Ideal LC oscillator and barkhausen criterion

In summary, the Barkhausen criterion for oscillations in a feedback system is used in the Ideal LC oscillator to sustain oscillations. However, in a parallel combination of LC with an initial condition, there is no feedback system present. In order to apply the Barkhausen criterion, a negative resistance can be used to cancel out losses in the inductor.
  • #1
asifshaik
7
0
I am unable to relate the Barkhausen criterion for oscillations to sustain to the Ideal LC oscillator with an initial condition.
Assume you have a parallel combination of LC(both with Q=infinity) with an initial condition say V volts on capacitor. Mathematically it will oscillate with the frequency 1/2/pi/sqrt(LC). Now I see no feedback here. where you apply barkhausen criterion for the oscillations in that feedback system?

Even if there is a loss in inductor and I keep a -ve resistance in parallel to cancel out that loss, how can i apply the Barkhausen criterion for this as well.
 
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  • #2
asifshaik said:
Now I see no feedback here. where you apply barkhausen criterion for the oscillations in that feedback system?

LC isn't a feedback system. A feedback system is when a sampled output of a network is fed back its input:

220px-Oscillator_block_diagram.svg.png



Oscillators work on the principle that the resonant element is amplified with an external amplifier, and then the amplified output is fed back to its input in correct phase as established by Barkhausen's criterion in order to sustain oscillations indefinitely.
 
  • #3
Thank you very much for the reply.
 

1. What is an ideal LC oscillator?

An ideal LC oscillator is an electronic circuit that uses an inductor (L) and a capacitor (C) to generate an oscillating signal at a specific frequency. It does not require any external power source and is considered to have no losses.

2. How does an ideal LC oscillator work?

An ideal LC oscillator works by storing energy in the inductor and capacitor, and then releasing it in a continuous cycle. The inductor and capacitor act as a feedback loop, causing the signal to oscillate at a specific frequency determined by the values of L and C.

3. What is the Barkhausen criterion?

The Barkhausen criterion is a mathematical condition that must be met for an electronic circuit to produce sustained oscillations. It states that the total phase shift around a feedback loop must be a multiple of 360 degrees and the loop gain must be equal to or greater than 1.

4. How is the Barkhausen criterion used in an ideal LC oscillator?

In an ideal LC oscillator, the Barkhausen criterion is used to determine the frequency at which the circuit will oscillate. By adjusting the values of L and C, the phase shift and loop gain can be manipulated to meet the criterion and produce sustained oscillations.

5. What are the advantages of an ideal LC oscillator?

The main advantages of an ideal LC oscillator are its simplicity and low cost. It also produces a pure sine wave output, making it useful for applications that require a stable and precise frequency. Additionally, since it does not require an external power source, it can be used in remote or portable devices.

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