# Electrical – Gain factor in real Resistance and Reactance (AD5933)

fftfourierimpedancereactanceresistance

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.