Measuring Complex Impedance
Here we measure the complex impedance
of a 1uF polypropylene capacitor and then check its deviation from the
rated value using the equation for capacitive reactance.
First we measured the capacitor with a
precision LC meter. It came in at 1.017uF. A 994W resistor will be used as the reference impedance. This
resistor was measured with a precision ohmmeter. We will use "32768_MLS_Impedance_Measure.process"
to perform the measurement. This process ships with the release version
of this product. It consists of four modules. The first is
the signal generator, which generates a 32768 length MLS stimulus to
excite the DUT. Second is the SoundIO module, which plays the stimulus
and records the response of the capacitor. Third is the Oscilloscope
module, which allows us to view the time domain response of the
capacitor. Finally is the Spectrum Analyzer, which performs an FHT/ FFT
on the time domain data and allows us to view impedance vs. frequency and
phase vs. frequency graphs.
You must have a dual channel, duplex
sound card to perform this measurement.
Later a table showing the measured
impedance results using three different values of reference resistance
will be developed. This will illustrate some of the problems that may be
encountered in the transition from constant current to constant voltage
measurement.
1. Measure the value of
the reference resistor using a precision ohmmeter. Our reference was
994.482 ohms.
2. Wire the circuit as
shown in Figure 1. Use short low resistance wiring. Note that many sound
cards Speaker Outputs have more output swing than their respective Line
Outputs.
Figure 1: Capacitance Measurement Process Calibration
Wiring
3. Open “32768_MLS_Impedance_Measurement.process”
from the applications File…Open… menu. Press OK if a “No
Compatible Calibration File Present” message box appears.
4. Open the FFT
Options dialog from the applications Options…FFT… menu and
ensure the FFT Size is 32768 in the Frequency Resolution group.
Press OK in the FFT Options dialog box. Press OK
when the “No Compatible Calibration File Present” message box
appears.
5. Select 4 in
the SoundIO modules Repeat Sequence: combo box. This will
provide some MLS pre-excitement for the sound card and device under test.
This will help to stabilize high frequency phase calibration, which can
be erratic, depending on where the sound card triggers.
6. Press the Open
Mixer button the SoundIO modules Options group. Select
the Volume Controls Options… Properties… menu. Choose the sound
card from the Mixer Device and press the Recording radio
button in the Adjust Volume for group. Press the OK
button.
7. Deselect all Record
Control mixer paths except the Line-In. Adjust the Line-In
mixer setting to its one quarter setting and equalize its balance
setting.
8. Select the Record
Controls Options… Properties… menu. Press the Playback
radio button in the Adjust Volume for group. Press the OK
button.
9. Mute all Playback
mixer gain settings except Master Volume and Wave. Set both
volume controls to one quarter and equalize their balance settings.
10. Press the applications Run button.
You should be able to see the MLS sequence in the oscilloscope module as
shown in Figure 2. If a SoundIO “ No data in record buffer”
message appears first check that your wiring conforms to Figure 1. If it
is correct, increase the mixers Playback Volume Control and Wave
Out sliders or Recording Line controls.
10. If all three controls are at maximum you may
reduce the level at which the sound card triggers. When in Record/Play
mode, the SoundIO module sends a record buffer to the sound card that
is 1.4 longer than required. This is to compensate for various system
delays. It then scans the buffer for the first level that is greater than
the trigger level. It then marks this point as the beginning of the
record and returns the remainder of the record (up to the number of
samples required for the selected FFT size) to the application. This is
the record that the modules processes and sends to subsequent modules.
Trigger level is expressed in terms of percentage full scale. Check the Trig
Level (%F.S.) combo box in the SoundIO Trigger Parameters
group. If it is greater than 20 enter 10 in the edit control.
Press the Run button and check the oscilloscope display again. You
can reduce this value to as low as 1%. This corresponds to 1% of the
sound card full-scale output. You can estimate the length of the buffer
that is sent to the sound card for a given FFT Size from the equation
below.
If
you know the full scale output voltage of your sound card, you can
estimate the level that causes the SoundIO module to trigger from the equation
below. Sound cards have a typical input swing ranging from +0.5 to
+2.0 volts.
11. Once you have a valid trigger, adjust the Play
Control and the Wave sliders so that the signal in the
oscilloscope display is not clipped (as in Figure 2).
