2 Microelettronica – Circuiti integrati analogici 2/ed Richard C. Jaeger, Travis N. Blalock Copyright © 2005 – The McGraw-Hill Companies srl Chapter10

2 Microelettronica – Circuiti integrati analogici 2/edRichard C. Jaeger, Travis N. Blalock

Copyright © 2005 – The McGraw-Hill Companies srl

Chapter10Operational Amplifier Applications

Microelectronic Circuit Design

Richard C. Jaeger

Travis N. Blalock



• 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.

Chapter Goals



• Op amp is voltage follower with unity gain over a wide range of frequencies.

• Uses positive feedback through C1 at frequencies above dc to realize complex poles without inductors.

• Feedback network provides dc path for amplifier’s input bias currents.

The transfer function is:

21

21

1

21221

21

)(sV)(oV

)(

CC

GG

C

GGss

CC

GG

ss

sLPA

Active Filters: Low-pass (Transfer Function)

In standard form,

222

)(oQ

ossssLPA

2121

1CCRRo

21

21

2

1RR

RR

C

CQ

Often, circuits are designed with C1 = C2 = C.



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.

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:

At <<o, filter has unity gain.At >>o,response exhibits two-pole roll-off at 40dB/decade.At =o, gain of filter =Q. 2

1C

SRS



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.

CoR

21

21Q

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.At 5 kHz, for a 0.01 F capacitor,

Final values: = R1 = R2 = 2.26kC1 = 0.02 F, C2 = 0.01 F

22502

3180

3180)810(410

11

R

Co



Active Filters: High-pass with Gain (Transfer Function)

• 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.

222

)(oQ

ossssHPA

The transfer function is:

RCo1

1

11

22)1(

21

21

2

1

CR

CRK

CC

CC

R

RQ

For R1 = R2 = R and C1 = C2 = C,

RCo1

KQ

31

For K=3, Q is infinite, poles are on j axis causing sinusoidal oscillations. K>3 causes instability due to right-half plane poles.

31 K



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.



Active Filters: Band-pass (Transfer Function)

221122

313

)(th

V)(oV

)(

)(oV1

)(1

V21th

V

oQossos

CRCR

RRR

ss

sBPA

ssCsth

GCCsth

G

212

1CCR

thRo

21

212CC

CC

thR

RQ

For C1 = C2 = C,

2

1R

thRCo

thR

RQ 2

CR2

2BW

Uses inverting op amp and its full loop gain (ideally infinite).

2

)(oV)(

1V

2 Rs

ssC



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.



Active Filters: Tow-Thomas Biquad

2201

22)(

oQoss

asasasT

General biquadratic transfer function to represent low-pass, high-pass, band-pass, all-pass and notch filters:

In Tow-Thomas biquad, first op amp is a multi-input integrator and third op amp is simply an inverter.

22)(

)(bp

V1

)(lp

V

)(bp

V

2

1)(

lpV-

1)(sV

1

1)(

bpV

oQossos

Ksbp

A

ssRC

s

sCsR

ssRC

sCsR

s

1R

RK

RCo

1RR

Q 2 CRBW

2

1

222

)(oQ

ossoKs

lpA

Thus, center frequency, Q and gain can each be adjusted independently.

Continua…

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2 Microelettronica – Circuiti integrati analogici 2/ed Richard C. Jaeger, Travis N. Blalock Copyright © 2005 – The McGraw-Hill Companies srl Chapter10