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Copyright 1978 by Analog Devices, Inc. Printed in U.S.A.

All rights reserved. This publication, or parts thereof, must not be reproduced in any form without permission of the copyright owner.

Information furnished by Analog Devices, Inc., is believed to be accurate and reliable. However no responsibility is assumed by Analog Devices, Inc. , for its use.

Analog Devices, Inc., makes no representation that the intercon-nection of its circuits as described herein will not infringe on ex-isting or future patent rights, nor do the descriptions contained herein imply the granting of licenses to make, use , or sell equipment constructed in accordance therewith .

Specifications and prices are subject to change with out notice. We are pleased to acknowledge the invaluable contr ibu tions of James Williams and Barrie Gilbert, who have contributed to the design, testing, and/ or documentation of many of these circuits.

Edited by D. H. Sheingold.

i

P R E F A C E

C l o s e t e d i n P r o d u c t G u i d e s b e t w e e n " O p e r a t i o n a l A m p l i f i e r s " a n d " D a t a C o n v e r t e r s " i s

u s u a l l y a s e c t i o n c a l l e d " S p e c i a l " o r " F u n c t i o n " c i r c u i t s . W i t h i n t h i s e c l e c t i c f a m i l y o f d e -

v i c e s , t h e r e l i v e s t h e a n a l o g m u l t i p l i e r . M u l t i p l i e r s a r e p e r h a p s t h e m o s t g e n e r a l l y u s e f u l

m e m b e r o f t h e g r o u p , b u t t h e y a r c s c a r c e l y e v e r r e c o g n i z e d a s s o l u t i o n s - i n - w a i t i n g , a s

o p a m p s h a v e b e c o m e .

A s k a n e n g i n e e r w h a t c a n b e d o n e w i t h o p e r a t i o n a l a m p l i f i e r s o r w i t h s y s t e m s u s i n g d a t a

c o n v e r t e r s , a n d t h e r e s p o n s e w i l l b e l e n g t h y , f l u i d , a n d e n t h u s i a s t i c . T h e s a m e q u e r y w i t h

r e g a r d t o m u l t i p l i e r s i s l i a b l e t o y i e l d ( p a r t i c u l a r l y i n t h e w o r s t c a s e ) a b l a n k s t a r e , a l o n g

( t h o u g h t f u l ) p a u s e , a n d t h e b a r e l y a u d i b l e r e s p o n s e . . . " m u l t i p l y ( ? ) " O t h e r s m a y m e n t i o n

g e n e r a l c a s e s , l i k e a m p l i t u d e m o d u l a t o r s o r f u n c t i o n s y n t h e s i s , b u t t h e d e t a i l e d , i n s p i r e d t o r -

r e n t s o f a p p l i c a t i o n s t h a t d i s c u s s i o n s o f o p a m p s e v o k e s i m p l y a r e n ' t t h e r e .

W h y n o t ?

T w o r e a s o n s s u g g e s t t h e m s e l v e s . F i r s t , m u l t i p l i e r s an~ a d m i t t e d l y n o t a s b r o a d l y a p p l i c a b l e

a s a r e o p a m p s - w h i c h d o m i n a t e t h e a n a l o g w o r l d b e c a u s e o f t h e a b i l i t y o f e v e n t h e n e o -

p h y t e d e s i g n e r ( f r e s h f r o m a n u n d e r g r a d u a t e o p - a m p c o u r s e ) t o s e e t h e i r r e l e v a n c e a n d i m -

m e d i a t e a p p l i c a b i l i t y t o m e a s u r e m e n t a n d c o n t r o l p r o b l e m s . W i t h t h e a d v e n t o f d i g i t a l c o m -

p u t e r s a n d m i n i c o m p u t e r s , d i g i t a l i n s t r u m e n t s , a n d m i c r o p r o c e s s o r s , d a t a c o n v e r t e r s h a v e

a s s u m e d a r e a d i l y i d e n t i f i a b l e f u n c t i o n a l i t y . M u l t i p l i e r s - a n d o t h e r a n a l o g f u n c t i o n a l c o m -

p o n e n t s - c o n c e i v e d o r i g i n a l l y t o p e r f o r m c i r c u m s c r i b e d t a s k s i n a n a l o g c o m p u t i n g , s i m p l y

a p p e a r t o h a v e b e e n b o r n w i t h o u t c h a r i s m a .

S e c o n d , h i g h - p e r f o r m a n c e , e a s y - t o - i m p l e m e n t . l o w - c o s t m u l t i p l i e r s ( o n - a - c h i p ) h a v e o n l y

b e e n a v a i l a b l e f o r a f e w y e a r s . O p a m p s a n d d a t a c o n v e r t e r s h a v e b e e n m a t u r e p r o d u c t s f o r

m u c h l o n g e r . I t ' s i n t e r e s t i n g t o n o t e t h a t e v e n t h e n o w - u b i q u i t o u s o p a m p w a s a r o u n d f o r

q u i t e a w h i l e b e f o r e i t s c a p a b i l i t i e s w e r e w i d e l y r e c o g n i z e d a n d e x p l o i t e d . 1 t m i g h t a l s o b e

n o t e d t h a t t h e m a r k e t f o r d a t a c o n v e r t e r s w a s n ' t j u s t c r e a t e d , i t w a s d e m a n d e d b y t h e d i g i t -

a l r e v o l u t i o n o f t h e ' 6 0 ' s , a s t h e o n l y r a t i o n a l w a y o f i n t e r f a c i n g d i g i t a l s y s t e m s t o t h e R e a l

( a n a l o g ) W o r l d .

