Op-amps that enter instability will exhibit oscillations and ringing, which might persist or grow depending on reactances in the feedback loop. To help deal with these problems, there are additional components or circuits that can be added to an op-amp that will force the circuit into stability conditions. These additional circuit blocks are known as op-amp compensation circuits, which are named because they apply some compensation to the phase margin in the op-amp’s closed loop gain.
In this article, we will outline a few common methods that will help ensure stability of an op-amp circuit with minimal impact on the functionality of the circuit. These methods can be applied in addition to the internal compensation that is used on op-amp packages.
Op-Amp Frequency Compensation Circuits
In general, there is an instability condition reached when the op-amp’s phase margin between the output and non-inverting input passes below a 45° benchmark and eventually approaches 0°. Compensation is intended to overcome poles in the loop gain transfer function when the transfer function contains some reactances. This is done by adding some components that will manipulate the transfer function in some way, which pushes off instability oscillations to higher frequencies or significantly reduces them.
The three common methods that will be discussed below are:
- Isolation resistor compensation
- Dominant pole compensation
- Gain compensation
Isolation Resistor Compensation
This method can be used in instances where the feedback loop has a reactive component, such as when the feedback loop is being used to implement low-pass filtering with gain. Depending on where roll-off arises in the loop gain transfer function, the signal is not sufficiently attenuated to prevent negative feedback. Adding an isolation resistor as shown below allows the loop gain transfer function to be modified.
Isolation resistor placement in two situations.
In the method on the right, the function of this resistor is to dampen the output before it reaches the capacitive load. In the method on the left, the isolation resistor is used to set a zero in the transfer function right at the point of instability. The resistor can be sized by examining the modified transfer function in an AC sweep.
Dominant Pole Compensation
A simple method for enforcing stability in the loop gain is by intentionally introducing a pole into the open-loop transfer function. By introducing a pole into the transfer function, it is possible to induce early rolloff in the open-loop gain curve, which will then severely attenuate any oscillation that occurs near the instability point. This is done by placing a low-pass filter circuit between the output and the load.
The transfer function for the feedback loop can be calculated or measured, and in general it will have the following form:
Closed-loop gain transfer function.
In general, the open-loop transfer function can have multiple poles, which are indexed by the integer i → N above. When a transfer function with the cascaded low-pass form above includes these multiple poles, there will be a series of roll-off frequencies beginning with the lowest pole frequency. An example with a modified open-loop transfer function is shown below.
Open-loop gain curve with an RC circuit used for dominant pole compensation.
The open-loop transfer function is modified by setting the new pole value as follows:
The new dominant pole frequency should be less than the lowest-order frequency.
Once the pole is added with the RC circuit on the output, the closed-loop gain will begin to attenuate significantly before the instability point is reached, and there will likely be negative gain at instability. This method is typically used when the signal being amplified is wideband or operating close to instability. The compensation applied in this case could be sized to still enable considerable gain at the operating frequency while also forcing attenuation in the instability.
Gain compensation is probably the simplest method to use in uncompensated op-amps. In these op-amps, there may be a minimum closed-loop gain specification but the device may have very high open-loop gain, and a high closed-loop gain could result in a wideband signal or strong noise triggering an instability.
Gain compensation refers to simply reducing the gain by adjusting feedback resistor values. By bringing down the gain, the frequency limit where the onset of instability would occur is increased, and one would more stable operation of the circuit even with lower gain.
These are not the only compensation methods that can be applied in op-amp circuits, but they are known to be effective for all three types of op-amp instabilities (sustained oscillation, ringing, and oscillation with gain). Technically, any method that modifies the transfer function is a candidate for op-amp compensation. Make sure to simulate your proposed compensation technique and understand in which situations these techniques will be most useful.
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