# The transient response of parallel RLC circuit

I have simulated a transient and steady state response of below circuit. For the transient response the frequency is lower than the steady state. Is there any physics behind this? I was wondering if one could determine the transient and steady state of this circuit only by inspection and not by plotting the output response?

simulate this circuit – Schematic created using CircuitLab

• "For the transient response the frequency is lower than the steady state." Can you show us what you mean? Post a second chart and caption them so we know which is which. You can be sure there's physics and maths behind it! Commented Apr 2, 2016 at 22:46
• What do you mean by: "transient response"? Commented Apr 2, 2016 at 23:53
• I am assuming you are measuring the output as the current through the inductor, is that correct? Or the sourced current? Commented Apr 3, 2016 at 11:58
• Yes current through the inductor Transient response means the current before the system reaches the steady state response.
– Jack
Commented Apr 3, 2016 at 15:01
• @JoshJobin, yes current through the inductor
– Jack
Commented Apr 3, 2016 at 15:15

During the initial transient it's quite hard to measure/compute the real ringing frequency compared to the more steady state scenario. As with all 2nd order filters (LP, BP, Notch and HP) the ringing frequency (damped resonant frequency) and the peaking frequency can be slightly different and, these can both be slightly different to the natural resonant frequency (always the highest).

The natural resonant frequency of this circuit (or a series LC) is: -

$f_n = \dfrac{1}{2\pi\sqrt{LC}}$

The damped (or ringing or transient) frequency is: -

$f_d = f_n\sqrt{1 - \zeta^2}$ where zeta is the damping factor and for a parallel RLC circuit is: -

$\zeta = \dfrac{1}{2R}\cdot\sqrt{\frac{L}{C}}$

See this wiki page for further clarification.

Is there any physics behind this?

There's always physics and math behind problems like this.