LC series oscillator with DC supply

In summary, the conversation discusses a question about LC series oscillators and the behavior of the circuit when a DC supply is applied. The solution to the differential equation shows that the circuit oscillates with an amplitude of 2*Vdc. However, there is confusion about the circuit impedance and the behavior in steady state. The expert explains that in an ideal case with R=0, the circuit would act like an open circuit. However, in a real circuit, the resistance would dampen out the oscillation. The expert also explains that the transient caused by the step input signal is what allows the oscillator to start oscillating. In conclusion, the circuit behaves as expected with a DC component on the capacitor and a transient oscillation caused by the
  • #1
Shinji83
10
1
Hi, I have a question about LC series oscillators. Specifically when a DC supply is applied.
Solving the differential equation for such circuit using as initial conditions at t=0 that Vc=0 and I=0 I get as a solution that the circuit oscillates and the voltage across the capacitor has an amplitude of 2*Vdc.
Solution is:
Vdc*(1-cos (t/sqrt (LC))
This is also confirmed using Pspice simulation.

Now my doubt is that if I consider the circuit impedance j (ωL -1/ωC) of course for ω=0 it goes to infinite which means that with a step signal applied to the curcuit (starting from zero state at t=0) after a transient I should get zero current in steady state. The circuit is not an oscillator but acts like an open circuit in steady conditions according to circuit analysis theory.

So what's happening? Thanks.
 
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  • #2
What is the resistance of your circuit?
If you suddenly turn on a DC source you do not really have a static situation, the transient in fact a broadband frequency pulse and that is what is causing your oscillator to get going.
In any real circuit this will be rapidly damped out by the resistance.
 
  • #3
f95toli said:
What is the resistance of your circuit?
If you suddenly turn on a DC source you do not really have a static situation, the transient in fact a broadband frequency pulse and that is what is causing your oscillator to get going.
In any real circuit this will be rapidly damped out by the resistance.

Thank you for your reply.
I was considering the ideal case with R=0.
But you gave me the right hint and I think that I get it now.
Impedance at ω=0 (ideal costant signal of infinite duration) is infinite and gives me a DC component on the capacitor.
The transient in this case doesn't go to zero on steady state but it's a permanent oscillation because the step input signal has a Fourier transform with a component at ω=1/sqrt (LC) and at that frequency impedence is zero and the circuit oscillates.
So on the capacitor I get an oscillation on top of a DC component which is what I was expecting.
 

What is an LC series oscillator with DC supply?

An LC series oscillator with DC supply is a type of electronic oscillator that uses a combination of an inductor (L) and a capacitor (C) in series with a direct current (DC) power supply to generate a continuous sinusoidal signal.

How does an LC series oscillator with DC supply work?

In an LC series oscillator with DC supply, the inductor and capacitor combination forms a resonant circuit that allows the signal to oscillate at a specific frequency. The DC supply provides the initial energy needed to start the oscillations, and the feedback mechanism between the inductor and capacitor helps to sustain the oscillations.

What are the advantages of using an LC series oscillator with DC supply?

Some advantages of using an LC series oscillator with DC supply include its simplicity, low cost, and stability. It also has a wide frequency range and can generate signals with relatively low distortion.

What are the main applications of an LC series oscillator with DC supply?

LC series oscillators with DC supply are commonly used in electronic devices such as radios, televisions, and computers. They are also used in measurement and testing equipment, as well as in communication systems.

How can one adjust the frequency of an LC series oscillator with DC supply?

The frequency of an LC series oscillator with DC supply can be adjusted by changing the values of the inductor and capacitor, which affect the resonant frequency of the circuit. It can also be adjusted by changing the supply voltage or by using a variable resistor in the circuit.

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