# Hartley Oscillator

Discussion in 'Homework Help' started by circuit2000, Apr 21, 2007.

1. ### circuit2000 Thread Starter Active Member

Jul 6, 2006
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Why does Hartley Oscillator produce a sine wave?Is it because Barkhausen condition is satisfied?

2. ### recca02 Senior Member

Apr 2, 2007
1,211
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according to my knowledge barkhausen criteria is required to be fulfilled by
+ve feedback ckt so that it can sustain the oscillation (so that they dont die out) .
the shape of oscillation depend on the tank ckt components.

3. ### circuit2000 Thread Starter Active Member

Jul 6, 2006
33
0
If the tank circuit is responsible for shape of oscillation,how does a phase shift oscillator produce sine waves without a tank circuit?

4. ### recca02 Senior Member

Apr 2, 2007
1,211
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well my knowledge in this case is limited but about barkhausen's criteria
if u r still unsure u must read abt he criteria itself which states that the gain of
should be equal greater than unity and phase shift produced by the feedback network should be 180 deg so that the amplifier again inverts it for a zero phase diff (360 deg). hence feedback is positive.
here is an explanation abt phase shift oscillator from some site.

"An oscillator is a circuit, which generates ac output signal without giving any input ac signal. This circuit is usually applied for audio frequencies only. The basic requirement for an oscillator is positive feedback. The operation of the RC Phase Shift Oscillator can be explained as follows.
The starting voltage is provided by noise, which is produced due to random motion of electrons in resistors used in the circuit. The noise voltage contains almost all the sinusoidal frequencies. This low amplitude noise voltage gets amplified and appears at the output terminals. The amplified noise drives the feedback network which is the phase shift network. Because of this the feedback voltage is maximum at a particular frequency, which in turn represents the frequency of oscillation. Furthermore, the phase shift required for positive feedback is correct at this frequency only. "
http://www.visionics.ee/curriculum/...ft Oscillator/RC Phase Shift Oscillator1.html

5. ### circuit2000 Thread Starter Active Member

Jul 6, 2006
33
0
Sorry for my delayed response. Thats cool!Thanx.

6. ### Papabravo Expert

Feb 24, 2006
10,340
1,850
I was drawn to this thread like a moth to a flame. I believe the reason an oscillator produces sine waves is because it is a linear system. Just as there is more than one type of oscillator, there is more than one way to construct a linear system with L's, and R's, and C's. The solutions to 2nd order linear differential equations are - sines and cosines. We know tha no systems of order zero or one can oscillate. If the roots of the characteristic equation are in the left half plane we have damped sinusoids. If the roots are on the j-omega axis then we have sustained oscillations. In control theroy we have a saying that

"The positive real part of the roots must vanish, or the system WILL."

We also know that if we introduce non-linearities, as for example in the Van der Pol oscillator, the solutions are no longer sines and cosines. We get a phenomenon called limit cycling, which occurs only in non linear systems.

So my conjecture is that the simplest oscillator is represented by a second order linear differential equation with constant coefficients whose solution contains sines and cosines.