# Controller requirements#

## Accuracy, bandwidth and frequency stability of negative feedback amplifiers#

Download the poster: "Derive Controller Requirements from Amplifier Specifications"

Bandwidth of a negative feedback amplifier

For design purposes it is convenient to decouple the definition of the bandwitdth of a negative feedback amplifier from its desired frequency characteristic. This can be achieved by defining the bandwidth of a negative feedback amplifier by that of its servo function.

**Presentation**

The presentation Bandwidth of a negative feedback amplifier shows that the bandwidth of a negative feedback amplifier will be defined as that of its servo function.

**Presentation in parts**

Bandwidth of a negative feedback amplifier (parts)

**Video**

Bandwidth definition for negative feedback amplifiers (3:40)

**Study**

Chapter 11.4.1

Example: Bandwidth of a negative feedback transimpedance integrator

**Presentation**

The presentation Bandwidth Transimpedance Integrator shows the bandwidth definition for a negative feedback transimpedance integrator.

**Presentation in parts**

Bandwidth Transimpedance Integrator (parts)

**Video**

Example Bandwidth definition for an OpAmp Integrator Circuit (7:12)

**study**

Chapter 11.4

Butterworth or Maximally Flat Magnitude (MFM) responses

The -3dB cut-off frequency of systems with a Butterworth or MFM transfer equals the Nth root of the magnitude of the product of their N poles, where N is the order of the system.

In this course we will design the frequency response of a feedback amplifier in such a way that the servo function obtains an MFM or Butterworth filter characteristic over the frequency range of interest. Design procudures for other filter characteristics, such as, Bessel or Chebyshev do not differ. Only the numeric relation between the -3dB bandwidth and the gain-poles product of the loop gain will be different.

**Presentation**

The presentation Butterworth or Maximally Flat Magnitude (MFM) responses shows the Laplace transfer functions, the pole patterns and the magnitude characteristics of first, second and third order Butterworth transfers.

**Presentation in parts**

Butterworth or Maximally Flat Magnitude (MFM) responses (parts)

**Video**

Butterworth frequency responses (4:07)

**Study**

Chapter 11.4.3

MFM bandwidth of an all-pole feedback amplifier

The product of the loop gain and the magnitude of the dominant poles of the loop gain is a design parameter for the -3dB MFM bandwidth of an all-pole negative feedback amplifier .

**Presentation**

The presentation All-pole loop gain and servo bandwidth proofs the above.

**Presentation in parts**

All-pole loop gain and servo bandwidth (parts)

**Video**

All-pole Loop Gain and Servo Bandwidth (5:13)

**Study**

Chapter 11.4.3

Determination of the dominant poles of the loop gain

**Presentation**

The presentation Dominant and non-dominant poles in feedback systems illustrates the procedure for separating dominant poles and non-dominant poles on feedback systems.

**Presentation in parts**

Dominant and non-dominant poles in feedback systems (parts)

**Video**

Dominant poles and non-dominant poles of the loop gain (8:53)

**Study**

Chapter 11.4.3

Determination of the requirement for the gain-bandwidth product of an operational amplifier

The requirement for the GB-product of an operational amplifier can be derived from the loop gain-poles product (for dominant poles only).

**Presentation**

The presentation Determination of OpAmp GB-product requirement illustrates the procedure for deriving the requirement for the gain-bandwidth product of the operational amplifier from the expression of the loop gain.

**Presentation in parts**

Determination of OpAmp GB-product requirement (parts)

**Video**

Determination of GB product requirements for operational amplifiers (5:35)

**Study**

Chapter 11.4.3

Frequency stability of negative feedback systems

A system is stable if its responses to bounded excitations are also bounded.

A lumped system is said to be stable if the solutions of its characteristic equation (the poles) all have a negative real part.

**Presentation**

The presentation Frequency stability of feedback amplifiers presents three ways to determine the stability of feedback systems.

**Presentation in parts**

Frequency stability of feedback amplifiers (parts)

**Video**

EE3C11 lecture 14: The Root locus technique

**Study**

Chapter 11.5

## Downloads#

The presentations are summarized on the poster: "Derive Controller Requirements from Amplifier Specifications"