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## AD5934 Datasheet(HTML) 15 Page - Analog Devices

 15 / 31 page Data SheetAD5934Rev. E | Page 15 of 31IMPEDANCE CALCULATIONMAGNITUDE CALCULATIONThe first step in the impedance calculation for each frequencypoint is to calculate the magnitude of the DFT at that point.The DFT magnitude is given by22IRMagnitude+=where:R is the real number stored at Register Address 0x94 andRegister Address 0x95.I is the imaginary number stored at Register Address 0x96 andRegister Address 0x97.For example, assume the results in the real data and imaginarydata registers are as follows at a frequency point:Real Data Register = 0x038B = 907 decimalImaginary Data Register = 0x0204 = 516 decimal1043.506)516(90722=+=MagnitudeTo convert this number into impedance, it must be multipliedby a scaling factor called the gain factor. The gain factor iscalculated during the calibration of the system with a knownimpedance connected between the VOUT and VIN pins.Once the gain factor is calculated, it can be used in thecalculation of any unknown impedance between the VOUT andVIN pins.GAIN FACTOR CALCULATIONAn example of a gain factor calculation follows, with theseassumptions:Output excitation voltage = 2 V p-pCalibration impedance value, ZCALIBRATION = 200 kΩPGA gain = ×1Current-to-voltage amplifier gain resistor = 200 kΩCalibration frequency = 30 kHzThe typical contents of the real data and imaginary dataregisters after a frequency point conversion would then beReal Data Register = 0xF064 = −3996 decimalImaginary Data Register = 0x227E = +8830 decimal()106.9692)8830(399622=+−=MagnitudeMagnitudeImpedance1CodeAdmittanceFactorGain==1210819.515106.9692kΩ2001−×==FactorGainIMPEDANCE CALCULATION USING GAIN FACTORThe next example illustrates how the calculated gain factorderived previously is used to measure an unknown impedance.For this example, assume that the unknown impedance is 510 kΩ.After measuring the unknown impedance at a frequency of30 kHz, assume that the real data and imaginary data registerscontain the following data:Real Data Register = 0xFA3F = −1473 decimalImaginary Data Register = 0x0DB3 = +3507 decimal3802.863)(3507)1473)((22=+−=MagnitudeThe measured impedance at the frequency point is then given byMagnitudeFactorGainImpedance×=1Ω3802.86310515.819273112 ××=−= 509.791 kΩGAIN FACTOR VARIATION WITH FREQUENCYBecause the AD5934 has a finite frequency response, the gainfactor also shows a variation with frequency. This variation ingain factor results in an error in the impedance calculation overa frequency range. Figure 18 shows an impedance profile basedon a single-point gain factor calculation. To minimize this error,the frequency sweep should be limited to as small a frequencyrange as possible.101.598.55466FREQUENCY (kHz)101.0100.5100.099.599.05658606264VDD = 3.3VCALIBRATION FREQUENCY = 60kHzTA = 25°CMEASURED CALIBRATION IMPEDANCE = 100kΩFigure 18. Impedance Profile Using a Single-Point Gain Factor Calculation