1. Two-Port Network 1

2. 2 TWO PORT NETWORKS Two port networks are a useful tool for describing idealized components. The basic device schematics are simple, but each set of parameters views the device differently. The basic device is seen below, along with the various parameter sets, I1I1 I2I2 s-domain circuit v1v1 v2v2 + - + -

3. 3 z-parameters y-parameters a-parameters b-parameters

4. 4 PARAMETER VALUES Obviously some of the parameters are impedance, while others are admittance. They can be easily determined by setting other parameters to zero, and measuring relevant voltages/currents. h-parameters g-parameters

5. 5 z-Parameters (impedance) The values are as below,

6. 6 The equivalent circuit for the z-parameters is shown below, z 11 I 2 z 21 I 1 z 11 z 22 V1V1 V2V2 I1I1 I2I2 + - + - + - + -

7. 7 Find the z parameters for the circuit shown EXAMPLE SOLUTION

8. 8 When port 1 is open, I 1 is zero and the voltage V 1 is

9. 9 The following measurements pertain to a two-port circuit operating in the sinusoidal steady state. With port 2 open, a voltage equal to 150 cos 4000t V is applied to port 1. The current into port 1 is 25 cos (4000t - 45°) A, and the port 2 voltage is 100 cos (4000t + 15°) V. With port 2 short-circuited, a voltage equal to 30 cos 4000t V is applied to port 1. The current into port 1 is 1.5 cos (4000t + 30°) A, and the current into port 2 is 0.25 cos (4000t + 150°) A. Find the a parameters that can describe the sinusoidal steady-state behavior of the circuit.

10. 10 SOLUTION

11. 11 The following measurements were made on a two-port resistive circuit. With 10 mV applied to port 2 and port 1 open, the current into port 2 is 025 µA, and the voltage across port 1 is 5 µV. With port 2 short-circuited and 50 mV applied to port 1, the current into port 1 is 50 µA, and the current into port 2 is 2 mA. Find the h parameters of the network. Drill Exercise

12. 12 RELATIONSHIPS AMONG THE TWO-PORT PARAMETERS

13. 13 To find the z parameters as functions of the a parameters,

14. 14

15. 15 EXAMPLE 1. 2.

16. 16 1. The parameters h 12 and h 22 cannot be obtained directly from the open circuit test.

17. 17

18. 18 Analysis Of The Terminated Two Port Circuit Two-port model of network VgVg ZgZg I1I1 V1V1 + - I2I2 V2V2 + - ZLZL Six characteristics of the terminated two-port circuit define its terminal behavior: 1.The input impedance Z in = V 1 /I 1, or the admittance Y in =I 1 /V 1 ; 2.The output current I 2 ; 3.The Thevenin voltage and impedance (V Th, Z Th ) with respect to port 2 ; 4.The current gain I 2 / I 1 ; 5.The voltage gain V 2 / V 1 and 6. the voltage gain V 2 / V g.

19. 19

20. 20 The Thevenin voltage with respect to port 2 Thevenin or output impedance is ratio V 2 / I 2 when V g is replace by short cicuit.

21. 21 The current gain The voltage gain V 2 / V 1

22. 22 The voltage ratio V 2 / V g

23. 23

24. 24 y parameters

25. 25 a parameters

26. 26 b parameters

27. 27 [b] 500Ω 5kΩ + - V1V1 + - V2V2 I1I1 I2I2 The two port circuit shown above is described in term of its b parameters, the values of which are b 11 = -20, b 12 = -3000Ω, b 21 = -2 mS, and b 22 = -0.2. a.Find the phasor voltage V 2. b.Find the average power delivered to the 5 kΩ load. c.Find the average power delivered to the input port. d.Find the load impedance for maximum average power transfer. ZgZg ZLZL Example

28. 28 e. To find he maximum average power delivered to the load in (d) Solution a. b. The average power delivered to the 5000 Ω load is c. To find the maximum average power delivered to the input port

29. 29 d. The load impedance for maximum power transfer e. The maximum average power delivered to Z L

30. 30 The b parameters of the two-port network are : b 11 =2000/3, b 12 =2/3 MΩ, b 21 =1/15 S, and b 22 =-100/3. The network is driven by a sinusoidal current source having a maximum amplitude of 100 μA and an internal impedance of 1000+j0 Ω. It is terminated in a resistive load of 10 kΩ. a.Calculate the average power delivered to the load resistor. b.Calculated the load resistance for maximum average power. c.Calculate the maximum average power delivered to the resistor in (b). Two port model of a network VgVg ZgZg ZLZL I1I1 I2I2 V1V1 V2V2 ++ - -