Lecture 21: Two Port Linear NetworksVijay Singh∗May 1, 20031 IntroductionOften, a system designer or a system analyst is interested only in the input and output charac-teristics of a “box” and does not want to be bothered with the details of circuits and components(like resistors, capacitors, etc) inside the “box”.A two p ort linear network containing R, L, C elements, tranformers, op-amps, anddependent sources (but no independent sources) can be described by:1. four admittance parameters, or2. four impedance parameters, or3. four hybrid parmeters, or4. four transmission (ABCD) parameters.2 Admittance ParametersLinear NetworkABFigure 1: Single Port.Current I1is controlled by two independant sources, V1and V2. Since the network is linear andcontains no independant sources, we can find I1by using the principle of superposition:I1= y11V1+ y12V2(1)where y11and y12are proportionality constants and have the units of siemens.∗Professor and Chairman, Department of Electrical & Computer Engineering, University of Kentucky, Lex-ington, KY, USA. E-mail: [email protected]. Document prepared using LATEX and figures created usingMetagraf by Ramprasad Potluri ([email protected]).1Linear NetworkABCDFigure 2: Two Port.Linear NetworkV1I1I1+−ABCDV2I2I2+−Figure 3: Two Port.Similarly,I2= y21V1+ y22V2(2)Alternatively,·I1I2¸=·y11y12y21y22¸·V1V2¸(3)Here, y11, y12, y21, and y22are called the admittance paramters or Y-parameters. Inputand output characterstics of the network or the “box” are completely defined once the fourY-parameters are known.Clearly,y11=I1V1¯¯¯¯V2=0(4)is the short-circuit input admittance.y12=I1V2¯¯¯¯V1=0(5)is the short-circuit transfer admittance.y21=I2V1¯¯¯¯V2=0(6)is the short-circuit transfer admittance.y22=I2V2¯¯¯¯V1=0(7)is the short-circuit output admittance.3 ExampleFind the Y-parameters of the circuit of Figure 321212 12I1I2ABCDV1V2+ +−−Figure 4: Example.y11=I1V1¯¯¯¯V2=0=16Sy12=I1V2¯¯¯¯V1=0=−112Sy21=I2V1¯¯¯¯V2=0=−112Sy22=I2V2¯¯¯¯V1=0=16SHere, S (siemens) is the SI unit of admittance.4 Other 2-port parameters4.1 Impedance ParametersV1= z11I1+ z12I2V2= z21I1+ z22I24.2 Hybrid ParametersV1= h11I1+ h12V2V2= h21I1+ h22V24.3 Transmission ParametersV1= AV2− BI2I1= CV2−
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