Digital process for determining the effective value of a periodic electric test signal

An arrangement for producing a measurement quantity which provides an effective value of an electric test signal applied to an input of the arrangement, the arrangement comprising:

• a sampling device sampling the periodic electric test signal during a sampling interval to produce M samples, wherein the sampling interval corresponds to at least two periods of the periodic electric signal and wherein N samples of the M samples correspond to a first one of the at least two periods of the periodic test signal;
• an analog-to-digital converter downstream from the sampling device and digitizing the M samples;
• and
• an arithmetic block downstream from the analog-to-digital converter, the arithmetic block producing the measurement quantity by:
• squaring and adding the digitized samples up to and including the Nth digitized sample to produce a first resulting total;
• multiplying the first resulting total by two to produce a second resulting total;
• adding to the resulting total a correction factor to produce a third resulting total, wherein the correction factor corresponds to a square of a subtotal obtained from one-quarter of the Nth sample and three-quarters of the (N+1)th sample;
• dividing the third resulting total by M to produce a fourth resulting total;
• and
• extracting a square root of the fourth resulting total to produce the effective value of the periodic test signal.

A method of determining an effective value of a periodic electric test signal, comprising:

• sampling with a sampling device and an analog-digital converter the periodic electric test signal during a sampling interval to produce M samples, wherein M is an odd number, wherein the sampling interval corresponds to at least two periods of the periodic electric signal, and wherein N samples of the M samples correspond to a first one of the at least two periods of the periodic electric signal;
• and
• determining a corrected effective value of the periodic electric test signal according to the equation:
• I corrected = 2 M ⁢ ( [ ∑ k = 1 N ⁢ i 2 ⁢ ( n ) ] + 1 2 ⁡ [ 1 4 ⁢ i ⁢ ( N ) + 3 4 ⁢ i ⁢ ( N + 1 ) ] 2 ) ;
• wherein i(n) is a value of the nth sample of the periodic electric test signal.