Multipliers Applications

7/25/2019 Multipliers Applications

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IC MultipliersApplicatrions

Recommended Text: Sergio Franco, Design with

Operational Amplifiers and Analog Integrated

Circuits. McGraw-Hill, (1988) pp. 538-548


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Introduction

Nonlinear operations on continuous-valued analogsignals are often required in instrumentation,

communication, and control-system design. These operations include

rectification,

modulation - demodulation, frequency translation,

multiplication - division.

non-linear function In this chapter we analyze the most commonly used

techniques for performing this within a monolithic

integrated circuit


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In analog-signal processing the need often arises for a circuit

that takes two analog inputs and produces an output proportional

to their product. Such circuits are termed analog multipliers.

There are two different approaches to analog multipliers

One of them is based on log/antilog amplifiers Another utilizes the exponential transfer function of bipolar

transistors (Gilbert cell) .

In following sections we consider applications of IC multipliersbased on both approaches


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Log/Antilog Converter

The log and antilog functions can be combined in slide rule

fashion to perform such operations as

multiplication, division,

exponentiation, and

root computation.

Two of the most useful functions are

multifunction conversion and

true rms-to-dc conversion



Multifunction Converters

A multifunction converter (4302) is a circuit that accepts three inputs, Vx, Vy,

and Vz and yields an output Vo of the type: m

x

zyo

V

VKVV

=

where Kis a suitable scale factor (typically K = 1),

and m is a user-programmable exponent, in therange 0.2 < m < 5

where K is a suitable scalefactor (typically K = 1),

and m is a user-programmable exponent, inthe range 0.2 < m < 5

By proper selection of

input configuration andexponent, the circuit can beprogrammed for a varietyof operations:

etc./1,,,/, xn

z

m

zzxyxo VVVVVVVV =



With the help of simple op amp circuitry it can be configured

for additional operations, such as

non-integer exponent approximations, coordinate conversion, and

true rms-to-dc conversion.

Although now the tendency is to implement these functions

digitally, considerations of cost and speed often require their

implementation in analog hardware.



4302 block diagram

The circuit diagram of 4302 is shown with frequency compensation and

reverse-polarity protection omitted for simplicity.

By op amp action, we have

x

x

x R

VI =

y

y

y R

VI =

z

zz

R

VI =

o

oo

R

VI =

The voltages at pins 6

and 12 are proportional

to the log ratios of thecorresponding currents:

=

x

zTI

IVV ln6

=

y

o

T I

IVV ln

12



m=1

V6

and V12

are derived directly from V11

so that V6

= V12

= V11

.

By this impliesIz/I

x= I

o/I

ythat is,

Vz/V

x= V

o/V

y.

Thus,

( ) yoTxzT IIVVIIVV /ln/ln 126 ===

=

x

z

yo V

VVV



m1

m < 1: V6

is derived directly from V11

while V12

is derived from V11

via a

voltage divider, V12

=mV11

, where m=R2/(R1+R2).

Letting V12

=mV6

yields ,

that is,

This, in turn, yields ,

that is,

3. m > 1: V12 is derived directly from V11 while V6 is derived from V11 via avoltage divider, V6=(1/m)V

11, where (1/m)=R2/(R1+R2).

Letting V6=V

12/m yields

m

xzxzyo IIIImII )/ln()/ln()/ln( ==m

xzyo IIII )/()/( =m

xzyo VVVV )/()/( =

121

2where, +=

=

RRRm

VVVV

m

x

zyo



Multiplication and Division

E ti t d


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Exponentiator andRoot Extractor


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4302 Adjustment

In each con-figuration the scale factor is calibrated by setting the input(s) to

10 V and adjustingRy for Vo = 10 V.

To maintain the accuracy of division at low signal levels, the input offset

errors of the X and Z op amps must be nulled as follows

1. With Vz = Vx = 10.0 V, adjust R1 for Vo = 10.0 V.

2. With Vz = Vx = 100 mV, adjustR2 for Vo = 10.0 V.

3. With Vx = 100 mV and Vz = 10.0 mV, adjust R3 for Vo = 1.00 V. Repeat the procedure, if necessary.

The 4302 provides the following typical accuracies expressed as a percent of

the output full scale:

multiply, 0.25 percent;

divide, 0.25 percent;

square, 0.03 percent;

square root, 0.07 percent.

F d t lti li


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Four-quadrant multiplierAD534

Figure shows the complete multiplier AD534.

Four-quadrant operation is achieved by using two transconductance pairs

with the bases driven in antiphase and the emitters driven by a second V-I

converter. ))(( 212121 YYXXKZZ =

xxy

z

IRR

RK =


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AD534 Basic Configuration

The basic connection for four-quadrant multiplication, is used in

amplitude modulation,

voltage-controlled amplification, and

instantaneous power measurements.

When one of the inputs is zero,

the output should also be zero,

regardless of the signal at the other input. In practice, a small fraction of the other input will feed through to the output,

causing an error.

This can be minimized by applying an external voltage to theX2 or Y2 input.

This basic configuration has a number of useful variations.

For instance, tying the inputs together yields the squaring function.

Deriving Z1 from Vo via a voltage divider allows for scale factors other than

1/(10 V). Applying a signal to theZ1 terminal will cause it to be summed to the output


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AD534 Applications

))(( 212121 YYXXKZZ =

)()10/1( oxz VVV =

ozo VVV /10=

)()10/1( ooz VVV =

zo VV = 10


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Show that ( ) 10/22 yxo VVV =

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