Every amplifier has some capacitance between each input

and AC ground, and also some differential capacitance be-

tween the inputs. When the feedback network around an

amplifier is resistive, this input capacitance (along with any

additional capacitance due to circuit board traces, the

socket, etc.) and the feedback resistors create a pole in the

feedback path. In the following General Operational Amplifier

circuit,

Figure 2 the frequency of this pole is

where C

cluding amplifier input capcitance and any stray capacitance

from the IC socket (if one is used), circuit board traces, etc.,

and R

mula, as well as all formulae derived below, apply to invert-

ing and non-inverting op-amp configurations.

When the feedback resistors are smaller than a few k

Ω, the

frequency of the feedback pole will be quite high, since C

generally less than 10 pF. If the frequency of the feedback

pole is much higher than the “ideal” closed-loop bandwidth

(the nominal closed-loop bandwidth in the absence of C

the pole will have a negligible effect on stability, as it will add

only a small amount of phase shift.

However, if the feedback pole is less than approximately 6 to

10 times the “ideal” −3 dB frequency, a feedback capacitor,

C

ing input of the op amp. This condition can also be stated in

terms of the amplifier’s low-frequency noise gain: To main-

tain stability a feedback capacitor will probably be needed if

where

is the amplifier’s low-frequency noise gain and GBW is the

amplifier’s gain bandwidth product. An amplifier’s low-

frequency noise gain is represented by the formula

regardless of whether the amplifier is being used in inverting

or non-inverting mode. Note that a feedback capacitor is

more likely to be needed when the noise gain is low and/or

the feedback resistor is large.

If the above condition is met (indicating a feedback capacitor

will probably be needed), and the noise gain is large enough

that:

the following value of feedback capacitor is recommended:

If

the feedback capacitor should be:

Note that these capacitor values are usually significant

smaller than those given by the older, more conservative for-

mula:

Using the smaller capacitors will give much higher band-

width with little degradation of transient response. It may be

necessary in any of the above cases to use a somewhat

larger feedback capacitor to allow for unexpected stray ca-

pacitance, or to tolerate additional phase shifts in the loop, or

excessive capacitive load, or to decrease the noise or band-

width, or simply because the particular circuit implementa-

tion needs more feedback capacitance to be sufficiently

stable. For example, a printed circuit board’s stray capaci-

tance may be larger or smaller than the breadboard’s, so the

actual optimum value for C

estimated using the breadboard. In most cases, the values

of C

the computed value.

Capacitive Load Tolerance

Like many other op amps, the LMC660 may oscillate when

its applied load appears capacitive. The threshold of oscilla-

tion varies both with load and circuit gain. The configuration

most sensitive to oscillation is a unity-gain follower. See

Typical Performance Characteristics.

The load capacitance interacts with the op amp’s output re-

sistance to create an additional pole. If this pole frequency is

sufficiently low, it will degrade the op amp’s phase margin so

that the amplifier is no longer stable at low gains. As shown

in

Figure 3, the addition of a small resistor (50

Ω to 100Ω)in

series with the op amp’s output, and a capacitor (5 pF to

10 pF) from inverting input to output pins, returns the phase

margin to a safe value without interfering with lower-

frequency circuit operation. Thus larger values of capaci-

tance can be tolerated without oscillation. Note that in all

cases, the output will ring heavily when the load capacitance

is near the threshold for oscillation.

DS008767-6

FIGURE 2. General Operational Amplifier Circuit

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