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# AE_Lecture11_Part1_Audio Oscillators

Module by: Bijay_Kumar Sharma. E-mail the author

Summary: AE_lecture11_Part1 describes a feedback system and the Barkhausen Criteria for sustained oscillation.It describes the circuit diagram and working of Audio Oscillators.

AE_LECTURE 11_Part1.

Section 1. FEEDBACK SYSTEMS STABILITY AND OSCILLATORS

Figure 1. Block Diagram of feedback system.

Here ‘s’ implies s-domain and s=σ+jω. Just as we have time domain, we have frequency domain, s-domain and z-domain.

In Time-domain we study the response of a system with respect to time.

In Frequency-domain we study the steady state sinusoidal response of a system.

In s-domain we get to see the total response of the system. Whenever a certain input is applied we have a transient response and steady state response. Total response is the sum total of transient plus steady state response.

z-domain is for discrete time systems and s-domain is for continuous time systems.

In the Block Diagram of a feedback system, we have the Basic Amplifier Block A(s) , the feedback network block f(s) and comparison node. f(s) can be frequency independent or frequency selective.

In negative feed back

In positive feed back

Negative feed back system is a degenerative system:

And Aclosed < Aopen Hence a degenerate system.

Positive feedback system is a regenerative system:

Aclosed = Aopen/[1- |L(s)|]

If

then Hence regenerative system

then and system becomes unstable and oscillatory.

We can take advantage of instability and realize a pure sine wave oscillator.

When

. This is BARKHAUSEN CRITERIA.

Then we realize a pure sine wave oscillator.

For self starting condition we allow

to be slightly greater than .This will ensure self starting condition but it will cause a slight distortion.

Section 2. Class of audio oscillators(1 Hz 100kHz)

Wien Bridge Oscillator, Phase-Shift Oscillator and Quadrature Oscillator.

2.1. Wien Bridge Oscillator.

Here Op.Amp is connected as an Non-inverting amplifier with a gain of 3/_0º. The feedback network is a notch filter providing a dip of exactly 1/3 and phase angle 0º at an angular frequency of

. Thus an exact loop gain of unity with 0º phase shift is achieved. But for selfstarting condition the non-inverting gain is kept slightly larger than 3.

Figure 2. Circuit Diagram of Wien Bridge Oscillator.

Replacing s by jω,

At

Then Loop Gain=

Oscillation Frequency=

; This gives a non-inverting gain of 3.

2.2. RC PHASE SHIFT OSCILLATOR

Figure 3. Circuit Diagram of RC phase shift oscillator.

Here Op Amp is connected as an inverting amplifier providing a gain of 29 and phase shift of 180º.

The RC phase shift network gives an attenuation of 1/29 and a phase shift of another 180º.

Thus an exact Loop Gain of 1/_0º is achieved. But for self starting condition the inverting gain is kept slightly larger than 29.

Figure 4. The feed back network.

The Loop Gain expression is:

L(jω) =

where ∆ = and = ;

Re(∆) =

Im(∆)=

To satisfy the Barkhausen Criteria, Re(∆) = 0;

But Re∆=

Therefore by cancelling

through out, we get

Therefore

= ;

Second part of the Barkhausen Criteria says that at oscillatory frequency the phase angle should be zero.

L(ω=

) = = = )

L(ω=

) = ) = 1 ;

Therefore

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