Analog Circuits and Systems

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1 Analog Circuits and Systems Prof. K Radhakrishna Rao Lecture 30: Automatic Tuning of Filters (PLL) and Review of Filter Design 1

2 Review Frequency Compensation 2

3 Review (contd.,) Switched Capacitor Filters Manual Tuning of a second-order filter f 0 of the filter to be tuned to f ref, specified frequency, by trial and error adjustment of V c to make V av = 0 Use an oscillator with frequency f ref 3

4 Automatic Tuning of Filters (Phase Locked Loop) V adjusts itself to make c input to the comparator (integrator) go to zero C = 0.1 µ ;R = 1k;Q = 5;H = 1 0 V C = 10RC where ω ω ref ref of the input. This is known as is the frequency Phase Locked Loop (PLL) 4

5 Phase Locked Loop (PLL) Phase Follower Dynamic Characteristic Loop Gain = K K VCF PD ω s 0 φ o = φ i 1 s 1 + K K ω VCF PD 0 The Bandwidth of the PLL=K K ω rad/sec VCF PD 0 5

6 Simulation 1 Sine wave input; 1 V, f ref =1 khz 6

7 Simulation 2 Sine wave input; 1 V, f ref =2 khz 7

8 Simulation 3 Square wave input; 1 V, f ref =1 khz 8

9 Simulation 4 Square wave input; 1 V, f ref =2 khz 9

10 Phase Locked Loop Static Characteristics: The phase is locked to 90 O independent of the frequency of the input signal Lock Range: The system has a lock range that is decided by the range of control voltage Dynamics of PLL: Capture Range: Range of frequencies over which the loop can have loop gain much greater than 1 while starting 10

11 Time Multiplexing for Calibration and Use C = 0.1 µ ;R = 1k;Q = 5;H =

12 Master-Slave Tuning (Continuous-time filters) V 10R C V = = Cm ω ; Cs ref 10R C m m s s ω s ω ω RC = as V = V RC Cs ref s s s m m Cm 12

13 Design of 4 th order Band-pass and Band-stop Filter Centre Frequency: 5.3 khz Maximally flat magnitude (Butterworth) Second order state-space filter will have for R = 30 kw and C=1nF Use UAF 42 13

14 2 nd Order BPF Q =10; H 0 = 1 14

15 Cascading two 2 nd order BPFs Bandwidth gets reduced and gain at centre frequency is (H 0 Q) 2 15

16 Wideband Amplifier Cascading BPFs with staggered centre frequencies known as Distributed Amplifiers 16

17 Wideband Amplifier Two 2 nd order BPFs cascaded Centre frequencies of the two filters are staggered by 10% 17

18 Wideband Amplifier with staggering >10% 18

19 Notch filter 2 nd Order and 4 th Order 4 th order filter has narrower stop band 19

20 Broad Band band-stop filter Centre frequencies are staggered by 5% 20

21 Review of Filter Structures 21

22 Butterworth and Chebyschev Filters All pole filters Useful when white noise dominates over signal Rates of attenuation at thee pass band edge are slow Dominant coloured noise is not effectively removed by these filters 22

23 Inverse Chebyschev and Elliptic Filters Have poles and zeros. Presence of zeros helps in eliminating narrow band dominant noise components in the stop band Attenuation in the stop band is decided by n-m ( number of poles number of zeros) When white noise dominant signal-to-noise ratio improvement is not as much as that of all pole filters 23

24 Second-order Filter Input-output relationship of a second order filter with a zero ( 2 1 αx ) ( 2 1 X ) 2 + Input-output relationship of all-pole filter 2 X Q 2 2 p 1 ( 2 1 X ) 2 + X Q 2 2 p ( 2 ) Zero: 1 0.5X 2 ω X= where ωp is the normalizing frequency. ω p Zero to be located beyond the pass band 24

25 Responses For Q p =2 and a=0.5 25

26 Responses For Q p =1 and 2 with a=0.5 White noise still comes through in our attempt to remove the coloured noise 1 Q 2 p ( ) = 21 α for maximum flatness in the pass-band 26

27 Addition of another first order filter For Q p =1/ 2 with a=b=0.5 Both coloured noise and white noise are attenuated 1 Q 2 p ( ) = 21 α β where β is the scalling factor in the first order 1 low pass= 1+ β X 2 27

28 How should filters be designed at present? Present day electronic systems have both digital and analog subsystems Many of the present systems are portable and hence battery operated Analog sub-systems have to be designed using the digital device technologies for single chip solutions Analog sub-systems have to be designed using low voltage (3V at present) 28

29 How should filters be designed at present? (contd.,) With leaky switches and switching noise switched-capacitor filter is not a viable option While L-replacement method provides a reliable filter it is less flexible (in terms of selecting the parameters Q, f 0 and H 0 independently) beside high component count Q-enhancement method can lead to active filter with single active device, but less reliable than multi-active device based filter. It is also less flexible. 29

30 How should filters be designed at present? (contd.,) State-space filters offer the best solution in terms of reliability and flexibility. While Biquad IC based state-space filter is convenient but more expensive at present compared to state-space filter designed using quad Op Amp IC State-space filters can be tuned precisely using either a multiplier and multiplying DAC. State-space filters with provision for tuning offer the best solution to filtering 30

31 Conclusion 31

32 Conclusion 32

Analog Circuits and Systems

Analog Circuits and Systems Prof. K Radhakrishna Rao Lecture 31: Waveform Generation 1 Review Phase Locked Loop (self tuned filter) 2 nd order High Q low-pass output phase compared with the input 90 phase