EVAL-AD5934EB
Preliminary Technical Data
Rev. PrC | Page 20 of 32
GAIN FACTOR CALCULATION
The code in the Evaluation Board Source Code Extract section
for the impedance sweep is based on a single-point gain factor
calculation, which is determined at the midpoint sweep frequency
with a known impedance connected between VOUT and VIN.
The gain factor for this example is calculated by exciting the
calibration impedance using a 2 V p-p sinusoid with a frequency
of 30.750 kHz, a PGA setting of ×1, a 100 kΩ resistor connected
between VOUT and VIN, and a feedback resistor of 100 kΩ.
The magnitude of the real and imaginary components at the
calibration frequency is given by the formula:
2
2
I
R
Magnitude
+
=
where
R
is the real component, and
I
is the imaginary
component of the calibration code.
The gain factor is then given by
Magnitude
Magnitude
Impedance
Code
Admittance
Factor
Gain
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
=
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
=
⎟
⎠
⎞
⎜
⎝
⎛
=
kΩ
100
1
1
Refer to the
data sheet for more details.
IMPEDANCE MEASUREMENT TIPS
This section outlines some of the workarounds for using the
AD5934 to measure impedance profiles under certain conditions.
Calibrating the AD5934
When calculating the calibration term (that is, the gain factor;
see the
data sheet for further details), it is important
that the receive stage is operating in its linear region. This
requires careful selection of the system gain settings. The
system gain settings are
•
Output excitation voltage range
•
Current-to-voltage gain setting resistor
•
PGA gain
The gain through the system shown in Figure 27 is given by
Gain
PGA
Z
Resistor
Setting
Gain
Range
Voltage
Excitation
Output
UNKNOWN
×
×
V
IN
V
DD
R
FB
ADC
LPF
Z
UNKNOWN
V
OUT
CURRENT TO VOLTAGE
GAIN SETTING RESISTOR
PGA
(X1 OR X5)
0
544
9-
02
7
Figure 27. AD5934 System Voltage Gain
For example, assume the following system calibration settings:
VDD = 3.3 V
Gain setting resistor = 200 kΩ
Z
UNKNOWN
= 200 kΩ
PGA setting = ×1
Range 1 = 2 V p-p
The peak-to-peak voltage presented to the ADC input is 2 V p-p.
However, if a programmable gain amplifier setting gain of ×5
is chosen, the voltage saturates the ADC, and, as a result, the
calculated calibration term (that is, the gain factor) is inaccurate.
The gain factor should be calculated when the largest response
signal is presented to the ADC while ensuring that the signal
is maintained within the linear range of the ADC over the
impedance range of interest. (The reference range of the ADC
is the supply AVDD.)
Therefore, based on your knowledge of the unknown
impedance span over the frequency range of interest, correctly
configure the system gain settings (see Figure 27). These
settings include the output excitation voltage range (Range 1,
Range 2, Range 3, or Range 4), the current-to-voltage amplifier
gain setting resistor, and the programmable gain amplifier
setting (either ×1 or ×5) that precedes the ADC.
Select a calibration impedance value that is approximately
halfway between the limits of the unknown impedance
(therefore, the impedance limits must be known to correctly
calibrate the system). Then, choose a value for the I-V gain
setting resistor that is equal to the calibration impedance. This
results in a unity gain condition on the receive side of the
current-to-voltage amplifier.
For example, assume the following:
•
The unknown test impedance limits are defined by
kΩ
220
kΩ
180
≤
≤
UNKNOWN
Z
•
The frequency range of interest is 30 kHz and 32 kHz
•
The following are the system calibration gain settings:
VDD = 3.3 V
Gain setting resistor (RFB) = 200 kΩ
Z
CALIBRATION
= 200 kΩ
PGA setting = ×1
Calibration frequency = 31 kHz (midpoint frequency)
The gain factor calculated at the midpoint frequency of 31 kHz
can be used to calculate any impedance in the 180 kΩ to 220 Ω
range. If the unknown impedance span or the frequency sweep
is too large, the accuracy of the calculated impedance
measurement degrades. In addition, if any of the calibration
system gain settings change, you must recalibrate the AD5934
and recalculate the gain factor (see the
data sheet for
further details).