Signals and Network Analysis

1. Signals and Network Analysis Target group 3rd year ECED Students 2 Lecture Hours 3 Tutorial Hours Contact hours: School of Computing and Electrical Engineering Eeng-3121

2. Reading Assignment • Generalized 1-port RLCM network synthesis procedures • Brune’s RLCM synthesis method

3. Signals and Network Analysis Chapter 4 Synthesis of 2-port networks

4. synthesis of 2-port networks I1 I2 + V1  + V2  Linear network I1 I2 Two Port Networks Output port Input port - Two pairs of terminal : two-ports - Current entering a port = current leaving a port - V1,V2, I1and I2 are related using two-port network parameters

5. synthesis of 2-port networks • Deriving point and transfer network functions I1 I2 The Network + + Input Port Output Port V1 V2 _ _ Deriving point functions

6. synthesis of 2-port networks • Deriving point and transfer network functions Current Gain I1 I2 The Network + + Input Port Output Port V1 V2 _ _ Transfer functions Voltage Gain

7. synthesis of 2-port networks • Two-port network parameters A two-port has four variables (voltages and currents at the two ports. Two of them can be expressed in terms of the other two using network parameters/functions. By taking any two variables as dependant and the other two as independent, different network parameter can be obtained V1 = z11I1 + z12I2 V2 = z21I1 + z22I2 Transmission A, B, C, D parameters V1 = AV2 - BI2 I1 = CV2 - DI2 Impedance Z parameters V1 = h11I1 + h12V2 I2 = h21I1 + h22V2 I1 = y11V1 + y12V2 I2 = y21V1 + y22V2 Admittance Y parameters Hybrid H parameters

8. synthesis of 2-port networks I2 I2 I1 I1=0 + V2  V1 + V1  V2 • Two-port network parameters V1 = z11I1 + z12I2 V2 = z21I1 + z22I2 Impedance Z parameters Output port : open I2 = 0 Input port : opened I1 = 0 Impedance parameters are called open-circuit parameters

9. synthesis of 2-port networks Z11-z12 Z22-z12 + V2  + V1  Z12 • Two-port network parameters V1 = z11I1 + z12I2 V2 = z21I1 + z22I2 Open-circuit impedance matrix For reciprocal network Z12 = Z21 Passive networks are reciprocal so that they can be replaced by equivalent T-network

10. synthesis of 2-port networks I2 I2 I1 I1 + V2 = 0  + V1  + V1=0  + V2  • Two-port network parameters I1 = y11V1 + y12V2 I2 = y21V1 + y22V2 Admittance Y parameters Output port : shorted Input port : shorted V2 = 0 V1 = 0 Admittance parameters are called short-circuit parameters

11. synthesis of 2-port networks -y12 + V1  + V2  y11+ y12 y22+ y12 • Two-port network parameters I1 = y11V1 + y12V2 I2 = y21V1 + y22V2 Short-circuit admittance matrix For reciprocal network Y12 = Y21 Passive networks are reciprocal so that they can be replaced by equivalent Π-network

12. synthesis of 2-port networks • Two-port network parameters Recall that where

13. synthesis of 2-port networks • Two-port network parameters similarly

14. synthesis of 2-port networks • Two-port network parameters Transmission A, B, C, D parameters V1 = AV2 - BI2 I1 = CV2 - DI2 For reciprocal network AD – BC = 1

15. synthesis of 1-port dp functions Example 1 Find the equivalent Π-network for the following T-network

16. synthesis of 2-port networks • Series, parallel and cascade interconnections Complex large network can be modeled with interconnected two-port networks • Simplify the analysis /synthesis • Simplify the design Parameters of interconnected two-port networks can be obtained easily: depending on the type of parameters and type of connections: • Series: z parameters • Parallel: y parameters • Cascade: transmission parameters

17. synthesis of 2-port networks I2 + V1  + V2  z I1 • Series, parallel and cascade interconnections za Series – Z parameters zb

18. synthesis of 2-port networks • Series, parallel and cascade interconnections ya Parallel – Y parameters yb

19. synthesis of 2-port networks • Series, parallel and cascade interconnections Cascade – T parameters Ta Tb