EVAL-AD5933EBZ Datasheet, PDF (27/32 Pages) Analog Devices – Evaluation Board for the 1 MSPS 12-Bit Impedance Converter Network Analyzer

Preliminary Technical Data
Because the AD5933 returns a complex output code composed
of real and imaginary components, the user can calculate the
phase of the response signal through the AD5933 signal path.
The phase is given by the following formula.
Phase (rads) = tan^−1(I / R)
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 AD5933, the low-pass
filter, and the impedance connected between the VOUT and
VIN pins of the AD5933.
The parameters of interest for many users of the AD5933 are the
magnitude of the impedance (|ZUNKNOWN|) and the impedance
phase (ZØ). The measurement of the impedance phase (ZØ) is
a two-step process.
The first step involves calculating the AD5933 system phase.
The AD5933 system phase can be calculated by placing a
resistor across the VOUT and VIN pins of the AD5933, 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 AD5933 signal path. Therefore, the
resulting phase, that is, the system phase, is due entirely to the
internal poles of the AD5933.
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 AD5933, 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.
ZØ = (ΦUnknown− ∇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 (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 AD5933.
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
EVAL-AD5933EB
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 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 34.
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 (ZØ) of the capacitor and is shown in
Figure 35.
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 34. System Phase Response vs. Capacitive Phase
–100
–90
–80
–70
–60
–50
–40
–30
–20
–10
0
0
15k 30k 45k 60k 75k 90k 105k 120k
FREQUENCY (Hz)
Figure 35. Phase Response of a Capacitor
It is important to note that the formula used to calculate the phase
and to plot Figure 34 is based on the arctangent function, which
returns a phase angle in radians. Therefore, it is necessary to
convert the calculated phase angle from radians to degrees.
Rev. PrC | Page 27 of 32