T h e a v a i l a b i l i t y o f g o o d m u l t i p l i e r s i n p r o f u s i o n e v o k e s t h e n e e d f o r a p p l i c a t i o n s l i t e r a t u r e .

T h e p r e s e n t e f f o r t c o m p l e m e n t s e a r l i e r p u b l i c a t i o n s ' i n d o c u m e n t i n g t h e s p r e a d i n g u s e s o f

a n a l o g m u l t i p l i c a t i o n , b u t t h e r e i s a d i f f e r e n c e o r a p p r o a c h . H e r e . t h e b u l k o f t h e e f f o r t h a s

g o n e i n t o t h e s e c t i o n o n A p p l i c a t i o n s . a l t h o u g h t h e r e i s s o m e r e v i e w o f b a s i c s a n d g e n e r a l -

i t i e s . T h e o b j e c t i v e h e r e i s t o c r e a t e a w a r e n e s s i n t h e r e a d e r th~1t t h e a n a l o g m u l t i p l i e r i s a

u n i v e r s a l l y a p p l i c a b l e p r o b l e m s o l v e r . T h a t i s , m u l t i p l i e r s d o n ' t " j u s t m u l t i p l y " i n t h e s a m e

w a y t h e o p a m p s d o n ' t " j u s t a m p l i f y " . T h e s e d e v i c e s m a k e p o s s i b l e a n a l o g s o l u t i o n s t o a n a -

l o g p r o b l e m s w i t h s i m p l i c i t y , s o p h i s t i c a t i o n , a n d l o w c o s t .

T h e d e p t h o f d e t a i l i n t h e t r e a t m e n t o r m a n y o f t h e a p p l i c a t i o n s i s i n t e n d e d t o a t t r a c t t h e

e n g i n e e r - a t - t h e b e n c h , w h o i s p a i n f u l l y aw~1re o f t h e g u l f b e t w e e n c o n c e p t s a n d c i r c u i t s - t h a t -

w o r k i n t h e c o l d , c r u e l w o r l d . T h o s e w h o a r c c h a r g e d ( o r w i l l b e ) w i t h d e s i g n i n g a p r o d u c t i o n

i n s t r u m e n t . a t e s t f i x t u r e , or~~ f u l l y i n s t r u m e n t e d s y s t e m . a r c t l w i n t e n d e d b e n e f i c i a r i e s o f

t h i s b o o k . N o r e a d e r c a n f a i l t o b e i m p r e s s e d b y t h e f a c t t h a t . i n m a n v o f t h e a p p l i c a t i o n s ,

t h e m u l t i p l y i n g f u n c t i o n , w h i c h i s t h e k e y t o p e r f o r m i n g t h e o v e r , J I I f u n c t i o n o r t h e s y s t e m .

c o m p r i s e s b u t a s m a l l p a r t o f t h e o v e r a l l c i r c u i t : t h e r e ' s p l e n t y o f r o o m f o r t h e r e a d e r t o e x -

e r c i s e h i s o w n e n g i n e e r i n g c r e a t i v i t y a n d j u d g m e n t o v e r t h e ~ 1 ctual i m p l e m e n t a t i o n o f t h e r e s t

o f i t . W e h o p e , t h e n . t h a t t h e p r e s e n t p u b l i c a t i o n w i l l s e r w b o t h n o v i c e a n d v e t e r a n a s a

g e n e r a t o r o f i d e a s

" . . . B e f r u i t f u l a n d m u l t i p l y . . . " ( G e n e s i s 1 - 2 2 )

1

1: 1 1 r c ' \ . l l l l p k . t h e 1\ n " l " " D e v i c e ' N O N I . I N L / \ 1{ C I I { C l i i T S 1 1 / \ N D i l O U K , , d i t c d h y D . I I . S h cin~ JJi d. c t v c t i l ; t h l c i ' u r

\ : " . 9 5 i ' r o l l l P . O . B ' " 7 ' J h . N n r w o o d M i \ 0 2 1 1 6 2 .

