Analog Filter Design

Transcription

1 Analog Filter Deign Part. 3: Time ontinuou Filter Implementation Sect. 3-a: General conideration Paive filter P. Bruchi - Analog Filter Deign

2 Deign approache H() V V S Paive (R) ladder filter acade of Biquadratic (Biquad) and Bilinear cell State Variable Filter Simulation of filter with active R network P. Bruchi - Analog Filter Deign

3 Filter Parameter For a given tranfer function H(), a particular implementation i characterized by everal FOM (Figure Of Merit). The mot frequently ued are: Dynamic Range: DR max v Senitivity to component variation omponent value pread, e.g. V nout out max min v n-out = output noie S S x Q x d / d P. Bruchi - Analog Filter Deign 3 x Q dx dq dx / x x dx

4 paive filter: "The Prototype filter" ladder filter are ynthetized in normalized ( rad/, W) and lowpa form (prototype filter) Tranformation rule are ued to derive the required filter function (e.g. band-pa) and parameter (e.g. actual operating frequencie) from the prototype filter H N () V V S Normalized ow-pa Function P. Bruchi - Analog Filter Deign 4

5 Paive ole adder Filter Doubly terminated ladder network Advantage: minimum enitivity to component variation in the paband The lowet enitivity i achieved with equally terminated network (R =R ). an be ued a tarting point for the ynthei of active R filter Drawback: tuning require change of all component. order (N) = number of capacitor + number of inductor P. Bruchi - Analog Filter Deign 5

6 adder network: driving point impedance (d.p.i.) Driving point impedance (or d.p. admittance) Tranfer impedance (or t. admittance) Z () Z Z () Z Y V Y Z V Y V Z V Z () Z Y Z Y "ontinued fraction" Z 3 Y 3 Z 4 Y 4 P. Bruchi - Analog Filter Deign 6

7 auer ynthei approach for d.p.i. Z() Z () 3 3 Z 3 3 YV Y 3 / In the end.. Z Y 3 3 Z () 4 V Z /6 Y P. Bruchi - Analog Filter Deign 7

8 Prototype Filter onfiguration (all pole) N=M+ (odd order) N=M (even order) R Pa-band gain: k R R (.5 for equally terminated network) P. Bruchi - Analog Filter Deign 8

9 Alternate olution (all pole) N=M+ (odd order) N=M (even order) R Pa-band gain: k R R (.5 for equally terminated network) P. Bruchi - Analog Filter Deign 9

10 ladder network for TF with imaginary zero (e.g. Invere hebyhev and auer Elliptic filter) P. Bruchi - Analog Filter Deign

11 Frequency caling rule Frequency caling allow to change the normalization frequency, allowing tranformation of the characteritic frequencie of the filter n N N n n N N N R R P. Bruchi - Analog Filter Deign

12 Impedance Scaling Rule Impedance caling i ued to change component value leaving the tranfer function unaltered. The target i finding feaible component value for the choen technology If the network include only: Two terminal impedance (,R, component) Voltage ontrolled Voltage Source (VVS) i.e Ideal voltage amplifier. urrent ontrolled urrent Source (S) i.e. ideal current amplifier Then: the Vout/VS tranfer function i unchanged when all the impedance are multiplied by the ame function f() P. Bruchi - Analog Filter Deign

13 Impedance caling: component tranformation An important cae i when the function f() i a contant factor K: n K K K K R KR P. Bruchi - Analog Filter Deign 3

14 Element tranformation P. Bruchi - Analog Filter Deign 4 B n N n B n High-Pa Band-Pa Band -Stop Goal: to change the filter repone from low-pa to the other three poibilitie (high-pa, etc.) and perform frequency caling at the ame time. et u recall the following tranformation: From ow-pa to:

15 Element Tranformation P. Bruchi - Analog Filter Deign 5 N n N N n N N n R R ow-pa to High-pa

16 Element Tranformation P. Bruchi - Analog Filter Deign 6 ow-pa to Band-pa B B B n n P P n B B S S n B B B B P P B B S S

17 Element Tranformation P. Bruchi - Analog Filter Deign 7 ow-pa to Band-top B n B B S S B B P P

18 Deign of ladder paive filter A procedure that allow deigning an arbitrary tranfer function with a ladder tructure doe not exit. All-pole function (e.g. Butterworth, hebyhev I, Beel) can be deigned with a tandard approach, where the branche of the ladder (Z and Y element) are pure capacitor or inductor. Given a cla of network, not all function are feaible. The rigorou deign of auer (elliptic) filter i le traightforward. Table are available for the mot frequently ued ladder topologie and tranfer function. Several AD deign tool are alo available. P. Bruchi - Analog Filter Deign 8

19 Table example William & Taylor «Electronic Filter Deign Handbook» 6, McGraw-Hill P. Bruchi - Analog Filter Deign 9

20 Example: Butterworth Prototype Filter radian per - econd = N P. Bruchi - Analog Filter Deign

21 hebyhev db ripple Note: In thee table, generally = i the -3 db angular frequency, regardle of ripple (and A p ) e.g. William & Taylor «Electronic Filter Deign Handbook» P. Bruchi - Analog Filter Deign

22 Example Deign a ladder hebyhev filter with the following characteritic: f_pa = khz, Maximum Pa-band attenuation db f_top = khz Minimum Stop-Band Attenuation: 4 db Python: chebord: Order=5, P =6.8 krad/ But: table are normalized to -3dB. From the magnitude plot: f.34 khz ' N 3dB 3dB 65 krad/ P. Bruchi - Analog Filter Deign

23 Filter deign uing Table From table: prototype filter N = -3dB = rad/ =.7 F =.8 H =3.3 F =.8 H 3=.7 F ' N ' N -3dB =65 krad/ =33.9 mf =7.35 mh =47.7 mf =7.35 mh 3=33.9 mf Frequency caled filter P. Bruchi - Analog Filter Deign 3