frequency responses and active filter circuitsee321/spring99/lect/lect6jan29.pdflecture 6-1...
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Lecture 6-1
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 6-2
Ideal Filters
H jω( )Vout jω( )Vin jω( )
----------------------= Vout jω( )Vin jω( )
A
0ωH
Pass Stop
ω
|H(jω)|
A
0ωL
Stop Pass
ω
|H(jω)|
A
0ωL
Stop Pass
ω
|H(jω)|
Stop
ωH
A
0ωL
Pass Stop
ω
|H(jω)|
Pass
ωH
Lecture 6-3
Ideal Filters
A
0
ωH ω
|H(jω)|
• We know that a first order filter will not look like an ideal model:
• Higher order filters will attempt to have sharper transitions at the cut-off frequencies, but sometimes at the expense of increased ripple
A
0
ωH ω
|H(jω)|
Lecture 6-4
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
C
R1
vin
vout
R2
Lecture 6-5
First-Order Low Pass Filter
530pF
100k
vin
vout
200k
• Will the frequency dependence of the open loop gain present a problem for this circuit using a 741 opamp?
frequency
e-1 e0 e1 e2 e3 e4 e5 e6 e7
-100dB
0dB
100 dB
200dB
DB(VMOUT/VMIN)
Lecture 6-6
First-Order Low Pass Filter
• SPICE results for magnitude using 741 opamp model
frequencye0 e1 e2 e3 e4 e5
-40
-30
-20
-10
0
10
DB(VMOUT/VMIN)
Lecture 6-7
First-Order Low Pass Filter
• SPICE results for phase using 741 opamp model
frequencye0 e1 e2 e3 e4 e5
80
100
120
140
160
180
PH(VMOUT/VMIN)
Lecture 6-8
First-Order High Pass Filter
• Calculate a transfer function to approximate the cut-off frequency
10kΩ
vin
vout
40kΩ
0.0159µF
Lecture 6-9
First-Order High Pass Filter
10kΩ
vin
vout
40kΩ
0.0159µF
• What is the high frequency gain for this circuit?
Lecture 6-10
First-Order High Pass Filter
• SPICE results for magnitude using 741 opamp model
frequencye0 e1 e2 e3 e4 e5
-50
-40
-30
-20
-10
0
10
20
DB(VMOUT/VMIN)
Lecture 6-11
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
frequencye0 e1 e2 e3 e4 e5 e6 e7
-50
-40
-30
-20
-10
0
10
20e0
DB(VMOUT/VMIN)
Lecture 6-12
First-Order High-Pass Filter
• SPICE results for phase using 741 opamp model
• Why the discontinuity?
frequencye0 e1 e2 e3 e4 e5
-200
0.0
200
PH(VMOUT/VMIN)
Lecture 6-13
Band Pass Filter
• Design for a mid-band frequency gain of 5 (volts/volt), and fL=500Hz and fH=5kHz.
R1
vin
vout
R2
C1
C2
Lecture 6-14
Band-Pass Filter
R1
vin
vout
R2
C1
C2
Lecture 6-15
Band Pass Filter
• SPICE results for magnitude using 741 opamp model
frequencye0 e1 e2 e3 e4 e5 e6
-50
-40
-30
-20
-10
0
10
20
DB(VMOUT/VMIN)
Lecture 6-16
Band-Pass Filter
• SPICE results for phase using 741 opamp model
frequencye0 e1 e2 e3 e4 e5 e6
-200
0.0
200
PH(VMOUT/VMIN)
Lecture 6-17
Noninverting Opamp
• Most of the circuits that we’ve seen so far can also be designed in a non-inverting configuration too
R2
R1
Vin
Vo
Lecture 6-18
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
VoR1
R2
V1
V2
Lecture 6-19
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
+ SINVIN C2
1214E-12F+
-
R2100E3Ω
R1100E3Ω
+ -
-15VVC8
+ 15VVC9
741
+
-
C1927E-12F+ -
RA100E3Ω
RB100E3Ω
Suggested configurationand element values from a book
Lecture 6-20
Second-Order Low Pass Filter
• SPICE results for magnitude using 741 opamp model
• Input impedance “magnitude” as a function of frequency
frequencye2 e3 e4 e5 e6 e7
90
100
110
K
VMIN/IMIN
Lecture 6-21
Second-Order Low Pass Filter
• Input impedance “phase” as a function of frequency
frequencye2 e3 e4 e5 e6 e7
-90
-80
-70
-60
-50
-40
-30
-20
-10
0
PH(VMIN/IMIN)
Lecture 6-22
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
frequencye0 e1 e2 e3 e4 e5 e6
-70
-60
-50
-40
-30
-20
-10
0
10
DB(VMOUT)
Lecture 6-23
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?
+ SINVIN C2
1214E-12F+
-
R2100E3Ω
R1100E3Ω
+ --15VVC8
+ 15VVC9
741+
-
C1927E-12F+ -
RA100E3Ω
RB100E3Ω
Lecture 6-24
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
+ SINVIN C2
1960E-12F+
-
R2100E3Ω
R1100E3Ω
+ -
-15VVC8
+ 15VVC9
741
+
-
C1900E-12F+ -
RA100E3Ω
RB100E3Ω
Lecture 6-25
Second-Order Low Pass Filter
frequencye0 e1 e2 e3 e4 e5 e6
-80
-70
-60
-50
-40
-30
-20
-10
0
10
DB(VMOUT)
3dB is now at 1.5kHz