Active Filters an Introduction

Transcription

1 Active Filter an Introduction + Vin() - Filter circuit G() + Vout() - Active Filter. Continuou-time or Sampled-data. Employ active element (e.g. tranitor, amplifier, op-amp) a. inductor-le (continuou-time) b. inductor-le & reitor-le (ample-data) c. G(jω) in paband 8 Kenneth R. Laker (baed on P. V. Lopreti 6) updated Dec8 KRL

2 Active Filter an Introduction + Vin() - Filter circuit G() + Vout() - G = a M M a M M... a a N b N N... b b a M z z... z M G = p p... p N M N Filter Order = N 8 Kenneth R. Laker (baed on P. V. Lopreti 6) updated Dec8 KRL

3 Ideal Filter Repone Characteritic G G Paband Stop-band Stop-band Paband P High-pa (HP) Low-pa (LP) G G Paband Lower Stop-band P PL Stop-band Upper Stop-band PH Upper Paband Lower Paband SL SH Bandtop (BS) V j G = G j = out V in j Bandpa (BP) 8 Kenneth R. Laker (baed on P. V. Lopreti 6) updated Dec8 KRL 3

4 Practical Lowpa Filter Specification S electivity factor = P G (db) Tranition band Amax Amin Stop-band Paband P S Key pec:. f B= P /. Amax 3. f S =S / 4. Amin Filter cot increae!. Amax -> lower. Amin -> larger 3. P -> larger 4. S / P -> z z 8 Kenneth R. Laker (baed on P. V. Lopreti 6) updated Dec8 KRL 4

5 Filter Approximation Deign G() G a M z z... z M => G = p p... p N MatLab i a good tool for thi tak. 8 Kenneth R. Laker (baed on P. V. Lopreti 6) updated Dec8 KRL 5

6 Practical Bandpa Filter Specification G (db) Selectivity factor SL SU PL PU Tranition band Amax Symmetric bandpa filter SL SU = PL PU Amin Lower Stop-band Paband Upper Stop-band PU PL Q= PU SU SL PL SL PL 8 Kenneth R. Laker (baed on P. V. Lopreti 6) updated Dec8 KRL 6

7 Cacade Filter Deign If N = odd G = a M M a M M... a a N b N N... b b (N- )/ (N- )/ a a a i a i a i = = G i b i = bi bi i = If N = even a M M a M M... a a N/ a i a i a i N/ G = N = = G i N b N... b b i = bi b i i = Vin G() Vo G() Vo G3() Vo3 Vo(N-)/... GN/() Vout Gi() are nd order ( pole + zero) with at mot one t order 8 Kenneth R. Laker (baed on P. V. Lopreti 6) updated Dec8 KRL 7

8 Filter Type -plane zero/pole order low-pa (LP) a Q a G j = G = nd order high-pa (LP) a G = Q G j = a X a Q a Q G j = j G z= z = max Gmax j X O max max = Q max = / 4Q Q a Q / Gmax G z= z = 4Q a Q / a X Q X Q o O a X Q X a Q Gmax G z= z = nd order bandpa (LP) G = G j nd a Q /.77 Gmax / Q 8 Kenneth R. Laker (baed on P. V. Lopreti 6) updated Dec8 KRL = 8

9 Filter Type -plane zero/pole order Notch (N) O nd N N N Q N = G =a N G =a Q N nd order HP Notch (HPN) N G =a Q N G a X X Q O nd order LP Notch (LPN) j O G a = a j G Q a N max N O j X O X G N N QO a G j = a N a 8 Kenneth R. Laker (baed on P. V. Lopreti 6) updated Dec8 KRL N G j = a a max N G j = a G j = a Gmax N G j = a Gmax X N X N G j = a N G j = a G j = a 9

10 nd order All-Pa (AP) Q G =a Q G j = G j = a G a j X O X Q Q O Ideal tranmiion: j t vo t = K v I t t d T j = T j e Group Delay T j = K d = j = t d d j =t d d 8 Kenneth R. Laker (baed on P. V. Lopreti 6) updated Dec8 KRL

11 Delay Equalization Concept delay ditorted data Cable or Filter equalized data Delay Equalizer Total Equalized Delay tot = C DE Delay Equalizer DE Cable or Filter tot = C DE 8 Kenneth R. Laker (baed on P. V. Lopreti 6) updated Dec8 KRL

12 OP Amp Integrator t vo t = v I t dt CR i i Vo db Vi Bode plot R C vi(t) V vo(t) Vo int = = Vi CR int = - 6 db/octave CR (log cale) CR 8 Kenneth R. Laker (baed on P. V. Lopreti 6) updated Dec8 KRL

