1. Design a 3rd order Butterworth low-pass filters having a dc gain of unity and a cutoff frequency, fc, of khz.

Transcription

1 ECE 34 Experiment 6 Active Filter Design. Design a 3rd order Butterworth low-pass ilters having a dc gain o unity and a cuto requency, c, o.8 khz. c :=.8kHz K:= The transer unction is given on page 7 j := T B ( ) := K This is the product o a st order LPF & nd order j + j LPF. + j + c c c T B ( ) T B ( ) To implement this with a circuit cascade the circuit on page 8 with that on page 83. For each the dc gain is unity (K) which means that RF is zero (a wire) and the resistor rom the inverting input to ground is ininity (nothing there). Start by picking two o the capacitors to be.μf. For the Butterworth ilter ωc & ωo are the same. So or the circuit on page 8 C :=.μf R := R =.48 3 Ω This is a st order LPF π c C For the circuit shown on page 83, the nd order LPF, pick C :=.μf C :=.C then Eq applies with Q= and ωo=ωc Q:= := π C R 4 Q := + R := 4Q Q ω o C C Q ω o C R = Ω R =.74 3 Ω C = 8 F C = 9 F Now that all o the component values have been determined it's time to simulate it with SPICE ω o c C C

2 Butterworth Filter Gain (Linear) Frequency (Hz) The next step is to head to the lab and build the circuits. Use 74s, LF3s, LF347s. The resistors or your use are %. The caps are %. Try to ind 3 caps reasonably close to the design values.

3 φ( ) := 8 π arg ( T B( )) τ p ( ) φ( ) := τ g ( ) := π π d d φ( ) τ p ( ) τ g ( )

4 . Design a 3rd order unity dc gain Chebyshev LPF with a -3 requency o.8 khz and. db ripple in the pass band. db :=. 3 :=.8kHz K:= n:= 3 t 3 () x := 4x 3 3x j:= db ε := Eq must be solved to obtain the relationship between ωc & ω3 which requires that Eq be solved which is a cubic polynomial g(x) gx () 4x 3 := 3x Since t3()= To solve this orm the vector v ε v := ε 3 4 This is done with the Insert Matrix selection rom the toolbar. The roots are now obtained with the polyroots(.) unction. With MathCad the index on arrays in a matrix begin with. Since this is a cubic polynomial it will have at least one real root and its the one required..84.i u := polyroots ( v) u =.84 +.i x:= u, x = c 3 := c = The transer unction is Eq. 6.6 which x s requires h, a, a, & b a := h tanh n asinh π := ε =.349 h =.3 θ := ε 3 h h a := h ( sin( θ )) b := + ( htan( θ )) a =.66 a =.69 b =.76 The transer unction then becomes T C () := K y ( ) := log T C () j + j j a c + + a c b a c ( ) For a check o the solution the magnitude o the transer unction in db will be plotted vs

5 y ( ) Equiripple box y ( ) db box Note that it is 3 db down at.8 khz Now the circuit must be designed. This requires a st order lp cascaded with a 3rd order lp. This can be done by cascading the circuit shown in Fig. 6.9.a (page 83) with Fig. 6. (page 83). For the st order ilter, since the dc gain is unity, K=, pick RF= (a wire) and R ininity. Pick C :=.μf R := R =.88 3 Ω πa c C For the nd order ilter, K=, pick RF= & R3 open ckt. o := c a ω o := π o Q:= b Pick C :=.μf C :=.C R := + Q ω o C 4Q C C R = Ω C = 7 F 4Q C R := Q ω o C C R = 97.4 Ω C = 9 F

6 . Chebyshev -. - Gain Frequency

7 Chebyshev - - Gain -3-4 φ( ) := π 4 Frequency arg ( T C( )) τ p ( ) φ( ) := τ g ( ) := π π d d φ( ) 3 3 τ p ( ) τ g ( )

8 Page 86, Fig 6-4 Second Order Sallen Key BPF c :=.8kHz K:= Q:= j := := o c Q j o T ( ) := K φ( ) := j Q j + + o o 8 π arg( T( )) T ( ). φ( ). 3 4 R 4 := 3kΩ R := 3kΩ C := nf C := nf ω o := π o R :=.8kΩ R :=.8kΩ R 3 :=.8kΩ K o := Given + R R 4 K = R R + R R R R + R K o R 3 C ( C + C ) + R 3 C K o R R + R ( )

9 ω o = R R R 3 C C R + R Q = R R R + R R R R + R C + C R 3 C C ( ) + R 3 C K o R R + R ( ) Find R, R, R 3 = Ω

10 Sallen Key BPF Gain Frequency

11 Second Order Initite Gain Multiple Feedback BPF, page 87, Exp 6 o :=.8kHz Q:= K:= ω o := π j := T ( ) := K j o Q j o Q j + + o o T ( ). 8arg( T( ) ) π C :=.μf C := C R := kω R := 4Ω R 3 := kω Given R 3 C R C + C ( ) = K R R R 3 C C R + R = ω o ( ) R 3 C C R + R ( R R ) C + C = Q ( ) Find R, R, R 3 = Ω

