Re: Transformation from TDR to FDR
Here is an example in which I measured the TDR reflection signal (7S12/S-52/S-6) *and* the reflection coefficient at several distinct frequencies:
pictures LCR_TDR.png and LCR_FDR.png .
For the FDR measurement I used my GR 1602-B Admittance Meter. As a DUT I soldered a parallel LC circuit in series with an R in a Pomona box with BNC connector. R = 50 Ohm deliberately chosen such that the TDR reflection would be a (smooth) curve starting at zero and damping to zero again as time elapses. C = 47 pF, L was a small air coil of a few turns of copper wire. So in this example I can compare the transformed TDR data directly with the observed FDR data from the 1602.
I would say the correspondence in LCR_FDR.png appears to be quite good.
Most surprising perhaps is that the real DUT curves drift up at higher frequencies, contrary to expectation if the DUT behaves as an ideal LCR circuit. Also the real DUT shows a rather steep drop after the resonance peak. For comparison, the curve labeled "Ideal LCR" is the theoretical reflection curve of an ideal LCR circuit, with component values R = 50 Ohm and L and C chosen by eye for best correspondence with the observed TDR reflection curve. The resonance frequency is about 87 MHz.
To a large extend the deviaton from ideal is due to the "spike" in the original TDR record. When I "photoshop" the spike away then there is much better resemblance between transformed TDR curve and Ideal LCR curve; the transformed TDR returns to about zero at higher frequencies and the steep drop gets somewhat less steep. The spike is probably caused by component lead inductions and/or geometry changes at the BNC connector. Though the spike width is less than 1 ns, its effects are felt already at relatively low frequencies.