Analog Devices EVAL-AD5933EBZ User Manual page 22

UG-364
Figure 29 shows the AD5933
using a 220 kΩ calibration resistor (R
and the repeated phase measurement with a 10 pF capacitive
impedance.
200
180
160
220kΩ RESISTOR
140
120
100
80
10pF CAPACITOR
60
40
20
0
0 15k 30k 45k
FREQUENCY (Hz)
Figure 29. 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 30.
–100
–90
–80
–70
–60
–50
–40
–30
–20
–10
0
0 15k 30k 45k
FREQUENCY (Hz)
Figure 30. Phase Response of a Capacitor
Note that the phase formula used to plot Figure 29 uses the
arctangent function that returns a phase angle in radians and,
therefore, it is necessary to convert from radians to degrees.
system phase response calculated
= 220 kΩ, PGA = ×1)
FB
60k 75k 90k 105k 120k
60k 75k 90k 105k 120k
In addition, take care when using the arctangent formula when
using the real and imaginary values to interpret the phase at
each measurement point. 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 taken counter clockwise
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 a further 180°
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, the arctangent formula
returns a positive angle, and it is necessary to add 180° to 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, the arctangent
formula returns a negative angle, and it is necessary to add 360° to
the angle to calculate the correct phase angle.
Therefore, the correct standard phase angle is dependent on the
sign of the real and imaginary component and is summarized in
Table 3.
Table 3. Phase Angle
Real Imaginary
Positive Positive
Positive Negative
Negative Negative
Positive Negative
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
projection of the impedance magnitude onto the real and
imaginary impedance axis using the following formulas:
The real component is given by
| Z | = | Z | × cos( ZØ )
REAL
The imaginary component is given by
| Z | = | Z | × sin( ZØ )
IMAG
Rev. 0 | Page 22 of 28
Evaluation Board User Guide
Quadrant Phase Angle (Degrees)
First
−
1
Tan ( I
Second ⎛
+
⎜
180 Tan
⎝
Third ⎛
+
⎜
180 Tan
⎝
Fourth ⎛
+
⎜
360 Tan
⎝
UNKNOWN
180
×
/ R )
π
⎞
180
−
×
1 ⎟
( I / R )
π
⎠
⎞
180
−
×
1
⎟
( I / R )
π ⎠
⎞
180
−
×
1
⎟
( I / R )
π ⎠
) by the vector