Ease Capacitor ESL/ESR Measurement With Mercury-Wetted Relay

Taking the ratio of two successive current peaks of the oscillating waveform:

where

and

In each case, effective L, R, and C components for ESL/ESR measurement (Fig. 2) are:

1. when C2 is not connected (short circuit):

L1 = ESL1+LS,
R1 = ESR1+RS
C1 = C1 

2. when C2, similar to C1, is connected:

L2 = 2ESL1 + Ls
R2 = 2ESR1+RS
C = (C1)/2 

Using basic circuit equations:

Similarly,

are determined from the monitored waveform in the respective cases.

and

ESL1=L2 - L1

Similarly,

and

ESR1=R2 - R1

Thus, the ESL and ESR values of the capacitor under test can be determined simply by measuring the waveforms (Fig. 3) and using the above formulas. The initial charging voltage of the capacitor must be adjusted to accommodate the peak current rating of the mercury-wetted relay. Implementing readily available relays, this circuit targets capacitor values up to about 10 nF. Because the measured current is always used in ratio, absolute calibration of the current probe isn't necessary. Generally, ESL values up to tens of nanohenries and ESR values up to hundreds of milliohms can be measured precisely with this simple setup.

Taking the ratio of two successive current peaks of the oscillating waveform:

where

and

In each case, effective L, R, and C components for ESL/ESR measurement (Fig. 2) are:

1. when C2 is not connected (short circuit):

L1 = ESL1+LS,
R1 = ESR1+RS
C1 = C1 

2. when C2, similar to C1, is connected:

L2 = 2ESL1 + Ls
R2 = 2ESR1+RS
C = (C1)/2 

Using basic circuit equations:

Similarly,

are determined from the monitored waveform in the respective cases.

and

ESL1=L2 - L1

Similarly,

and

ESR1=R2 - R1

Thus, the ESL and ESR values of the capacitor under test can be determined simply by measuring the waveforms (Fig. 3) and using the above formulas. The initial charging voltage of the capacitor must be adjusted to accommodate the peak current rating of the mercury-wetted relay. Implementing readily available relays, this circuit targets capacitor values up to about 10 nF. Because the measured current is always used in ratio, absolute calibration of the current probe isn't necessary. Generally, ESL values up to tens of nanohenries and ESR values up to hundreds of milliohms can be measured precisely with this simple setup.