EVALAD5933EB datasheet(27/32 Pages) AD

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Preliminary Technical Data

EVAL-AD5933EB

Rev. PrC | Page 27 of 32

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.

)

(

tan

)

rads

(

Phase

−

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.

)

(

System

Unknown

∇

−

where:

System is the phase of the system with a calibration resistor

connected between VIN and VOUT.

Unknown 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

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

140

120

100

15k

30k

45k

60k

75k

90k

105k

120k

FREQUENCY (Hz)

220kΩ RESISTOR

10pF CAPACITOR

Figure 34. System Phase Response vs. Capacitive Phase

–100

–90

–80

–70

–60

–50

–40

–30

–20

–10

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.

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