AD5934 Datasheet, PDF (14/32 Pages) Analog Devices – 250 kSPS, 12-Bit Impedance Converter, Network Analyzer

AD5934
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 = R² + I²
where R is the real number stored at Register Address 94 h and
Register Address 95 h and I is the imaginary number stored at
Register Address 96 h and Register Address 97 h.
For example, assume the results in the real and imaginary registers
are as follows at a frequency point:
Real register: = 038B hex = 907 decimal
Imaginary register: = 0204 hex = 516 decimal
Magnitude = (907² + 516²) = 1043.506
To convert this number into an 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 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 these
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 and imaginary register after a
frequency point conversion would be
Real register: = F9C hex = -3996 decimal
Imaginary register: = 227E hex = 8830 decimal
Magnitude = (−3996² + (8830)² = 9692.106
GAIN
FACTOR
= ⎜⎛
ADMITTANCE
⎟⎞ =
⎜⎜⎝⎛
1
Impedance
⎟⎟⎠⎞
⎝
Code
⎠ Magnitude
GAIN
FACTOR
=
⎜⎛
⎜
⎜
⎜
1
200 kΩ
9692 .106
⎟⎞
⎟
⎟
⎟
=
515 .819
E
−
12
⎝
⎠
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 and imaginary registers contain the
following data:
Real register: = 0AEB hex = −1473 decimal
Imaginary register: = 0DB3 hex = 3507 decimal
Magnitude = ((−1473)² + (3507)²) = 3802.863
Then the measured impedance at the frequency point is given by
Impedance =
1
GAIN FACTOR × Magnitude
=
1
Ω
515.819273 E − 12 × 3802.863
= 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 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
101.0
VDD = 3.3V
CALIBRATION FREQUENCY = 60kHz
T_A = 25°C
MEASURED CALIBRATION IMPEDANCE = 100kΩ
100.5
100.0
99.5
99.0
98.5
54
56
58
60
62
64
66
FREQUENCY (kHz)
Figure 18. Impedance Profile Using a Single-Point Gain Factor Calculation
Rev. 0 | Page 14 of 32