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. gain in paband 8 Kenneth R. Laker updated 7Dec9 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 8 Kenneth R. Laker updated 7Dec9 KRL Filter Order = N

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 updated 7Dec9 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 8 Kenneth R. Laker updated 7Dec9 KRL z 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 updated 7Dec9 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 updated 7Dec9 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 ai ai = = G i b i = bi bi i = If N = even a M M a M M... a a N/ a i ai ai 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 N = odd => G() t order N = even => G() nd order 8 Kenneth R. Laker updated 7Dec9 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 = o O max j G z = z = O X Q 8 Kenneth R. Laker updated 7Dec9 KRL 4Q max max = Q a Q / a Gmax X Q X a X Q X a Q Gmax G z = z = nd order bandpa (LP) G = G j nd max = / 4Q Q a Q / Gmax a Q /.77 Gmax / Q = 8

9 Filter Type -plane zero/pole order Notch (N) O nd X Q O nd order LP Notch (LPN) N G =a Q N nd order HP Notch (HPN) G a X j N G =a Q N O G a = a j G Q a N max N O j X O X N N QO 8 Kenneth R. Laker updated 7Dec9 KRL G a G j = a N a G j = a a max N N Gmax N Gmax X N X N G j = a N 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 v O t =K v I t t d T j = T j e Group Delay 8 Kenneth R. Laker updated 7Dec9 KRL T j =K d = j = t d d j =t d d

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 updated 7Dec9 KRL

12 OP Amp Building Block Inverting Integrator t v O t = v I t dt CR Summer v v V o = = int V i CR int = R f R3 Rf V = V V. R R R3 R R Rf V 3 R R3 R CR 8 Kenneth R. Laker updated 7Dec9 KRL

13 Two-Integrator-Feedback-Loop Active Filter V hp int = = CR Vi V hp - => V hp V hp V hp =K V i Q => K K V hp = V i = V i Q Q V hp = V hp V hp K V i Q V hp hp V V hp V hp V hp Vi /Q Q K V hp 8 Kenneth R. Laker updated 7Dec9 KRL V hp K V hp=v lp V hp=v bp 3

14 Feedback Equation V hp = V hp K V i Q V hp G hp = = Vi K K = Q Q 8 Kenneth R. Laker updated 7Dec9 KRL 4

15 Feedback Equation II High Pa Output: Bandpa Output: Lowpa Output: 8 Kenneth R. Laker updated 7Dec9 KRL V hp = Vi K = K Q Q V bp V hp = = Vi Vi V lp V bp = = Vi Vi K Q K Q 5

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17 Implementation R Rf Vi C R R R Inverting Integrator C V lp V hp V bp R3 V hp = V hp V hp K V i Q Summing Amp V hp=v bp V hp=v lp R f R Rf R3 Rf V hp = V hp V hp Vi R R R 3 R R R 3 R 8 Kenneth R. Laker updated 7Dec9 KRL 7

18 Implementation II R f R Rf R3 Rf V hp = V hp V hp Vi R R R 3 R R R 3 R R f = R Set: V hp = R R3 V hp V hp V R R3 R R3 i V hp = And compare term: V hp V hp K V i Q R R3 R3 Q= Q= R R 8 Kenneth R. Laker updated 7Dec9 KRL => circuit ymbolic Eq. pec/numerical Eq. R3 = Q R 8

19 K Q Dependence From previou lide: R3 = Q R R3 K= R R 3 R3 R3 R Q K= = = = R3 R R 3 Q Q R Only Q or K can be the independent variable! 8 Kenneth R. Laker updated 7Dec9 KRL 9

20 Deign Equation RC = R f = R Given = f, chooe C, calculate 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 independent parameter ( and Q, or K) and three independent component (C, Rf (or R), and R(or R3)). 8 Kenneth R. Laker updated 7Dec9 KRL

21 Retriction Since K = Q / Q When 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 updated 7Dec9 KRL

22 Adding Finite Zero (Notche) To be able to create notche in the repone, we need another umming amplifier: V hp V bp V lp Vo Where the weighted input come from the highpa, bandpa, and lowpa output of the feedback circuit. 8 Kenneth R. Laker updated 7Dec9 KRL

23 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 R F / R H R F / R B R F / R L /Q For a notch at = N, no connection i made to Vbp, i.e. R B = 8 Kenneth R. Laker updated 7Dec9 KRL 3

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25 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 updated 7Dec9 KRL 5

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29 R n =R fn =Rn = 8 Kenneth R. Laker updated 7Dec9 KRL 9

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32 (MFM) 8 Kenneth R. Laker updated 7Dec9 KRL 3