Analog Devices EVAL-AD5933EBZ User Manual page 21

Evaluation Board User Guide
Measuring the Phase Across an Impedance
The AD5933 returns a complex output code made up of a separate
real and imaginary component. The real component is stored at
Register 0x94 and Register 0x95, and an imaginary component
is stored at Register 0x96 and Register 0x97 after each sweep
measurement. These correspond to the real and imaginary
components of the DFT and not the resistive and reactive
components of the impedance under test.
For example, it is a common misconception that when analyzing a
series RC circuit that the real value stored in Register 0x94 and
Register 0x95 and the imaginary value stored at Register 0x96
and Register 0x97 corresponds to the resistance and capacitive
reactance, respectfully. However, this is incorrect; the magnitude of
the impedance (|Z|) can be calculated by calculating the magnitude
of the real and imaginary components of the DFT given by
2 2
= +
Magnitude R I
After each measurement, multiply it by the calibration term
(see gain factor calculation in
the product. The magnitude of the impedance is therefore given by
=
Impedance
Gain Factor
where the Gain Factor is given by
⎛
Admittance
=
⎜
Gain Factor
⎝
Code
Before any valid measurement can take place, the
must be calibrated for a know impedance range to determine
the gain factor. Therefore, the impedance limits of the complex
impedance (Z ) for the sweep frequency range of interest
UNKNOWN
must be known. Place known impedance between the input/output
of the AD5933 and measure the resulting magnitude of the code
to determine what the gain factor is. The
settings must be chosen to place the excitation signal in the
linear region of the on-board ADC (refer to the
sheet for further details).
Because the AD5933 returns a complex output code made up of a
real and an imaginary component, the phase of the response
signal through the AD5933 signal path can be calculated. The
phase is given by Phase (rads) = Tan
The phase measured by the previous formula accounts for the
phase shift introduced to the DDS output signal as it passes
through the internal amplifiers on the transmit and receive side
of the AD5933 along with the low-pass filter and the impedance
connected between the VOUT and VIN pins of the AD5933.
AD5933 data sheet) and invert
1
×
Magnitude
⎛ ⎞
1
⎜ ⎜ ⎟ ⎟
⎞
⎝ Impedance ⎠
=
⎟
⎠
Magnitude
AD5933 system
AD5933 system gain
AD5933 data
−1
(I/R).
The AD5933 parameters of interest are the magnitude of the
impedance (|Z
UNKNOWN
measurement of ZØ is a two-step process. The first step
involves calculating the
system phase can be calculated by placing a resistor across the
VOUT and VIN pins of the
(using the previous formula) 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 to the
signal path, and the resulting phase is due entirely to the internal
poles of the AD5933, that is, the system phase.
Once the system phase has been calibrated using a resistor, the
phase of any unknown impedance can be calculated by inserting
the unknown impedance between the VIN and VOUT terminals
of the AD5933
phase due to the impedance) using the previous formula. The
phase of the unknown impedance (ZØ) is given by
ZØ = (Φ unknown −
where:
∇
is the phase of the system with a calibration resistor
system
connected between VIN and VOUT.
Φ unknown 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 both 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°; therefore, before any measurement
is taken, expect to see an approximate −90° phase difference
between the system phase responses measured with a resistor
and the system phase responses measured with capacitive
impedance.
As previously outlined, to determine the phase angle of capacitive
impedance (ZØ), the system phase response ( system
determined and subtracted from the phase calculated with the
capacitor connected between VOUT and VIN (Φ unknown ).
Rev. 0 | Page 21 of 28
|) and the impedance phase (ZØ). The
AD5933 system phase. The
AD5933 and calculating the phase
and by recalculating the new phase (including the
∇
)
system
UG-364
AD5933
AD5933
∇
) must be