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Hi,
In a word, "no". This is because that formula works in the
frequency domain.
If you want to understand how the capacitor works with other
waveforms you should look into complex number solutions.
This will allow you to calculate what a circuit is doing even
with other waveforms.
To elaborate, Fourier transforms describe the frequency content of an arbitrary waveform in the frequency domain, but Laplace transforms are used to calculate how the waveform behaves in an arbitrary circuit.So if one considers all the frequency componets then a prediction in terms of Xc could be approximated. Of course Fourier transform would be the method used by designers.
every body knows that capacitor act as freq dependent resistances in response to sinosoidal signals following the formaula
Xc=1/(2*π*f*c)
i wanted to know whether this rule is valid for other waveforms i-e sqaure,triangular,sawtooth??
A complex waveform like a squarewave can still be analyzed in the frequency domain. It is simply the fundamental with decreasing odd harmonics. The Xc component will still be a function of frequency. In the case of the sqr wave this would be multiple frequencies.
The images below illustrates this.
So if one considers all the frequency componets then a prediction in terms of Xc could be approximated. Of course Fourier transform would be the method used by designers.
**broken link removed**
**broken link removed**
images from
i wanted to know whether this rule is valid for other waveforms i-e sqaure,triangular,sawtooth??
He is apparently asking for the REACTANCE to an arbitrary waveform
using this formula:
Xc=1/(2*π*f*c)
So perhaps you can tell me what the *reactance* is to a 1uf capacitor
with a *square wave* of 1kHz is?
Also, what units is this in?
Also, what good would it do to calculate the reactance of a capacitor
to the various odd harmonics of a square wave when trying to find
a 'reactance' to a 'square wave' ?
Hi again Mike,
Ok, no problem there, and dont forget i also said it's probably a good idea
that someone brought this stuff up.
The only problem i wanted to avoid is to give the impression that we
can use that formula with say a square wave and expect to get good
results for any application under the sun.
For example if we are working with a filter we might get
a ball park result, but if we are working with (a different example) say
the output from a square wave output inverter our circuit would be
constantly banged by steep wavefronts which would give rise to
sharply rising high current surges which could easily blow something out
or at least overheat it, if we fall back onto the 'reactance' formula without
knowing its limitations. That's my main concern.
Oh yeah, after posting this i realized the simplest example is probably
the offline LED night light, or offline LED area light, where the LED
is powered via a series capacitor to keep efficiency high rather
than a simple series resistor which burns up lots of power.
If we calculate the value of the cap based on it's reactance, it
'might' work, but if we use complex math it will 'definitely' work,
and not only that, if we are not familiar with the limitations of
using the reactance alone as a circuit parameter we would not
think to analyze the time domain transient response, which
could be TOTALLY different due to the fact that at some
point in time we would eventually decide to plug this thing in,
and if we do this enough eventually we will plug it in when the
line is at 170v peak (USA), and that means a steep wavefront
to deal with as well, which is also not a sine wave.
If we want to really look closely at this circuit, it is also possible
to unplug it and plug it back in fast enough to keep roughly 170v
on the cap, while when we plug it back in the line is at -170v peak,
which means 340v across the cap for a short time.
Understanding these kinds of things is what i believe is necessary
to go with understanding the frequency domain response so that
something doesnt go wrong.