Capacitance proportionality to circuit frequency?

[LuxFestinus]

The way I understand extremely high frequency circuits to work is that in the design consideration it has to be considered capacitance across the traces. This becomes especially true as you increase the frequency.
According to this website: http://www.adras.com/Impedance.t647-89-2.html
capacitance is indeed proportional to frequency. I need a discussion on this please.

 

[Averagesupernova]

What exactly do you want to discuss? You need to be more specific. Otherwise, what you have posted is really all there is to know. You did see the formula used to find capacitive reactance didn't you? In one place they call it capacitive imedance. That is technically incorrect.

 

[LuxFestinus]

Some people say that capacitance is not proportional to frequency of a circuit. I scoured the web looking for proof and found the one site above. I have heard and understood that as the frequency of a circuit increases so does capacitive bleed across the traces. If this is not correct please inform me. Thanks.

 

[berkeman]

Some people say that capacitance is not proportional to frequency of a circuit. I scoured the web looking for proof and found the one site above. I have heard and understood that as the frequency of a circuit increases so does capacitive bleed across the traces. If this is not correct please inform me. Thanks.

Capacitance is determined purely by geometry, and has nothing to do with frequency. The "bleed" current that you are referring to is better just described as the current though the capacitor. Yes, the current does change with the excitation frequency, and is dependent on the complex impedance of the capacitor with respect to frequency. In general, the current that goes "through" the capacitor is composed of the reactive "displacement" current and the real "leakage" current. The displacement current is generally higher at the frequency increases. Any basic EE or E&M textbook that covers capacitance will describe this.

 

[dlgoff]

I have heard and understood that as the frequency of a circuit increases so does capacitive bleed across the traces. If this is not correct please inform me. Thanks.

Are you asking if circuit board designers need to consider the frequency of the circuits that will populate the board? If so, yes. You can take advantage of trace layouts to create capacitors. Look up the specs. of the board material you're going to use/or need.

Regards

 

[Averagesupernova]

Berkeman while you are correct in saying that capacitance does not change with frequency, at the same time you are not quite correct.

In the real world, a 1 uF capacitor may look like it is indeed 1 uF at 1000 hertz, it will not necessarily look like it at 10 Mhz. In larger capacitors it is quite common that the ESL (equivalent series inductance) becomes significant. The inductance cancels out some of the capacitance. This is a real consideration especially in RF circuits. Have you ever seen on a schematic where there are several capacitors in parallel with different values? This is to make sure that a large spectrum of frequencies are passed or bypassed depending on the application. I'd check the link but am working from a slow internet connection tonight and just don't want to bother.

 

[berkeman]

Supernova, while you are correct that the reactance changes with frequency, it is not because of any geometric change in the capacitive structure. Yes, there are inductive structures and leakage mechanisms (and even more exotic stuff like dielectric absorption), but the capacitive portion of the complex reactance is constant, and determined 100% by the geometry of the conductors. It's important to understand what the various components of the complex reactance are, in order to optimize the circuit at hand. Even weirder is when the size of the components gets to be a significant portion of a wavelength -- then you use stripline analysis more to model the complex reactance and transmission line characteristics. Like when you use a chip capacitor as an inductor...

PS -- I think we are saying the same thing. It's important to model components and their parasitics well, or we risk missing out on predicting the real behavior at high frequencies.

 

[Averagesupernova]

Yes Berkeman we are in fact saying the same thing. I was just trying to avoid having someone think that they can use a 1 uF electrolytic as power supply bypass capacitor in a UHF circuit. At a single given frequency we still really can't tell if a particular capacitor is just slightly out of tolerance or if it's capacitive reactance is being canceled by inductance. I'm not saying it is impossible to determine it, but if all we have to work with is one frequency, a voltmeter and current meter it is impossible to tell.

 

[abdo375]

I Can't see what are you arguing about, capacitance does not change with frequency, capacitnace is constant value you buy a capacitor with, what changes with the frequency is the impedance,
that is the whole idea of filters....

 

[LuxFestinus]

So from what I understand from all this is that as the frequency changes so does impedance. Then increased leakage with increased frequency occurs because of a change in impedance? I thought signals bled across wire traces more with increased frequency. Seems like they would do this less if resistance was higher.

 

[Averagesupernova]

abdo375, apparently you haven't read or at least understood what I have said in my posts. Yes, capacitance cannot change over frequency. BUT, it is impossible to build a capacitor without building some inductance in series with it. Knowing that, we can say that the effective capacitance of a real world capacitor does in fact go down as the frequency increases. The inductance is there all the time, but it has such a small effect on lower frequencies that it is not noticed. It is the same way with traces on a circuit board. The capacitance is always there, but it is not significant until the frequency is high enough.

 

[berkeman]

So from what I understand from all this is that as the frequency changes so does impedance. Then increased leakage with increased frequency occurs because of a change in impedance? I thought signals bled across wire traces more with increased frequency. Seems like they would do this less if resistance was higher.

Lux, I share Supernova's frustration here. Do you know the differential equation that defines the behavior of voltage and current for a capacitor? That shows the frequency dependence of impedance directly. Check out any basic EE or E&M text for a tutorial on caps.

The basic equation for a capacitor is written I = C dv/dt

That means that the current "through" the capacitor (the displacement current, not any resistive leakage current) is proportional to the capacitance and also proportional to the rate of change of the voltage with respect to time. Given a constant C and a constant amplitude sine wave, the higher the frequency of the sine wave, the higher dv/dt is. Thus, the displacement current through a capacitor is proportional to the frequency of excitation, and since Z = dV/dI, the impedance of a capacitor is inversely proportional to frequency and inversely proportional to C.

And as Supernova says, if you add into your model the series inductance associated with the real capacitor (whether from ESL inside an electrolytic cap, or from the leads and traces going into SMT ceramic caps), the inductive impedance (which is proportional to frequency and L, as opposed to the impedance of capacitors, which is inversely related to frequency and C) will make the overall impedance have a different shape from just the ideal capacitor. This is easiest to see if you have either a SPICE package to simulate the series L-C connection, or access to an impedance analyzer like an HP 4194. Plot Z(f) for some different combinations of R,L,C with either of these tools, and you will start to get a better feel for the "impedance" characteristics of real circuits.