Circuits II EE221 Unit 8 Instructor: Kevin D. Donohue2-Port Circuits2-Port Circuits:Inverse Transmission -Parameter Model:ExampleSummary Formula for Inverse Transmission Parameters:Equivalent Circuit for Inverse Transmission Parameter Model:SPICE Solutions for Two-Port Parameters:Slide 9Slide 10Transmission -Parameter Model:Impedance/Admittance-Parameter Model:Hybrid (h)/Inverse Hybrid (g)-Parameter Model:Relationship Between 2 Sets of Port Parameters:Slide 15Solving for Terminal Currents and Voltages from Port Parameters:Combinations of Two-Port Networks:Slide 18Circuits IIEE221Unit 8Instructor: Kevin D. Donohue2 Port Networks –Impedance/Admittance, Transmission, and Hybird Parameters2-Port CircuitsNetwork parameters characterize linear circuits that have both input and output terminals, in terms of linear equations that describe the voltage and current relationships at those terminals. This model provides critical information for understanding the effects of connecting circuits, loads, and sources together at the input and output terminals of a two-port circuit. A similar model was used when dealing with one-port circuits.Review example: Thévenin and Norton Equivalent Circuits:10 V50 100 100 10 i1i1abShow that Voc=8 V, Isc = 0.08 A, and Rth = 1002-Port Circuits:Now take away the source from the previous example:Why wouldn't it make sense to talk about a Thévenin or Norton equivalent circuit in this case?The Thévenin and Norton models must be extended to describe circuit behavior at two ports.Label the terminal voltage and currents as v1, i1, v2, and i2 and develop a mathematical relationship to show their dependencies. 50 100 100 10 ia iaInverse Transmission -Parameter Model:If the circuit is linear, then a general linear relationship between the terminal voltages and currents can be expressed as: Geometrically each equation forms a planar surface over the v1-i1 plane, therefore, only three points on the surface are necessary to uniquely determine a, b, c, d, V2, and I2. So if the circuit response is known for three different values of the v1-i1 pairs, six equations with six unknowns can be generated and solved.This problem can be simplified by strategically setting v1 and i1 to zero in order to isolate unknown parameters and simplify the resulting equations. In general, if there are no independent sources in the circuit then V2, and I2 will be 0. This will be the case for the problems considered in this unit.21122112IdicviVbiavvExampleDetermine the inverse transmission parameter model for the given circuit.50 100 100 10 iaiai1+v1-i2+v2-Show that a =18/5, b= 100, c = 7/250 Siemens, d= 1.Summary Formula for Inverse Transmission Parameters:If all independent sources are deactivated, set i1 = 0 to find:If all independent sources are deactivated, set v1 = 0 to find:01201211 iivicvva01201211 vviidivbEquivalent Circuit for Inverse Transmission Parameter Model:If inverse transmission parameters are known, then the following circuit can be used as an equivalent circuit: 21ic cd 1av 1bi i1 + v1 - i2 + v2 - + - + - + - This circuit is helpful when implementing in SPICE withoutknowledge or details of circuit from which parameterswere derived.SPICE Solutions for Two-Port Parameters:As shown on previous slides, by strategically selecting the constraints on certain port variables, the two-port parameters are equal to ratios of other port variables. Therefore:Port variables can be constrained by attaching a zero-valued voltage or current source. The other port can be excited by a unity-valued source (or some other convenient value).Place meters at the remaining values need to evaluate the ratios.The two-port parameter can be found computing the ratio values from those found directly by SPICE. Example: Determine the SPICE commands to find the abcd parameters for the circuit below.50 100 100 10 iaiai1+v1-i2+v2-SPICE Solutions for Two-Port Parameters:1) Consider setting v1=0, then 2) Excite the circuit with i2=1 then3) Use SPICE to compute v2 and i1 to solve for b and d.12iid 12ivb 110012ivb11112iid 50 R1 100 R2 100 R3H116.67nVAma1I2100.00IVm2 0V1-1000.00mVAm1SPICE Solutions for Two-Port Parameters:4) Consider setting i1=0, then 5) Excite the circuit with v2=1, then6) Use SPICE compute v1 and i2 to solve for a and c.12vva 12vic 6.32778.0111vam282778.000778.12vic 50 R1 100 R2 100 R3H1 5.56mVAma0I1277.78mIVm1 7.78mVAm2 1V2Transmission -Parameter Model:Transmission parameters are related to the inverse transmission parameters by reversing the independent and dependent variables: 1122112112ivdcbaivdicvibiavv221221112211221DiCviBiAvvivivDCBAivivdcbaTransmissionParametersInverse TransmissionParametersImpedance/Admittance-Parameter Model:21222112112122212122121111iizzzzvvizizvizizvImpedance ParametersAdmittance Parameters222121221211112121222112112121122211211vyvyivyvyiiivvyyyyiivvzzzzHybrid (h)/Inverse Hybrid (g)-Parameter Model: 21222112112122212122121111vihhhhivvhihivhihvHybrid Parameters Inverse Hybrid Parameters222121221211112121222112112121122211211igvgvigvgiviivggggviivhhhhRelationship Between 2 Sets of Port Parameters:Since a single set of network parameters characterize the linear circuits completely at the input and output terminals, it is possible to derive other network parameters from this set.Example: Consider the z and y parameter characterization of a given circuit with no independent sources:Show that:vvz zz zii1211 1221 2212iiy yy yvv1211 1221 2212z zz zy yy yyy y y yyy y y yyy y y yyy y y y11 1221 2211 1221 2212211
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