Data Sheet

AD736

Rev. I | Page 11 of 20

Mathematically, the rms value of a voltage is defined (using a

simplified equation) as

rms

V

Avg

V

=

This involves squaring the signal, taking the average, and

then obtaining the square root. True rms converters are smart

rectifiers; they provide an accurate rms reading regardless of the

type of waveform being measured. However, average responding

converters can exhibit very high errors when their input signals

deviate from their precalibrated waveform; the magnitude of

the error depends on the type of waveform being measured. For

example, if an average responding converter is calibrated to

measure the rms value of sine wave voltages and then is used to

measure either symmetrical square waves or dc voltages, the

converter has a computational error 11% (of reading) higher

than the true rms value (see Table 5).

CALCULATING SETTLING TIME USING FIGURE 16

Figure 16 can be used to closely approximate the time required

for the AD736 to settle when its input level is reduced in amplitude.

The net time required for the rms converter to settle is the

difference between two times extracted from the graph (the

initial time minus the final settling time). As an example, consider

the following conditions: a 33 µF averaging capacitor, a 100 mV

initial rms input level, and a final (reduced) 1 mV input level.

From Figure 16, the initial settling time (where the 100 mV line

intersects the 33 µF line) is approximately 80 ms.

The settling time corresponding to the new or final input level

of 1 mV is approximately 8 seconds. Therefore, the net time for

the circuit to settle to its new value is 8 seconds minus 80 ms,

which is 7.92 seconds. Note that because of the smooth decay

characteristic inherent with a capacitor/diode combination, this

is the total settling time to the final value (that is, not the settling

time to 1%, 0.1%, and so on, of the final value). In addition, this

graph provides the worst-case settling time because the AD736

settles very quickly with increasing input levels.

RMS MEASUREMENT—CHOOSING THE OPTIMUM

rectified input signal during rms computation, its value directly

affects the accuracy of the rms measurement, especially at low

frequencies. Furthermore, because the averaging capacitor

appears across a diode in the rms core, the averaging time

constant increases exponentially as the input signal is reduced.

This means that as the input level decreases, errors due to

nonideal averaging decrease, and the time required for the

circuit to settle to the new rms level increases. Therefore, lower

input levels allow the circuit to perform better (due to increased

averaging) but increase the waiting time between measurements.

accuracy and settling time is required.

Table 5. Error Introduced by an Average Responding Circuit when Measuring Common Waveforms

Waveform Type 1 V Peak Amplitude

Crest Factor

True RMS

Value (V)

Average Responding Circuit

Calibrated to Read RMS Value of

Sine Waves (V)

% of Reading Error Using

Average Responding Circuit

Undistorted Sine Wave

1.414

0.707

0.707

0

Symmetrical Square Wave

1.00

1.00

1.11

+11.0

Undistorted Triangle Wave

1.73

0.577

0.555

−3.8

Gaussian Noise (98% of Peaks <1 V)

3

0.333

0.295

−11.4

Rectangular

2

0.5

0.278

−44

Pulse Train

10

0.1

0.011

−89

SCR Waveforms

50% Duty Cycle

2

0.495

0.354

−28

25% Duty Cycle

4.7

0.212

0.150

−30