ll

CONTENTS

PREFACE

CONTENTS

MULTIPLIERS - SOME BASICS

MULTIPLICATION

DIVISION AND ROOTING

POLARITY

SPECIAL MULTIPLICATION-DIVISION FUNCTIONS

SCALING

BRIEF DEFINITIONS

APPLICATIONS

ii

2

2

3

3

3

4

INSTRUMENTA TION FUNCTIONS 5

WATTMETERS 5

WATT-HOUR METER 6

FLOWMETER 7

DENSITOMETER 9

PHASE MEASUREMENT AND PHASE-SENSITIVE DETECTION 10

ACOUSTIC THERMOMETER 11

SIGNAL GENERATORS AND FILTERS 13

WIEN-BRIDGE OSCILLATOR 13

VOLTAGE-CONTROLLED SINE-WAVE OSCILLATOR 14

CRYSTAL OSCILLATOR WITH AMPLITUDE-MODULATED OUTPUT 14

LOW-DISTORTION OSCILLATOR 16

VOLTAGE-CONTROLLED LOW-PASS FILTER 17

DERIVATIVE-CONTROLLED LOW-PASS FILTER 17

MISCELLAN EOUS MULTIPLIER APPLICATIONS 19

% DEVIATION - RATIO COMPUTER 19

COMPONENTSORTER 19

BRIDGE LINEARIZATION 21

H I G H - P E R F O R M A N C E R M S - T O - D C C O N V E R S I O N C I R C U I T

2 1

F R E Q U E N C Y D O U B L I N G

2 2

F I L T E R T E S T E R U S I N G W I D E B A N D M U L T I P L I E R 2 4

P E R F O R M A N C E A U G M E N T A T I O N

2 5

I N C R E A S E D A C C U R A C Y W I T H M U L T I P L Y I N G D A C ' S

2 5

C U R R E N T O U T P U T S

2 7

C U R R E N T B O O S T I N G

2 7

A U D I O P O W E R B O O S T E R 2 7

H I G H - V O L T A G E B O O S T E R 2 9

M U L T I P L I E R M E D L E Y

3 1

D I F F E R E N C E O F T H E S Q U A R E S

3 1

A U T O M A T I C L E V E L C O N T R O L 3 2

A U T O M A T I C G A I N C O N T R O L 3 2

A M P L I T U D E M O D U L A T O R 3 2

V O L T A G E - C O N T R O L L E D A M P L I F I E R 3 3

P O L Y N O M I A L S - P O W E R S E R I E S 3 3

A R B I T R A R Y ( N O N - I N T E G R A L ) P O W E R S

3 3

S I N E O F A V O L T A G E

3 4

S Q U A R E - R O O T O F T H E S U M O F S Q U A R E S ( V E C T O R S U M ) 3 5

. . _

V E C T O R O P E R A T I O N S - P O L A R - T O - R E C T A N G U L A R 3 5

C A R E A N D F E E D I N G A N D A L I T T L E T H E O R Y

3 7

B R I E F B I B L I O G R A P H Y

4 0

T E C H N I C A L D A T A v

i i i

t

M U L T I P L I E R S

S O M E B A S I C S

I n i t s s i m p l e s t c o n c e p t u a l f o r m , a n a n a l o g m u l t i p l i e r i s a t h r e e - t e r m i n a l ( p l u s c o m m o n ) d e v i c e

t h a t w i l l p e r f o r m t h e m a t h e m a t i c a l o p e r a t i o n s o f m u l t i p l i c a t i o n a n d d i v i s i o n , b y a p p r o p r i a t e

t e r m i n a l c o n n e c t i o n s . F i g u r e 1 s h o w s t h e c o n c e p t u a l b l o c k r e p r e s e n t i n g a m u l t i p l i e r .

V x

O U T

E = V x V y

o E R

V y

F i g u r e 1 . C o n c e p t u a l m u l t i p l i e r . E R i s a d i m e n s i o n a l s c a l e c o n s t a n t ,

u s u a l l y 1 0 V

F o r g i v e n v a l u e s o f t h e i n p u t s , Y x a n d Y y , t h e o u t p u t w i l l b e Y x Y y / E R , w h e r e E R i s a d i -

m e n s i o n a l c o n s t a n t , u s u a l l y e q u a l t o 1 0 v o l t s . S i n c e s q u a r i n g i s s i m p l y a m u l t i p l i c a t i o n o f a n

i n p u t b y i t s e l f , i t f o l l o w s t h a t t y i n g X a n d Y t o g e t h e r w i l l y i e l d a s q u a r e d t e r m a t t h e o u t p u t ,

i . e . , i f Y x = Y y = Y i n , t h e o u t p u t w i l l b e Y i n

2

/ E R .

D i v i s i o n a n d s q u a r e - r o o t i n g , b e i n g i n v e r s e s o f t h e a b o v e o p e r a t i o n s , c a n b e i m p l e m e n t e d b y

p l a c i n g t h e m u l t i p l i e r i n t h e f e e d b a c k p a t h o f a n o p e r a t i o n a l a m p l i f i e r , a s F i g u r e 2 s h o w s .

S i n c e m o s t m u l t i p l i e r s u s e a n o p e r a t i o n a l a m p l i f i e r a s t h e o u t p u t c i r c u i t , a s e t o f s i m p l e

e x t e r n a l j u m p e r c o n n e c t i o n s p e r m i t t h e s a m e ( c o m p l e t e ) d e v i c e t o p e r f o r m i n a n y o f t h e

f o u r m o d e s .

( N U M E R A T O R ) V , R

R

INPUT,V,~

E ' Y . . L

V x Eo = - V z . E

0

= - R v . .

