Circuits Ci it II EE221 Unit 8 Instructor Kevin D D Donohue 2 Port Networks Impedance Admittance p Transmission and Hybird Parameters 2 Port Circuits Network parameters characterize linear circuits that have both input and output terminals in terms of linear equations that describe the voltage g and current relationships p 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 twoport circuit i i A similar i il model d l was used d when h d dealing li with i h oneport circuits Review example p Th venin and Norton Equivalent q Circuits 100 10 i1 a i1 10 V 50 100 b Show that Voc 8 V Isc 0 08 A and Rth 100 2 Port Circuits Now take away the source from the previous example 100 10 ia ia 50 100 Why wouldn t it make sense to talk about a Th venin or Norton equivalent circuit in this case The Th venin and Norton m models must m 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 d dependencies d i Inverse Transmission Parameter Model If the circuit is linear then a general linear relationship between the terminal voltages and currents can be expressed as v2 av1 bi1 V2 i2 cv1 di1 I 2 Geometrically each equation forms a planar surface over the v1 i1 plane therefore only p y three points p on the surface are necessary y 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 bl can be b simplified si lifi d by b strategically st t i ll setting s tti v1 and d i1 to t 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 Example Determine the inverse transmission parameter model for the given circuit 100 10 ia i1 v1 ia 50 100 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 a v2 v1 c i1 0 i2 v1 i1 0 If all independent sources are deactivated set v1 0 to find b v2 i1 d v1 0 i2 i1 v1 0 Equivalent Circuit for Inverse Transmission Parameter Model If inverse transmission parameters are known then the following circuit can be used as an equivalent circuit i1 v1 i2 1 i2 c d c av1 bi1 v2 This circuit Thi i it is i helpful h l f l when h implementing i l ti in i SPICE without ith t knowledge or details of circuit from which parameters were 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 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 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 f f found directly y by y SPICE Example Determine the SPICE commands to find the abcd parameters for the circuit below 100 10 ia i1 v1 ia 50 100 i2 v2 SPICE Solutions for Two Port Parameters 1 Consider setting v1 0 then i v b 2 d 2 i1 i1 2 Excite the circuit with i2 1 then v 100 b 2 i1 1 d i2 1 1 i1 1 3 Use SPICE to compute v2 and i1 to solve for b and d VAm1 H1 R2 1000 00m 100 0 V1 R1 50 VAma 16 67n R3 100 1 IVm2 100 00 I2 SPICE Solutions for Two Port Parameters 4 Consider setting i1 0 then i2 c v1 v2 a v1 5 Excite the circuit with v2 1 then a 6 1 1 3 6 v1 0 2778 i2 00778 c 28m v1 0 2778 Use SPICE compute v1 and i2 to solve for a and c H1 R2 VAm2 7 78m 100 0 I1 IVm1 277 78m R1 50 VAma 5 56m R3 100 1 V2 Transmission Parameter Parameter Model Transmission parameters are related to the inverse transmission parameters by reversing the independent and dependent variables Transmission Parameters v2 av1 bi1 i2 cv1 di1 v2 a b v1 i c d i 1 2 Inverse Transmission Parameters 1 a b v2 v1 c d i i 2 1 A B v2 v1 C D i i 2 1 v1 Av2 Bi2 i1 Cv2 Di2 Impedance Admittance Parameter Impedance Admittance Parameter Model Impedance Parameters v1 z11i1 z12i2 v2 z 21i1 z 22i2 v1 z11 v z 2 21 z12 i1 z 22 i2 Admittance Parameters 1 z11 z12 v1 i1 z 21 z 22 v2 i2 y11 y12 v1 i1 y 21 y22 v2 i2 i1 y11v1 y12 v2 i2 y21v1 y22 v2 Hybrid h Inverse Hybrid g Parameter M d l Model Hybrid Parameters v1 h11i1 h12 v2 i2 h21i1 h22 v2 v1 h11 i h 2 21 h12 i1 h22 v2 Inverse Hybrid Parameters 1 h11 h12 v1 i1 h 21 h22 i2 v2 g11 g12 v1 i1 g 21 g 22 i2 v2 i1 g11v1 g12i2 v2 g 21v1 g 22i2 Relationship 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 v v 1 2 z z z i z i 11 12 21 i y i y 1 22 2 Sh Show th that t z z 11 21 z y z y 12 22 11 21 y y 1 12 1 11 2 21 y y y y y y y y y y 11 21 y z y z 11 12 22 11 21 12 22 1 22 2 22 21 12 21 22 z z 12 22 11 y y y v y v 1 22 21 12 z z z z z z z z z z 22 11 22 21 12 21 11 22 21 12 y y y y y y y y y y 12 11 22 21 12 21 12 11 11 22 z z z z z z z z z z 12 11 22 21 12 21 12 11 11 22 Relationship Between 2 Sets of Port Parameters Example Consider the abcd and h parameter characterization …
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