[SI-LIST] Re: From spectrum of i(t) to spectrum of d(i(t))/dt
- From: "Andrew Ingraham" <a.ingraham@xxxxxxxx>
- To: "si-list" <si-list@xxxxxxxxxxxxx>
- Date: Fri, 18 May 2007 15:45:33 -0400
> I have some questions on the spectrum translation. Recently, I measured
> the spectrum of power supply current i(t) ( very long time range ) with
> current probes, then I would like to transfer it to the spectrum of di/dt. I
> know thoeretically F( di(t)/dt ) = j w F ( i(t) ). My question is : Does it
> mean at every frequency point, the spectrum level is multiplied by the
> corresponding frequency for di/dt signal ? If this is the case, the I end
> up with quite large spectrum value in di/dt which is definitly not
> reasonable. For instance, at 1 GHz, the spectrum level is increase by 180
> dB. I am quite confused about this. Is my derivation wrong ?
Yes, it is correct; no your calculation is not wrong.
Take care of your units! When you differentiate amperes, the result is not in
amperes. The spectrum contribution at 1 GHz doesn't increase by 180 dB
because that would be "comparing apples to oranges," even though the raw
(unit-less) numbers might happen to be that way.
Andy
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