Electronic – A transmission line with continuously varying impedance, how would reflection occur in this case

characteristic-impedancetransmission line

Alright folks here it is, another transmission line question that has been bothering me. I understand the case where there is an abrupt change in impedance along a transmission line that leads to reflection of portion (or even all) of the signal.

Now, what is bothering me for a while is the case where we have a transmission line who's impedance varies in a predictable manner over its length. Lets suppose that we have a PCB trace who's characteristic impedance depends on it's width as per physics. Now suppose that this width is increasing linearly as the signal travels on it which leads to a continuosly linear change in it's impedance. I expect that signal would be reflected in this case too but continuously! But what I cannot imagine is how would the reflection look like in this case on the transmitting end and what the signal would look like on the receiving end. Besides this, how can one mitigate this type of impedance mismatch, I suppose that getting the correct receiver termination would be tricky in this case. hmmmmmmm…

Best Answer

Continuous varying impedances are used all the time for impedance matching. If you have a very capacitive part of a trace (for example, where a large component pad might be), you can have a relatively inductive transition before or after it to "balance" it out.

What will end up happening is that the reflections will "stack up" but, instead of being at one point (a VSWR peak), it will be moderately spread out. You can still imagine it discretely, but in small steps.

And also remember, if you have a small reflection point, any backward reflection after THAT will be reflected slightly FORWARD, and so on.

Anyway, the good gents at http://www.microwaves101.com/encyclopedia/klopfenstein.cfm always have a nice, in depth explanation.

edit: I didn't completely answer your question. "How it would look" is dependent a bit on how you are describing it. In the frequency domain, what you'll probably get is a VSWR that is "de-Q'd". You'll go from a nice sharp peak at midband to a more gradual, broader band response.

In the time domain....well, I don't work with the time domain as much but I would imagine you would have a lower amplitude, longer pulsewidth "ringing" or reflection.