Capacitor Measurement Mode

Setup
The equation for capacitive reactance Xc=1/(2*PI*F*C) shows that capacitor reactance approaches infinity at 0 Hz.  The WT2's constant current source output is voltage limited by the USB supply rail, so this must be considered as it would cause clipping. This issue is easily solved with an additional external resistor placed across the tester terminals as shown below.  In most cases a 1k-10k resistor will work, but sizing the resistor to match the capacitor will result in an improved test range.  The general goal in this case is to pick a resistor value equal the capacitors reactance in the middle of the desired test frequency range.

           
WARNING
DISCHARGE CAPACITORS BEFORE
CONNECTING THEM TO THE TESTER		                      


       
Cmin
 Cmax Range
 Rp
 Resulting Drive
         

1
 10000
 pF
 10k
 2%

0.01
 10
 uF
 1K
 20%

10
 1000
 uF
 220
 100%

 
Automatic Parallel Resistance and Parasitic Capacitance Nulling
Given the testers ability to measure impedance and capacitance, it is also possible to null the effects of the parallel resistance and any lingering parasitic capacitance.   Simply connect the parallel resistor, select Tools->Capacitor Measurement Setup from the pull down menus, and select the Auto Complete button.  The auto-null will then measure Rp, set the drive level for maximum output and find the parasitic jig capacitance.  When this feature is enabled, the measured complex impedance of the parallel combination of the test load and parasitic values are reverse calculated revealing the test load. 


CapAutoAlign

Auto Alignment: Note 10k resistor and Cp=7pF



MeasuringCap

Physical Connections: Note the short (non-existent) test leads

Notes
  • Best results occur when the component and test lead lengths are minimized
  • In the example above, the inductance and contact resistance of the 10k resistor banana jack will be inline with test load.  This increases D.F. when Xc and ESR are very low.  Be sure to clean the contacts and (if needed) do a full calibration using the 10k banana jack as the test leads.
  • As frequency increases, Xc decreases.  Since capacitive and lead inductance are out of phase, they cancel causing Xc to decrease and phase to move more positive (toward capacitance).  Eventually this will become the self inductance of the capacitor.
  • Deep sine signal mode averaging will improve range and resolution
  • Capacitance measurement works for all signal types but swept sine is significantly better.  The accuracy in these tables was achieved by using the sine signal mode, 8k buffer and 32 averaging frames.  Real time 'FFT' modes, smaller frames and less averaging can also be used to speed up the tests with a corresponding decrease in precision.
  • The WT2 port output is a constant current source resulting in a -6dB/octave voltage roll off when Xc<Rp. 
100pF 2% Silver Mica capacitor
This is the capacitor shown in the connection diagram above.  The capacitive reactance is
very high, so Rp=10k is used.  Though the capacitor value is quite low, the useful accurate
measurement range is 200-20 kHz.  The measurements are however at this point probably not
good enough to calculate dissipation factor (except maybe above 10kHz).

