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 an invert-

ing 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 significantly

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 value of

C

computed value.

CAPACITIVE LOAD TOLERANCE

Like many other op amps, the LMC6032 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 the

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 ca-

pacitance 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.

Capacitive load driving capability is enhanced by using a pull

up resistor to V

ducting 500 µA or more will significantly improve capacitive

load responses. The value of the pull up resistor must be de-

termined based on the current sinking capability of the ampli-

fier with respect to the desired output swing. Open loop gain

of the amplifier can also be affected by the pull up resistor

(see Electrical Characteristics).

PRINTED-CIRCUIT-BOARD LAYOUT

FOR HIGH-IMPEDANCE WORK

It is generally recognized that any circuit which must operate

with less than 1000 pA of leakage current requires special

layout of the PC board. When one wishes to take advantage

of the ultra-low bias current of the LMC6032, typically less

DS011135-4

FIGURE 2. General Operational Amplifier Circuit

DS011135-5

FIGURE 3. Rx, Cx Improve Capacitive Load Tolerance

DS011135-22

FIGURE 4. Compensating for Large Capacitive

Loads with a Pull Up Resistor

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