Measuring Power Ground Impedance
Dr. Johnson - thanks for your newsletter, I have just subscribed. I completely agree with the comments pertaining to power plane impedance and the 'single node' assumption below the frequency where the board resonates (Vol. 2 Issue 4). We have checked the impedance of power planes with a network analyzer. With no capacitors present, you can see interesting resonances that depend on the 1/4 wavelength from the probes to the card edge (valleys) and half wavelengths that fit into the card dimensions. But these measurements always come in dB and my spice simulations come out in ohms (after I force 1 Amp). Do you have any ideas on how t correlate between them? I would like to be able to measure the plane impedance in Ohms!
A minor point... We are looking at using HIGHer dielectric constants for the material between power planes in order to gain more decoupling capacitance. That is going to lower the resonant frequencies of the power planes, possibly into frequencies of interest (near the clock).
Thanks for your interest in High-Speed Digital Design.
When using a network analyzer to measure power and ground impedance, we drive the power and ground planes at one point on the board with a sine wave, and the measure how much voltage appears at a different point.
Don't set the IN and OUT cable attachment points on the board too close together or else their local crosstalk will pollute your measurement.
In this setup, we can relate ohms to dB if (1) we know the driving point impedance of the network analyzer test setup and (2) the network analyzer is calibrated in terms of dB gain, where 0 dB means there is no device under test connected (that is, the IN cable is directly connected to the OUT cable).
To establish this relation, we just use the resistance divider theorem:
dB gain = 20*log(Vmeasured / Vreference)
dB gain = 20*log( Rpwr-gnd / (Rpwr-gnd + Rsource) )
Where:
- Rsource is the driving point impedance of the test setup.
If your network analyzer has a 50-ohm output, and a 50-ohm input, then the driving point impedance at the device-under- test point is 25 ohms. Rsource = 25 ohms.
Now we can simplify things a little if we use the fact that, even when resonating, the power and ground planes have an impedance much less than 25 ohms (if they didn't the whole system wouldn't even come close to working). Therefore we can ignore the term Rpwr-gnd in the denominator, and just use the approximation:
dB gain = 20*log( Rpwr-gnd / Rsource )
Converting this formula to express Rpwr-gnd in terms of dB, we get:
Rpwr-gnd = Rsource *{10 (raised to the power of) [(dB gain)/20]}
Best regards,
Dr. Howard Johnson