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AD5934 Datasheet(PDF) 15 Page  Analog Devices 

AD5934 Datasheet(HTML) 15 Page  Analog Devices 
15 / 31 page Data Sheet AD5934 Rev. E  Page 15 of 31 IMPEDANCE CALCULATION MAGNITUDE CALCULATION The first step in the impedance calculation for each frequency point is to calculate the magnitude of the DFT at that point. The DFT magnitude is given by 2 2 I R Magnitude + = where: R is the real number stored at Register Address 0x94 and Register Address 0x95. I is the imaginary number stored at Register Address 0x96 and Register Address 0x97. 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 1043.506 ) 516 (907 2 2 = + = Magnitude 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. Once the gain factor is 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 these assumptions: Output excitation voltage = 2 V pp Calibration impedance value, ZCALIBRATION = 200 kΩ PGA gain = ×1 Currenttovoltage amplifier gain resistor = 200 kΩ Calibration frequency = 30 kHz The typical contents of the real data and imaginary data registers after a frequency point conversion would then be Real Data Register = 0xF064 = −3996 decimal Imaginary Data Register = 0x227E = +8830 decimal ( ) 106 . 9692 ) 8830 ( 3996 2 2 = + − = Magnitude Magnitude Impedance 1 Code Admittance Factor Gain = = 12 10 819 . 515 106 . 9692 kΩ 200 1 − × = = 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 is 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 3802.863 ) (3507) 1473) (( 2 2 = + − = Magnitude The measured impedance at the frequency point is then given by Magnitude Factor Gain Impedance × = 1 Ω 3802.863 10 515.819273 1 12 × × = − = 509.791 kΩ GAIN FACTOR VARIATION WITH FREQUENCY Because the AD5934 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 18 shows an impedance profile based on a singlepoint 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 54 66 FREQUENCY (kHz) 101.0 100.5 100.0 99.5 99.0 56 58 60 62 64 VDD = 3.3V CALIBRATION FREQUENCY = 60kHz TA = 25°C MEASURED CALIBRATION IMPEDANCE = 100kΩ Figure 18. Impedance Profile Using a SinglePoint Gain Factor Calculation 
