How Can Transmission Lines Be Modeled and Matched?

[likephysics]

I have two questions about Tx lines

1. Can we think of the Tx line in terms of just LC ladder. If yes, why can't this be thought of as a LC filter. In that case, the tx line would be a low pass filter. Increasing C would make the cut off freq even lower.

2. If I don't terminate at the load and have a high impedance load, then I would see 2x the incident voltage at the load. If there is undershoot/overshoot, can I use a stub to eliminate this?
I am aware of the stub matching, smith chart etc. I am unable to apply this technique to PC board.
What I did in class was rotate towards generator/load and place the stub at a point along the tx line. How do I apply that here!?

 

[Bob S]

See telegrapher's equations in

http://en.wikipedia.org/wiki/Transmission_line

Transmissions lines are broad band, non-resonant lines, unless the termination does not match the characteristic impedance, Z₀ = sqrt(L/C). The signal velocity is determined by the dielectric constant of the dielectric. Increasing C just reduces Z₀. Increasing C will increase skin effect losses at high frequencies, because the ratio of voltage over current is decreased (V/I = Z₀)..

Open or shorted stubs will make the transmission line characteristics frequency dependent. I have used shorted stubs as a termination to clip (shorten) fast pulses (e.g., from 10 ns to 2 ns). In this case, the source impedance should be Z₀ to absorb the reflected pulse.

Bob S

 

[jsgruszynski]

I have two questions about Tx lines

1. Can we think of the Tx line in terms of just LC ladder. If yes, why can't this be thought of as a LC filter. In that case, the tx line would be a low pass filter. Increasing C would make the cut off freq even lower.

You can. But remember LC ladders are Lumped Equivalent model while transmission liens are Distributed model. The boundary between when you have to use one or the other is when the wavelength is within 10x of the physical dimensions of the circuit.

2. If I don't terminate at the load and have a high impedance load, then I would see 2x the incident voltage at the load.
If there is undershoot/overshoot, can I use a stub to eliminate this?
I am aware of the stub matching, smith chart etc. I am unable to apply this technique to PC board.
What I did in class was rotate towards generator/load and place the stub at a point along the tx line. How do I apply that here!?

You have to match the transmission line termination or you'll see reflected power. You mention undershoot/overshoot so you are talking about pulses. Reflections are another way of describing why you get these.

Strictly all of the Distributed model concepts and tools like s-parameters and Smith charts presume a single frequency. Pulses imply multiple frequencies (the Fourier components of the pulse).

For this reason you need to do your analysis with enough components. The rule of thumb is 10x the rise/fall time is required for equivalent transmission line bandwidth. So you need to think about the termination (and flatness of match) up to that frequency.

So since stubbing in the Distributed model is akin to adding an in-line filter, and with that you can flatten your mismatch (Lumped model filters can be thought of as "matching networks" for Distributed model), then yes, in principle you can. It may not be that easy - there are physical constraints of filter implementation.

You can use a Smith chart to do that but you 1) have to do each frequency of interest and 2) have to make some assumptions about the frequency response of your load; a Smith chart assume ideal Lumped terminations are present. Which at high enough frequencies may need explicit measurement confirmation - 50 ohm resistive loads are seldom such at high enough frequency. And if your load is an active device it get real fun because it's not even linear anymore.

 

[likephysics]

Hi Guys, thanks for the reply.
ppl around me think of the strip line as a PCB trace having capacitance. So wider trace = more capacitance.
Is that the right way?
I am thinking in terms of transmission line impedance and trying to match the strip line impedance with the source impedance, which is very low(15ohms).
Would a wider trace really reduce the rise time of a signal.

How can I reduce the overshoots in high speed digital circuits. I cannot match on both sides(source+load).

This is something like a PCI bus on a motherboard. They don't use termination, they use reflected wave switching. So cannot terminate at the load.

 

[JimmyAlz]

If you google AppCad you will find a free RF design package with calculators for different transmission lines.

 

[likephysics]

Thanks for the appcad suggestion.
My question was can you think of transmission line as a Capacitor.
If I make a strip line trace thicker, trace capacitance increases. So the driver should charge a higher value capacitor.
Is it the correct way or should I stick to impedance matching of driver impedance to trace impedance without worrying about the trace capacitance.

 

[sophiecentaur]

A short length of line can behave as a capacitor but lengthening the line will alter that. A quarter wavelength, open-circuited at the end, will look like a short circuit and various lengths can look inductive or capacitive. If the line is terminated with its characteristic impedance then it will behave as if it's not there (/ of zero length) and the input to the line is that impedance (just resistive).

 

[likephysics]

A short length of line can behave as a capacitor but lengthening the line will alter that. A quarter wavelength, open-circuited at the end, will look like a short circuit and various lengths can look inductive or capacitive. If the line is terminated with its characteristic impedance then it will behave as if it's not there (/ of zero length) and the input to the line is that impedance (just resistive).

How much is short length?

 

[sophiecentaur]

Fair enough question!

I mean an open circuited line, much shorter than one wavelength - say up to an eighth of a wavelength. If it's correctly terminated, it just looks like a resistance, however long it is.
You really have to read up on some actual transmission line theory - it isn't a very intuitive business. Google is full of the stuff. Go and find something that is approachable for you, personally - it's in there at all levels.

 

[likephysics]

I actually know transmission line theory. Not an expert, but enough to do impedance matching, smith chart etc. But I need some help in convincing people around me that you cannot think of tx line as a capacitor.
Is the criteria same as in the case of when you need to be concerned about reflections. I use wavelength/10.

At high frequencies tx line is just resistive. I can't convince this to people without EM background. I need some graph which shows frequency behavior of a coax cable or a transmission line.

 

[Bob S]

Here is a comprehensive lecture on transmission line theory (click on Full Screen to view):

http://www.docstoc.com/docs/12213145/Transmission-Line-Theory

It includes the ladder network equations (telegrapher's equations) to develop the transmission line characteristics (impedance and signal velocity), skin effect (proportional to √f) and dielectric (proportional to f) losses, effects of load mismatches, reflections, open and shorted stubs, Smith charts, stub matching (single frequency) etc.

Bob S

 

[sophiecentaur]

At high frequencies tx line is just resistive. I can't convince this to people without EM background. I need some graph which shows frequency behavior of a coax cable or a transmission line.

There is a limit to how simple an explanation can be given about the action of a transmission line. If these people can't be convinced then wave a Smith Chart at them, show them what it tells you and let them argue with that - it will show exactly what you want to tell them. We can't expect everything to be intuitive can we? Why demand 'Noddy' explanations for things that are just not 'noddy'?