Analog Circuits and Systems

Transcription

1 Analog Circuits and Systems Prof. K Radhakrishna Rao Lecture 11: Feedback in Systems 1

2 Previous lecture Applications of multipliers and comparators Macro models of BJTs and FETs Realizations of voltage buffer, current buffer, trans-conductance amplifier and trans-resistance amplifiers using nullator-norator models of transistors 2

3 What is Feedback? Dynamic system with feedback 1 represents the forward path of the system 2 represents the feedback path of the system 1 and 2 are unilateral (transmission from input to output only) X i is the input variable and is X o the output variable 3

4 What is Feedback? (contd.,) ( ) X + X = X i 2 o 1 o X = X ; X = X + X f o 2 es i f f 1 X o 1 2 = = = X 1 1 i X X f = 1 2 ;X i es = i X 1 1 4

5 What is Feedback? (contd.,) 1 2 L If is called loop gain. is negative the dynamic system is called Negative Feedback System If L is positive the dynamic system is called Positive Feedback System 5

6 Negative Feedback System L is negative If magnitude of the loop gain? Xo 1 X f f = - ; 1 X X i 2 i becomes independent of, and X 0 f 1 es 6

7 Positive Feedback System Positive feedback system When is positive and 0 <1 L L X X o i becomes highly sensitive to variations in L Regenerative feedback When ispositive and 1 L L X X o i and a practical dynamic system goes into saturation 7

8 Sensitivity in Negative Feedback Systems S f 1 Sensitivity of the response to changes in 1 S as Δ 1 f = f 1 = 1 Δ1 f 1 12 f L S 0 1 8

9 Sensitivity in Negative Feedback Systems S f 2 Sensitivity of the response to changes in 2-1 S f = ; Any variations in 2 cause inverse variations in f 9

10 Example: Sensitivity and Negative Feedback Voltage Amplifier 10

11 Example: Sensitivity and Negative Feedback Voltage Amplifier 1 f Sensitivity S = for L = Xo 10 f = = = Xi x 10 1 f Sensitivity S = for L = Xo f = = X i 11

12 Simulation: Voltage Amplifier L =- 100 L =

13 Example: Sensitivity and Negative Feedback Current Amplifier 13

14 Current Amplifier Sensitivity S f 1 = 1 21 for = - 20 L X = o = f X i 14

15 Simulation: Current Amplifier L =- 100 L =

16 Sensitivity and Positive Feedback = 0.9 L V 9 o = = V i 90 = 0.5 L V 5 o = = V i 10 Open loop gain in each case is less than closed loop gain It is highly sensitive tovariations in openloop gain 16

17 Example: Negative Feedback and Inversion Multiplier in feedback path results in a divider V C has to be kept positive to ensure loop gain L to be negative V V=10 i o V C 17

18 Example: Negative Feedback and Inversion Squarer in the feedback path results in a square rooter V i needs to be maintained positive V= 10V o i 18

19 Example: Negative Feedback and Inversion Square rooter through squarer V po = 20V ref As the output is independent of control input it is an AC 19

20 Example: Negative Feedback and Inversion 20

21 Simulation with V ref = 0.8 and V po = 4 volts V pi = 10 V pi = 8 21

22 Simulation with V ref = 0.8 and V po = 4 volts V pi = 5 V pi = 4 22

23 Example: Negative Feedback and Inversion True RMS enerator True RMS value of any periodic waveform can be generated using squarer, averages (low pass filter and a square rooter) 23

24 Feedback System 1 is the forward path of the system 2 is the feedback path X f follows the input X i precisely if the loop gain 1 2 is very large 24

25 Encoder-Decoder Feedback System Feedback systems with 1 as an encoder then 2 as a decoder, and vice-versa Input variable to 1 is of the same dimension as that of output variable of 2, and input variable 2 is of the same dimension as that of output variable of 1 Enables realization of a large number of communication functions 25

26 Current-to-Voltage Converter and Current Follower 1 is Trans-resistance (R f ) amplifier and 2 is Trans-conductance ( m ) amplifier The loop gain m R f >> 1 26

27 Voltage-to-Current Converter and Voltage Follower 1 is Trans-conductance ( m ) amplifier and 2 is Transresistance (R f ) amplifier The loop gain m R f >> 1 27

28 AC to DC converter and AC Follower 1 is AC to DC converter and 2 is DC to AC converter The loop gain 1 2 >> 1 28

29 DC to AC Converter and DC Follower 1 is AC to DC converter and 2 is DC to AC converter 29

30 Phase to Voltage Converter and Phase Follower 1 is Phase to Voltage converter and 2 is Voltage to Phase converter 30

31 Voltage to Phase Converter and Voltage Follower 1 is Voltage to Phase converter and 2 is Phase to Voltage converter 31

32 Voltage to Frequency Converter and Voltage Follower 1 is Voltage to Frequency converter and 2 is Frequency to Voltage converter 32

33 Frequency to Voltage Converter and Frequency Follower Frequency Follower and FM Detector 1 is Frequency to Voltage converter and 2 is Voltage to Frequency converter 33

34 Frequency Locked Loop 34

35 Simulation: Quiescent frequency = 10kHz for V cq =0 V T = 0.1 ms T = ms 35

36 Simulation: Quiescent frequency = 10kHz for V cq =0 V T = ms 36

37 A to D Converter Analog Voltage Follower 1 is A to D Converter and 2 is D to A Converter 37

38 D to A Converter Digital Follower 1 is D to A Converter and 2 is A to D Converter 38

39 Conclusion Negative feedback makes the output less sensitive or insensitive to the variations of parameters associated with active devices in the forward path Negative feedback makes the output sensitive to parameter variations associated with the feedback path Positive feedback can make the output very sensitive to parameter variations associated with the loop Encoder-Decoder feedback systems enable us to realize a wide range of analog signal processing functions 39