Aalog Filter Deig Part. 3: Time otiuou Filter Implemetatio P. ruchi - Aalog Filter Deig
Deig approache Paive (R) ladder filter acade of iquadratic (iquad) ad iliear cell State Variable Filter Simulatio of filter with active R etwork P. ruchi - Aalog Filter Deig 2
Filter Parameter For a give trafer fuctio H(), a particular implemetatio i characterized by everal FOM (Figure Of Merit). The mot frequetly ued are: Dyamic Rage: DR max v Seitivity to compoet variatio ompoet value pread, e.g. V out out max mi v -out = output oie S S x Q x d / d P. ruchi - Aalog Filter Deig 3 x Q dx dq dx / x x dx
Paive ole adder Filter Doubly termiated ladder etwork Advatage: miimum eitivity to compoet variatio i the pabad The lowet eitivity i achieved with equally termiated etwork (R =R 2 ). a be ued a tartig poit for the ythei of active R filter Drawback: tuig require chage of al compoet. order () = umber of capacitor + umber of iductor P. ruchi - Aalog Filter Deig 4
Prototype Filter ofiguratio (all pole) =2M+ (odd order) =2M (eve order) R2 Pa-bad gai: k R R 2 (.5 for equally termiated etworl) P. ruchi - Aalog Filter Deig 5
Alterate olutio (all pole) =2M+ (odd order) =2M (eve order) R2 Pa-bad gai: k R R 2 (.5 for equally termiated etworl) P. ruchi - Aalog Filter Deig 6
ladder etwork for TF with imagiary zero (e.g. Ivere hebyhev ad auer Elliptic filter) P. ruchi - Aalog Filter Deig 7
Frequecy calig rule P. ruchi - Aalog Filter Deig 8 ladder filter are ythetized i ormalized ( rad/, W) ad lowpa form Frequecy calig allow to chage the ormalizatio frequecy, allowig traformatio of the characteritic frequecie of the filter R R
Impedace Scalig Rule Impedace calig i ued to chage compoet value leavig the trafer fuctio ualtered. The target i fidig feaible compoet value for the choe techology If the etwork iclude oly: Two termial impedace (,R, compoet) Voltage otrolled Voltage Source (VVS) i.e Ideal voltage amplifier. urret otrolled urret Source (S) i.e. ideal curret amplifier The: the Vout/VS trafer fuctio i uchaged whe all the impedace are multiplied by the ame fuctio f() P. ruchi - Aalog Filter Deig 9
Impedace calig: compoet traformatio A importat cae i whe the fuctio f() i a cotat factor K: K K K K R KR P. ruchi - Aalog Filter Deig
Elemet traformatio P. ruchi - Aalog Filter Deig High-Pa ad-pa ad -Stop Goal: to chage the filter repoe from low-pa to the other three poibilitie (high-pa, etc.) ad perform frequecy calig at the ame time. et u recall the followig traformatio: From ow-pa to:
Elemet Traformatio P. ruchi - Aalog Filter Deig 2 R R ow-pa to High-pa
Elemet Traformatio P. ruchi - Aalog Filter Deig 3 ow-pa to ad-pa 2 P P 2 S S 2 P P 2 S S 2
Elemet Traformatio P. ruchi - Aalog Filter Deig 4 ow-pa to ad-top S S 2 2 P P
Deig of ladder paive filter A procedure that allow deigig a arbitrary trafer fuctio with a ladder tructure doe ot exit. All-pole fuctio (e.g. utterworth, hebyhev I, eel) ca be deiged with a tadard approach, where the brache of the ladder (Z ad Y elemet) are pure capacitor or iductor. Give a cla of etwork, ot all fuctio are feaible. The rigorou deig of auer (elliptic) filter i le traightforward. Table are available for the mot frequetly ued ladder topologie ad trafer fuctio. Several AD deig tool are alo available. P. ruchi - Aalog Filter Deig 5
Example: utterworth Prototype Filter 2 2 3 3 4 4 5 5 P. ruchi - Aalog Filter Deig 6
hebyhev d ripple 2 2 3 3 7 P. ruchi - Aalog Filter Deig 7
Example Deig a ladder hebyhev filter with the followig characteritic: f_pa = khz, Maximum Pa-bad atteuatio d f_top = 2 khz Miimum Stop-ad Atteuatio: 4 d Pytho: chebord: Order=5, = P =62.8 krad/ P. ruchi - Aalog Filter Deig 8
Filter deig uig Table = P = rad/ =2.27 F =.28 H 2=3.3 F 2=.28 H 3=2.27 F = P =62.8 krad/ =35. mf =8. mh 2=49.4 mf 2=8. mh 3=35. mf P. ruchi - Aalog Filter Deig 9