Introduction

Negative feedback is an error reduction technique that uses the available power gain of a controller for quality improvement of the transfer of the feedback amplifier. With a high-gain controller, the bandwidth, the linearity and the accuracy of a negative feedback amplifier are primarily defined by the feedback network(s). In the following sections, we will discuss to what extent performance limitations of the controller affect those of the negative feedback amplifier. This knowledge will help us in setting up the performance requirements for the controller.

We have already seen that the controller adds noise to the signal. For given noise sources of the controller, the smallest noise contribution can be achieved with nonenergic feedback. With other implementations of feedback, the feedback network enlarges this contribution and possibly adds noise itself. This deterioration of the noise behavior can be kept small by placing only relatively small impedances in series with the signal path and/or small admittances in parallel with the signal path. These small impedances and admittances can have a large effect on the port impedances of the feedback amplifier (see section Impedance model). Hence, when compared with the use of brute-force techniques, we are able to design the port impedances, the transfer and the signal-to-noise ratio of a feedback amplifier almost independently. We will see that this is also true for other performance aspects, such as the static accuracy, the nonlinearity and the bandwidth of feedback amplifiers.

With the aid of the asymptotic gain model, the source-to-load transfer of a feedback amplifier can be approximated by the product of its ideal transfer and the servo function.

If the loop gain reference variable has been selected properly and if the direct transfer can be neglected.

With a nullor as controller the servo function equals unity and the source-to-load transfer equals the ideal transfer. A practical controller cannot behave as a nullor; it will have a finite available power gain and suffer from speed and power limitations. Therefore, in practice, the servo function will only approximate unity over a limited operating range of the controller. Since the servo function is completely determined by the loop gain, designing the servo function means designing the loop gain. The elements that contribute to the loop gain are:

1. The controller

2. The feedback network

3. The source and the load impedance

The source and the load impedances are part of the application specification of the amplifier. The feedback network has been designed on grounds of the desired transfer, its noise contribution and its effect on the power efficiency. Design or selection of the controller is what remains. This starts with setting up its performance requirements. The specification of the controller requirements in relation to the performance of the amplifier is the main topic of this chapter.

This chapter

In the following sections, we will study the influence of the following performance limitations:

1. Finite static loop gain

   A finite static (DC) loop gain can be caused by:

   1. A finite static gain of the controller

   2. One or more zeros in the loop gain at \(s=0\)

   3. One or more zeros at \(s=0\) in the impedance or in the admittance of the source and/or the load

   The effect on the static accuracy of the feedback amplifier will be discussed in section Accuracy design considerations.

2. Nonlinear loop gain

   Nonlinearity of the loop gain can be caused by:

   1. Nonlinear transfer of the controller

   2. Nonlinearity in the transfer of the feedback network

   3. Nonlinear behavior of the source or the load

   The relation between nonlinear behavior of the loop gain and that of the feedback amplifier will be discussed in section Nonlinearity design consideration.

3. Bandwidth limitation of the loop gain

   Bandwidth limitation of the loop gain can be caused by:

   1. Bandwidth limitation of the controller gain

   2. Bandwidth limitation in the transfer of the feedback network

   3. Dynamic character of the source and/or the load

   The relation between the dynamic behavior of the loop gain and that of the feedback amplifier will be discussed in section Bandwidth design considerations.