Reduction of the servo bandwidth#
We have seen that a large loop gain is beneficial to almost all performance aspects of a feedback amplifier. The only performance degradations that cannot be cured by a large loop gain are:
The addition of noise at the input of the controller and in the feedback network.
The addition of DC offset at the input of the controller and associated temperature effects.
Energy storage and power losses that occur in (parasitic) impedances in series and/or in parallel with the load, the source or elements of the feedback network.
There may be situations in which the loop gain needs to be very large, yielding servo bandwidth that is much larger than required. If the order of the servo function exceeds two or three, frequency compensation while maintaining the bandwidth may become difficult or even impossible.
Consider, for example, an audio power amplifier that needs to drive electrodynamic loudspeakers. Such an amplifier needs to have a large power gain, a very low distortion at low frequencies, and a very low output impedance, but a rather modest frequency range. The requirements for the low distortion combined with the large power gain and the low output impedance, often result in a feedback amplifier with a very large loop gain. As a result, the servo bandwidth may be much larger than required and the number of dominant poles may be too large to deal with during frequency compensation.
In the above situations, it may be a useful approach to limit the number of dominant poles without limiting the low-frequency loop gain. This can be achieved with the aid of pole-splitting techniques or by using brute force methods.
Excessive pole-splitting#
In sections Pole-splitting and Pole-zero canceling, we have introduced two pole splitting techniques that can be applied for increasing the sum of two dominant poles of the loop gain, without changing their product. If two dominant poles after splitting are still dominant poles of the loop gain, the bandwidth of the servo function will be preserved. The splitting of the poles can also be performed in such a way that one of the poles is moved out of the dominant group. If so, the order of the servo function is decreased by one and the bandwidth of the servo function will be reduced. Such a reduction of the bandwidth may be desired in the situation described above. Fig. 432 shows the intended effect on the magnitude characteristics of the loop gain and the servo function.
Pole frequency reduction#
Instead of splitting one of the poles out of the dominant group, the bandwidth can also be reduced by moving a pole of the dominant group closer to the origin or by adding a dominant pole. This can be achieved by inserting a capacitance in parallel with the signal path. Fig. 433 illustrates the reduction of the bandwidth of the servo function by moving the most dominant pole closer to the origin. In cases in which the most dominant pole is associated with an independent capacitor voltage, this can be achieved by placing a capacitor in parallel with the existing capacitor.
Fig. 434 illustrates the effect of the addition of a new dominant pole. This can be achieved by insertion of a capacitor in parallel with the signal path in a resistive network with a nonzero resistance.
DC loop gain reduction#
In section Non-observable and non-controllable states, we studied a balanced voltage amplifier that exhibited a common-mode loop gain much larger than the differential-mode loop gain. Since the common-mode DC performance is usually of less interest than the differential-mode DC performance the common-mode frequency compensation may be accomplished by reduction of the common-mode DC loop gain. The effect of this compensation method is illustrated in Fig. 435.
Interaction with other performance aspects#
Reduction of the loop gain in some frequency range generally causes deterioration of accuracy and linearity in this frequency range. If the reduction of the loop gain is achieved by brute force insertion of impedances in series or in parallel with the signal path, it may result in degradation of the signal-to-noise ratio and/or an increase of power losses and/or energy storage. The latter may result in an increase of the overdrive recovery error.