The high input resistance of the LMC603x op amps allows the use of large feedback and source resistor values without losing gain accuracy due to loading. However, the circuit can be especially sensitive to the printed circuit board (PCB) layout when these large-value resistors are used.

Every amplifier has some capacitance between each input and ac ground, and also some differential capacitance between 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, and so on) and the feedback resistors create a pole in the feedback path. In Figure 6-2, the frequency of this pole is:

where C_S is the total capacitance at the inverting input, including amplifier input capacitance and any stray capacitance from the IC socket (if one is used), circuit board traces, and so on, and R_P is the parallel combination of R_F and R_IN. This formula, as well as all the following formulas, apply to inverting and noninverting op-amp configurations.

When the feedback resistors are smaller than a few kΩ, the frequency of the feedback pole can be quite high, since C_S is generally less than 10pF. If the frequency of the feedback pole is much greater than the ideal closed-loop bandwidth (the nominal closed-loop bandwidth in the absence of C_S), the pole has a negligible effect on stability, as only a small amount of phase shift is added.

However, if the feedback pole is less than approximately 6 to 10 times the ideal ?3dB frequency, add a feedback capacitor, C_F, between the output and the inverting input of the op amp. This condition can also be stated in terms of the amplifier low-frequency noise gain: To maintain stability, a feedback capacitor is probably needed if:

where

• $\left(\frac{R_F}{R_{IN}}+1\right)$ is the amplifier low-frequency noise gain.
• GBW is the amplifier gain bandwidth product.

An amplifier low-frequency noise gain is represented by the following formula:

regardless of whether the amplifier is being used in an inverting or noninverting mode. A feedback capacitor is more likely to be needed when the noise gain is low, the feedback resistor is large. or both.

If the previous condition is met (indicating a feedback capacitor is probably be needed), and the noise gain is large enough that $\left(\frac{R_F}{R_{IN}}+1\right)\ge 2\sqrt{GBW\times R_F\times C_S}$ , the following value of feedback capacitor is recommended:

If $\left(\frac{R_F}{R_{IN}}+1\right)< 2\sqrt{GBW\times R_F\times C_S}$ , the feedback capacitor is:

These capacitor values are usually significantly smaller than those given by the older, more conservative formula:

C_S consists of the amplifier input capacitance plus any stray capacitance from the circuit board and socket. C_F compensates for the pole caused by C_S and the feedback resistor.

Figure 6-2 General Operational Amplifier Circuit

Using the smaller capacitors give much higher bandwidth with little degradation of transient response. Using a somewhat larger feedback capacitor can be necessary in any of the above cases to allow for unexpected stray capacitance, or to tolerate additional phase shifts in the loop, or excessive capacitive load, or to decrease the noise or bandwidth, or simply because the particular circuit implementation needs more feedback capacitance to be sufficiently stable. For example, a PCB stray capacitance can be larger or smaller than the breadboard capacitance, so the actual preferred value for C_F can be different from the one estimated using the breadboard. In most cases, check the value of C_F on the actual circuit, starting with the computed value.