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 out ( jω )
H ( jω ) = ---------------------V in ( jω )
V in ( jω )
V out ( jω )
|H(jω)|
|H(jω)|
A
A
Pass
Stop
Stop
0
0
ω
ωH
|H(jω)|
ω
ωL
|H(jω)|
A
A
Stop
0
Pass
Pass
ωL
Stop
ωH
Pass
ω
0
Stop
ωL
Pass
ωH
ω
Lecture 6-2
Ideal Filters
• We know that a first order filter will not look like an ideal model:
|H(jω)|
A
0
ωH
ω
• Higher order filters will attempt to have sharper transitions at the cut-off
frequencies, but sometimes at the expense of increased ripple
|H(jω)|
A
0
ωH
ω
Lecture 6-3
First-Order Low Pass Filter
• Design for a 3dB cut-off frequency of 3000π (radians/second), a dc gain of 2,
and an input impedance of at least 100kΩ
R2
C
R1
vout
vin
Lecture 6-4
First-Order Low Pass Filter
200k
530pF
• Will the frequency dependence of
the open loop gain present a
problem for this circuit using a
741 opamp?
200dB
e-1
e0
e1
e2
e3
e4
e5
100k
vout
vin
e6
e7
100 dB
0dB
-100dB
DB(VMOUT/VMIN)
frequency
Lecture 6-5
First-Order Low Pass Filter
• SPICE results for magnitude using 741 opamp model
e0
e1
e2
e3
e4
frequency
e5
10
0
-10
-20
-30
-40
DB(VMOUT/VMIN)
Lecture 6-6
First-Order Low Pass Filter
• SPICE results for phase using 741 opamp model
e0
e1
e2
e3
e4
frequency
e5
180
160
140
120
100
80
PH(VMOUT/VMIN)
Lecture 6-7
First-Order High Pass Filter
• Calculate a transfer function to approximate the cut-off frequency
40kΩ
0.0159µF
10kΩ
vout
vin
Lecture 6-8
First-Order High Pass Filter
• What is the high frequency gain for this circuit?
40kΩ
0.0159µF
10kΩ
vout
vin
Lecture 6-9
First-Order High Pass Filter
• SPICE results for magnitude using 741 opamp model
e0
e1
e2
e3
e4
frequency
e5
20
10
0
-10
-20
-30
-40
-50
DB(VMOUT/VMIN)
Lecture 6-10
First-Order High Pass Filter
• Note that the low-pass nature of the opamp makes this high-pass filter a band-
pass filter when using a 741-type opamp
e0
e1
e2
e3
e4
e5
frequency
e6
e7
20
e0
10
0
-10
-20
-30
-40
-50
DB(VMOUT/VMIN)
Lecture 6-11
First-Order High-Pass Filter
• SPICE results for phase using 741 opamp model
• Why the discontinuity?
e0
e1
e2
e3
e4
frequency
e5
200
0.0
-200
PH(VMOUT/VMIN)
Lecture 6-12
Band Pass Filter
• Design for a mid-band frequency gain of 5 (volts/volt), and fL=500Hz and
fH=5kHz.
C2
R2
C1
R1
vout
vin
Lecture 6-13
Band-Pass Filter
C2
R2
C1
R1
vout
vin
Lecture 6-14
Band Pass Filter
• SPICE results for magnitude using 741 opamp model
e0
e1
e2
e3
e4
e5
frequency
e6
20
10
0
-10
-20
-30
-40
-50
DB(VMOUT/VMIN)
Lecture 6-15
Band-Pass Filter
• SPICE results for phase using 741 opamp model
e0
e1
e2
e3
e4
e5
frequency
e6
200
0.0
-200
PH(VMOUT/VMIN)
Lecture 6-16
Noninverting Opamp
• Most of the circuits that we’ve seen so far can also be designed in a non-
inverting configuration too
R2
R1
Vo
Vin
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?
R4
R3
V1
V2
R1
Vo
R2
Lecture 6-18
Second-Order Low Pass Filter
• Design for a 3dB cut-off frequency of 3000π (radians/second), a dc gain of 2,
and an input impedance of 100kΩ
RB
100E3Ω
RA
100E3Ω
Suggested configuration
and element values from a
book
VC8
-15V
+R1
100E3Ω
R2
100E3Ω
-
741
+
+
VIN
SIN
+ C2
+
VC9
15V
1214E-12F
-
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
e2
e3
e4
e5
e6
frequency
e7
110
K
100
90
VMIN/IMIN
Lecture 6-20
Second-Order Low Pass Filter
• Input impedance “phase” as a function of frequency
e2
e3
e4
e5
e6
frequency
e7
0
-10
-20
-30
-40
-50
-60
-70
-80
-90
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
e0
e1
e2
e3
e4
e5
frequency
e6
10
0
-10
-20
-30
-40
-50
-60
-70
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?
RB
100E3Ω
RA
100E3Ω
VC8
-15V
+R1
100E3Ω
R2
100E3Ω
-
741
+
+
VIN
SIN
+ C2
+
VC9
15V
1214E-12F
-
C1
927E-12F
+
-
Lecture 6-23
Second-Order Low Pass Filter
• Design for a 3dB cut-off frequency of 3000π (radians/second), a dc gain of 2,
and an input impedance of 100kΩ using values determined by pole analysis
RB
100E3Ω
RA
100E3Ω
VC8
-15V
+R1
100E3Ω
R2
100E3Ω
741
+
+
VIN
SIN
+ C2
+
VC9
15V
1960E-12F
-
C1
900E-12F
+
-
Lecture 6-24
Second-Order Low Pass Filter
3dB is now at 1.5kHz
e0
e1
e2
e3
e4
e5
frequency
e6
10
0
-10
-20
-30
-40
-50
-60
-70
-80
DB(VMOUT)
Lecture 6-25