3 Sensitivity of PCB Rogowski coils used in energy metering vs. ADC noise performance

PCB Rogowski coil sensitivity is typically specified in microvolts per ampere and depends on the geometry (number of turns, coil dimension); core material (if any); current frequency; and environmental factors (temperature, humidity, external magnetic fields) [9]. Common sensitivities range from tens to a few hundred microvolts per ampere [9].

It’s a common accuracy requirement for residential electricity meters to measure a 250mA root-mean-square (RMS) phase current with 2% accuracy [1]. For example, with a 200μV/A Rogowski coil, the signal at the input of the ADC is only 200μV/A × 0.250A = 50μV for this phase current. The required ADC performance (that is, the noise which determines the effective resolution) to measure this signal with 2% accuracy is as low as 0.02 × 200μV/A × 0.250A = 1μV, as defined by Equation 1:

where, V_nADC is the required noise level of the ADC, tol is the specified measurement accuracy in percentage for a given phase current, I_phase-rms in amperes, and k is the sensitivity constant of the Rogowski coil in microvolts per ampere.

Therefore, in this example, the total noise of the ADC (the quantization noise plus white noise) needs to be lower than 1μV.

Comparing the 1μV ADC noise requirement to the specification of a precision ADC such as the Texas Instruments (TI) ADS131M08 [10], it is clear that achieving the intended performance level may require additional averaging of the ADC samples. Table 2 illustrates this averaging, and also shows the total ADC noise in RMS microvolts for various gain settings and data rates as defined by the oversampling ratio (OSR). With gain of 1 and a sample rate of 4kSPS (OSR = 1,024), the ADC noise is approximately 5μVrms. As noise improves at a factor of √2 for doubling the time of averaging, achieving the requirement of <1μV of ADC noise requires a time period of ≥16ms. This is acceptable for most energy metering systems, which commonly require an update rate of 20ms [1]. This type of averaging may be practically implemented with a combination of ADC internal oversampling using the delta-sigma ADC’s internal oversampling ratio (OSR ) feature and external post-averaging.

Another option suggested by Table 2 is to select a higher gain for the programmable gain amplifier (PGA) internal to the ADC, as it reduces the noise referred to the input [10]. Alternatively, you could precondition the signal with an external gain stage before it arrives at the ADC. An external gain stage increases the cost of the signal chain significantly, however.