the g of overall parallelseries network Conversion Table (from text book): Cal Poly State University, SLO 19

20 Example: For the parallel-series connection of the two twoports below, find the g parameters. Recall, for Parallel-Series connection, it is most convenient to use the g parameters Use conversion table to obtain the g parameters from the given parameters ] = 5 10, = = 150 a [ a ] = 25 30, = = 875 b [ b [g] = g ] =, [ g = b ] [ a 0.06 S g] = [ g a ] + [ g ] = 0.7 [ b Ω Cal Poly State University, SLO 20

21 Cal Poly State University, SLO 21 Example: Find the transmission parameters. Finding Y parameters are easiest, but this is a series connection so use Z parameters, then use conversion table to obtain the T parameters The y parameters for the upper network is = ] [y, y = = = = ] [ y 11 y 21 y 12 y 22 a y y y y = ] [ b = + = ] [ ] [ ] [ b a = = = = ] [ T Ω S

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