E R

V , ( D E N O M I N A T O R )

' : ) 0 O U T P U T ( A N S W E R ! )

E o

( a ) D i v i s i o n

E 2

~A= - V z

E

0

= J - V , E R

I V , < O)

" ) 0 E

0

O U T P U T

( b ) S q u a r e R o o t

F i g u r e 2 . F e e d b a c k c o n n e c t i o n o f c o n c e p t u a l m u l t i p l i e r f o r d i v i s i o n

a n d s q u a r e - r o o t i n g

O f w h a t u s e i s s u c h a d e v i c e ? M u l t i p l i e r s s e r v e w e l l i n a n u m b e r o f a r e a s i n c l u d i n g a n a l o g

c o m p u t i n g ( e . g . , r a t i o d e t e r m i n a t i o n , f u n c t i o n s , r m s c o n v e r s i o n ) , s i g n a l p r o c e s s i n g ( a m p l i -

t u d e m o d u l a t i o n , f r e q u e n c y m u l t i p l i c a t i o n , s e r v o m e c h a n i s m s ) , m e a s u r e m e n t ( w a t t m e t e r s

2

and phase-sensitive detectors), and in a miscellany of useful functions (linearization of trans-ducers , percentage computing, bridge linearizi ng). T he Table of Contents gives a reasonably full list at a glance.

The designer , be he battle-scarred veteran , or astute neophyte , well-alerted to the difficulties of applying theoretical models to Real Solutions, will wonder what circuit contortions arc required to transform the black boxes on the diagrams into Real Multipliers. Happily, very little . High performance multipliers, such as the AD532 and AD534, are completely self-contained IC's, laser-trimmed at the factory, whose actual implementation schematic is joyfully close to the theoretical. In fact, in some ways even better. The ADS 3 5 is very similar to the AD534, only it is trimmed, tested and specified in the divide mode.

MULTIPLICATION Practical use of an AD534 in the multipl y mode is shown in Figure 3. No trims, capacitors, or other appendages are required. In addition , the AD534 is even more versatile than the theoretical version introduced in Figure I , since all the inputs are differential (including the feedback circuit). This allows such multipliers to be used in systems having grounds of less than impeccable character and permits direct subtraction, where needed , as well as permitting other terms (additive constants or variables) to be included in the transfer function.

AD534

BASIC RE LATIONSHI P' (X1 X21 (Y 1 Y2) = 10V (Z1- Z2) VVv = 10V E0

Figure 3. Signal connections of an actual multiplier

Many of the other multipliers in our catalog do require a set of external trims, for scale factor and/ or output/ input offsets, but offer compensating advantages, such as extra-low cost , wide bandwidth , an active division terminal (for YZ/ X function s) , or the like . Even pre-trimmed units can be ex ternally trimmed where th e application calls for optimization "to a gnat's eyelash."

DIVISION AND ROOTING Division with the AD534 or AD535 is configured with equal ease (Figure 4). In division circuits, where the multiplying operation comprises the feedback path , only one polarity of denominator is permitted , since reversal of th e denominator reverses th e sense of the feed-back loop. In addition , the closed-loop gain is inversely proportional to the denominator voltage (approaching "infinity" at zero input). This - in general - causes increased noise, error, and output lag, for small values of denominator, in inverse proportion to Vz.

Xl

X2 OUT!--1~-0UTPUT. E0 AD534

OR AD535 + Zlt----ir---

- NUMERATOR. V, Z2 ........,,__..,... (EITHER Yl \7 POLARITY)

Figure 4. Connection of the AD534/AD535 for division

The AD534/AD535 square-roots easily, but requires a diode- connected as shown in Figure 5 - to prevent latchup, which can occur in such configurations if the input were to change polarity , even momentarily . As shown in Figure 5, the device is set up for the positive square root. The output may be made negative by reversing the diode polarity and inter-

c h a n g i n g t h e X i n p u t l e a d s . S i n c e t h e s i g n a l i n p u t i s d i f f e r e n t i a l , a l l c o m b i n a t i o n s o f i n p u t

a n d o u t p u t p o l a r i t i e s c a n b e r e a l i z e d .

r-a---------------~~-1~-ClOUT,E

0

R L O A D

( M U S T B E P R O V I D E D )

Z1~+

_ I N P U T , V z

Z 2

' \ 7 E o J - 1 0 V V ,

E

0

( - E

0

) 1 0 V V ,

F i g u r e 5 . C o n n e c t i o n o f t h e A D 5 3 4 / A D 5 3 5 f o r s q u a r e r o o t i n g

I f t h e o u t p u t c i r c u i t d o e s n o t p r o v i d e a r e s i s t i v e l o a d t o g r o u n d , o n e s h o u l d b e c o n n e c t e d

( a b o u t 1 O H 2 ) t o m a i n t a i n d i o d e c o n d u c t i o n . F o r c r i t i c a l a p p l i c a t i o n s , t h e Z o f f s e t c a n b e

a d j u s t e d f o r g r e a t e r a c c u r a c y b e l o w 1 V .

P O L A R I T Y

T h e A D 5 3 4 i s a 4 - q u a d r a n t m u l t i p l i e r . T h i s m e a n s t h a t , f o r i t s t w o i n p u t s , t h e r e a r e f o u r p o s -

s i b l e p e r m u t a t i o n s o f p o l a r i t y , a n d t h e o u t p u t p r o d u c t w i l l a l w a y s b e o f t h e c o r r e c t p o l a r i t y .

