Getting time domain current from impedance and voltage measurement?

  1. I'm working on a high power multi-phase DC/DC converter where the load current has some fast transients. We can easily measure the output voltage in the time domain, and also measure the power distribution network impedance in the frequency domain.

    So, I think I would try converting the time-domain output voltage to frequency-domain, and then do I = V/Z. Now I'm a little confused, because in the frequency domain, does this mean I should convolve V with 1/Z? After getting the frequency-domain current, then I'll convert this back into time-domain with ifft.

    Or can anyone suggest any other methods to measure the current using another method? This is possibly in the 0-100A range going through tons of BGA balls so I don't think I can measure it directly.
  2. jcsd
  3. berkeman

    Staff: Mentor

    I would suggest putting a 0.1 Ohm precision resistor in series with the output of the power supply, and digitizing the differential voltage drop across the resistor along with the input voltage to the resistor. That should give you what you need.
  4. Can't do that, the power supply is 1V and the load is almost 100A. The power trace is an entire internal plane to minimize I^2 R loss, so I think the only way to measure the current is indirectly.
  5. berkeman

    Staff: Mentor

    Nope. Next choice is using a Hall Effect current probe:

    Can you rent one of those?
  6. Yeah, but I can only measure the input current into the switcher, and that's not useful for getting transient data. The actual load is a BGA chip so I can't use a current probe directly.
  7. berkeman

    Staff: Mentor

    The switcher feeds the plane with the BGA contacts. There is an output from the switcher. Is it a buck or multiple bucks? Clamp the output inductors...
  8. It could be okay to just divide the values of the frequency components of voltage by the value of the impedance at that frequency, and then perform the inverse transform to get current. This should be done element-wise in the frequency domain and not by using convolution.

    You may think of the time domain voltage signal source as of as a number of sinusoidal voltage sources in series, with amplitude and phase that may be determined by the DFT of the measured voltage. The theoretical time domain current at the input to the network could be found by superposition, by adding the currents through the load from each of the voltage sources.

    There are elements for negative frequencies in the vector that results from the FFT, though.

    Perhaps something like this:

    1. Divide the elements for zero and positive frequencies by the corresponding impedance at that frequency.
    2. In the resulting (transformed current) vector, set the elements for negative frequencies equal to the complex conjurgate of the corresponding positive frequency.
    3. Perform the inverse transform.
    Last edited: Jun 4, 2011
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