ADE7978 datasheet(49/120 Pages) AD

49 / 120 page

Data Sheet

ADE7978/ADE7933/ADE7932

Rev. 0 | Page 49 of 120

ROOT MEAN SQUARE MEASUREMENT

Root mean square (rms) is a measurement of the magnitude of

an ac signal. Its definition can be both practical and mathematical.

Defined practically, the rms value assigned to an ac signal is the

amount of dc required to produce an equivalent amount of power

in the load. Mathematically, the rms value of a continuous signal

f(t) is defined as

dt

rms





(18)

For time sampled signals, rms calculation involves squaring the

signal, taking the average, and obtaining the square root.







rms

(19)

Equation 19 implies that for signals containing harmonics, the

rms calculation contains the contribution of all harmonics, not

only the fundamental.

The method used by the ADE7978 to compute the rms values is

to low-pass filter (LPF) the square of the input signal and take

the square root of the result (see Figure 66). If the input signal

f(t) is written as a sum of harmonic components, then













sin

)

(

(20)

The square of f(t) is















































sin

)

cos(

)

(

(21)

After the LPF and the execution of the square root, the rms

value of f(t) is obtained by







(22)

The rms calculation based on this method is simultaneously

processed on all current and voltage input channels. The results

are available in the following 24-bit registers: AIRMS, AVRMS,

AV2RMS, BIRMS, BVRMS, BV2RMS, CIRMS, CVRMS, CV2RMS,

and NIRMS (Address 0x43C0 to Address 0x43C9) and NVRMS

and NV2RMS (Address 0xE530 and Address 0xE531).

In addition, the ADE7978 computes the fundamental rms value of

the phase currents and voltages and makes them available in the

following 24-bit registers: AFIRMS, BFIRMS, CFIRMS, AFVRMS,

BFVRMS, and CFVRMS (Address 0xE537 to Address 0xE53C).

CURRENT RMS CALCULATION

This section describes how the rms values of all phase and neutral

currents are computed. Figure 66 shows the signal processing chain

for the rms calculation on one phase of the current channel. The

current channel rms value is processed from the samples used

in the current channel.

The current rms values are signed 24-bit values and are stored

in the AIRMS, BIRMS, CIRMS, and NIRMS registers. The rms

values of the fundamental components are stored in the AFIRMS,

BFIRMS, and CFIRMS registers. The update rate of the current

rms measurement is 8 kHz.

0xAED2C0 =

–5,320,000

0x512D40 =

+5,320,000

CURRENT

SIGNAL

FROM HPF

LPF

xIRMSOS[23:0]

xIRMS[23:0]

Figure 66. Current RMS Signal Processing

When Bit 14 (INSEL) of the CONFIG register is cleared to 0 (the

default value), the NIRMS register contains the rms value of the

neutral current. When the INSEL bit is set to 1, the NIRMS reg-

ister contains the rms value of the sum of the instantaneous values

of the phase currents. Note that in 3-phase, 3-wire delta configura-

tion, the Phase B current is not measured, and its estimated rms

value is equal to NIRMS when the INSEL bit is set to 1. See the

Neutral Current Mismatch section for more information.

With the specified full-scale analog input signal of 31.25 mV, the

ADC produces an output code that is approximately 5,320,000.

The equivalent rms value of a full-scale sinusoidal signal is

3,761,808, independent of the line frequency.

The accuracy of the current rms is typically 0.1% error from

the full-scale input down to 1/1000 of the full-scale input. This

measurement has a bandwidth of 3.3 kHz.

To ensure rms measurement stability, follow these steps:

Read the rms registers at least once per line cycle over 1 sec.

Average the readings to obtain the rms value.

The settling time for the current rms measurement is 580 ms for

both 50 Hz and 60 Hz input signals. The current rms measurement

settling time is the time it takes for the rms register to reflect the

value at the input to the current channel when starting from 0.

The serial ports of the ADE7978 work with 32-, 16-, or 8-bit

words, whereas the DSP works with 28-bit words. The 24-bit

signed xIRMS and xFIRMS registers are transmitted as 32-bit

registers with the eight MSBs padded with 0s (see Figure 67).

3124 23

24-BIT NUMBER

0000

Figure 67. 24-Bit xIRMS and xFIRMS Registers Transmitted as 32-Bit Words

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