NETWORK FILTERS AND TRANSMISSION LINE

1. NETWORK FILTERS AND TRANSMISSION LINE

2. TWO PORT NETWORKS

3. SUB - TOPICS • Z – PARAMETER • Y – PARAMETER • T (ABCD) – PARAMETER • TERMINATED TWO PORT NETWORKS

4. OBJECTIVES • TO UNDERSTAND ABOUT TWO – PORT NETWORKS AND ITS FUNTIONS. • TO UNDERSTAND THE DIFFERENT BETWEEN Z – PARAMETER, Y – PARAMETER, T – PARAMETER AND TERMINATED TWO PORT NETWORKS. • TO INVERTIGATE AND ANALYSIS THE BEHAVIOUR OF TWO – PORT NETWORKS.

5. TWO – PORT NETWORKS • A pair of terminals through which a current may enter or leave a network is known as a port. • Two terminal devices or elements (such as resistors, capacitors, and inductors) results in one – port network. • Most of the circuits we have dealt with so far are two – terminal or one – port circuits.

6. A two – port network is an electrical network with two separate ports for input and output. • It has two terminal pairs acting as access points. The current entering one terminal of a pair leaves the other terminal in the pair.

7. I + V - Linear network I I1 I2 + V2 - + V1 - Linear network I1 I2 One – port network Two – port network

8. Two (2) reason why to study two port – network: • Such networks are useful in communication, control system, power systems and electronics. • Knowing the parameters of a two – port network enables us to treat it as a “black box” when embedded within a larger network.

9. From the network, we can observe that there are 4 variables that is I1, I2, V1and V2, which two are independent. • The various term that relate these voltages and currents are called parameters.

10. Z – PARAMETER • Z – parameter also called as impedance parameter and the units is ohm (Ω) • Impedance parameters is commonly used in the synthesis of filters and also useful in the design and analysis of impedance matching networks and power distribution networks. • The two – port network may be voltage – driven or current – driven.

11. I1 I2 V1 V2 Linear network +  +  + V1 - + V2 - I1 I2 Linear network • Two – port network driven by voltage source. • Two – port network driven by current sources.

12. I2 I1 Z11 Z12 + V1 - + V2 - Z21 Z22 (1) (2) • The “black box” is replace with Z-parameter is as shown below. • The terminal voltage can be related to the terminal current as:

13. In matrix form as: • The Z-parameter that we want to determine are z11, z12, z21, z22. • The value of the parameters can be evaluated by setting: 1. I1= 0 (input port open – circuited) 2. I2= 0 (output port open – circuited)

14. Thus,

15. Where; z11 = open – circuit input impedance. z12 = open – circuit transfer impedance from port 1 to port 2. z21 = open – circuit transfer impedance from port 2 to port 1. z22 = open – circuit output impedance.

16. I2 I1 + V1 _ + V2 _ 240Ω 120Ω 40Ω Example 1 Find the Z – parameter of the circuit below.

17. Ia I1 + V1 _ + V2 _ 240Ω Ib 120Ω 40Ω Solution • I2 = 0(open circuit port 2). Redraw the circuit.

19. Iy I2 + V1 _ + V2 _ 240Ω 120Ω Ix 40Ω ii) I1 = 0 (open circuit port 1). Redraw the circuit.

20. In matrix form:

21. I1 2Ω 10Ω I2 j4Ω + V1 _ + V2 _ 10I2 + _ -j20Ω Example 2 Find the Z – parameter of the circuit below

22. I1 2Ω j4Ω I2 = 0 + V2 _ + V1 _ Solution i) I2 = 0 (open circuit port 2). Redraw the circuit.

23. I1 = 0 10Ω I2 + V1 _ + V2 _ + _ 10I2 -j20Ω ii) I1 = 0 (open circuit port 1). Redraw the circuit.

24. I2 I1 Y11 Y12 + V1 - + V2 - Y21 Y22 Y - PARAMETER • Y – parameter also called admittance parameter and the units is siemens (S). • The “black box” that we want to replace with the Y-parameter is shown below.

