LM108AHRQMLV - National Semiconductor

TL/H/8726

Predicting Op Amp Slew Rate Limited Response LB-19

National Semiconductor

Linear Brief 19

August 1972

Predicting Op Amp Slew

Rate Limited Response

The following analysis of sine and step voltage responses

applies to all single dominant pole op amps such as the

LM101A, LM107, LM108A, LM112, LM118 and the LM741.

Each of these op amps has an open loop response curve

with a shape similar to the one shown in

Figure 1

. The dis-

tinguishing feature of this curve is the single low frequency

turnover from a flat response to a uniform b20 dB per dec-

ade of frequency (b6 dB/octave) drop in gain, at least until

the curve passes through the 0 dB line. Closing the loop to

40 dB (X100) as shown with a dotted line on

Figure 1

does

not change the shape of the curve, but it does move the

turnover to a higher frequency. These open loop and closed

loop response curves determine the gain applied to small

signal inputs. The logical question then arises as to when a

signal can no longer be treated as a small signal and the

amplifier response begins to deviate from this curve.

TL/H/8726–1

FIGURE 1. Open and Closed Loop Frequency Response

The answer lies in the slew rate limit of the op amp. The

slew rate limit is the maximum rate of change of the amplifi-

er’s output voltage and is due to the fact that the compensa-

tion capacitor inside the amplifier only has finite currents1

available for charging and discharging. A sinusoidal output

signal will cease being a small signal when its maximum rate

of change equals the slew rate limit Srof the amplifier. The

maximum rate of change for a sine wave occurs at the zero

crossing and may be derived as follows:

voeVPsin 2qft (1)

dvo

dt e2qfV

Pcos 2 qft (2)

dvo

dt Àte0

e2qfV

p(3)

Sre2qfmax Vp(4)

where: voeoutput voltage

Vpepeak output voltage

Sremaximum dvo

The maximum sine wave frequency an amplifier with a given

slew rate will sustain without causing the output to take on a

triangular shape is therefore a function of the peak ampli-

tude of the output and is expressed as:

fmax eSr

2qVp

(5)

Equation 5 demonstrates that the borderline between small

signal response and slew rate limited response is not just a

function of the peak output signal but that by trading off

either frequency or peak amplitude one can continue to

have a distortion free output.

Figure 2

shows a quick refer-

ence graphical presentation of equation 5 with the area

above any VPEAK line representing an undistorted small sig-

nal response and the area below a given VPEAK line repre-

senting a distorted sine wave response due to slew rate

limiting.

TL/H/8726–2

FIGURE 2. Sine Wave Response

As a matter of convenience, amplifier manufacturers often

give a ‘‘full-power bandwidth’’ or ‘‘large signal response’’ on

their specification sheets.

C1995 National Semiconductor Corporation RRD-B30M115/Printed in U. S. A.

LB-19 Predicting Op Amp Slew Rate Limited Response

This frequency can be derived by inserting the amplifier

slew rate and peak rated output voltage into equation 5. The

bandwidth from DC to the resulting fmax is the full-power

bandwidth or ‘‘large signal response’’ of the amplifier. For

example the full-power bandwidth of the LM741 with a 0.5V

msS

ris approximately 6 kHz while the full-power bandwidth

of the LM118 with an Srof 70 V/ms is approximately 900

kHz.

The step voltage response at the output of an op amp can

also be divided into a small signal response and a slew rate

limited response. The signal turnover and uniform b20 dB/

decade slope shown in the small signal frequency response

curve of

Figure 1

are also characteristic of a low pass filter

and one can in fact model an op amp as a low pass RC filter

followed by a very wideband amplifier.

Figure 3

shows a

model of a X100 circuit witha3dBdown rolloff frequency of

TL/H/8726–3

FIGURE 3. Small Signal Op Amp Model

10 kHz. From basic filter theory2the 10% to 90% rise time

of single pole low pass filter is:

tre0.35

f3dB

(6)

which for this example would be 35 ms. Again this small

signal or low pass filter response ceases when the required

rate of change of the output voltage exceeds the slew rate

limit Srof the amplifier. Mathematically stated:

VSTEP

tSr(7)

This means that as soon as the amplitude of the output step

voltage divided by the rise time of the circuit exceeds the Sr

of the amplifier, the amplifier will go into slew rate limiting.

The output will then be a ramp function with a slope of Sr

and a rise time equal to:

tÊreVSTEP

(8)

Subsituting equation 6 into equation 7 gives the critical val-

ue of VSTEP directly in terms of f3dB:

VSTEP f3db

0.35

tSr(9)

which can be graphed as shown in

Figure 4

. Any point in the

area above a VSTEP line represents an undistorted low pass

filter type response and any point in the area below a given

VSTEP line represents a slew rate limited response.

TL/H/8726–4

FIGURE 4. Step Voltage Response

The above equations and graphs should allow one to avoid

the pitfalls of slew rate limiting and also provide a means of

using engineering tradeoffs to extend the response of the

single dominant pole type of ampilfier.

REFERENCES

1. Solomon, J. E.; Davis, W. R.; and Lee, P. L.:

‘‘A Self-Com-

pensated Monolithic Operational Amplifier With Low Input

Current and High Slew Rate’’,

pp. 14– 15, ISSCC Digest

Tech. Papers, February 1969.

2. Millman, J. and Hawkias, C. C.:

‘‘Electronic Devices and

Circuits’’,

pp. 465– 466, McGraw-Hill Book Company,

New York, 1967.

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