Buffer[3] 100pF Silver Mica                                              Ver 5.01    
Completed: Mon Nov 28 14:40:11 2011
Drive level 2.133% [73.134 uA]
Sine,LoZP(LV/LA)->Buf03,22 pts
Shunts: Rp=10.046 kohm, Cp=6.979 pF
;--------------------------------------------------------------------------------
;   Freq     Impedance         Phase          Real          Imag        Series
;     Hz    Z=mag(R,I)       Degrees      Z*cos(P)      Z*sin(P)        L or C
;--------------------------------------------------------------------------------
   20.00   34.474 Mohm -151.033  deg  -30.161 Mohm   16.696 Mohm  476.627 p  C
   28.28   31.217 Mohm -139.085  deg  -23.590 Mohm   20.445 Mohm  275.221 p  C
   40.00   27.564 Mohm -139.155  deg  -20.851 Mohm   18.027 Mohm  220.722 p  C
   56.57   22.966 Mohm -123.247  deg  -12.591 Mohm   19.207 Mohm  146.490 p  C
   80.00   17.152 Mohm -112.953  deg   -6.689 Mohm   15.794 Mohm  125.970 p  C
  113.13   13.158 Mohm -108.788  deg   -4.238 Mohm   12.457 Mohm  112.931 p  C
  159.99    9.449 Mohm -103.899  deg   -2.270 Mohm    9.172 Mohm  108.458 p  C
  226.26    6.757 Mohm  -98.334  deg -979.397 kohm    6.686 Mohm  105.209 p  C
  319.98    4.821 Mohm  -96.420  deg -539.039 kohm    4.790 Mohm  103.832 p  C
  452.51    3.406 Mohm  -94.342  deg -257.857 kohm    3.396 Mohm  103.562 p  C
  639.94    2.431 Mohm  -92.972  deg -126.082 kohm    2.428 Mohm  102.422 p  C
  905.00    1.716 Mohm  -91.869  deg  -55.967 kohm    1.715 Mohm  102.515 p  C
 1279.85    1.216 Mohm  -91.512  deg  -32.091 kohm    1.216 Mohm  102.270 p  C
 1809.97  860.773 kohm  -90.831  deg  -12.485 kohm  860.683 kohm  102.166 p  C
 2559.66  609.742 kohm  -90.613  deg   -6.525 kohm  609.707 kohm  101.981 p  C
 3619.86  431.466 kohm  -90.357  deg   -2.690 kohm  431.458 kohm  101.904 p  C
 5119.21  305.379 kohm  -90.205  deg   -1.094 kohm  305.377 kohm  101.808 p  C
 7239.59  216.262 kohm  -90.068  deg -257.935  ohm  216.262 kohm  101.654 p  C
10238.23  153.079 kohm  -89.982  deg   47.902  ohm  153.079 kohm  101.550 p  C
14478.90  108.361 kohm  -89.917  deg  156.599  ohm  108.361 kohm  101.441 p  C
20000.00   78.537 kohm  -89.901  deg  135.126  ohm   78.537 kohm  101.325 p  C

50uF 10% Non-Polarized Electrolytic
This is a fairly high value capacitor, so it is not surprising the ESR is also low.  However,
a closer examination also indicates the phase is beginning to increase above 300Hz.  There are
however two causes.

First, the real resistive part of the impedance goes no lower than about 50 milliohms.  Unlike
ESR that is frequency dependent, this resistance intercepts at a constant level.  As the reactive
part continues to decrease, the ratio is more and more purely resistive and the phase increases.
A second capacitor was checked, and it measured about the same.  These values also halved when
the two capacitors were measured in parallel.

Second, even though the capacitor is directly mounted using a banana jack the component leads
have formed an inductive loop that is about 60mm in diameter, resulting in approximately 80 nH
of lead inductance.  This would account for about +j0.010 ohms @ 20kHz and though this may seem insignificant, the capacitor reactance is also becoming smaller with increasing frequency. 
Since the phase angles cancel (-j for caps and +j for inductors), the imaginary reactive part
of the impedance at 20k would be 0.010 higher.  This again pushes the phase upward.  This is
essentially the beginning of self resonance.

In either case, this clearly shows the importance of short, or non-existent, test leads when
measuring higher value capacitors.

