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Two-port networks Review of one ports Various two-port descriptions Terminated nonlinear two-ports Impedance and admittance matrices of two-ports Other two-port parameter matrices The hybrid matrices The transmission matrices

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1-port2-port 1-port

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Thevenin’s Equivalent Circuit Norton’s Equivalent Circuit

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NNONO For LTI network In frequency domain 0 No independent sources

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Nonlinear one port

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For small

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For DC bias For DC bias + small signal From Taylor’s series expansion

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Where

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0.75 0.5 0.550.60.650.7 0 1 1.5 2 2.5 3 3.5 0.5 v D (V) i D (mA) t t Bias point Q V D I D Slope at Q point =

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Example If find

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Two-port networks LTI one ports Input impedance Input admittance Fig. 1

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Two-port networks Example 1 Determine the input impedance of the circuit in Fig. 2 Fig. 2

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Example 2 Determine the output impedance of the circuit in Fig. 3 Fig. 3

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Two-port networks Circuits can be considered by theirs terminal variables Voltages and currents are terminal’s variables Complex circuit can be analyzed more easily. There are many kinds of two port parameters. Fig. 4 A two port network

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Common-Emitter (CE) Fixed-Bias Configuration

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Removing DC effects of VCC and Capacitors

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Small signal equivalent circuit

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Hybrid equivalent model r e equivalent model

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Various two-port descriptions or Port current Port voltage Or hybrid

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Two-port networks The Y parameter The admittance or Y parameter of a two port network is defined by or in scalar form

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The Y parameter The Y parameters can found from These parameters are call short-circuited admittance parameters

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The Y parameter Example 3 Determine the admittance parameters from the circuit in Fig 5. Fig 5.

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The Y parameter Example 4 Compute the y-parameter of the circuit in Fig.6 Fig.6

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Y parameter analysis of terminated two-port Fig. 9 Terminated two-port Y-parameter equations

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Y parameter analysis of terminated two-port From Crammer’s rules The input admittance Y in and

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Y parameter analysis of terminated two-port Gain: Fig 10 Terminated two-port Y-parameter model

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Two-port networks The Z parameter The impedance or Z parameter of a two port network is defined by or in scalar form

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The Z parameter The Z parameters can be found from These parameters are call open circuit impedance parameters

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The Z parameter Example 6 Determine the impedance parameters from the circuit in Fig 11 Fig 11. In frequency domain

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The Y parameter Example 7 Compute the z-parameter of the circuit in Fig.12 Fig.12

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The Z parameter

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Z parameter analysis of terminated two-port Fig. 14 Terminated two-port Z-parameter equations

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Z parameter analysis of terminated two-port From Crammer’s rules The input impedance Z in and

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Z parameter analysis of terminated two-port Gain: Fig 15 Terminated two-port Z-parameter model

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Z parameter analysis of terminated two-port Example 9 The circuit in Fig 16 is a two-stage transistor amplifier. The Z-parameters for each stage are Determine a) The input impedance and b) The overall voltage gain c) Check the matching of the load and output impedance Fig 16

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Z parameter analysis of terminated two-port Solution

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Z parameter analysis of terminated two-port 0.902225.6

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Z parameter analysis of terminated two-port The overall voltage gain Out put impedance The detail is left to the student to show that

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Z parameter analysis of terminated two-port Therefore the load is closely matched to the output impedance

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The h-parameter (Hybrid parameter) H-parameter is the combination of Z and Y parameter defined by or in scalar form H-parameter is commonly used in transistor modeling.

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The h-parameter The h parameters can found from

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The h-parameter Fig 17 Hybrid parameter model

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The h-parameter Example 10 Determine the h-parameter of the two-port circuit shown in Fig. 18 Fig. 18

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The h-parameter Example 10 Find the h-parameter of the circuit in Fig. 19 assuming L 1 =L 2 =M=1H Fig. 19 In frequency domain

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The h-parameter In matrix form

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The h-parameter With L 1 =L 2 =M=1 H

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The inverse hybrid parameter (g- parameter) g-parameter is defined by or in scalar form g-parameter is an alternative form of hybrid representation.

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The g parameters can found from

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Inverse hybrid parameter model

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Conversion of Two-port parameters Two port parameters can be converted to any form as follows From And and

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where

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Conversion of Two-port parameters From y to h

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Conversion of Two-port parameters Henc e

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Conversion of Two-port parameters It can be shown that for the terminated two-port with h-parameter the following equations can be derived and

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Transmission parameter The t-parameter or transmission parameters are used in power system and it is called ABCD parameter. The transmission parameter is defined by This means that the power flows into the input port and flow out to the load from the output port. t-parameter can be calculated from Open or short circuit at the output port or

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Transmission parameter Example 11 Fig 20 Determine the t-parameter of the circuit shown in Fig 20.

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Transmission parameter One of the most importance characteristics of the two-port circuit with t-parameter is to determine the overall cascade parameter. Therefore

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Inverse Transmission parameter

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Interconnection of two-port network Two port networks can be connected in series parallel or cascaded Series and parallel of two-port have 4 configurations Series input-series output (Z-parameter) Series input-parallel output (h-parameter) Parallel in put-series output (g or h -1 -parameter) Parallel input-parallel output (Y-parameter) With proper choice of parameters the combined parameters can be added together.

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Interconnection of two-port network

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Example Bridge-T network

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N1 // N2

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For network N2 For network N1

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Y-parameters of the bridge-t network are

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