EVAL-AD5933EB Datasheet, PDF (20/40 Pages) Analog Devices – 1 MSPS, 12-Bit Impedance Converter, Network Analyzer

AD5933
new phase (including the phase due to the impedance) using
the same formula. The phase of the unknown impedance (ZØ)
is given by the following formula:
ZØ = (Φ unknown − ∇system)
where:
∇system is the phase of the system with a calibration resistor
connected between VIN and VOUT.
Φunknown is the phase of the system with the unknown
impedance connected between VIN and VOUT.
ZØ 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 AD5933, 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 degree phase difference exists between the system phase
responses measured with a resistor and that of the system phase
responses measured with a capacitive impedance.
As previously outlined, if the user would like to determine the
phase angle of capacitive impedance (ZØ), the user first has to
determine the system phase response ( ∇system ) and subtract
this from the phase calculated with the capacitor connected
between VOUT and VIN (Φunknown).
A plot showing the AD5933 system phase response calculated
using a 220 kΩ calibration resistor (RFB = 220 kΩ, PGA = ×1)
and the repeated phase measurement with a 10 pF capacitive
impedance is shown in Figure 26.
One important point to note about the phase formula used to
plot Figure 26 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.
200
180
160
220kΩ RESISTOR
140
120
100
80
10pF CAPACITOR
60
40
20
0
0
15k 30k 45k 60k 75k 90k 105k 120k
FREQUENCY (Hz)
Figure 26. System Phase Response vs. Capacitive Phase
Data Sheet
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 (see Figure 27).
–100
–90
–80
–70
–60
–50
–40
–30
–20
–10
0
0
15k 30k 45k 60k 75k 90k 105k 120k
FREQUENCY (Hz)
Figure 27. Phase Response of a Capacitor
Also when using the real and imaginary values to interpret
the phase at each measurement point, take care when using
the arctangent formula. The arctangent function returns the
correct standard phase angle only 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 the angle 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, then the arctangent formula returns a negative angle
and it is necessary to add a further 180 degrees to calculate the
correct standard angle. Likewise, when the real and imaginary
components are both negative, that is, when the coordinates lie
in the third quadrant, then the arctangent formula returns a
positive angle and it is necessary to add 180 degrees from the
angle to return the correct standard phase. Finally, when the
real component is positive and the imaginary component is
negative, that is, the data lies in the fourth quadrant, then the
arctangent formula returns a negative angle. It is necessary to
add 360 degrees to the angle to calculate the correct phase
angle.
Therefore, the correct standard phase angle is dependent upon
the sign of the real and imaginary component and is summa-
rized in Table 7.
Rev. E | Page 20 of 40