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Rule of thumb: Frequency of S21 dip in microstrip

02 Feb 2015  | Eric Bogatin

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In every measurement of the single ended insertion loss of a microstrip differential pair, there is a sharp dip. This is a natural feature of all microstrips. It is not a resonance, but related to far end cross talk. Here's how you can estimate at what frequency you expect to see it.

Spoiler summary: When you measure the single-ended insertion loss of a tightly coupled microstrip differential pair, the frequency of the dip is roughly: f = 50 GHz/Len[in].

When you measure the 4-port S-parameters of a tightly coupled microstrip differential pair, you always see a sharp dip in S21. An example is shown in the figure.

What could possibly be causing this dip? Your first thought is that it is due to some sort of resonance, or maybe there is a stub in the circuit you hadn't noticed. Both of these explanations are wrong.

When we drive one line in the differential pair with a single-ended signal, we can describe the signal as a combination of a differential and common signal component, each exactly in phase at the source. The differential and common components on line 1 add at the source, while the differential and common components of the signal on line 2 subtract and cancel out to zero. The resulting signal looks like a single-ended signal on line 1.

If the differential and common signals propagate down the line at the same speed, the single-ended signal will always look like a single ended signal. But, if the differential signal travels a little faster than the common signal, after some distance traveling down the line, the differential and common signals will be shifted exactly 180° out of phase.

When they are out of phase, they will now subtract and cancel out on line 1, and add on line 2. This looks like all the energy on line 1 has now coupled to line 2. The S21 insertion loss will be a tiny signal, or a large, negative value in decibels.

If we can estimate the frequency of the dip, based on this root cause, we can use it in debugging a problem. If our estimate of the dip frequency matches the measured dip, this is strong evidence we have the root cause. Using this rule of thumb, we can anticipate where the dip frequency might be, and it will not be a mystery.

At the end of the line, the difference in time delay between the arrival of the differential and common signal is:

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