13 Two-Integrator-Feedback-Loop Active Filter K K V hp = V i = Vi Q Q V hp int = = CR - Vi Vbp V hp V hp = V hp V hp K V i Q Vlp V hp V hp V hp / Q V hp Vi K Q K V hp V hp= Vlp V hp= Vbp 8 Kenneth R. Laker (baed on P. V. Lopreti 6) updated Dec8 KRL 3

14 Feedback Equation Vi V hp =V bp V hp = V bp V lp Q V hp =V lp V hp = V hp K V i Q V hp K K G = = = Vi Q Q 8 Kenneth R. Laker (baed on P. V. Lopreti 6) updated Dec8 KRL 4

15 Feedback Equation II High Pa Output: Bandpa Output: Lowpa Output: V hp = Vi K = K Q Q V bp V hp = = Vi Vi V lp V bp = = Vi Vi 8 Kenneth R. Laker (baed on P. V. Lopreti 6) updated Dec8 KRL K Q K Q 5

16 Implementation R Rf Vi R C R Integrator R C V lp V hp V bp R3 V hp = V hp V hp K V i Q 8 Kenneth R. Laker (baed on P. V. Lopreti 6) updated Dec8 KRL Summing Amp V hp= Vbp V hp= V lp 6

17 Implementation II R f R Rf R3 Rf V hp = V hp V hp Vi R R R3 R R R3 R R f = R Set: V hp = And compare term: R R3 V hp V hp V R R3 R R3 i V hp = V hp V hp K V i Q R R3 R3 Q= Q = R R => R3 = Q R 8 Kenneth R. Laker (baed on P. V. Lopreti 6) updated Dec8 KRL 7

18 Deign Equation RC = Given = f, chooe C, calculate R R f = R Chooe Rf, Calculate R (or vice-vera) R3 = Q Given Q, chooe R, calculate R3 (or vice-vera). R R3 KQ= = Q K = R Q K i fixed by choice of Q. We have two deign parameter ( and Q, or K) and three free component (C, Rf, and R) or independent variable. 8 Kenneth R. Laker (baed on P. V. Lopreti 6) updated Dec8 KRL 8

19 Retriction Since K mut be poitive, Q MIN =.5 At thi value of Q: V hp K K = = V i We have real and equal pole. For Q > /, we are retricted to complex conjugate pole. 8 Kenneth R. Laker (baed on P. V. Lopreti 6) updated Dec8 KRL 9

20 Adding Finite Zero (Notche) To be able to create notche in the repone, we need another umming amplifier: Where the weighted input come from the highpa, bandpa, and lowpa output of the feedback circuit. 8 Kenneth R. Laker (baed on P. V. Lopreti 6) updated Dec8 KRL

21 Notch Creation All the output point tranfer function contain the ame denominator, o only the numerator term will be affected: V hp V bp V lp RH RF RB RL G = K RF RF RF V o G = V hp V bp V lp RH RB RL RF / RH RF / RB RF / RL / Q For a notch at = N, no connection i made to Vbp. 8 Kenneth R. Laker (baed on P. V. Lopreti 6) updated Dec8 KRL

22 8 Kenneth R. Laker (baed on P. V. Lopreti 6) updated Dec8 KRL

23 Big Picture Filter Deign Tak. Deign G() from filter pec.. Determine filter tructure (block diagram) to realize G(). 3. Determine filter circuit() to implement tructure. 4. Determine component value. Filter Deign CAD Tool on the Market. MatLab - Mathwork. FILTER PRO Texa Intrument 3. Aktiv Filter New Wave Intrument 4. Filter Lab Microchip 5. Filter Wiz Pro Schematica 6. FilterCAD Linear Technology 8 Kenneth R. Laker (baed on P. V. Lopreti 6) updated Dec8 KRL 3

24 Numerical 8 Kenneth R. Laker (baed on P. V. Lopreti 6) updated Dec8 KRL 4

25 Normalizing R and C value - cont. 8 Kenneth R. Laker (baed on P. V. Lopreti 6) updated Dec8 KRL 5

26 lp 8 Kenneth R. Laker (baed on P. V. Lopreti 6) updated Dec8 KRL 6

27 8 Kenneth R. Laker (baed on P. V. Lopreti 6) updated Dec8 KRL 7

28 8 Kenneth R. Laker (baed on P. V. Lopreti 6) updated Dec8 KRL 8

29 8 Kenneth R. Laker (baed on P. V. Lopreti 6) updated Dec8 KRL 9

30 8 Kenneth R. Laker (baed on P. V. Lopreti 6) updated Dec8 KRL 3

31 (MFM) 8 Kenneth R. Laker (baed on P. V. Lopreti 6) updated Dec8 KRL 3