T h e i n p u t s c a n b e m a p p e d o n t h e f o u r q u a d r a n t s o f a n X - Y p l a n e , a s s h o w n i n F i g u r e 6

( h e n c e t h e t e r m " 4 - q u a d r a n t " ) . S o m e m u l t i p l i e r s w i l l o p e r a t e i n o n l y o n e o r t w o q u a d r a n t s .

A t w o - q u a d r a n t m u l t i p l i e r w i l l a c c e p t a s i g n a l a t o n e i n p u t a n d a u n i p o l a r s i g n a l a t t h e

o t h e r ; i n t h e s i n g l e - q u a d r a n t c a s e , t h e i n p u t s a r e r e s t r i c t e d t o a s i n g l e p o l a r i t y f o r e a c h i n p u t .

V y M A X

I I

v x M I N I I I . . . v x M A X

I l l

I V

V y M I N

F i g u r e 6 . I n p u t p l a n e s h o w i n g m u l t i p l i c a t i o n q u a d r a n t s

D i v i d e r s a r e e i t h e r t w o - q u a d r a n t o r o n e - q u a d r a n t d e v i c e s , b e c a u s e , a s n o t e d e a r l i e r , t h e d e -

n o m i n a t o r m a y h a v e o n l y o n e p o l a r i t y . H o w e v e r , i n t h e c a s e o f d e v i c e s h a v i n g t h e e x t r a

d e g r e e s o f f r e e d o m p r o v i d e d b y d i f f e r e n t i a l i n p u t s , t h e X i n p u t m a y b e o f e i t h e r p o l a r i t y ,

a s l o n g a s i t i s c o n n e c t e d t o X

1

a n d X

2

i n t h e p r o p e r s e n s e .

S P E C I A L M U L T I P L I C A T I O N - D I V I S I O N F U N C T I O N S

T h e 4 3 6 i s a n e x a m p l e o f a s p e c i a l i z e d , d e d i c a t e d , h i g h - p e r f o r m a n c e , t w o - q u a d r a n t d i v i d e r

o n l y . T h e 4 3 3 a n d 4 3 4 a r e e x a m p l e s o f t h r e e - i n p u t s i n g l e - q u a d r a n t h i g h - a c c u r a c y m u l t i p l i e r

d i v i d e r s ( Y Z / X ) ; t h e 4 3 3 h a s t h e f u r t h e r d i s t i n c t i o n t h a t t h e e x p o n e n t o f t h e r a t i o ( Z / X )

c a n b e a d j u s t e d f r o m 1 / 5 t o 5 i . e . , Y ( Z / X )

1 1 1

I n t h e A D 5 3 ! I C , t h e i n t e r n a l r e f e r e n c e c u r r e n t

m a y b e m a n i p u l a t e d e x t e r n a l l y , p e r m i t t i n g a f o r m o f t h r e e - v a r i a b l e m u l t i p l i e r - d i v i d e r , i n

w h i c h t h e s c a l e c o n s t a n t c a n b e v a r i e d .

S C A L I N G

A s m e n t i o n e d e a r l i e r , m u l t i p l i e r s a r e a l m o s t a l w a y s d e s i g n e d ( b u t n o t n e c e s s a r i l y c o n s t r a i n e d )

t o h a v e a d i m e n s i o n a l s c a l e c o n s t a n t , E R , o f 1 O V . T h i s p e r m i t s e i t h e r i n p u t t o h a v e a n y

v a l u e i n t h e I O V f u l l - s c a l e r a n g e , w i t h o u t c a u s i n g t h e o u t p u t t o e x c e e d 1 O V . F o r a p p l i c a t i o n s

i n w h i c h t h e m a x i m u m r a n g e o f t h e i n p u t s i s s u b s t a n t i a l l y l e s s t h a n I O V , o r i f t h e m u l t i p l i e r

i s u s e d f o r d i v i s i o n a n d t h e n u m e r a t o r c a n e x c e e d t h e d e n o m i n a t o r , i t i s h e l p f u l t o u s e a

s m a l l e r v a l u e o f E R . T h i s c a n b e d o n e w i t h t h e A D 5 3 4 , t h e A D 5 3 1 , t h e 4 3 3 , a n d t h e 4 3 4 .

3

4

BRIEF DEFINITIONS2

The most obvious specification of importance is accuracy , which may be defined in terms of the total error of the multiplier at room temperature and constant nominal supply voltage. Such errors include input and output de imperfections , plus nonlinearity , plus feed through. Temperature dependence and supply variation effects are specified separately. Scale Factor The scale-factor error is the difference between the average scale factor and the ideal scale factor of (1 OVr 1 . It is expressed in % of the output signal and can be trimmed for critical applications . Temperature dep endence is specified. Output Offset refers to the offset voltage at the output-amplifier stage. This is usually mini-mized at manufacture and can be trimmed where high accuracy is desired. Remember that the output offset will drift with temperature.

