Analog Devices AD5934, Manual, Page: 19 / 40

AD5934
Rev. A | Page 19 of 40
MEASURING THE PHASE ACROSS AN IMPEDANCE
The AD5934 returns a complex output code made up of a
separate real and imaginary components. The real component is
stored at Register Address 0x94 and Register Address 0x95, and
the imaginary component is stored at Register Address 0x96
and Register Address 0x97 after each sweep measurement. These
correspond to the real and imaginary components of the DFT
and not the resistive and reactive components of the impedance
under test.
For example, it is a common misconception to assume that if a
user was analyzing a series RC circuit that the real value stored
in Register Address 0x94 and Register Address 0x95 and the
imaginary value stored in Register Address 0x96 and Register
Address 0x97 would correspond to the resistance and capacitive
reactance, respectfully. However, this is incorrect because the
magnitude of the impedance (|Z|) can be calculated by calculating
the magnitude of the real and imaginary components of the
DFT given by the following formula:
2 2
I R Magnitude
+ =
After each measurement, multiply it by the calibration term and
invert the product. Therefore, the magnitude of the impedance
is given by the following formula:
Magnitude Factor Gain
Impedance
×
=
1
Where the gain factor is given by
Magnitude
Impedance
1
Code
Admittance
Factor Gain
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
=
⎟
⎠
⎞
⎜
⎝
⎛
=
The user must calibrate the AD5934 system for a known
impedance range to determine the gain factor before any valid
measurement can take place. Therefore, the user must know
the impedance limits of the complex impedance (Z
UNKNOWN
) for
the sweep frequency range of interest. The gain factor is simply
determined by placing a known impedance between the input/
output of the AD5934 and measuring the resulting magnitude of
the code. The AD5934 system gain settings need to be chosen to
place the excitation signal in the linear region of the on-board ADC.
Because the AD5934 returns a complex output code made up of
real and imaginary components, the user is also able to calculate
the phase of the response signal through the signal path of the
AD5934. The phase is given by the following formula:
Phase (rads) = tan
−1
( I / R ) (3)
The phase measured by Equation 3 accounts for the phase
shift introduced to the DDS output signal as it passes through the
internal amplifiers on the transmit and receive side of the AD5934,
along with the low-pass filter, and also the impedance connected
between the VOUT and VIN pins of the AD5934.
The parameters of interest for many users are the magnitude of
the impedance (|Z
UNKNOWN
|) and the impedance phase (ZØ).The
measurement of the impedance phase (ZØ) is a 2-step process.
The first step involves calculating the AD5934 system phase.
The AD5934 system phase can be calculated by placing a
resistor across the VOUT and VIN pins of the AD5934 and
calculating the phase (using Equation 3) after each measurement
point in the sweep. By placing a resistor across the VOUT and
VIN pins, there is no additional phase lead or lag introduced to
the AD5934 signal path, and the resulting phase is due entirely
to the internal poles of the AD5934, that is, the system phase.
Once the system phase is calibrated using a resistor, the second
step involves calculating the phase of any unknown impedance
can be calculated by inserting the unknown impedance between
the VIN and VOUT terminals of the AD5934 and recalculating
the new phase (including the phase due to the impedance) using
the same formula. The phase of the unknown impedance (ZØ)
is given by
Z Ø = (Φ unknown − ) system
∇
where:
system
∇
is the phase of the system with a calibration resistor
connected between VIN and VOUT.
Φ
unknown is the phase of the system with the unknown
impedance connected between VIN and VOUT.
Z Ø is the phase due to the impedance, that is, the impedance phase.
Note that it is possible to calculate the gain factor and to calibrate
the system phase using the same real and imaginary component
values when a resistor is connected between the VOUT and
VIN pins of the AD5934, for example, measuring the impedance
phase (ZØ) of a capacitor.
The excitation signal current leads the excitation signal voltage
across a capacitor by −90 degrees. Therefore, an approximate
−90 degrees phase difference between the system phase responses
measured with a resistor and the system phase responses measured
with a capacitive impedance exists.
As previously outlined, if the user wants to determine the phase
angle of the capacitive impedance (ZØ), the user first must
determine the system phase response (
) and subtract
this from the phase calculated with the capacitor connected
between VOUT and VIN (Φunknown).
system
∇
Figure 28 shows the AD5934 system phase response calculated
using a 220 kΩ calibration resistor (R
FB
= 220 kΩ, PGA = ×1)
and the repeated phase measurement with a 10 pF capacitive
impedance.
One important point to note about the phase formula used to
plot Figure 28 is that it uses the arctangent function that returns
a phase angle in radians and, therefore, it is necessary to convert
from radians to degrees.