AD8436

Data Sheet

Rev. B | Page 10 of 24

THEORY OF OPERATION

OVERVIEW

The AD8436 is an implicit function rms-to-dc converter that

renders a dc voltage dependent on the rms (heating value) of an

ac voltage. In addition to the basic converter, this highly integrated

functional circuit block includes two fully independent, optional

amplifiers, a standalone FET input buffer amplifier and a precision

dc output buffer amplifier (see Figure 1). The rms core includes

a precision current responding full-wave rectifier and a log-antilog

transistor array for current squaring and square rooting to imple-

ment the classic expression for rms (see Equation 1). For basic

applications, the converter requires only an external capacitor, for

averaging (see Figure 31). The optional on-board amplifiers

offer utility and flexibility in a variety of applications without

incurring additional circuit board footprint. For lowest power,

the amplifier supply pins are left unconnected.

Why RMS?

The rms value of an ac voltage waveform is equal to the dc voltage

providing the same heating power to a load. A common measure-

ment technique for ac waveforms is to rectify the signal in a

straightforward way using a diode array of some sort, resulting in

the average value. The average value of various waveforms (sine,

square, and triangular, for example) varies widely; true rms is

the only metric that achieves equivalency for all ac waveforms.

See Table 5 for non-rms-responding circuit errors.

The acronym “rms” means root-mean-square and reads as follows:

“the square root of the average of the sum of the squares” of the

peak values of any waveform. RMS is shown in the following

equation:

1

T

0

T

∫

(1)

the Analog Devices RMS-to-DC Applications Guide.

RMS Core

The core consists of a voltage-to-current converter (precision

resistor), absolute value, and translinear sections. The translinear

section exploits the properties of the bipolar transistor junctions

for squaring and root extraction (see Figure 24). The external

capacitor (CAVG) provides for averaging the product. Figure 20

shows that there is no effect of signal input on the transition times,

as seen in the dc output. Although the rms core responds to input

voltages, the conversion process is current sensitive. If the rms

input is ac-coupled, as recommended, there is no output offset

voltage, as reflected in Table 1. If the rms input is dc-coupled, the

input offset voltage is reflected in the output and can be calibrated

as with any fixed error.

V–

AC IN

V+

OUT

+

V +

5kΩ CAVG

ABSOLUTE

VALUE

CIRCUIT

V-TO-I

16kΩ

Figure 24. RMS Core Block Diagram

Table 5. General AC Parameters

Waveform Type (1 V Peak)

Crest Factor

RMS Value

Reading of an Average Value Circuit

Calibrated to an RMS Sine Wave

Error (%)

Sine

1.414

0.707

0.707

0

Square

1.00

1.00

1.11

11.0

Triangle

1.73

0.577

0.555

−3.8

Noise

3

0.333

0.295

Rectangular

2

0.5

0.278

−11.4

Pulse

10

0.1

0.011

−44

SCR

−89

DC = 50%

2

0.495

0.354

−28

DC = 25%

4.7

0.212

0.150

−30