capacitor reactance?

Wond3rboy · Oct 10, 2008

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??

MrAl · Oct 10, 2008

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.

crutschow · Oct 10, 2008

The easiest way to determine what a capacitor circuit will do with a complex waveform is to let the computer do the calulations with a circuit simulator.

Mikebits · Oct 10, 2008

MrAl said:
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.

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

crutschow · Oct 10, 2008

Mikebits said:
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.

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.

MrAl · Oct 11, 2008

Hi Mikebits,

Wond3rboy said:
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??

Mikebits said:
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

Mikebits,

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' ?

Even so, i dont think it's a bad idea that you brought this up, as
the OP may wish to know about Fourier techniques for analyzing a
circuit as i think you were alluding to, and that's one of the reasons
i mentioned complex number solutions.

As crutschow mentioned, Laplace techniques would probably be
a good idea too, but again for the circuit analysis, not for calculating
the so called "reactance" to a "square wave", of which i dont even
think it's defined.

I was hoping to persuade the OP to look into circuit analysis in general,
so that's what my post was about. I assumed Fourier and Laplace as
well as State Vector Differential Equations would come up eventually,
but as i was saying, this wont help calculate the reactance because
there is no such thing for a square wave...that's why i answered "No".

Willbe · Oct 11, 2008

Wond3rboy said:
i wanted to know whether this rule is valid for other waveforms i-e sqaure,triangular,sawtooth??

You use Laplace analysis to figure this out using the s operator, and then go back into the time domain.
Partial fractions, the whole bit. By hand, it is tedious.
Someone may have tabulated commonly used solutions for this, if you can find them.

Mikebits · Oct 11, 2008

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' ?

Lets face it. Were not trying to build the Hubble transceiver here. For general hobby use, one can take the fundamental frequency, plug it into the XC formula and make a good prediction of it's response for the waveform. Take my excel spreadsheet as an example. Using your values. A 1KHz sqr wave and a 1 uf cap. Consider cap in series, I can see from the graph that I have a high pass filter, and that the fundamental would be rolled off. I could tweak my C value higher to pass more of the fundamental. That is all I am saying. To ball park a series cap for example...

MrAl · Oct 11, 2008

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.

Space Varmint · Oct 11, 2008

MrAl said:
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.

If there is such a thing as pure square wave than both would be right. He's just saying the formula does apply. I think that was the original question

capacitor reactance?

Wond3rboy

Member

MrAl

Well-Known Member

crutschow

Well-Known Member

Mikebits

Well-Known Member

crutschow

Well-Known Member

MrAl

Well-Known Member

Willbe

New Member

Mikebits

Well-Known Member

Attachments

MrAl

Well-Known Member

Space Varmint

New Member

Similar threads

capacitor reactance?

Member

Well-Known Member

Well-Known Member

Well-Known Member

Well-Known Member

Well-Known Member

New Member

Well-Known Member

Attachments

Well-Known Member

New Member

Similar threads

Privacy & Transparency

Privacy & Transparency