Buffer[3] Arb1                                                      Ver 5.01    
Completed: Tue Nov 29 11:13:04 2011
Drive level 2.201% [75.512 uA]
Sine,LoZP(LV/LA)->Buf03,22 pts
Shunts: Rp=10.047 kohm, Cp=6.918 pF
;---------------------------------------------------------------------------------------------
;   Freq     Impedance         Phase          Real          Imag        Series    *Dissipation
;     Hz    Z=mag(R,I)       Degrees      Z*cos(P)      Z*sin(P)        L or C     Factor
;---------------------------------------------------------------------------------------------
   20.00  142.950  ohm  -88.436  deg    3.901  ohm  142.897  ohm   55.689 u  C     27.3018E-03
   28.28  101.714  ohm  -88.346  deg    2.936  ohm  101.672  ohm   55.345 u  C     28.8798E-03
   40.00   72.416  ohm  -88.263  deg    2.195  ohm   72.382  ohm   54.971 u  C     30.3201E-03
   56.57   51.583  ohm  -88.195  deg    1.624  ohm   51.557  ohm   54.572 u  C     31.5086E-03
   80.00   36.751  ohm  -88.165  deg    1.177  ohm   36.732  ohm   54.163 u  C     32.0307E-03
  113.13   26.188  ohm  -88.161  deg  840.621 mohm   26.175  ohm   53.747 u  C     32.1160E-03
  159.99   18.646  ohm  -88.177  deg  593.164 mohm   18.636  ohm   53.378 u  C     31.8282E-03
  226.26   13.282  ohm  -88.192  deg  419.158 mohm   13.275  ohm   52.987 u  C     31.5741E-03
  319.98    9.448  ohm  -88.187  deg  298.944 mohm    9.444  ohm   52.670 u  C     31.6553E-03
  452.51    6.724  ohm  -88.154  deg  216.653 mohm    6.720  ohm   52.336 u  C     32.2382E-03
  639.94    4.773  ohm  -88.074  deg  160.401 mohm    4.770  ohm   52.141 u  C     33.6283E-03 <-NOTE 1
  905.00    3.388  ohm  -87.940  deg  121.786 mohm    3.386  ohm   51.939 u  C     35.9683E-03
 1279.85    2.414  ohm  -87.669  deg   98.154 mohm    2.412  ohm   51.562 u  C     40.6988E-03
 1809.97    1.712  ohm  -87.310  deg   80.325 mohm    1.710  ohm   51.431 u  C     46.9809E-03
 2559.66    1.218  ohm  -86.680  deg   70.551 mohm    1.216  ohm   51.120 u  C     58.0039E-03
 3619.86  866.341 mohm  -85.885  deg   62.167 mohm  864.108 mohm   50.882 u  C     71.9436E-03
 5119.21  607.568 mohm  -84.845  deg   54.590 mohm  605.110 mohm   51.379 u  C     90.2145E-03
 7239.59  436.813 mohm  -82.469  deg   57.250 mohm  433.045 mohm   50.766 u  C    132.2044E-03 <-NOTE 2
10238.23  304.969 mohm  -80.711  deg   49.228 mohm  300.970 mohm   51.650 u  C    163.5655E-03
14478.90  215.300 mohm  -75.863  deg   52.587 mohm  208.780 mohm   52.650 u  C    251.8759E-03
20000.00  153.198 mohm  -69.636  deg   53.311 mohm  143.623 mohm   55.407 u  C    371.1893E-03

Notes
1 Lead inductance is beginning to have an effect. Dissipation Factor is .033 (3.3%)
2 Lead inductance and internal resistance are now both significant, affecting phase.  The real
  component intercepts at ~0.05 ohm
3 The Dissipation Factor column (DF=ESR/Xc=Real/Imag) was calculated and added manually
  The effect of lead inductance and internal resistance has not been backed out

4.00uF 1% Polyester Film
This capacitor has a phase angle considerably closer to 90' indicating a correspondingly better
Dissipation Factor (DF=ESR/Xc).  However, as in the example above, lead inductance begins to
have a significant effect at the higher frequencies.

