Aug 28, 2013

This note describes using the Analog Discovery design kit along with the

Obtaining a more accurate measurement of complex impedance requires

The DC resistance of the pickup was measured to be Rp=8.5kΩ using a multimeter.

Since both voltage measurements in the configuration above are relative to the same input voltage, the phase angle is the DIFFERENCE in phase between the phase measured in the voltage measurement and the phase measured in the current measurement. To calculate and display the magnitude and phase of the pickup impedance, the following simple procedure was used for Excel:

- from the Network Analyzer, for each of the two measurements, after the Bode scan is complete, disable the Cl 1 view (since it is not needed) and EXPORT the data to a .csv file, using GAIN (instead of db). The exported file will contain frequency, gain (or amplitude relative to the C1 source voltage) and phase (relative to the C1 voltage source)
- import the first .csv file into Excel. The first few information lines can be either removed from the file or can be skipped in Excel
- import the second .csv file for the current measurments into Excel. Then copy the current measurements and phase from that file into the voltage measurement csv file as an additional 2 separate columns
- in an additional new column, create an Excel formula to calculate the impedance magnitude, for example as
**=B1*10000/D1**if the pickup voltage data is in column B and the pickup current data is in column D. The 10000 is the value of Rs to convert the "current measurement" in column D from an actual measured voltage to current - in another additional column, create an Excel formula to calculate the impedance phase angle as described above, for example as
**=C1 - E1**if the pickup voltage phase angle is in column C and the pickup current phase angle is in column E - create a separate scatter chart in Excel for each of the two new column results which are the complex impedance magnitude and phase

- There is a strong resonant peak in impedance at 5.5 kHz
- The peak impedance magnitude is over 200 kΩ, typical of pickups. This is why electric guitars usually require high-impedance input amplifiers to prevent loading
- At the resonant peak, the phase angle is almost zero. At this point the current and voltage are in phase and the pickup looks "resistive"
- At frequencies lower than the resonant peak, the phase angle of the impedance is positive, meaning that the voltage leads the current (inductive-like)
- At frequencies higher than the resonant peak, the phase angle of the impedance is negative, meaning that the voltage lags the current (capacitive-like)
- At very low frequency, the phase angle again approaches zero as the impedance approaches the value of the pickup coil's DC resistance (8.5kΩ for this pickup)

The resonant peak occurs at approximately:

The pickup parameters are:

An alternate simple spot measurement for measuring impedance magnitude without scope loading across a high-impedance device is to measure the input W1 voltage with C1 and the (current-determining) voltage across a smaller series resistor with C2 as above but using the Discovery oscilloscope and the Waveform Generator instead of the Network analyzer. Then an additional Math channel can be added in Discovery and used to calculate and display the true vector voltage across the pickup using the Math function