12 Ininite Gain Multiple Feedback BPF Gain Frequency

13 General Bi Quadratic Filter Ts () = s ω o s ( α γ) + Q ω ( β γ) + γ o s ω o s + + Q ω o o :=.8kHz N := i :=.. N start := khz j := stop := khz stop := i start start i N Allpass Q:= 3 α := β := γ := T ( ) := j j ( α γ) + o Q ( β γ) + γ o j o j + + Q o

14 T ( i ) ( ( )) 8 arg T i π i i Notch α := β :=. γ := Q:= 3 o :=.8kHz T ( ) := j j ( α γ) + o Q ( β γ) + γ o j o j + + Q o T ( i ) ( ( )) 8 arg T i π. 3 4 i 3 4 i Bandpass α := β :=. γ := o :=.8kHz Q:= 3

15 T ( ) := j j ( α γ) + o Q ( β γ) + γ o j o j + + Q o T ( i ) ( ( )) 8 arg T i π. 3 4 i 3 4 i Highpass α :=. β := γ := o :=.8kHz Q:= 3 T ( ) := j j ( α γ) + o Q ( β γ) + γ o j o j + + Q o T ( i ) ( ( )) 8 arg T i π i i

16 Lowpass α :=. β :=. γ := o :=.8kHz Q:= 3 T ( ) := j j ( α γ) + o Q ( β γ) + γ o j o j + + Q o T ( i ) ( ( )) 8 arg T i π i i Third Order Elliptic Filter with. db ripple unity dc gain with stop band to cuto ratio o. with a min attenuation in the stop band o.9 db rom page 79 in the lab manual Ts () = s ω c s.7ω c s.67ω c + s ω c

17 this requires that a irst order ilter be cascaded with a bi quad or a notch at p this means c :=.8kHz γ := β := o :=.7 c.7 γ +.67 α := =.7 Q :=.367 T ( ) := j o j ( α γ) + Q ( β γ) + γ o j o j + + Q o or the irst order ilter :=.7669 c T ( ) := + j T ( ) := T ( ) T ( ) T ( i ) φ( ) := τ g ( ) 8 π arg( T( )) := π d d φ( ) 3 4 i τ p ( ) := φ( ) π

18 ( ) M ( ) := log T( ) M ( i ) φ( i φ( ) τ g ( ) := 8 π arg( T( )) φ( ) τ p ( ) := π d π d φ( ) :=

19 M ( i ) i Third Order Bessel Filter 3 :=.8kHz a :=.3 a :=.4 b :=.69 3 c :=.77

20 T ( ) := j + a c j a c + j + b a c ( ) M ( ) := log T( ) φ( ) := 8 π arg( T( )) φ( ) τ g ( ) := 8 π arg( T( )) φ( ) τ p ( ) := π d π d φ( ) := 3 3 M ( i ) 3 3 4

21 i n = 3 3 =.77 a :=.4 c a :=.3 b :=.69 Ts () = st Order LPF s + s s nd Order LPF a ω c a ω + + c b a ω c 3 :=.8kHz 3 c := ω.77 c := π c C 3 := nf Use Sallen Key R 3 := a ω c C 3 =.7 4 Ω C :=.μf C :=.C C R := + 4b b a ω c C =.47 4 Ω C C R := 4b b a ω c C C = 778. Ω

22 4 3 R7 D 4.44k U D + C3 OUT Vac Vdc V R8.k C4 n U3 + - OUT OPAMP.7n R4 68.4k R 4.44k C n - OPAMP R 4.44k V R3 4.44k C R 68.4k C.9n OPAMP OUT - C + U B B Third Order Elliptic Filter A A Title Third Order Elliptic Filter Size Document Number Rev A Active Filters 4 3 Date: Tuesday, March, 8 Sheet o

23 ** Proile: "SCHEMATIC-sweep" [ G:\brewdoc\ece34hwk\WA_Sprg8_Filter\Elliptic\elliptic-pspiceiles\s... Date/Time run: 3/3/8 :3:4 Temperature: 7. (A) sweep (active).v.8v (.8374K,943.87m) (.6K,94.47m).6V Third Order Elliptic Filter Goal CutO Frequency=.8k.4V.V (7.9K,.87m) V.KHz 3.KHz KHz 3KHz KHz V(R:) Frequency Date: March 3, 8 Page Time: :33:44

24 ** Proile: "SCHEMATIC-sweep" [ G:\brewdoc\ece34hwk\WA_Sprg8_Filter\Elliptic\elliptic-pspiceiles\s... Date/Time run: 3/3/8 :3:4 Temperature: 7. (A) sweep (active) (.86K,-9.469m) - Third Order Elliptic Filter (.733K,-3.m) - (6.97K,-.98) -3-4 (7.378K,-46.3) -.KHz 3.KHz KHz 3KHz KHz db(v(r:)) Frequency Date: March 3, 8 Page Time: :39:7