Linearity error , or nonlinearity , is th e maximum difference between actual and th eoretical output, for all pairs of input values, expressed as a percentage of full scale, with all other de errors nulled, i.e ., the irreducible minimum error. It is usually expressed in terms of X and Y nonlinearity , with the named input swinging over its full-scale range , and the oth er input at lOY. If the user recognizes that linearity errors are usually largest at large input values, im-provement in predicted linearity can be gained, for small inputs , using the approximate non-linearity equation: f(X ,Y) = IVx lEx +IVY lEy , where Ex and Ey are the specified linearity errors, and Yx and Yy are the maximum respective input signal ranges.

X or Y Feedthrough is the signal at the output for any value of X or Y input when the other input is zero . It has two components, a linear one corresponding to an offset at the zero in-put, which may be trimmed out (but can drift) , and a nonlinear one which is irreducible. Feedthrough is usually specified at one frequency (50Hz) for a 20V p-p sinewave input and increases with frequency.

Dynamic parameters include small-signal bandwidth , full-power response, slew( ing) rate , small-signal amplitude error , and settling time . These terms should be familiar to all but the most de-minded op-amp users. Small-signal bandwidth is the frequency at which the output is down 3dB from its low-frequency value (i.e. , by about 30%), for a nominal output amplitude of 10% of full scale. Full-power response is the maximum frequency at which the multiplier can produce full-scale voltage into its rated output load without noticeable distortion. Slew(ing) rate is the maximum rate of change of output voltage for a large input-signal step change . Small-signal amplitude error is defined in relation to the frequency at which the am-plitude response , or scale factor , is in error by 1%, measured with a small ( 10% of full scale) signal. Settling time (for a 1 OV step, multiplied by 1 OV) , is the total length of time the out-put takes to respond to an input change and stay within some specified error band of its

fin~! value. Settling time cannot be accurately predicted from any other dynamic specifica-tions ; it is specified in terms of a prescribed measurement. Vector error is the most-sensitive measure of dynamic error. It is usually specified in terms of the frequency at which a phase error of 0.01 radian (0.57) occurs. In variable-transconductance multipliers, the most-significant lags occur in the output stage, with considerably smaller differential lags between the inputs. Thus, they are well-suited to such applications as power measurement , where input phase may be important, but the output is usually filtered.

2 Complctc definitions and tests can be found in the NONLINEAR CIRCUITS HANDBOOK.

A P P L I C A T I O N S

I N S T R U M E N T A T J O N F U N C T I O N S

W A T T M E T E R S

M u l t i p l i e r s a r e w e l l s u i t e d f o r w a t t m e t e r d e s i g n s . F i g u r e 7 s h o w s a s i m p l e a r r a n g e m e n t t h a t

m e a s u r e s t h e p o w e r o u t p u t o f a n a u d i o a m p l i f i e r i n t o a l o a d . T h e 1 8 k . s 1 - l O k . Q d i v i d e r s c a l e s

t h e a m p l i f i e r ' s o u t p u t v o l t a g e s w i n g t o a m a x i m u m o f 1 O V ( f r o m a m a x i m u m o f 2 8 V , r e p r e -

s e n t i n g a b o u t l O O W p e a k p o w e r ) , w e l l w i t h i n t h e A D S 3 4 ' s i n p u t r a n g e . T h e v o l t a g e i s m e a s -

u r e d a c r o s s t h e l o a d , w i t h t h e t a p o f t h e d i v i d e r c o n n e c t e d t o X

1

a n d t h e l o w e r e n d o f t h e

l o a d t o X

2

. T h e p o w e r d i s s i p a t e d i n t h e d i v i d e r i s n e g l i g i b l e ( 1 / 3 5 0 0 o f t h e p o w e r i n t h e l o a d ) .

1 8 k " E "

~ I X l

I N P U T

' ' P " O U T

r-----------------~X2

O U T

A D 5 3 4

Z l

\ ) t I " I " I Y l Z 2

Y 2

F i g u r e 1 . W a t t m e t e r m e a s u r e s a u d i o - a m p l i f i e r o u t p u t p o w e r i n t o

d u m m y l o a d

C u r r e n t i s m e a s u r e d w i t h a 4 - t e r m i n a l , O . l n s h u n t . T h e O . l . Q " s t e a l s " o n l y a b o u t 1 / 8 0 o f

t h e v o l t a g e c o m i n g o u t o f t h e a m p l i f i e r , b u t t h e d i f f e r e n t i a l v o l t a g e m e a s u r e m e n t e n s u r e s

t h a t e v e n t h i s s m a l l d i f f e r e n c e b e t w e e n t h e a m p l i f i e r o u t p u t a n d t h e l o a d v o l t a g e d o e s n o t

a f f e c t t h e m e a s u r e m e n t o f t h e p o w e r d i s s i p a t e d i n t h e l o a d . T h e A D 3 0 l A o p a m p i s u s e d t o

a m p l i f y t h e s i g n a l u p t o m a n a g e a b l e l e v e l s a n d t o p r e s e n t i t t o t h e m u l t i p l i e r ' s Y i n p u t . T h e

o u t p u t o f t h e m u l t i p l i e r i s ( X

1

- X

2

) ( Y ) / 1 0 , w h i c h i s p r o p o r t i o n a l t o t h e p r o d u c t o f l o a d

v o l t a g e a n d c u r r e n t , h e n c e t h e p o w e r d i s s i p a t e d i n t h e l o a d .

