Resistors in high-speed I/O trace when impendance mismatching

Question

I am little bit confused over impedance matching when dealing with high-speed digital I/Os. I would like to share some perspectives in hope to clarify a few things.

Let's consider a digital output with a known impedance Zt=50 Ohm. If the transmission line (PCB trace) is designed with Z0=50 Ohm, then there are no ringing/reflection phenomena, beside the expected one.

Now, let's say that Z0=80 ohm. In that case, a series R of 30 Ohm is placed in the trace, and here my confusion begins. What exactly happens? By reading material, I have gained two perspectives, of which either one is wrong or both are wrong and I have completely missed the points.

• Perspective 1: By applying a 30 Ohm R, then there is a correct termination because Ztt = Zt+ 30 =80 Ohm, which matches trace impedance.

But then, I question myself, why the 30 Ohm add to Zt and mitigate the problem, and not add up to Z0, and further amplify the problem? What's the difference of having a trace with Z0=110 ohm and a trace with Z0=80 Ohm plus a 30 Ohm series resistor? Also, with that logic, the series R should be placed as close to the output pin as possible, whereas I have see designs that place it in the middle or even at the end of the trace, next to the input pin.

• Perspective 2: By applying a 30 Ohm R, you limit the output current, thus increasing the rise time which in turn increases the maximum conductor length before the undesired high speed phenomena affect the line.

In that perspective, the R can be place anywhere in the trace. Also, you essentially trade between rise time and max length. So, if you have a clock, let's say, with 200 MHz freq (5 ns period) and rise time of 1 ns, then it could have an impact on setup and hold times: now there is less pulse width time due the increased rise time, whereas in a correctly matched trace impedance the additional time could be used and the overall design would be limited only by the propagation speed of PCB material. Additionally, if that's the case, then a series R could be placed based on the max length desired to be achieved: if, for example, Zt=50 Ohm, Z0 = 80 Ohm and rise time is 1 ns, in that case max length is ~4.5cm, then if the trace is 4.9 cm, a R=30Ohm is more than enough, so it could be lowered to 10Ohm, thus preserving some pulse width time.

To sum up, my question essentially boils down to these:

When I am placing a series R, am I doing impedance matching, am I doing a rise time increase or have I completely misunderstood everything?

Answer 1

By applying a 30 Ohm R, then there is a correct termination because Ztt = Zt+ 30 =80 Ohm, which matches trace impedance.

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why the 30 Ohm add to Zt and mitigate the problem, and not add up to Z0, and further amplify the problem? What's the difference of having a trace with Z0=110 ohm and a trace with Z0=80 Ohm plus a 30 Ohm series resistor?

This is called "source series termination". You allow a reflection due to the mismatch at the load end of the line, but there are no multiple reflections because when the reflection returns to the source end it sees a matched termination so that it is fully absorbed at the source (the source itself and the added series termination resistor).

This is often done when the source is a digital driver with low output impedance. In that case the termination resistor value will be approximately equal or just a bit less than the transmission line \$Z_0\$.

By applying a 30 Ohm R, you limit the output current, thus increasing the rise time which in turn increases the maximum conductor length before the undesired high speed phenomena affect the line.

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In that perspective, the R can be place anywhere in the trace.

You should still place the resistor near the source. If you place the resistor in the middle of the trace you will have several sets of multiple reflections in different parts of the line (before and after the resistor). You could do a careful analysis and possibly come up with an ideal resistor value for this scenario that produces acceptable reflections, but it would be easier to just put the resistor near the source.

So, if you have a clock, let's say, with 200 MHz freq (5 ns period) and rise time of 1 ns, then it could have an impact on setup and hold times: now there is less pulse width time due the increased rise time, whereas in a correctly matched trace impedance the additional time could be used and the overall design would be limited only by the propagation speed of PCB material.

You are correct. Both solutions (source series termination or rise-time restriction) are second-best solutions compared to just using a trace with matched \$Z_0\$.

When I am placing a series R, am I doing impedance matching, am I doing a rise time increase or have I completely misunderstood everything?

You are doing impedance matching (sort-of).

Thinking of it as increasing the rise time is an approximate analysis that will be accurate enough for most designs if the trace length is not too long. (Say, for cases where \$\ell < \lambda/2\$, where \$\lambda\$ is the characteristic wavelength associated with the rise and fall times of the signal)