25. (1) (2) • The terminal current can be expressed in term of terminal voltage as: • In matrix form:

26. The y-parameter that we want to determine are Y11, Y12, Y21, Y22. The values of the parameters can be evaluate by setting: i) V1 = 0 (input port short – circuited). ii) V2 = 0 (output port short – circuited). • Thus;

27. 5Ω I2 I1 + V1 _ + V2 _ 15Ω 20Ω Example 1 Find the Y – parameter of the circuit shown below.

28. 5Ω I2 I1 + V1 _ 20Ω Ia Solution • V2 = 0

29. I1 5Ω I2 + V2 _ 15Ω Ix ii) V1 = 0 In matrix form;

30. I1 2Ω 10Ω I2 j4Ω + V1 _ + V2 _ 10I2 + _ -j20Ω Example 2 (circuit with dependent source) Find the Y – parameters of the circuit shown.

31. I1 2Ω 10Ω j4Ω I2 + V1 _ + _ 10I2 Solution i) V2 = 0 (short – circuit port 2). Redraw the circuit.

32. I1 2Ω 10Ω I2 j4Ω + V2 _ 10I2 -j20Ω + _ ii) V1 = 0 (short – circuit port 1). Redraw the circuit.

33. T (ABCD) PARAMETER • T – parameter or ABCD – parameter is a another set of parameters relates the variables at the input port to those at the output port. • T – parameter also called transmission parameters because this parameter are useful in the analysis of transmission lines because they express sending – end variables (V1 and I1) in terms of the receiving – end variables (V2 and -I2).

34. I2 I1 A11 B12 + V1 - + V2 - C21 D22 • The “black box” that we want to replace with T – parameter is as shown below. • The equation is:

35. In matrix form is: • The T – parameter that we want determine are A, B, C and D where A and D are dimensionless, B is in ohm (Ω) and C is in siemens (S). • The values can be evaluated by setting i) I2 = 0 (input port open – circuit) ii) V2 = 0 (output port short circuit)

36. Thus; • In term of the transmission parameter, a network is reciprocal if;

37. I1 2Ω 4Ω I2 + V1 _ + V2 _ 10Ω Example Find the ABCD – parameter of the circuit shown below.

38. I1 2Ω + V1 _ + V2 _ 10Ω Solution i) I2 = 0,

39. I1 2Ω 4Ω I2 + V1 _ 10Ω I1 + I2 ii) V2 = 0,

40. Zg I1 I2 + V1 - + V2 - Two – port network Vg ZL +  TERMINATED TWO – PORT NETWORKS • In typical application of two port network, the circuit is driven at port 1 and loaded at port 2. • Figure below shows the typical terminated 2 port model.

41. Zg represents the internal impedance of the source and Vg is the internal voltage of the source and ZL is the load impedance. • There are a few characteristics of the terminated two-port network and some of them are;

42. The derivation of any one of the desired expression involves the algebraic manipulation of the two – port equation. The equation are: 1) the two-port parameter equation either Z or Y or ABCD. For example, Z-parameter,

43. 2) KVL at input, 3) KVL at the output, • From these equations, all the characteristic can be obtained.

44. ATTENUATORS

45. Attenuators are simple but very important instruments. Unlike an amplifier, which is ordinarily used to increase a signal level by a given amount, the attenuator is used to reduce the signal level by a given amount

46. The use of attenuators has become so widespread that a study of their design and use is important in the study of electronic instruments. Attenuators may be constructed in many ways. We will confine our discussion to lumped-resistance attenuators.

47. The L-type Attenuator • One of the simplest types of attenuators is the L type or the ordinary voltage divider. The voltage gain of this network is the out­put voltage divided by the input voltage.

48. Usually, the term attenuator refers to a device that not only introduces a precise amount of attenuation but also provides an impedance match on the input and output terminals. The Characteristic Resistance of Symmetrical Attenuators