I n p r a c t i c e , t h e o u t p u t o f t h e a m p l i f i e r u n d e r t e s t s h o u l d b e c o n n e c t e d t o t h e i n p u t o f t h e

c i r c u i t t h r o u g h n u m b e r 1 6 w i r e . C o n n e c t i o n s s h o u l d b e m a d e w i t h s o l d e r e d l u g s t o m i n i m i z e

c o n t a c t r e s i s t a n c e , a n d t h e l o a d s h o u l d b e a h i g h - w a t t a g e - c a p a c i t y , n o n - r e a c t i v e 8 . s 1 r e s i s t o r .

A n u m b e r o f v e n d o r s s u p p l y 8 . s 1 , 1 O W r e s i s t o r s , e n c a s e d i n f i n n e d , i n t e g r a l h e a t s i n k s , w h i c h

m a y b e b o l t e d t o a l u m i n u m p l a t e s f o r o p t i m u m d i s s i p a t i o n c h a r a c t e r i s t i c s . A n 8 . s 1 l o u d -

s p e a k e r c o u l d b e u s e d a s a l o a d , b u t t h e c o s t o f t h e n e c e s s a r y a n e c h o i c c h a m b e r o r c o n c e r t

h a l l ( t o a v o i d l o s s o f f r i e n d s i n t h e l a b o r a t o r y - o r o n e ' s h e a r i n g ) s h o u l d b e c o n s i d e r e d . T h i s

s y s t e m c a n b e u s e d t o t e s t i n s t a n t a n e o u s a m p l i f i e r p o w e r i n t o a r e s i s t i v e l o a d a s a f u n c t i o n

o f f r e q u e n c y a n d w a v e f o r m . W i t h a n a v e r a g i n g o u t p u t , i t w i l l t e s t a v e r a g e p o w e r . W i t h a

l o u d s p e a k e r , i t w i l l d e t e r m i n e h o w m u c h p o w e r i s d e l i v e r e d t o a r e a l l o a d .

S o m e i n t e r e s t i n g c h a r a c t e r i s t i c s o f i n c a n d e s c e n t l a m p s c a n b e o b s e r v e d i f t h e 8 . s 1 l o a d i s

5

6

replaced by a light bulb and a transistor switch . This configuration was used to determine th e optimum price-performance breakpoint in a computer-controlled scoreboard. Trace A of F igure 8 is the bulb voltage, trace B is th e AD30 1 A "current" amplifier output, and trace C is the AD534 "power" output.

A 10V/DIV

B

c 2V/DIV

20ms/DIV

Figure 8. Turn-on power of cold incandescent lamp

The waveforms show that the bulb pulls almost 2. 5 times the power at turn-on as it does in the steady state. In Figure 9, the bulb has been pre-biased just below the illumination level by connecting a "leak" resistor across the switch. This pre-heating of the filament dramati-cally reduces th e turn-on power requirements , which results in an increase of bulb life. In ad-dition, the transient demand on the power supply (which also runs the computer) is reduced , eliminating logic-deranging spikes.

20ms/DIV

Figure 9. Turn-on power of incadescent lamp from standby

For three-phase wattage measurements, voltages proportional to the voltages and currents in each phase are multiplied in each of three analog multipliers and summed in an operational amplifier. 3

WATT-HOUR METER A power-measuring circuit similar to that used in Figure 8 is employed in the watt-hour meter circuit of Figure 10. An isolation amplifier allows the multiplier output to be measured without safety hazard. The Model 284J isolation amplifier is chosen for economy and because it furnishes a fully floating dual supply , which drives the active circuitry. The output of the 284J represents the instantaneous power delivered to th e load , which is a "40-watt" light bulb .

3 "Detection and Measurement of Three-Phase Power, Reac tive Power, and Power Factor, with Minimum Time Delay ," by

l. R. Smith and L. A. Snyder , Proc. IEEE, November, 1970, p. 1866 .

8 0 k

" E "

~ I X 1

I S O L A T E D

P O W E R

F O R A 0 5 3 4

A N D A D 3 0 8

, . - - - - - - - - - - - 1 X 2

" I "

" > I I Y 1

Y 2

A D 5 3 4

1 k

6 7

A D 5 3 7

+ 1 5 V

F R E Q U E N C Y O U T P U T T O C O U N T E R S ,

C O M P U T E R , E T C .

A N A L O G O U T

I N S T A N T A N E O U S P O W E R

F i g u r e 1 0 . L i n e w a t t m e t e r - w a t t - h o u r m e t e r

T o o b t a i n t h e w a t t - h o u r f u n c t i o n , t h i s s i g n a l i s a v e r a g e d a n d c o n v e r t e d t o f r e q u e n c y b y a n

A D 5 3 7 V / f c o n v e r t e r . T h e p u l s e r e p e t i t i o n r a t e o f t h e A D 5 3 7 w i l l v a r y i n d i r e c t p r o p o r t i o n

t o t h e a v e r a g e p o w e r c o n s u m e d b y t h e l o a d . A c o u n t e r w i l l d e t e r m i n e t h e t o t a l e n e r g y c o n -

s u m e d o v e r t h e d e s i r e d i n t e r v a l .

