Calculating the Quality Factor Q for Capacitors

Introduction

• The bridge meters ST2827 and ST2829 behave differently in the low D-range. The ST2829 consistently delivers more stable values.
• The ST2827 shows a slight phase shift compared to the ST2829, resulting in a larger angle in the C-range and a smaller one in the L-range.
• The formula De = Ae/100 does not yield a relative error in %, but an absolute one!
• So the error in D, even in the best accuracy range, is ±0.05/100 = ±0.0005 – which is significant for values between 0.00236 and 0.00239, expanding the interval to at least 0.00189 to 0.00286. (Capacitors with values below 0.0005 may even fall into the negative.)
• Since Q = 1/D, this results in a Q range from 350 to 529 around a nominal value of 422.

The formula for Qe only applies when Qx * De < 1 (i.e. the error is smaller than D itself). 422 × 0.0005 = 0.211

Qx² × De
Qe = ± ——————————————
      1 ± Qx × De

= ±(422²×0.0005)/(1±0.211) = +89.042/0.789 and -89.042/1.211 = +112 and -73

However, we are not in the best accuracy range. At 57Ω and 260kHz, the diagram shows A = 0.65. With 100mV, a factor of 3 is added, totaling 1.95. Kb is 0.0000003 and negligible, Ka is 0.00007, Kc is 0.0003, Kd is 0.0035, Ke is 1.

This gives Ae = ±[A + (Ka + Kb + Kc)×100 + Kd]×Ke = ±(1.95 + 0.00037×100 + 0.0035) = ±1.9905, and thus De ≈ ±0.02. Therefore, Qx × De > 1, making the formula above invalid. If ignored, the Q range stretches from 45 to extremely large values (tan 90°).

In practice, however, we observe that the devices deliver much more stable readings than the accuracy specs suggest. Inductance and capacitance values, for instance, are often far better than 2%, even over many hours.

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