Analog Devices AD5934 Manual page 20

AD5934
200
180
160
220kΩ RESISTOR
140
120
100
80
60 10pF CAPACITOR
40
20
0
0 15k 30k 45k
FREQUENCY (Hz)
Figure 28. 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 29.
–100
–90
–80
–70
–60
–50
–40
–30
–20
–10
0
0 15k 30k 45k
FREQUENCY (Hz)
Figure 29. Phase Response of a Capacitor
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
60k 75k 90k 105k 120k
60k 75k 90k 105k 120k
Rev. A | Page 20 of 40
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.
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
Positive Positive First
Positive Negative Second
Negative Negative Third
Positive Negative Fourth
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
Phase Angle
°
180
−
×
1
tan ( I / R )
π
°
⎛ ⎞
180
−
° + ×
1
⎜ ⎟
180 tan ( I / R )
π
⎝ ⎠
°
⎛ ⎞
180
−
° + ×
1
⎜ ⎟
180 tan ( I / R )
π
⎝ ⎠
°
⎛ ⎞
180
−
° + ×
1
⎜ ⎟
360 tan ( I / R )
π
⎝ ⎠
) by the vector
UNKNOWN