# AD5933 gain factor and impedance calculation

Question asked by andrewbourhis on Aug 31, 2017
Latest reply on Sep 1, 2017 by Snorlax

Hello,

I am looking to use the AD5933 in a portable network analyzer application and am confused on a couple of things. Referring to the user guide for the eval board (UG-364), Figure 1 shows an analog front-end using the AD8606 opamp. I am curious about a couple things here. For your reference, I plan to use two multiplexers to allow for 16 impedances to be connected in place of Z_unknown and 4 devices to be connected in place of Rfb. I am trying to figure out a couple of things and was hoping to get some advice/insight if possible! Thanks in advanced for your help.

1. My first question pertains to calculating the impedance. I understand that this device takes a 1024 point DFT at the excitation frequency of the analog signal and then places the result of this calculation in the real and imaginary registers.  The datasheet says that the result of this calculation is the power in the signal at the excitation frequency. Maybe I am confused, but it was my understanding that you need to square the absolute value of the DFT to get an estimate of power? Nevertheless, if we accept that the result of this DFT is the power at the excitation frequency, then I am confused on how we are able to obtain impedance from this? The answer seems to be that we calculate impedance using the gain factor, which leads to my second question.

2. What the heck is this gain factor term and where did it come from? I understand it may be a number that accounts for device nonlinearity, unit conversion, and impedance offsets. Could you please clarify what exactly this number represents and describe the mathematics that lead us from the DFT of our signal at the excitation frequency to the impedance of Z_unknown? The datasheet does not go beyond stating that a simple scalar value converts this DFT calculation into a measure of impedance, but I am not why this works exactly. Perhaps including units in these values would help clarify?

3. My last question is regarding Figure 1 of the user guide again. The analog front-end uses the AD8606 opamp which seems to have fairly low output impedance for the frequency range used in the AD5933. I am trying to figure out the lowest Z_unknown I can measure accurately with this setup and was hoping someone could validate my thinking here: If I choose the excitation amplitude range to be 0.2 Vp-p and use Rfb = 100 ohms, I think I should be able to measure down to ~6 ohms (with Vdd = 3.3v) and still be within the linear region of the internal ADC. Disregarding the fact that the multiplexers will likely introduce impedances that significantly offset the measurements, I am concerned that using such low resistors in the feedback loop of the second op-amp will draw too much current.

Any advice or insight into these three questions would be greatly appreciated!

Thank you,

Andrew