Transcript Document

Chapter10
Operational Amplifier Applications
Microelectronic Circuit Design
Richard C. Jaeger
Travis N. Blalock
2 Microelettronica – Circuiti integrati analogici 2/ed
Richard C. Jaeger, Travis N. Blalock
Copyright © 2005 – The McGraw-Hill Companies srl
Chapter Goals
• Continue study of methods to determine transfer functions
of circuits containing op amps.
• Introduction to active filters and switched capacitor circuits
• Explore digital-to-analog converter specifications and
basic circuit implementations.
• Study analog-to-digital converter specifications and
implementations.
• Explore applications of op amps in nonlinear circuits, such
as precision rectifiers.
• Provide examples of multivibrator circuits employing
positive feedback.
• Demonstrate use of ac analysis capability of SPICE.
2 Microelettronica – Circuiti integrati analogici 2/ed
Richard C. Jaeger, Travis N. Blalock
Copyright © 2005 – The McGraw-Hill Companies srl
Active Filters: Low-pass (Transfer Function)
The transfer function is: G G
1 2
CC
Vo(s)
1 2
A ( s) 

LP
Vs(s) 2 G  G G G
s s 1 2  1 2
C
CC
1
1 2
In standard form,
s2
A ( s) 

LP
• Op amp is voltage follower with
s2  s o  o2
Q
unity gain over a wide range of
C RR
1
o 
1 2
frequencies.
Q 1
RR CC
R R
C
1
2
1
2
• Uses positive feedback through C1 at
2 1 2
frequencies above dc to realize
complex poles without inductors.
• Feedback network provides dc path
for amplifier’s input bias currents.
2 Microelettronica – Circuiti integrati analogici 2/ed
Richard C. Jaeger, Travis N. Blalock
Often, circuits are designed with C1 =
C2 = C.
Copyright © 2005 – The McGraw-Hill Companies srl
Active Filters: Low-pass (Frequency
Response)
For Q=0.71,magnitude response is
maximally flat (Butterworth Filter:
Maximum bandwidth without
peaking)
For Q>0.71, response shows
undesired peaking.
For Q<0.71: Filter’s bandwidth
capability is wasted.
At <<o, filter has unity gain.
At >>o,response exhibits twopole roll-off at 40dB/decade.
At =o, gain of filter =Q.
2 Microelettronica – Circuiti integrati analogici 2/ed
Richard C. Jaeger, Travis N. Blalock
Sensitivity, S represents fractional
change in parameter, P due to a given
fractional change in value of Z.
Sensitivity of with respect to R and
C is:
S  S  1
R C
2
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Active Filters: Low-pass (Example)
• Problem: Design second-order low-pass filter with
maximally flat response.
• Given data: fH = 5 kHZ
• Analysis:C1 = 2C2 = 2C and R1 = R2 = R.
Q 1
2oC
2
1/oC is the reactance of C at o, R is 30% smaller than this value. Thus
impedance level of filter is set by C. If impedance level is too low, op amp
will not be able to supply current required to drive feedback network.
1
At 5 kHz, for a 0.01 mF capacitor, 1 
 3180W
oC 104 (10 8)
3180W
R
 2250W
2
Final values: = R1 = R2 = 2.26kW, C1 = 0.02 mF, C2 = 0.01 mF
R
1
2 Microelettronica – Circuiti integrati analogici 2/ed
Richard C. Jaeger, Travis N. Blalock
Copyright © 2005 – The McGraw-Hill Companies srl
Active Filters: High-pass with Gain
(Transfer Function)
The transfer function is:
s2
1
A ( s) 


o

HP
RC
s2  s o  o2
Q
1


 R C C
R C 

Q   1 1 2  (1 K ) 2 2 
 R
CC
R C 

2
1 2
1 1

•
•
Voltage follower in low-pass
filter replaced by non-inverting
amplifier with gain K, which
gives an added degree of
freedom in design.
dc paths for both op amp input
bias currents through R2 and
feedback resistors.
2 Microelettronica – Circuiti integrati analogici 2/ed
Richard C. Jaeger, Travis N. Blalock
For R1 = R2 = R and C1 = C2 = C,
1
o  1
Q

RC
3 K
For K=3, Q is infinite, poles are on
j axis causing sinusoidal
oscillations. K>3 causes instability
due to right-half plane poles.
1 K  3
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Active Filters: High-pass with Gain
(Frequency Response)
• For Q=0.71,magnitude response is maximally flat
(Butterworth Filter response).
• Amplifier gain is constant at >o, the lower cutoff
frequency of the filter.
2 Microelettronica – Circuiti integrati analogici 2/ed
Richard C. Jaeger, Travis N. Blalock
Copyright © 2005 – The McGraw-Hill Companies srl
Active Filters: Band-pass (Transfer
Function)
Uses inverting op amp and its full loop gain
(ideally infinite).
V (s)
sC V (s)   o
2 1
R
2
 


G V   sC  C   G V (s)  sC Vo(s)
1
th th   1 2  th  1
R RC
Vo(s)
so
3
2 2
A ( s) 

BP
R  R R C s2  s o   2
V ( s)
1 3 1 1
th
o
Q
o 
1
R
CC
1 2
2
R R C C Q
th 2 1 2
R C1  C2
th
For C1 = C2 = C,
R
1
2 BW  2
o 
Q
C R R
R
R C
th 2
2
th
2 Microelettronica – Circuiti integrati analogici 2/ed
Richard C. Jaeger, Travis N. Blalock
Copyright © 2005 – The McGraw-Hill Companies srl
Active Filters: Band-pass (Frequency
Response)
• Response peaks at o and gain at center frequency is 2Q2.
• At <<o or >>o, filter response corresponds to
single-pole high-pass or low-pass filter changing at a rate
of 20dB/decade.
2 Microelettronica – Circuiti integrati analogici 2/ed
Richard C. Jaeger, Travis N. Blalock
Copyright © 2005 – The McGraw-Hill Companies srl
Active Filters: Tow-Thomas Biquad
General biquadratic transfer function
to represent low-pass, high-pass,
band-pass, all-pass and notch filters:
a s2  a s  a
0
T ( s)  2  1
s2  s o  o2
Q
In Tow-Thomas biquad, first op amp
is a multi-input integrator and third
op amp is simply an inverter.

1
1 
1

V ( s)  
Vs( s) 
V
(
s
)
V ( s)


bp
bp
lp
 sR C
sR C
sRC 
1
2
1
V ( s)  
V ( s)
lp
sRC bp
so
A ( s)   K

bp
s2  s o  o2
Q



R 
R BW  1
1

K  
o 
Q 2
R C
R
R 
RC
2
 1
o 2
A ( s)   K

lp
s2  s o  o2
Q
Thus, center frequency, Q
and gain can each be
adjusted independently.
Continua…
2 Microelettronica – Circuiti integrati analogici 2/ed
Richard C. Jaeger, Travis N. Blalock
Copyright © 2005 – The McGraw-Hill Companies srl