Analog Devices AD5934, Руководство пользователя, Страница: 15 / 40

AD5934
Rev. A | Page 15 of 40
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 p-p
Calibration impedance value, Z
CALIBRATION
= 200 kΩ
PGA gain = ×1
Current-to-voltage 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 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
54 66
0
532
5-
0
85
FREQUENCY (kHz)
IM
P
E
D
ANCE
(
k
Ω
)
101.0
100.5
100.0
99.5
99.0
56 58 60 62 64
VDD = 3.3V
CALIBRATION FREQUENCY = 60kHz
T
A
= 25°C
MEASURED CALIBRATION IMPEDANCE = 100k Ω
Figure 18. Impedance Profile Using a Single-Point Gain Factor Calculation