Preliminary Technical Data
EVAL-AD5934EB
Rev. PrC | Page 25 of 32
Measuring the Phase Across an Impedance
The AD5934 returns a complex output code composed of separate
real and imaginary components. The real component is stored
at Register Addresses 94h and 95h, and the imaginary component
is stored at Register Addresses 96h and 97h after each sweep
measurement. These correspond to the real and imaginary
components of the DFT, not to the resistive and reactive
components of the impedance being tested.
For example, it is a common misconception to assume that if a
customer is analyzing a series RC circuit, the real value stored in
94h and 95h and the imaginary value stored at 96h and 97h corres-
pond to the resistance and capacitive reactance, respectfully. This is
incorrect. However, the magnitude of the impedance (|Z|) can
be determined by first calculating the magnitude of the real and
imaginary components of the DFT by using the following formula:
2
2
I
R
Magnitude
+
=
Next multiply by the calibration term (see the Gain Factor
Calculation section in the
data sheet) and invert the
product gives the impedance. Therefore, the magnitude of the
impedance is given by the following formula:
Magnitude
Factor
Gain
Impedance
×
=
1
)
|
Z
|
(
The gain factor is given by the following formula:
Magnitude
Impedance
1
Code
Admittance
Factor
Gain
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
=
⎟
⎠
⎞
⎜
⎝
⎛
=
Before a valid measurement can occur, the user must calibrate
the AD5934 system for a known impedance range to determine
the gain factor. Therefore, the user of the AD5934 must know
the impedance limits of the complex impedance (Z
UNKNOWN
) for
the sweep frequency range of interest. The gain factor is
determined by placing a known impedance between the input
and output of the AD5934, and then measuring the resulting
magnitude of the code. The AD5934 system gain settings need
to be chosen so that the excitation signal is in the linear region
of the on-board ADC. (Refer to the data sheet for further details.)
Because the AD5934 returns a complex output code composed
of real and imaginary components, the user can calculate the
phase of the response signal through the AD5934 signal path.
The phase is given by the following formula.
)
/
(
tan
)
rads
(
1
R
I
Phase
−
=
This equation accounts for the phase shift introduced in the
DDS output signal as it passes through the internal amplifiers
on the transmit and receive sides of the AD5934, the low-pass
filter, and the impedance connected between the VOUT and
VIN pins of the AD5934.
The parameters of interest for many users of the AD5934 are the
magnitude of the impedance (|Z
UNKNOWN
|) and the impedance
phase (ZØ). The measurement of the impedance phase (ZØ) is
a two-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
then calculating the phase (using the formula above) 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 in the AD5934 signal path. Therefore, the
resulting phase, that is, the system phase, is due entirely to the
internal poles of the AD5934.
After the system phase is calibrated using a resistor, the phase of
any unknown impedance can be calculated by inserting it
between the VIN and VOUT terminals of the AD5934, and
then recalculating the new phase (including the phase due to
the impedance) by using the same formula. The phase of the
unknown impedance (ZØ) is given by the following formula.
)
(
Ø
System
Unknown
Z
∇
−
Φ
=
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 (impedance phase).
Note that it is possible to both calculate the gain factor and
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.
Example of Measuring the Impedance Phase (ZØ) of a
Capacitor
The excitation signal current leads the excitation signal voltage
across a capacitor by −90°. Therefore, before any measurement
is performed, one would intuitively expect to see approximately
a −90° phase difference between the system phase response
measured with a resistor and the system phase response
measured with a capacitive impedance.
As outlined in the Measuring the Phase Across an Impedance
section, if the user would like to determine the phase angle of a
capacitive impedance (ZØ), the user must first determine the
system phase response (
∇
System), and then subtract this from
the phase calculated with the capacitor connected between
VOUT and VIN (ΦUnknown).
A plot showing the AD5934 system phase response calculated
using a 220 kΩ calibration resistor (Rfb = 220 kΩ, PGA = ×1)