frequency responsepassive-networks
Reading Linear Circuit Transfer Functions and one of the graphs got me curious.
I've recreated the circuit (series RLC) and plotted the frequency response for a Q of 7.
We have a peak of ~16.3 dB when Q is 7 @ 10Khz.
Can this value be used (16.3 dB) to accurately predict something in the time domain – such as the value of Q or how long the oscillatory decay would take, the amplitude of the oscillations etc.. ?
Added in case its relevent
Every kind of waveform (square, triangle, etc) can be expressed in terms of the superposition of a number of sinusoidal components. Taking the Fourier transform of any waveform will find those sinusoidal components, their amplitudes, and their phases.
.gif#/media/File:Fourier_transform_time_and_frequency_domains_(small).gif)
By Lucas V. Barbosa - Own work, Public Domain, https://commons.wikimedia.org/w/index.php?curid=24830373
For example, this square wave is made from the fundamental frequency, plus all its odd harmonics. That is, if this is a 1000 Hz square wave, then it's a combination of sine waves at 1000 Hz, 3000 Hz, 5000 Hz, 7000 Hz, and so on. For an ideal square wave these harmonics go on forever, but as they get higher they decrease in amplitude.
The frequency response of something (like a filter) describes how it will affect each of these sinusoidal components. In a linear system (as most filters are), it's valid to consider what would happen to each component independently, given the frequency response, and then add all the results back together to see the net result.
These are time domain.
When talking about "time domain" or "frequency domain", or indeed any other "thing domain" we are talking about how something changes with respect to "time", "frequency", or "thing". In this case your x-axis is time, so you are in the time domain. A frequency domain analysis would typically involve graphs with frequency on the x-axis, and amplitude and/or phase as y axes.
This terminology is borrowed from maths, where domain has a more clearly defined meaning.
Note that a step response is an example of a time domain response, but other forms of time domain response also exist.
Best Answer
Q is (among other definitions) the voltage gain at resonance, and a voltage gain of 7 times is $$20 * \log(7) = 16.9dB$$ which seems close enough as your cursor is clearly not actually on resonance (phase would be -90 not -93). So dB of resonant gain is trivially converted to or from Q.
Q gives you risetime and whether the circuit is over/under or critically damped in the time domain, as well as how well damped the ringing in an under damped circuit is.