EVALAD5933EB datasheet(28/32 Pages) AD

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EVAL-AD5933EB

Preliminary Technical Data

Rev. PrC | Page 28 of 32

In addition, care must be taken with the arctangent formula

when using the real and imaginary values to interpret the phase

at each measurement point. The arctangent function returns the

correct standard phase angle only if the sign of the real and

imaginary values are positive, that is, if the coordinates lie in the

first quadrant.

Table 8. Phase Angle

Real

Imaginary

Quadrant

Phase Angle (Degrees)

Positive

First

−

180

)

(

tan

Positive

Negative

Second

⎟

⎠

⎞

⎜

⎝

⎛

−

180

)

(

tan

180

Negative

Third

⎟

⎠

⎞

⎜

⎝

⎛

−

180

)

(

tan

180

Positive

Negative

Fourth

⎟

⎠

⎞

⎜

⎝

⎛

−

180

)

(

tan

360

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 180°

to calculate the correct standard angle.

After 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 (ZUNKNOWN).

This is accomplished by the vector projection of the impedance

magnitude onto the real and imaginary impedance axes using

the following formulas:

Likewise, when the real and imaginary components are both

negative, that is, when the coordinates lie in the third quadrant,

the arctangent formula returns a positive angle, and it is

necessary to add 180° to the angle in order to determine 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,

and it is necessary to add 360° to the angle in order to calculate

the correct phase angle.

|ZREAL|= |Z| × cos(ZØ)

|ZIMAG|= |Z| × sin(ZØ)

where ZREAL is the real component, and ZIMAG is the imaginary

component.

Therefore, the correct standard phase angle is dependant on the

sign of the real and imaginary components (see Table 8 for a

summary).

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