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Data Sheet

AD5933

Rev. E | Page 17 of 40

IMPEDANCE CALCULATION

MAGNITUDE CALCULATION

The first step in impedance calculation for each frequency point

is to calculate the magnitude of the DFT at that point.

The DFT magnitude is given by

Magnitude

where:

R is the real number stored at Register Address 0x94 and

I is the imaginary number stored at Register Address 0x96 and

For example, assume the results in the real data and imaginary

data registers are as follows at a frequency point:

Real data register = 0x038B = 907 decimal

Imaginary data register = 0x0204 = 516 decimal

506

1043

)

516

907

(

Magnitude

To convert this number into impedance, it must be multiplied

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.

Once the gain factor has been calculated, it can be used in the

calculation of any unknown impedance between the VOUT and

VIN pins.

GAIN FACTOR CALCULATION

An example of a gain factor calculation follows, with the

following assumptions:

Output excitation voltage = 2 V p-p

Calibration impedance value, ZCALIBRATION = 200 kΩ

PGA Gain = ×1

Current-to-voltage amplifier gain resistor = 200 kΩ

Calibration frequency = 30 kHz

Then typical contents of the real data and imaginary data

registers after a frequency point conversion are:

Real data register = 0xF064 = −3996 decimal

Imaginary data register = 0x227E = +8830 decimal

106

9692

)

8830

(

)

3996

(

−

Magnitude

Impedance

Code

Admittance

Factor

Gain

























515.819

106

9692

200













Ω

Factor

Gain

IMPEDANCE CALCULATION USING GAIN FACTOR

The next example illustrates how the calculated gain factor

derived previously is used to measure an unknown impedance.

For this example, assume that the unknown impedance = 510

kΩ.

After measuring the unknown impedance at a frequency of

30 kHz, assume that the real data and imaginary data registers

contain the following data:

Real data register = 0xFA3F = −1473 decimal

Imaginary data register = 0x0DB3 = +3507 decimal

863

3802

)

3507

(

)

1473

((

−

Magnitude

Then the measured impedance at the frequency point is given

Impedance

Magnitude

Factor

Gain

Ω

−

791

509

863

3802

819273

515

GAIN FACTOR VARIATION WITH FREQUENCY

Because the AD5933 has a finite frequency response, the gain

factor also shows a variation with frequency. This variation in

gain factor results in an error in the impedance calculation over

a frequency range. Figure 22 shows an impedance profile based

on a single-point gain factor calculation. To minimize this error,

the frequency sweep should be limited to as small a frequency

range as possible.

101.5

98.5

FREQUENCY (kHz)

101.0

100.5

100.0

99.5

99.0

VDD = 3.3V

CALIBRATION FREQUENCY = 60kHz

TA = 25°C

MEASURED CALIBRATION IMPEDANCE = 100k

Ω

Figure 22. Impedance Profile Using a Single-Point Gain Factor Calculation

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