Frequency Responses and Active Filter Circuits

Frequency Responses and Active Filter Circuits Compensation capacitors and parasitic capacitors will influence the frequency response Capacitors are also purposely added to create certain functions; e.g. integrators The most common use of energy storage elements in opamp circuits is for filtering Inductors are not as often used as capacitors because they are much bulkier and more difficult to integrate on an IC The order of the filter depends on the number of energy storage elements that are used Lecture 6-1

Ideal Filters V in ( jω) Hjω ( ) V out ( jω) = --------------------- V V in ( jω) out ( jω) H(jω) H(jω) A Pass Stop A Stop Pass ω H ω ω L ω A H(jω) Stop Pass Stop A H(jω) Pass Stop Pass ω L ω H ω ω L ω H ω Lecture 6-2

Ideal Filters We know that a first order filter will not look like an ideal model: H(jω) A ω H ω Higher order filters will attempt to have sharper transitions at the cut-off frequencies, but sometimes at the expense of increased ripple A H(jω) ω H ω Lecture 6-3

First-Order Low Pass Filter Design for a 3dB cut-off frequency of 3π (radians/second), a dc gain of 2, and an input impedance of at least 1kΩ R2 C R1 v in v out Lecture 6-4

First-Order Low Pass Filter 2k 53pF Will the frequency dependence of the open loop gain present a problem for this circuit using a 741 opamp? v in 1k v out 2dB e-1 e e1 e2 e3 e4 e5 e6 e7 1 db db -1dB DB(VMOUT/VMIN) frequency Lecture 6-5

First-Order Low Pass Filter SPICE results for magnitude using 741 opamp model 1 frequency e e1 e2 e3 e4 e5-1 -2-3 -4 DB(VMOUT/VMIN) Lecture 6-6

First-Order Low Pass Filter SPICE results for phase using 741 opamp model 18 frequency e e1 e2 e3 e4 e5 16 14 12 1 8 PH(VMOUT/VMIN) Lecture 6-7

First-Order High Pass Filter Calculate a transfer function to approximate the cut-off frequency 4kΩ.159µF 1kΩ v out v in Lecture 6-8

First-Order High Pass Filter What is the high frequency gain for this circuit? 4kΩ.159µF 1kΩ v in v out Lecture 6-9

First-Order High Pass Filter SPICE results for magnitude using 741 opamp model 2 frequency e e1 e2 e3 e4 e5 1-1 -2-3 -4-5 DB(VMOUT/VMIN) Lecture 6-1

First-Order High Pass Filter Note that the low-pass nature of the opamp makes this high-pass filter a bandpass filter when using a 741-type opamp e 2 1-1 -2-3 -4-5 frequency e e1 e2 e3 e4 e5 e6 e7 DB(VMOUT/VMIN) Lecture 6-11

First-Order High-Pass Filter SPICE results for phase using 741 opamp model Why the discontinuity? 2 frequency e e1 e2 e3 e4 e5. -2 PH(VMOUT/VMIN) Lecture 6-12

Band Pass Filter Design for a mid-band frequency gain of 5 (volts/volt), and f L =5Hz and f H =5kHz. C2 R2 C1 R1 v in v out Lecture 6-13

Band-Pass Filter C2 R2 C1 R1 v in v out Lecture 6-14

Band Pass Filter SPICE results for magnitude using 741 opamp model 2 frequency e e1 e2 e3 e4 e5 e6 1-1 -2-3 -4-5 DB(VMOUT/VMIN) Lecture 6-15

Band-Pass Filter SPICE results for phase using 741 opamp model 2 frequency e e1 e2 e3 e4 e5 e6. -2 PH(VMOUT/VMIN) Lecture 6-16

Noninverting Opamp Most of the circuits that we ve seen so far can also be designed in a noninverting configuration too R 2 R 1 V o V in Lecture 6-17

Other Noninverting Configurations But sometimes they are a bit trickier to solve What is the transfer function of this circuit? How is it best evaluated? R 4 R 3 V 1 V 2 R 1 R 2 V o Lecture 6-18

Second-Order Low Pass Filter Design for a 3dB cut-off frequency of 3π (radians/second), a dc gain of 2, and an input impedance of 1kΩ RB 1E3Ω Suggested configuration and element values from a book R1 1E3Ω RA 1E3Ω R2 1E3Ω - 741 VC8-15V + - + VIN + SIN + C2 1214E-12F VC9 + 15V - C1 927E-12F + - Lecture 6-19

Second-Order Low Pass Filter SPICE results for magnitude using 741 opamp model Input impedance magnitude as a function of frequency 11 frequency e2 e3 e4 e5 e6 e7 K 1 9 VMIN/IMIN Lecture 6-2

Second-Order Low Pass Filter Input impedance phase as a function of frequency frequency e2 e3 e4 e5 e6 e7-1 -2-3 -4-5 -6-7 -8-9 PH(VMIN/IMIN) Lecture 6-21

Second-Order Low Pass Filter SPICE results for magnitude using 741 opamp model Fall-off is sharper for higher frequencies, but 3dB point is at 5.6kHz 1 frequency e e1 e2 e3 e4 e5 e6-1 -2-3 -4-5 -6-7 DB(VMOUT) Lecture 6-22

Second-Order Low Pass Filter 3dB cut-off frequency is slightly off from 1.5kHz target What parameters do we change to lower it 3dB slightly? R1 1E3Ω VIN + SIN RA 1E3Ω + - R2 1E3Ω C2 1214E-12F RB 1E3Ω - 741 + VC8-15V + - VC9 + 15V C1 927E-12F + - Lecture 6-23

Second-Order Low Pass Filter Design for a 3dB cut-off frequency of 3π (radians/second), a dc gain of 2, and an input impedance of 1kΩ using values determined by pole analysis RB 1E3Ω RA 1E3Ω VC8-15V + - R1 1E3Ω R2 1E3Ω - 741 + VIN + SIN + C2 196E-12F VC9 + 15V - C1 9E-12F + - Lecture 6-24

Second-Order Low Pass Filter 3dB is now at 1.5kHz 1-1 -2-3 -4-5 -6-7 -8 DB(VMOUT) frequency e e1 e2 e3 e4 e5 e6 Lecture 6-25