### Feedback and its application

By its definition, a feedback system is put between the output and input of the system transferring part of the output to the input. In designing amplifiers, feedback has a key role for many purposes. Feedback can be either negative or positive. The negative feedback is called degenerative, and the positive feedback is called regenerative.

**Negative feedback**

The negative feedback is applied to affect one or several of following properties:

- Make the value of the gain less sensitive to variations in the value of circuit components. Desensitization of the gain reduces the effect of temperature changing characteristics of components, on the signal shape and magnitude.
- Make the output proportional to the input to reduce the nonlinear distortion of the signal. In other words, make the gain constant independent of signal level.
- Minimize the contribution to the output of the unwanted electric signal generated by the circuit components. In other words, it reduces the effect of noise.
- By selection of appropriate feedback topology, input and output impedance of circuit raises or lowers. So the Control of input and output impedance could be provided.
- Extend the bandwidth of the amplifier.

All these benefits are achieved at the expense of a reduction in gain by a factor

called the amount of feedback. In other words, the idea of negative feedback is to trade off gain for some desirable properties.

**Positive feedback**

In a positive feedback, a small disturbance in the input leads to an increase in the magnitude of the disturbance. Unlike a negative feedback which stabilizes the system against such factors as temperature variation, environmental noises, etc., a positive feedback always leads to instability. This property of positive feedback is used in some applications such as active filters and oscillators. A common application of a positive feedback in digital electronics is forcing analog voltage values of a system far from their intermediate values into the digital state of 0 or 1.

**Basic terminology **

__Forward gain A__: This is the gain of an amplifier defined as Vo/Vi for voltage amplifiers.__Feedback gain β__: This is the gain of a feedback system or an element. The amount of feedback gain is defined as the ratio of the voltage feedback to the system with regards to the output voltage or V_{f}/V_{o}.__Loop gain (Aβ)__: For a negative feedback this value must be a positive number.

For a feedback system, the value of (1+Aβ) determines the gain reduction, gain de-sensitivity, bandwidth extension, and change in input and output impedances

**The four basic feedback topologies**

Based on the quantity that is amplified and the desired output, amplifiers can be classified into four categories:

- Voltage sampling series mixing (series- shunt)
- Current sampling shunt mixing (shunt- series)
- Current sampling series mixing (series- series)
- Voltage sampling shunt mixing (shunt- shunt)

**How can the Stability of an amplifier be determined?**

Stability of a feedback amplifier can be analyzed by constructing Bode plots for the forward and feedback gains using different software like MATLAB. If the plots for |A| and 1/|β| intersects with a difference in slope no greater than 6dB/octave the system is guaranteed to be stable.

To make a given amplifier stable for a given feedback factor β, the open loop frequency response can be suitably modified by a process known as frequency compensation. A popular method for frequency compensation involves connecting a feedback capacitor to an inverting stage in the amplifier. This causes the pole formed at the input of the amplifier stage to shift to a lower frequency and thus become dominant, while the pole formed at the output of the amplifier stage is moved to a very high frequency and become unimportant. This process is known as pole splitting.