# Gain factor in real Resistance and Reactance (AD5933)

I'm trying to develop a system for bioimpedance measurement with the IC AD5933.

The AD5933 is a high precision impedance converter system that combines a frequency generator with a 12-bit, 1 MSPS, Analog-to-Digital converter. The frequency generator allows an external complex impedance to be excited with a known frequency. The signal in response from the impedance is sampled by the on -board ADC and a discrete Fourier transform (DFT) is done by an on-board DSP engine.

The DFT algorithm returns both a real (R) and imaginary (I) data-word at each frequency point along the sweep. The impedance magnitude and phase are easily calculated using equations. To convert this number into impedance, it must be multiplied by a scaling factor called the gain factor. The gain factor is calculated during the calibration of the system with a known impedance connected between the VOUT and VIN pins. The measured impedance at the frequency point is given by:

My problem is that I need to use only the real (Resistance) and imaginary (Reactance) information, rather than the Impedance Magnitude.

Because the equations of body composition require, for example: So, my question is: How do I apply the gain factor only in real (Resistance) and imaginary (Reactance) values?

Tks!

If you do the math with real numbers you should see it comes to the same final number.

Sorry, but I didn't understand.

For example, in the Datasheet of the AD5933 there is the following example:

Gain Factor = 515,819 x 10 ^ (-12)

Real data register = -1473

Imaginary data register = 3507

So, the Magnitude of the impedance is: 3802,863

Then, applying the gain factor, the correct Magnitude of the impedance is: 509,791 k

. My point is:

If I just multiply the values of the registers -1473 and 3507 with the gain factor (515,819 x 10 ^ (-12)), and calculate the correct Magnitude of the Impedance: I can't get the correct impedance value, which was previously calculated 509,791 k.

• Your numbers don't add (or multiply) up - how can 3803 multiplied by 515.6E-9 equal 510 kohms? – Andy aka Aug 5 '17 at 18:29
• @Andyaka If I understand well, if I multiply the values of the registers -1473 and 3507 with the gain factor, I will get the resistance and reactance values corrected, right? So, with the values corrected and re-calculating the magnitude, I should get the value of the corrected impedance, that is, the value discovered by applying the gain factor: 509,791 k. – Dyarlen Aug 5 '17 at 19:44
• Yes you should but I think you need to look at your multiplication i.e. take note of my comment above. – Andy aka Aug 5 '17 at 20:01
• @Andyaka My calculations are correct, but if I divide by 1 the result of the magnitude obtained with the corrected Real and Imaginary values (1 / Magnitude), I will get the correct Impedance value 509.791 k. This is correct? Why? – Dyarlen Aug 6 '17 at 1:06

How do I apply the gain factor only in real (Resistance) and imaginary (Reactance) values?

Quite simply, you multiply the real value that is returned by the DFT with the gain factor that was calculated during calibration. If you do the math with real numbers you should see it comes to the same final number.

• "If you do the math with real numbers you should see it comes to the same final number." I didn't understand. I explained it better below. – Dyarlen Aug 5 '17 at 18:20