Basic feedback theory and Oscillators

by

D.V.KamatFaculty, Department of E&C Engg., MIT

Types of feedback

There are two types of feedback in amplifiers:• Positive feedback(regenerative feedback)• Negative feedback(degenerative feedback)

The difference between these two types is whether the feedback signal is in phase or out of phase with the input signal.

Negative feedback amplifier

A negative feedback amplifier is an amplifier in which a fraction of the output of which is combined with the input.

Negative feedback is used in many amplifiers and control systems.

A negative feedback amplifier is a system having three elements : an amplifier ,a feedback network ,a summing circuit

Block diagram of amplifier with negative feedback

Let AOL be the gain of the amplifier without

feedbackLet Afb the closed-loop gain(voltage gain of the amplifier with feedback)Let β is the feedback factor (β < 1)

,

V'in input applied directly to the amplifier without feedback

Then the gain of the amplifier with feedback, Afb is given by,

Advantages offered by Negative feedback system

The negative feedback when employed in amplifier provides following advantages :• improves performance factors like gain stability• improves the linearity• improves the frequency response (increases BW)• reduces the noise• reduces the distortion• reduces sensitivity to parameter variations due to manufacturing or environment. • increases Zin

• decreases Zout

,

If AOL >> 1, then Afb ≈ 1 / β The closed-loop gain Afb is set by the feedback constant β, and hence set by the feedback network.

If β AOL = −1, the amplifier has infinite amplification – it has become an oscillator, and the system is unstable.

Types of oscillatorsTwo general classes of oscillators exist:• Relaxation oscillator• Sinusoidal oscillator

Sinusoidal oscillators consist of amplifiers with RC or LC circuits that have adjustable oscillation frequencies. Relaxation oscillators generate triangular, sawtooth, square waveforms.

Barkhausen criterion for oscillation

Let A is the gain of the amplifying element in the circuit

is the transfer function of the feedback path

is the loop gain around the feedback loop of the circuit

It states that the circuit will sustain steady-state oscillations only at frequencies for which:(i) The loop gain is equal to unity in absolute magnitude, that is,

(ii) The phase shift around the loop is zero or an integer multiple of 2π:

Oscillator fundamentals

Op-amp based Relaxation oscillator(Astable multivibrator)

The non-sinusoidal waveform generators are also called Relaxation oscillators. The op-amp based relaxation oscillator is used to produce a square wave. In general, square waves are relatively easy to produce. The square wave oscillator is a simple two-state system. The square wave oscillator is also known as free-running or Astable multivibrator ,as it has two quasi-stable states (the states, neither one stable.)(A multivibrator is an electronic two state system such as oscillators, timers and flip flops etc).

Op-amp based square wave generator

The op-amp based square wave oscillator uses an inverting op-amp comparator. The comparator uses positive feedback, which offer two advantages:• the high gain causes the op-amp’s output to switch very quickly from one state to another and vice-versa.• the use of positive feedback gives the circuit hysteresis.

• A fraction of the output is fedback to the non-inverting (+) input terminal.

• The differential input voltage is given as vin = vc - β vout

• When vin is positive, vout = – Vz1 and when vin is negative vout = + Vz1

Op-amp based square wave generator

Op-amp based square wave generator

When vin < 0. At this instant vout = + Vz 2 , and the voltage at the non-inverting (+) input terminal is β Vz 2 , the capacitor C charges exponentially towards Vz 2, with a time constant Rf C. The output voltage remains constant at Vz2 until vc equal β Vz2. When it happens, comparator output reverses to – Vz1. Now vc changes exponentially towards -Vz1 with the same time constant and the output makes atransition from -Vz1 to + Vz 2. when vc equals -βVz 1

Op-amp based square wave generator

The frequency of oscillation is dependent on the charge and discharge of a capacitor C through feedback resistor R.

T = 2τ loge 1+β/1- β

In the op-amp square-wave generator circuit, the output voltage vout is shunted to ground by two Zener diodes Z1 and Z2 connected back-to-back and is limited to either VZ 2 or –VZ 1.

Op-amp based square wave generator

Op-amp based sinusoidal oscillators

• Op-amp sine-wave oscillators operate without an externally-applied input signal. Instead, some combination of positive and negative feedback is used to drive the op amp into an unstable state, causing the output to cycle back and forth.

• The frequency and amplitude of oscillation are set by the arrangement of passive and active components around a central op amp.

Two commonly used op-amp based sinusoidal oscillators at audio frequencies are :

• Phase-shift oscillator• Wien-bridge oscillator

Wien Bridge Oscillator

•Uses two RC networks connected to the positive terminal to form a frequency selective feedback network•It generates a sinusoidal oscillatory output signal without having any input source•The circuit amplifies the signal with the two negative feedback resistors•The oscillator is useful at audio frequency applications.

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