Jim Wilkins wrote:
On Feb 16, 10:38 am, wrote:

(...)

Right, but this isn't a 'pure' DC circuit.

By mentioning 'impedance' instead of just ESR, I hoped to remind us
that the current waveform into the battery is dependent on
it's Equivalent Series Resistance *as well as* how it 'looks'
to the pulses of D.C. from the rectifier, in the frequency domain.

See for example, Table 1 of:http://www.telepower.com.au/INT95b.PDF

Interesting.

The test I've seen and done for battery impedance is to measure the
voltage at a steady low-level current, then pulse on a higher load and
capture the voltage and current waveforms on a digital storage scope.
The impedance is the slope of the line between the low and high
current V and I, at a place on the waveform chosen by the battery
engineer.

Note how Hawkins and Barling used a one-step process
for each frequency of interest with their very low impedance
measuring circuit.

http://www.telepower.com.au/INT95b.PDF
By forcing a small, levelled, alternating broadband current
through the battery, they measured the resulting voltage
between 5 milli-Hz to 100 Hz in order to arrive at an
impedance reading, calculated by an attached PC.
They went on to measure impedance above 10 Hz (to 100 KHz)
using current-levelled sinewave excitation.

Impedance scaled directly with the voltage - to - current
ratio at any given frequency. Because current was known and
held constant, Z was directly proportional to V. Kewl!

The higher frequency effects which are relevant to PWM motor
drivers are easily removed with capacitors.

The low frequency impedance (mostly resistance) is a good
measure of the condition of the battery.

Abso-tively.

--Winston