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Rule of thumb: Frequency of S21 dip in microstrip

02 Feb 2015  | Eric Bogatin

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In this case, WD is the wiring delay, which is 1/speed for each of the signals. It is in ns/inch. The only way to know this is by calculating with a 2D field solver that takes into account the relative electric field distribution for the odd and even modes.

The frequency at which the dip will occur is when this time delay difference is half a cycle. This means that the time delay of a complete cycle would be 2 × DT. This allows us to estimate the frequency of the dip:

The measured example above was for a tightly coupled microstrip differential pair in FR4 of 50Ω. It was 4 inches long. We would expect the dip frequency to be 50 GHz/4 = 12.5 GHz. We measured it as about 12.8 GHz.

We also see that as the coupled length increases, the frequency of the dip decreases. However, it is not a physical resonance. The frequency of the dip also depends on the coupling. The smaller the coupling, the smaller the difference in the wiring delays between the differential and common signals. The smaller the difference, the higher the dip frequency.

Now you try it:

1. A tightly coupled microstrip differential pair is 10 inches long. At what frequency would you expect to see a sharp dip in the insertion loss?

2. Suppose the lines were loosely coupled: would you expect the dip frequency to be higher or lower than the estimate above?

About the author
Eric Bogatin is Signal Integrity Evangelist at Teledyne LeCroy.

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