Transcript Oscillators fundmentals

Basic feedback theory and Oscillators
by
D.V.Kamat
Faculty, 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
feedback
Let 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 oscillators
Two 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.
Oscillator fundamentals
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:
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.
Op-amp based square wave generator
• A fraction of the output is fedback to the noninverting (+) 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
When vin < 0. At this instant vout = + Vz 2 , and the voltage at the noninverting (+) 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 a
transition from -Vz1 to + Vz 2. when vc equals -βVz 1
Op-amp based square wave generator
T = 2τ loge 1+β/1- β
The frequency of oscillation is dependent on the charge and
discharge of a capacitor C through feedback resistor R.
Op-amp based square wave generator
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 sinusoidal oscillators
• Op-amp sine-wave oscillators operate without an externallyapplied 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.
END