Figure 2: MLS Sequence in the Oscilloscope Module
11. You now need to calibrate the frequency
response curve of the sound card if you do not already have a valid
calibration file loaded for the input and output devices selected in the
SoundIO module. Level and Latency calibration are not required for
complex impedance measurement. Press the Calibration button in the
SoundIO module. The SoundIO Module Calibration dialog box will
open.
12. Select Frequency from the Calibration
Type Select: combo box in the Calibration Status group box.
Select MLS from the Signal Type combo box in the Frequency
Calibration group box.
13. Press the Run button and wait for the
Frequency Calibration Complete status message to appear. If a “No
data in record buffer” message box appears Press the Open Mixer
button and increase the applications output level slider. The SoundIO
modules input device level may also be increased by right clicking on the
Windows Task Bar Sound icon and selecting the Recording and
Levels and adjusting the devices slider. Frequency calibration may
be restarted by pressing the Run button. If successful, the calibration
dialog should look as in Figure 3. The Calibration Progress bar may not
update in certain versions of Windows.
Figure 3: SoundIO Module Calibration Dialog Box After
Calibration
12. Press the OK button in the
calibration dialog and select Yes when the “Calibration
Parameter Has Changed Save To Process File” message box appears.
13. Now rewire the circuit as shown in Figure 4.
Figure 4: Capacitance Measurement Process Test Wiring
14. Select |Z| from the spectrum analyzers
Y-Axis Select combo box and change the Y-Axis Scale to 1000 ohms/div.
Enter the exact value of the reference resistor wired between Ch1 Line-In
and Ch2 Line-In in the Ref1: edit box in the spectrum analyzer.
Check the Apply Freq Cal. Checkbox in the Spectrum Analyzers Options
group. Change the smoothing factor to 7 in the Smth combo box of
in the spectrum analyzer. This will help smooth the low frequency
results.
15. Press the Run button on the
application toolbar and observe the trace in the spectrum analyzer. The
impedance and phase appear in channels one and two respectively. Pressing
the right mouse button at the desired frequency will show individual
values. For example at 1004 Hz we obtain a value of 157.0W. This is out
by 1.12W (0.724%) from the calculated value of 155.87W at that frequency.
Figure 5: Measured Impedance Results in Spectrum
Analyzer
Below is a table showing the measured
impedance results using three different values of reference resistance
(101W, 994W and 10,467W respectively). The process was re-calibrated for each new
reference resistor.
Using a 101W reference we see that low frequency data seems unreliable.
This is because the voltage on both sound card inputs is almost equal out
to about 1KHz, because the impedance of the capacitor is much larger than
that of the resistor. In this case even a small amount of sound card
noise can cause a very large error in the apparent measurement.
Using a 10,467W reference we see that high frequency data seems unstable.
This is because the voltage at the Channel 2 sound card input is almost
equal to zero because the impedance of the capacitor is much lower than
that of the resistor. In this case even a small amount of sound card
noise can cause a very large error in the apparent measurement
|
Reference
|
20Hz
|
50Hz
|
100Hz
|
500Hz
|
1Khz
|
5KHz
|
10KHz
|
|
Calculated
|
7,825W
|
3,129
W
|
1,565 W
|
313 W
|
157 W
|
31 W
|
16 W
|
|
101 W
|
8,069 W
|
2,751 W
|
1,633 W
|
313 W
|
158 W
|
32 W
|
15 W
|
|
994 W
|
6,788 W
|
3,074 W
|
1,557 W
|
310 W
|
156 W
|
32 W
|
16 W
|
|
10467 W
|
7,492 W
|
2,985 W
|
1,623 W
|
312 W
|
162 W
|
31 W
|
17 W
|
Below is a table showing the same measurements done with a
994W reference and a process FFT Size of 8192. This translates
to a spectral resolution of 10.77 Hz. We would expect low frequency
measurements to be inaccurate because of the decreased resolution. This
can be seen as an increased raggedness in the low frequency portion of
the curve
Figure 6: Measured Impedance Results
in Spectrum Analyzer at 8192 FFT Size
|
Reference
|
20Hz
|
50Hz
|
100Hz
|
500Hz
|
1Khz
|
5KHz
|
10KHz
|
|
Calculated
|
7,825W
|
3,129
W
|
1,565 W
|
313 W
|
157 W
|
31 W
|
16 W
|
|
994 W
|
7,886 W
|
2,770 W
|
1,533 W
|
315 W
|
157 W
|
33 W
|
15 W
|
|