25 ** Proile: "SCHEMATIC-sweep" [ G:\brewdoc\ece34hwk\WA_Sprg8_Filter\Elliptic\elliptic-pspiceiles\s... Date/Time run: 3/3/8 :4:3 Temperature: 7. (A) sweep (active) u Phase and Group Delays or 3rd Order Elliptic Filter 8u (.9K,73.78u) 6u Group Delay 4u (.69K,.867u) Phase Delay u (.9K,33.67u).KHz 3.KHz KHz 3KHz KHz -(P(V(R:))/Frequency)*(PI/8)/(*PI) G(V(R:)) Frequency Date: March 3, 8 Page Time: :7:

26 4 3 D D C R3 U.u C Vac Vdc V.7k C3 n + - OUT OPAMP R 4.7k R 778. C n U + - OUT OPAMP V C B Third Order Bessel Filter B A A Title Third Order Bessel Filter Size Document Number Rev A Active Filters 4 3 Date: Wednesday, March, 8 Sheet o

27 ** Proile: "SCHEMATIC-sweep" [ G:\brewdoc\ece34hwk\WA_Sprg8_Filter\Bessel\bessel-pspiceiles\schem... Date/Time run: 3/3/8 :4:9 Temperature: 7. (A) sweep (active) - (.86K,-3.6) - -3 Third Order Bessel Filter KHz 3.KHz KHz 3KHz KHz DB(V(U:OUT)) Frequency Date: March 3, 8 Page Time: :7:4

28 ** Proile: "SCHEMATIC-sweep" [ G:\brewdoc\ece34hwk\WA_Sprg8_Filter\Bessel\bessel-pspiceiles\schem... Date/Time run: 3/3/8 :4:9 Temperature: 7. (A) sweep (active) 4u 3u (.6K,7.88u) (.89K,6.88u) u (.89K,.47u) Phase Delay u Third Order Bessel Filter Group Delay.KHz 3.KHz KHz 3KHz KHz (P(V(U:OUT))/Frequency)*(PI/8)*(-/(*PI)) G(V(U:OUT)) Frequency Date: March 3, 8 Page Time: ::

29 Georgia Institute o Technology School o Electrical and Computer Engineering ECE 34 Microelectronic Circuits Laboratory Veriication Sheet NAME: GT NUMBER: SECTION: GTID: Experiment 6: Op Amp Active Filters Procedure Time Completed Date Completed Veriication (Must demonstrate circuit) Points Possible. Third Order Butterworth LPF 6. Third Order Chebyshev LPF 6 3. Second Order Band Pass 6 4. Second Order Notch 6. First Order All Pass 6 Points Received 6. Second Order All Pass Enter your critical requency below: crit To be permitted to complete the experiment during the open lab hours, you must complete at least three procedures during your scheduled lab period or spend your entire scheduled lab session attempting to do so. A signature below by your lab instructor, Dr. Brewer, or Dr. Robinson permits you to attend the open lab hours to complete the experiment and receive ull credit on the report. Without this signature, you may use the open lab to perorm the experiment at a % penalty. SIGNATURE: DATE:

30 ECE 34 Check o Requirements or Experiment 6 Make sure you have made all required measurements beore requesting a check o. For all check os, you must demonstrate the circuit or measurement to a lab instructor. All screen captures must have a time/date stamp. Do not ollow the procedures in the lab manual. Only Bode magnitude plots are required it is not necessary to measure the phase. Do not ollow the lab report ormat or this experiment. Instead, display two Bode plots and their associated tables per page.. Third Order Butterworth Low Pass Filter Bode gain magnitude plot over requency range o Hz to khz. Measurement o dc gain and 3dB requency. Table comparing these measured values to the design speciications. Show percent error.. Third Order Chebyshev Low Pass Filter Bode gain magnitude plot over requency range o Hz to khz. Measurement o dc gain, db ripple, and 3dB requency. Table comparing these measured values to the design speciications. Show percent error. 3. Second Order Bandpass Filter Bode gain magnitude plot over requency range o Hz to khz. Measurement o center requency o, 3dB bandwidth BW, and Q. Q is given by o /BW. Table comparing these measured values to the design speciications. Show percent error. 4. Second Order Notch Filter Implement ilter with the general biquad circuit rom the class notes. Save this ilter it can be modiied to obtain the second order all pass transer unction. Bode gain magnitude plot over requency range o Hz to khz. Measurement o center requency o, 3dB bandwidth BW, and Q. Q is given by o/bw. Table comparing these measured values to the design speciications. Show percent error.. First Order All Pass Filter Bode gain magnitude plot over requency range o Hz to khz. Measurement o dc gain. Scope screen capture showing measured crit, the requency at which the phase shit between input and output is 9 deg. Connect input to ch and output to ch. Display measured Vpp or each channel, the requency, and the phase. Table comparing these measured values to the design speciications. Show percent error. 6. Second Order All Pass Filter Bode gain magnitude plot over requency range o Hz to khz. Measurement o dc gain. Scope screen capture showing measured crit, the requency at which the phase shit between input and output is 8 deg. Connect input to ch and output to ch. Display measured Vpp or each channel, the requency, and the phase. Table comparing these measured values to the design speciications. Show percent error.