Characteristic impedance

[JamesCm]

Hello!

I'm routing a PCB that has a gigabit Ethernet, and that requires differential pairs with a target characteristic impedance. So I went studying about characteristic impedance, as it's something I never had to consider before, and although I understand it a little better now I still have a few questions about it in my PCB:

1) Does the distance between the 2 traces on the differential pairs affects their characteristic impedance?

2) Does the distance between the traces on the differential pairs and the GND polygon pour around those traces affects their characteristic impedance?

3) As far as my small knowledge of the subject, characteristic impedance does requires a return path, in order to form the capacitances along the conductors. Is that correct? Or does a single wire floating in space have characteristic impedance as well?

Thanks very much!

 

[barry]

1) Yes.
2) Yes.
3) A wire floating in space also has a characteristic impedance. this is due to the fact that although there may not be any capacitance, the wire still has some inductance.

 

[JamesCm]

2) But does the characteristic impedance of the differential pair changes a lot due to the ground plate?
3) That's something I don't understand. I thought characteristic impedance depended on the capacitances. So, will that wire's characteristic impedance change if I increase its length?

I don't fully understand characteristic impedance. How, for example, a coaxial cable will have the same characteristic impedance regardless of its length? Characteristic impedance is not even close to impedance then?

 

[crutschow]

So, will that wire's characteristic impedance change if I increase its length?

No.

How, for example, a coaxial cable will have the same characteristic impedance regardless of its length?

The characteristic impedance is caused by the distributed capacitance and inductance of the cable (as in F and L per unit length).
Since this does not change with cable length, neither does the characteristic impedance.

Characteristic impedance is not even close to impedance then?

If by impedance, you mean the cable's total resistance, capacitance, and inductance, not for high frequencies.
If the signal frequency wavelength is much longer than the cable length, then it will see this total impedance.

The characteristic impedance is only seen for fast rise pulses or frequencies that have a wavelength approaching or shorter than the cable electrical length (as determined by the speed of signal propagation in the cable).

 

[JamesCm]

No.

The characteristic impedance is caused by the distributed capacitance and inductance of the cable (as in F and L per unit length).

When you say "per unit length", it's not "impedance per meter or inch", right?

 

[KlausST]

Hi,

no, it´s not "per meter".

There are so much good tutorials, even videos in the internet. Why don´t you use this information?
It´s available for free. And they explain such behaviour much better than we can do as written text in a forum discusssion.
Out of curiosity I did an internet search for you... and found this within a couple of seconds.

Watch the video.
Every human has a different way to learn things. Thus you may search for more suitable videos.

If there still are questions, then feel free to ask more detailed, refer to a video (link) and to a special time in the video.

Klaus

 

[JamesCm]

Oh believe me, I've seen so many videos and read so many documents online trying to understand this. Most talk about an infinite array of inductors and capacitors, and most show inductors also on the bottom segment of the line (the video you posted shows inductors only on the top segment).

But still there's doubts, for example: I see on tutorials the formula to calculate characteristic inductance as: Zo=Sqrt(L/C), with L and C being per unit length. Looking at this transmission line at your video, how do you find the inductance and capacitance per unit length? Do I measure the inductance of the entire cable and then divide by the cable's length, then measure the capacitance of the entire cable and divide by the cable's length?

 

[KlausST]

Hi,

But still there's doubts, for example: I see on tutorials the formula to calculate characteristic inductance as: Zo=Sqrt(L/C), with L and C being per unit length.

Since L is divided by C ... the true length does not matter. Use 1meter, use 1 inch, use 1 foot --> the ratio will alwys be the same.
And that´s what it is: it´s independent of length.

Do I measure the inductance of the entire cable and then divide by the cable's length, then measure the capacitance of the entire cable and divide by the cable's length?

... it does not matter. See above. or do some calculations with different length. The ratio will always be the same.

Klaus

 

[JamesCm]

Hmmm... now I understand it! Thanks very much!

But just to make it absolutely clear:

1) The inductance (L) and capacitance (C) per unit length of an entire cable can indeed be obtained by measuring the inductance and capacitance of that entire cable and then dividing it by the cable's length?

2) If I cut that same cable in half and measure again the entire inductance (L) and capacitance (C) of one of the halves, then apply those new L and C values to the characteristic impedance formula Zo=Sqrt(L/C), I'll get the same Zo value as if I used the L and C values from the entire cable from question #1 above?

And yes, the unit used for length (meters, inch, etc) doesn't matter since we'll divide L by C.

 

[betwixt]

Correct!

Brian.

 

[FvM]

Due to the fact that L' and C' are frequency dependend, cable and PCB transmission line impedance is preferably measured with TDR instruments or simulated TDR of modern network analyzers.

 

[JamesCm]

Due to the fact that L' and C' are frequency dependend, cable and PCB transmission line impedance is preferably measured with TDR instruments or simulated TDR of modern network analyzers.

What I read is that characteristic impedance is very hard to measure, and is only measured with expensive instruments. Is that true?

It does seen kinda simple: measure the capacitance of the cable (charge it with constant current, then discharge it with constant current), and measure the inductance (knowing the capacitance, apply a sine wave to the cable and measure the phase shift between V and I), then calculate L knowing C already. And yes, you'd need the length of the cable.

Am I thinking right?