EEL 3923C. JD/ Module 3 Elementary Analog Filter Design. Prof. T. Nishida Fall 2010

Transcription

1 EEL 3923C JD/ Module 3 Elementary Analog Filter Design Prof. T. Nishida Fall 2010

2 Purpose Frequency selection Low pass, high pass, band pass, band stop, notch, etc. Applications II. Filter Fundamentals Many applications in communications, instrumentation, signal processing 2

3 Low Pass and High Pass Filter Single Time Constant (STC) Networks Attenuation beyond 3dB frequency not steep 3

4 LP HP BP BS Ideal Filter Frequency Response Ref. Sedra and Smith, Figure

5 Specifications of Non-ideal LP A max = maximum allowable attenuation in passband A min = minimum required attenuation in stopband ω p = passband edge ω s = stopband edge Ref. Sedra and Smith, Figure

6 Specifications of Non-ideal BP Amax = maximum allowable attenuation in passband Amin = minimum required attenuation in stopband ωp1, ωp2 = passband edges Ref. Sedra and Smith, Figure 12.4 ωs1, ωs2 = stopband edge 6

7 General Filter Transfer Function Transfer function in s-domain Transfer function for physical frequencies Polynomial expansion of T(s) N=1 filter order N M 7

8 General Filter Transfer Function Factor numerator and denominator Numerator roots: z 1, z 2,, z M Transfer function zeros (transmission zeros) Also, N-M transmission zeros at s= Denominator roots: p 1, p 2,, p N Transfer function poles (natural modes) 8

9 Characteristics of Trans. Fct. Poles, Zeros May be real or complex Complex zeros and poles occur in conjugate pairs Transmission zeros usually purely imaginary at stopband frequencies Poles have negative real part for stable filters Represent on pole-zero plot 9

10 N = M = N-M = Pole-Zero Pattern Poles and zeros plotted on complex s-plane All poles complex conjugate except for odd order filter (one pole on real axis) zeros at s= jω ο ο ο ο σ 10

11 Some Filter Types Ref. Application note: 11

12 Butterworth LP Filter Characteristics Monotonically decreasing transmisson All transmission zeros at ω= (all pole) Very flat response near ω=0 Transfer function Ref. Sedra and Smith, Figure

13 Butterworth LP Filter At ω=ω p T(ω) At ω=ω s 1 A max A min ω p ω s (ω) 13

14 Transfer function Butterworth LP Filter 1 T(ω) A max A min p 3 p 2 p 1 jω ω 0 σ ω p ω s (ω) p 4 p 5 14

15 Chebyshev LP Filter Characteristics: Equi-ripple response in passband Monotonically decreasing transmission in passband All transmission zeros at ω= Ref. Sedra and Smith, Figure

16 Chebyshev LP Filter At ω=0 At ω=ω p At ω=ω s 16

17 Transfer function Chebyshev LP Filter 17

18 Implementation of Higher Order Filters 1 st and 2 nd order filters may be cascaded to realize higher order filters Factor higher order transfer function into product of 1 st and 2 nd order functions Implement each 1 st and 2 nd order stage as an opamp circuit 18

19 1 st Order Filter Implementation Ref. Sedra and Smith, Figure

20 2 nd Order Filter Transfer Functions Ref. Sedra and Smith, Figure

21 2 nd Order Filter LCR Circuits Issue: Inductors expensive and large Ref. Sedra and Smith, Figure

22 Opamp Simulated Inductor Ref. Sedra and Smith, Figure

23 Feedback Implementation of 2 nd Order Filter Gain Inverting integrator Inverting integrator Ref. Sedra and Smith, Figure

24 Two Integrator Feedback Loop Circuit Example: Kerwin-Huelsman-Newcomb two-integrator circuit Ref. Sedra and Smith, Figure

25 Single Opamp 2 nd Order Filter Block Alternate approach Single opamp with RC network in feedback path Sallen-Key Filter Circuit Compare with 2 nd order T(s) 25

26 III. FilterPro TM Software Tool Purpose Although low-pass filters are vital in modern electronics, their design and verification can be tedious and time consuming. The FilterPro program is designed to aid in the design of lowpass filters implemented with the multiple feedback (MFB) and Sallen-Key topology. Ref. Application note: Download link: 26

27 Step 1: Select Filter Type 27

28 Step 2: Select Filter Specifications 28

29 Step 3: Filter Response 29

30 Step 4: Select Filter Topology 30

31 Design Results Main Page Component tolerances 31

32 Design Results Bill Of Materials Actual implementation depends on opamp specs 32

33 Simulate Design in LTSPICE 33

34 Step 1: Select Filter Type 34

35 Step 2: Select Filter Specifications 35

36 Step 3: Filter Response 36

37 Step 4: Select Filter Topology 37

38 Design Results Main Page Component tolerances 38

39 Design Results Bill Of Materials Actual implementation depends on opamp specs 39

40 Simulate Design in LTSPICE 40

41 Real Opamp Requirements Ref. Application note: 41

42 Real Opamp Requirements Ref. Application note: 42

43 Summary Assignment 3 (Active Filter) Filter fundamentals FilterPro TM Software Tool See detailed schedule in syllabus for assignment check-off process Also check for lab/ta hours at NEB 246 and E-learning 43