To measure the characteristic impedance of a pc-board trace, most engineers use a TDR (time-domain reflectometer). Connect the instrument to a long, unterminated trace, and it blasts into the trace one very quick, precise rising edge. By analyzing the signal that reflects back from the trace, you can deduce the trace impedance. Some instruments provide averaging capabilities to help reduce the noise floor during particularly fast measurements.
In the usual setup, a TDR instrument uses only the first few nanoseconds of your reflected signal. After the initial step edge propagates to the far end of the unterminated trace, it bounces and returns to the instrument, corrupting further readings of characteristic impedance. Figure 1 illustrates the typical result. The top curve (TDR, in red) illustrates the signal you typically observe at the front end of a pc-board trace. This plot displays the initial TDR step (first edge) and the signal that reflects from the far end of the trace (second edge).
You calculate the lower plot (blue, offset below for visual clarity) from the TDR plot. It is the step response of the S-parameter function, S11. The S11 step response shows only the signal reflected from the trace, in the absence of the outgoing signal. (Subtracting a half-sized step and then doubling the result accomplishes this conversion.)
The S11 step response displays a pedestal, from whose amplitude you may deduce the effective trace impedance over a scale of time of 1 nsec or so. After the pedestal, this S11 step response also displays a gentle upward tilt. The tilt is the hallmark of a trace marred by significant amounts of skin-effect loss.
Engineers usually consider the second edge the end of usable data in a TDR waveform. Even though the latter stages of the waveform contain a wealth of information about trace loss and impedance, these details are hidden from view—unless you learn to see beyond that second edge.
Here is the catch: You must make two measurements, not one. Make the first measurement as usual, with the trace open-circuited at the far end. Make the second measurement with the trace shorted to ground at the far end. Then, convert both measurements to the frequency domain using an FFT.
Next, convert each of your TDR results to S11 form using:
From the two S11 functions now in your possession and from knowledge of the source impedance, ZS(f), of your TDR tester (usually 50 Ω), you may now calculate the characteristic impedance, ZC(f), of your pc-board trace. This calculation works at extended frequencies corresponding to the full length of the waveform you capture and is not limited by the reflection time of your TDR-test coupon:
This clever frequency-domain technique derives from procedures that engineers commonly use to calibrate the SMA cables you use with a network analyzer.