Datasheet

AD5934 Data Sheet
Rev. C | Page 18 of 32
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 (
system∇
) and subtract
this from the phase calculated with the capacitor connected
between VOUT and VIN (Φunknown).
Figure 22 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 22 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.
0
20
40
60
80
100
120
140
160
180
200
SYSTEM PHASE (Degrees)
60k45k15k 30k0 75k 90k 105k 120k
FRE
QUENCY (Hz)
05325-090
220kΩ RESISTOR
10pF CAPACITOR
Figure 22. System Phase Response vs. Capacitive Phase
The phase difference (that is, ZØ) between the phase response
of a capacitor and the system phase response using a resistor is
the impedance phase of the capacitor (ZØ) and is shown in
Figure 23.
In addition, when using the real and imaginary values to interpret
the phase at each measurement point, care should be taken
when using the arctangent formula. The arctangent function
only returns the correct standard phase angle when the sign of
the real and imaginary values are positive, that is, when the
coordinates lie in the first quadrant. The standard angle is
taken counterclockwise from the positive real x-axis. If the sign
of the real component is positive and the sign of the imaginary
component is negative, that is, the data lies in the second
quadrant, the arctangent formula returns a negative angle, and
it is necessary to add an additional 180° to calculate the correct
standard angle. Likewise, when the real and imaginary components
are both negative, that is, when data lies in the third quadrant,
the arctangent formula returns a positive angle, and it is necessary
to add an additional 180° to calculate the correct standard
phase. When the real component is positive and the imaginary
component is negative, that is, the data lies in the fourth quadrant,
the arctangent formula returns a negative angle, and it is necessary
to add an additional 360° to calculate the correct standard phase.
PHASE (Degrees)
60k45k15k 30k0 75k 90k 105k 120k
FREQUENCY (Hz)
05325-091
–100
–90
–80
–70
–60
–50
–40
–30
–20
–10
0
Figure 23. Phase Response of a Capacitor
Therefore, the correct standard phase angle is dependent
upon the sign of the real and imaginary components, which is
summarized in Table 6.
Table 6. Phase Angle
Real Imaginary Quadrant Phase Angle
Positive Positive First
π
°
×
−
180
)/(tan
1
RI
Positive Negative Second






π
°
×+°
−
180
)/(tan180
1
RI
Negative Negative Third






π
°
×+°
−
180
)/(tan180
1
RI
Negative Positive Fourth






π
°
×+°
−
180
)/(tan360
1
RI
Once the magnitude of the impedance (|Z|) and the impedance
phase angle (ZØ, in radians) are correctly calculated, it is possible
to determine the magnitude of the real (resistive) and imaginary
(reactive) components of the impedance (Z
UNKNOWN
) by the vector
projection of the impedance magnitude onto the real and
imaginary impedance axis using the following formulas:
The real component is given by
|Z
REAL
| = |Z| × cos(ZØ)
The imaginary component is given by
|Z
IMAG
| = |Z| × sin(ZØ)