AD5933 datasheet(20/40 Pages) AD

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AD5933

Data Sheet

Rev. F | Page 20 of 40

new phase (including the phase due to the impedance) 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.

Φunknown 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 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 degrees. Therefore, an approximate

−90 degree phase difference exists between the system phase

responses measured with a resistor and that of the system phase

responses measured with a capacitive impedance.

As previously outlined, if the user would like to determine the

phase angle of capacitive impedance (ZØ), the user first has to

determine the system phase response (

system

∇

) and 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 26.

One important point to note about the phase formula used to

plot Figure 26 is that it uses the arctangent function that returns

a phase angle in radians and, therefore, it is necessary to convert

from radians to degrees.

200

180

160

140

120

100

15k

30k

45k

60k

75k

90k

105k

120k

FREQUENCY (Hz)

220kΩ RESISTOR

10pF CAPACITOR

Figure 26. 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 (see Figure 27).

–100

–90

–80

–70

–60

–50

–40

–30

–20

–10

15k

30k

45k

60k

75k

90k

105k

120k

FREQUENCY (Hz)

Figure 27. Phase Response of a Capacitor

Also when using the real and imaginary values to interpret

the phase at each measurement point, take care when using

the arctangent formula. 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 the angle taken

counterclockwise 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, then the arctangent formula returns a negative angle

and it is necessary to add a further 180 degrees 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, then the arctangent formula returns a

positive angle and it is necessary to add 180 degrees from 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, then the

arctangent formula returns a negative angle. It is necessary to

add 360 degrees to the angle to calculate the correct phase

angle.

Therefore, the correct standard phase angle is dependent upon

the sign of the real and imaginary component and is summa-

rized in Table 7.

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