# PCB dielectric and characteristic impedance with frequency

1. ## PCB dielectric and characteristic impedance with frequency

When typical trace impedance is specified at 50 Ohm or 100 Ohm for example, what is the actual complex impedance? Does it matter? I assume for PCB traces like a microstrip it would be mainly capacitive?

I'm also a little confused why frequency never seems to be factored into the calculations. Isn't the relative permittivity a function of frequency? Would the geometry be the same for 2.4GHz as it would for 100MHz?

I look at a stripline or microstrip as mainly a capacitor, which should have an impedance inversely proportional to the frequency. But wherever I look, frequency doesn't seem to be considered in the calculations, so clearly I'm missing something.

Thanks

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2. ## Re: PCB dielectric and characteristic impedance with frequency

Hi, you actually have three questions here here it goes..

Originally Posted by ARQuattr
When typical trace impedance is specified at 50 Ohm or 100 Ohm for example, what is the actual complex impedance? Does it matter? I assume for PCB traces like a microstrip it would be mainly capacitive?
Trace impedance can be expressed as (R ± JωXn. R is the ohmic part- which attributes to Copper's pure resistance. This is way too small to be considered for calculations. So its actually JωXn that forms the impedance- which is THE complex part of your impedance. So you are already using the "complex impedance" And this is calculated by √(L/C). And your assumption of Microstrip acting mainly as capacitive is not correct. Negative complex part of the impedance indicate that the trace is more of capacitive in nature and positive j indicates more of inductive nature of the trace. But that does not mean that the trace will be fully inductive or capacitive in nature. Depending on the frequency of the signal that is transferred in the trace, the trace act either inductive or Capacitive. Fundamentally any trace- whether Strip or Microstrip is a combination of lot of infinitesimal L & C parts.

Originally Posted by ARQuattr
I'm also a little confused why frequency never seems to be factored into the calculations. Isn't the relative permittivity a function of frequency? Would the geometry be the same for 2.4GHz as it would for 100MHz?
Well, frequency is always taken into account for impedance calculations. Z0 (characteristic impedance) = √ (jωL/jωC). where jω=2.Π.f, and f is the frequency. And in this process, since we have jω in both numerator and denominator, we do not explicitly mention about frequency. But Frequency plays a major role here because that's the key factor to decide the "REACTANCE" of the L & C parameters of a trace

Originally Posted by ARQuattr
I look at a stripline or microstrip as mainly a capacitor, which should have an impedance inversely proportional to the frequency. But wherever I look, frequency doesn't seem to be considered in the calculations, so clearly I'm missing something.

Hope this helps

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3. ## Re: PCB dielectric and characteristic impedance with frequency

Trace impedance can be expressed as (R ± JωXn. R is the ohmic part- which attributes to Copper's pure resistance. This is way too small to be considered for calculations. So its actually JωXn that forms the impedance- which is THE complex part of your impedance. So you are already using the "complex impedance" And this is calculated by √(L/C)....Fundamentally any trace- whether Strip or Microstrip is a combination of lot of infinitesimal L & C parts.
I understand that a strip is modeled as a chain of small ideal impedances, but if resistance is negligible, then the impedance vector must lie on the imaginary axis, and this suggests to me that the vector sum of the inductance and capacitance must result in an impedance of either j50 Ohm or -j50 Ohm (using the 50 Ohm example). So as lumped component it's either capacitive or inductive (not both), right?

1 members found this post helpful.

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4. ## Re: PCB dielectric and characteristic impedance with frequency

Hi,

Characteristic impedance √(L/C) remains same for a particular range of frequency- that is within the "Skin effect- or Knee frequency" of the material. Till this frequency, we can assume that frequency might not have any direct effect on trace Z0. This is the case of "Loss-less Transmission line".

And practically this frequency ranges from 100s or MHz to few GHz (approximately 3GHz). And beyond this frequency, PCB traces start exhibiting the property of either L or C, depending on the frequency. And this condition is the case of "Lossy Transmission line".
Factors adding to this behavior are :
Trace length, Loss tangent of dielectric material and Dielectric separation between two adjacent routing layers.

Right, as you have mentioned- Z0 will behave more in inductive or capacitive form at these frequencies. Smith chart will be the right way of finding out the behavior of the trace beyond knee frequency.

1 members found this post helpful.

5. ## Re: PCB dielectric and characteristic impedance with frequency

I know it is confusing, but transmission lines have to be modeled with respect to the frequency range you are using them in. A wavelength is the physical length one period of your frequency. In a PCB, a shorter, because the PCB dielectric material makes the speed of light slower.

So you need to calculate a wavelength in your board material for the highest frequency you are interested in. If the length of trace you are using is << than one wavelength (say ≦ 0.1 wavelengths or shorter) then you can model the transmission line as a lumped element effect. (although modeling it as a transmission like still works 100% fine too).

If, however, the trace length is ≧ than 0.1 wavelengths, you really should only model it as a transmission line. If you try to model this longer line as a lumped element effect, you will have very big errors.

The characteristic impedance is a ratio of the electric field/magnetic field, which is a real number for lossless lines, and almost a real number for lossy lines. Just think of it as either 50 or 100 ohms, respectively...with no imaginary part.

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6. ## Re: PCB dielectric and characteristic impedance with frequency

Sorry for the late reply (didn't get an email notification for some reason).

biff44,

transmission lines have to be modeled with respect to the frequency range you are using them in
This is my understanding, and it brings me back to my original question - why do the trace width calculators not factor in frequency? I understand as cks3976 notes that it might not be a strong influence in a commonly used band, but I'm surprised these calculators would assume anything about frequency. For example the trace width calculator built into Altium only uses impedance and PCB material and stack up properties as far as I can tell. There are also plenty of online calculators that do the same, again without any apparent regard for frequency.

I'm also still trying to mentally digest the concept of characteristic impedance of a lossless line being purely resistive. The DC resistance of an unterminated strip will be very high. At some frequency the impedance may be 50 Ohm, but it will vary between 0 and that frequency...and again, what IS that frequency for a given strip.

Sorry if I'm being dense here. I probably need to dust off some EM course textbooks.

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