If you can handle capacitive loads, improving amplifier performance is easy.

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The inherent output resistance, R _o, of the op amp , along with the capacitive load, forms another pole in the amplifier transfer function. As shown in the Bode plot, at each pole, the amplitude slope (negative value) decreases by 20 dB/decade. Note how each pole adds up to -90° of phase shift. We can look at the instability problem from two angles. Looking at the magnitude response on a logarithmic plot, the circuit becomes unstable when the sum of the open-loop gain and the feedback attenuation is greater than 1. Similarly, looking at the phase response, the op amp tends to oscillate at frequencies where the loop phase shift exceeds -180°, if this frequency is below the closed-loop bandwidth. The closed-loop bandwidth of a voltage feedback op amp circuit is equal to the op amp's gain-bandwidth product (GBP, or unity-gain frequency) divided by the circuit's closed-loop gain (A _CL ).

The phase margin of an op amp circuit can be thought of as the amount of additional phase shift above the closed-loop bandwidth required for timing that (i.e., phase shift + phase margin = -180°). As the phase margin approaches zero, the loop phase shift approaches -180°, and the op amp circuit becomes unstable. Generally speaking, phase margin values ​​much less than 45° can cause peaking in the frequency response, as well as overshoot or ringing in the step response. To maintain adequate phase margin, the pole created by the capacitive load should be at least 10 times higher than the closed-loop bandwidth of the circuit. If this is not the case, consider the possibility of circuit instability.

First, determine if the op amp can safely drive its own load. Many op amp data sheets specify "capacitive load drive capability," while others provide typical data on "small signal overshoot vs. capacitive load." Looking at these numbers, you can see that the overshoot increases exponentially as the load capacitance increases. As the overshoot approaches 100%, the op amp becomes unstable. If possible, keep the overshoot well below this limit. Also note that this graph is for a specific gain. For voltage feedback op amps, capacitive load drive capability increases as gain increases. So a voltage feedback op amp that can safely drive 100pF at unity gain should be able to drive 1000pF at a gain of 10.

Some op amp data sheets give the open-loop output resistance (Ro), from which the frequency of the additional pole can be calculated. If the frequency of the additional pole (fp ₎ is 10 times higher than the circuit bandwidth, the circuit will remain stable.

If the op amp data sheet does not specify capacitive load drive capability or open-loop output resistance, and does not provide a graph of overshoot vs. capacitive load, then it must be assumed that any load capacitance will require some compensation technique to ensure stability. There are many ways to make a standard op amp circuit stable driving capacitive loads, and here are a few:

This is an effective method for maintaining stability in low-frequency applications , but it is often overlooked by designers. The principle is to increase the closed-loop gain (also called "noise gain") of the circuit without changing the signal gain, thereby reducing the frequency at which the product of the open-loop gain and the feedback attenuation becomes 1. This can be achieved by connecting R _D between the op amp inputs of some circuits , as shown in the figure below. The "noise gain" of these circuits can be calculated using the formula given.

Since stability is governed by noise gain rather than signal gain, the above circuit improves stability without sacrificing signal gain. Stability is ensured by simply making the "noise bandwidth" (GBP/A _NOISE ) at least 10 times lower than the pole created by the load.

One drawback of this stabilization method is that the input-referred voltage noise and input offset voltage are further amplified, resulting in increased output noise and offset voltage. Placing capacitor C _D in series with R _D can eliminate the added dc bias voltage, but this technique adds noise that cannot be eliminated. The effective noise gain of these circuits with and without C _{D is} shown in the figure.

When used, CD _should be as large as possible; the minimum value should be 10A _NOISE / (2πRDGBP ₎ to make the "noise pole" at least 10 times lower than the "noise bandwidth".

This method is to add a resistor R _X between the output of the operational amplifier and the load capacitor , as shown in the figure below. This resistor is obviously outside the feedback loop, but together with the load capacitor, it can introduce a zero point into the transfer function of the feedback network, thereby reducing the loop phase shift at high frequencies.

To ensure stability, the value of R _X should be such that the added zero (f _Z ) is at least 10 times lower than the closed-loop bandwidth of the op amp circuit . By adding R _X , circuit performance is not affected as in the first approach, and output noise is not increased, but the output impedance relative to the load is increased. This may reduce signal gain because R _X and R _L form a resistor divider. If RL is known and reasonably stable, the gain of the op amp circuit can be increased to offset this gain loss.

This method works very well for driving transmission lines. To avoid standing waves, the values ​​of R _L and R _X must be equal to the characteristic impedance of the cable (usually 50Ω or 75Ω). Therefore, R _X is predetermined, and the remaining work is to double the gain of the amplifier to offset the signal loss caused by the resistor divider, and the problem is solved.

If R _L is unknown or varies dynamically, the effective output resistance of the gain stage must be kept low. In this case, it may be helpful to connect R _X inside the overall feedback loop, as shown in the figure below. With this configuration, the DC and low-frequency feedback comes from the load itself, so the signal gain from the input to the load remains unaffected by the voltage divider (R _X and R _L ).

_{The addition of capacitor CF} to this circuit cancels the poles and zeros created by _{CL . In simple terms,} the zero created by _CF coincides with the pole created by _CL , and the pole created by _{CF coincides with the zero created by CL} . Therefore, the overall transfer function and phase response are exactly the same as without the capacitor. To ensure that both pole and zero combinations cancel, the above equations must be solved exactly. Also note the conditions; these conditions are easily met if the load impedance is relatively large.

If R _O is unknown, it is difficult to calculate. In this case, the design process becomes a guessing game, which can be said to be a nightmare for circuit design. One thing that should be noted about SPICE is that the SPICE model of the op amp does not accurately simulate the open-loop output resistance (R _O ) and therefore cannot completely replace the empirical design of the compensation network.

Another important point to note is that C _L must be a known and constant value for this technique to work. In many applications, the amplifier drives unusual loads, and C _L can vary greatly from load to load. Using the above circuit is best done only when C _L is part of a closed-loop system.

One application is to buffer or invert a reference voltage to drive a large decoupling capacitor. In this case, C _L is a fixed value that precisely cancels the pole/zero combination. The low dc output impedance and low noise (compared to the previous two methods) of this approach are very beneficial. In addition, the reference voltage decoupling capacitor can be large (often several microfarads), making other compensation methods impractical.