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**Effects of Feedback Capacitance in Op Amps**
Fast op amps are useful as current-to-voltage converters in such applications as high speed photodiode preamplifiers and current-output DAC buffers. A typical application using a VFB op amp as an I/V converter is shown in Figure 1-117 on the following page.

The net input capacitance, C1, forms a pole at a frequency f_{P}in the noise gain transfer function as shown in the Bode plot, and is given by:
If left uncompensated, the phase shift at the frequency of intersection, f

_{x}, will cause instability and oscillation. Introducing a zero at f_{x}by adding feedback capacitor C2 stabilizes the circuit and yields a phase margin of about 45°.
The location of the zero is given by:

Figure 1-117: Compensating for input capacitance in a current-to-voltage converter using VFB op amp

Although the addition of C2 actually decreases the pole frequency slightly, this effect is negligible if C2 << C1. The frequency f

_{x}is the geometric mean of f_{p}and the unity-gain bandwidth frequency of the op amp, f_{u},
Combining Eq. 1-52 and Eq. 1-53 and solving for C2 yields:

This value of C2 will yield a phase margin of about 45°. Increasing the capacitor by a factor of 2 increases the phase margin to about 65° (Reference 3: James L. Melsa and Donald G. Schultz, Linear Control Systems, McGraw-Hill, 1969, pp. 196-220, ISBN: 0-07-041481-5).

In practice, the optimum value of C2 may be optimized experimentally by varying it slightly, to optimize the output pulse response.

A similar analysis can be applied to a CFB op amp as shown in Figure 1-118 below. In this case, however, the low inverting input impedance, R

_{O}, greatly reduces the sensitivity to input capacitance. In fact, an ideal CFB with zero input impedance would be totally insensitive to any amount of input capacitance!
Figure 1-118: Current-to-voltage converter using a CFB op amp

The pole caused by C1 occurs at a frequency f_{P}:
This pole frequency will generally be much higher than the case for a VFB op amp, and the pole can be ignored completely if it occurs at a frequency greater than the closed-loop bandwidth of the op amp.

We next introduce a compensating zero at the frequency f

_{x}by inserting the capacitor C2:
As in the case for VFB, fx is the geometric mean of f

_{p}and f_{cl}:
Combining Eq. 1-56 and Eq. 1-57 and solving for C2 yields:

There is a significant advantage in using a CFB op amp in this configuration as can be seen by comparing Eq. 1-58 with the similar equation for C2 required for a VFB op amp, Eq. 1-54. If the unity-gain bandwidth product of the VFB is equal to the closed-loop bandwidth of the CFB (at the optimum R2), then the size of the CFB compensation capacitor, C2, is reduced by a factor of √(R2/R

_{O}).
A comparison in an actual application is shown in Figure 1-119 below. The full scale output current of the DAC is 4mA, the net capacitance at the inverting input of the op amp is 20pF, and the feedback resistor is 500Ω. In the case of the VFB op amp, the pole due to C1 occurs at 16MHz. A compensating capacitor of 5.6pF is required for 45° of phase margin, and the signal bandwidth is 57MHz.

Figure 1-119: CFB op amp is relatively insensitive to input capacitance when used as an I/V converter

For the CFB op amp, however, because of the low inverting input impedance (R

_{O}= 50Ω), the pole occurs at 160Mhz, the required compensation capacitor is about 1.8pF, and the corresponding signal bandwidth is 176MHz. In practice, the pole frequency is so close to the closed-loop bandwidth of the op amp that it could probably be left uncompensated.
It should be noted that a CFB op amp's relative insensitivity to inverting input capacitance is when it is used in the inverting mode. In the non-inverting mode, however, even a few picofarads of stray capacitance on the inverting input can cause significant gain-peaking and potential instability.

Figure 1-120: Low inverting input impedance of CFB op amp helps reduce effects of fast DAC transients

Another advantage of the low inverting input impedance of the CFB op amp is when it is used as an I/V converter to buffer the output of a high speed current output DAC. When a step function current (or DAC switching glitch) is applied to the inverting input of a VFB op amp, it can produce a large voltage transient until the signal can propagate through the op amp to its output and negative feedback is regained. Back-to-back Schottky diodes are often used to limit this voltage swing as shown in Figure 1-120 above. These diodes must be low capacitance, small geometry devices because their capacitance adds to the total input capacitance.

A CFB op amp, on the other hand, presents a low impedance (RO) to fast switching currents even before the feedback loop is closed, thereby limiting the voltage excursion without the requirement of the external diodes. This greatly improves the settling time of the I/V converter.

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