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## AD5934 Datasheet(PDF) 18 Page - Analog Devices

 Part No. AD5934 Description Impedance Converter, Network Analyzer Download 31 Pages Scroll/Zoom 100% Maker AD [Analog Devices] Homepage http://www.analog.com Logo ## AD5934 Datasheet(HTML) 18 Page - Analog Devices           18 / 31 page AD5934Data SheetRev. E | Page 18 of 31Note that it is possible to calculate the gain factor and to calibratethe system phase using the same real and imaginary componentvalues when a resistor is connected between the VOUT andVIN pins of the AD5934, for example, measuring the impedancephase (ZØ) of a capacitor.The excitation signal current leads the excitation signal voltageacross a capacitor by −90 degrees. Therefore, an approximate−90 degrees phase difference between the system phase responsesmeasured with a resistor and the system phase responses measuredwith a capacitive impedance exists.As previously outlined, if the user wants to determine the phaseangle of the capacitive impedance (ZØ), the user first mustdetermine the system phase response ( system∇) and subtractthis from the phase calculated with the capacitor connectedbetween VOUT and VIN (Φunknown).Figure 22 shows the AD5934 system phase response calculatedusing a 220 kΩ calibration resistor (RFB = 220 kΩ, PGA = ×1)and the repeated phase measurement with a 10 pF capacitiveimpedance.One important point to note about the phase formula used toplot Figure 22 is that it uses the arctangent function that returnsa phase angle in radians and, therefore, it is necessary to convertfrom radians to degrees.02040608010012014016018020060k45k15k30k075k90k105k120kFREQUENCY (Hz)220kΩ RESISTOR10pF CAPACITORFigure 22. System Phase Response vs. Capacitive PhaseThe phase difference (that is, ZØ) between the phase responseof a capacitor and the system phase response using a resistor isthe impedance phase of the capacitor (ZØ) and is shown inFigure 23.In addition, when using the real and imaginary values to interpretthe phase at each measurement point, care should be takenwhen using the arctangent formula. The arctangent functiononly returns the correct standard phase angle when the sign ofthe real and imaginary values are positive, that is, when thecoordinates lie in the first quadrant. The standard angle istaken counterclockwise from the positive real x-axis. If the signof the real component is positive and the sign of the imaginarycomponent is negative, that is, the data lies in the secondquadrant, the arctangent formula returns a negative angle, andit is necessary to add an additional 180° to calculate the correctstandard angle. Likewise, when the real and imaginary componentsare both negative, that is, when data lies in the third quadrant,the arctangent formula returns a positive angle, and it is necessaryto add an additional 180° to calculate the correct standardphase. When the real component is positive and the imaginarycomponent is negative, that is, the data lies in the fourth quadrant,the arctangent formula returns a negative angle, and it is necessaryto add an additional 360° to calculate the correct standard phase.60k45k15k30k075k90k105k120kFREQUENCY (Hz)–100–90–80–70–60–50–40–30–20–100Figure 23. Phase Response of a CapacitorTherefore, the correct standard phase angle is dependentupon the sign of the real and imaginary components, which issummarized in Table 6.Table 6. Phase AngleRealImaginaryQuadrantPhase AnglePositivePositiveFirstπ°×−180)/(tan 1RIPositiveNegativeSecondπ°×+°−180)/(tan1801RINegativeNegativeThirdπ°×+°−180)/(tan1801RINegativePositiveFourthπ°×+°−180)/(tan3601RIOnce the magnitude of the impedance (|Z|) and the impedancephase angle (ZØ, in radians) are correctly calculated, it is possibleto determine the magnitude of the real (resistive) and imaginary(reactive) components of the impedance (ZUNKNOWN) by the vectorprojection of the impedance magnitude onto the real andimaginary impedance axis using the following formulas:The real component is given by|ZREAL| = |Z| × cos(ZØ)The imaginary component is given by|ZIMAG| = |Z| × sin(ZØ)

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