Buffer[4] Arb2                                                      Ver 5.01    
Completed: Tue Nov 29 11:13:04 2011
Drive level 2.201% [75.512 uA]
Sine,LoZP(LV/LA)->Buf04,31 pts
Shunts: Rp=10.047 kohm, Cp=6.918 pF
;---------------------------------------------------------------------------------------------
;   Freq     Impedance         Phase          Real          Imag        Series    *Dissipation*
;     Hz    Z=mag(R,I)       Degrees      Z*cos(P)      Z*sin(P)        L or C     Factor
;---------------------------------------------------------------------------------------------
    1.00   39.612 kohm  -89.931  deg   47.846  ohm   39.612 kohm    4.018 u  C      1.2079E-03
    1.41   27.917 kohm  -89.984  deg    7.736  ohm   27.917 kohm    4.031 u  C    277.1019E-06
    2.00   19.739 kohm  -89.976  deg    8.272  ohm   19.739 kohm    4.032 u  C    419.0484E-06
    2.83   13.958 kohm  -89.967  deg    7.985  ohm   13.958 kohm    4.031 u  C    572.0471E-06
    4.00    9.871 kohm  -89.962  deg    6.506  ohm    9.871 kohm    4.031 u  C    659.1325E-06
    5.66    6.980 kohm  -89.961  deg    4.730  ohm    6.980 kohm    4.031 u  C    677.6414E-06
    8.00    4.937 kohm  -89.959  deg    3.523  ohm    4.937 kohm    4.030 u  C    713.5941E-06
   11.31    3.491 kohm  -89.958  deg    2.589  ohm    3.491 kohm    4.029 u  C    741.5573E-06
   16.00    2.469 kohm  -89.956  deg    1.880  ohm    2.469 kohm    4.029 u  C    761.3979E-06
   22.63    1.746 kohm  -89.953  deg    1.420  ohm    1.746 kohm    4.028 u  C    813.0633E-06
   32.00    1.235 kohm  -89.950  deg    1.080  ohm    1.235 kohm    4.028 u  C    874.1829E-06
   45.25  873.382  ohm  -89.945  deg  835.019 mohm  873.382  ohm    4.027 u  C    956.0751E-06
   63.99  617.688  ohm  -89.939  deg  658.576 mohm  617.687  ohm    4.026 u  C      1.0662E-03
   90.50  436.869  ohm  -89.931  deg  524.601 mohm  436.869  ohm    4.026 u  C      1.2008E-03
  127.98  308.985  ohm  -89.921  deg  423.534 mohm  308.985  ohm    4.025 u  C      1.3707E-03
  180.99  218.546  ohm  -89.909  deg  346.041 mohm  218.546  ohm    4.024 u  C      1.5834E-03
  255.96  154.584  ohm  -89.895  deg  283.443 mohm  154.584  ohm    4.022 u  C      1.8336E-03
  361.98  109.348  ohm  -89.877  deg  234.642 mohm  109.347  ohm    4.021 u  C      2.1458E-03
  511.91   77.355  ohm  -89.856  deg  193.926 mohm   77.355  ohm    4.019 u  C      2.5070E-03
  723.94   54.734  ohm  -89.832  deg  160.160 mohm   54.734  ohm    4.017 u  C      2.9262E-03
 1023.80   38.717  ohm  -89.805  deg  131.948 mohm   38.716  ohm    4.015 u  C      3.4081E-03
 1447.86   27.395  ohm  -89.773  deg  108.419 mohm   27.395  ohm    4.013 u  C      3.9576E-03
 2047.57   19.382  ohm  -89.735  deg   89.733 mohm   19.382  ohm    4.010 u  C      4.6298E-03
 2895.67   13.716  ohm  -89.700  deg   71.815 mohm   13.716  ohm    4.007 u  C      5.2360E-03
 4095.05    9.719  ohm  -89.645  deg   60.151 mohm    9.718  ohm    3.999 u  C      6.1894E-03
 5791.22    6.867  ohm  -89.591  deg   49.056 mohm    6.867  ohm    4.002 u  C      7.1441E-03
 8189.95    4.868  ohm  -89.536  deg   39.405 mohm    4.868  ohm    3.992 u  C      8.0946E-03
11582.23    3.447  ohm  -89.420  deg   34.886 mohm    3.447  ohm    3.987 u  C     10.1209E-03
16379.58    2.438  ohm  -89.337  deg   28.230 mohm    2.438  ohm    3.986 u  C     11.5794E-03
20000.00    1.996  ohm  -89.325  deg   23.529 mohm    1.996  ohm    3.986 u  C     11.7865E-03

Note
1 The Dissipation Factor column (DF=ESR/Xc=Real/Imag) was calculated and added manually


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