D i f f e r i n g s e n s i t i v i t i e s ( w a t t - m i n u t e s , w a t t - m i l l i s e c o n d s , e t c . ) c a n b e o b t a i n e d b y a l t e r i n g t h e

s c a l e f a c t o r o f t h e A D 5 3 7 , t h e g a i n t o t h e 2 8 4 , o r t h e c o u n t r a t i o o n t h e A D 5 3 7 o u t p u t .

I f a n a n a l o g o u t p u t i s d e s i r e d , a n a n a l o g i n t e g r a t o r m a y b e s u c c e s s f u l l y e m p l o y e d w i t h i n t h e

l i m i t a t i o n s o f t h e c o m p o n e n t s c h o s e n . A c c u r a c i e s t o w i t h i n 1 % o r b e t t e r a r e a c h i e v a b l e

w i t h t i m e c o n s t a n t s o f 1 O O k s , b u t 1 O O O s i s p e r h a p s a m o r e p r a c t i c a l l i m i t .

F L O W M E T E R

T h e a c c u r a t e m e a s u r e m e n t o f t h e f l o w r a t e o f l i q u i d s f 1 o w i n g a t s l o w s p e e d s p r e s e n t s a d i f f i -

c u l t t r a n s d u c t i o n p r o b l e m . A f l o w t r a n s d u c e r o f w i d e d y n a m i c r a n g e a t l o w f l o w r a t e s m a y

b e c o n f i g u r e d w i t h t h e a i d o f a n a l o g m u l t i p l i e r s a n d a p a i r o f w e l l - m a t c h e d , l i n e a r - r e s p o n d i n g

t e m p e r a t u r e s e n s o r s .

T h e t h e o r y b e h i n d t h e f l o w m e t e r c a n b e u n d e r s t o o d b y r e f e r r i n g t o F i g u r e 1 1 . T h e c o n c e p -

t u a l t r a n s d u c e r i s c o m p o s e d o f a s e c t i o n o f t u b i n g , a h e a t e r d i s s i p a t i n g a c o n s t a n t a m o u n t o f

p o w e r i n t o t h e t u b i n g , a n d t w o t e m p e r a t u r e s e n s o r s . T h e e n t i r e a s s e m b l y i s w r a p p e d i n

F i b e r g l a s t o l i m i t a n d s m o o t h t h e t h e r m a l l o s s r a t e .

T 1

T 2

F L U I D - - - -

b

1 \

I

I

F L O W

I

I

t t

t

I

H E A T

F i g u r e 1 1 .

F l o w m e t e r p r i n c i p l e

W i t h n o f l o w t h r o u g h t h e p i p e , t h e p o w e r i s d i s s i p a t e d i n t o t h e m e d i u m i n a s y m m e t r i c a l

m a n n e r . U n d e r t h e s e c o n d i t i o n s , t h e t e m p e r a t u r e s e n s o r s , T 1 a n d T 2 , w i l l i n d i c a t e a n e t t e m -

p e r a t u r e d i f f e r e n c e o f z e r o . A s f l o w b e g i n s , T 1 w i l l c o n t i n u e t o a s s u m e t h e v a l u e o f t h e u p -

s t r e a m t e m p e r a t u r e , b u t T 2 w i l l b e i n f l u e n c e d b y t h e p o w e r d i s s i p a t e d i n t o t h e m o v i n g s t r e a m .

7

8

The temperature difference between T 1 and T 2 will be solely a function of flow rate, so long as the specific heat of the fluid remains constant. Changes in stream or ambient temper-ature will be effectively offset by T 1 , which serves as a baseline for the measurement. It is worth noting that the flowmeter is bidirectional. If the flow reverses direction, the meas-urement is still valid . By detecting which sensor is hotter, and by how much, the transducer will indicate what the flow rate is and which way it is going.

A working version of the theoretical model is shown in Figure 12. The transducer comprises a 1,4'' inside-diameter stainless steel tube which has been turned down and force fit through the core of a standard 20W ceramic-coated resistor. Silicon grease is used to facilitate thermal transfer between the resistor and the tubing. At each end of the tube , stainless-steel mesh has been inserted to break up the laminar flow of the liquid and promote mixing. The re-quirement for linear, matched temperature sensors is met with distinction by the ADS90 current-output temperature transducers.

Z1 = IN752 Z1 = IN752 CR 1 ~ IN4148 CR 1 ~ IN914 g;. ~otN~d5~ 2N2222

RA & R8 MATCH : 0.1 %

2.5k

MEASURED POWER

95k

FURNISHED BY J . WILLIAMS~ PATEN T PENDING

Figure 12. Flowmeter circuit

In theory, the power dissipated by the resistor can be held constant by driving it with a fixed voltage. In practice, changes in the resistor's value over time and temperature (remember, the resistor is being used as a heater, so the temperature rise will be quite substantial) mandate a requirement for a constant wattage regulator. The regulator determines the V I product at the load (in similar manner to the wattmeters described in Figures 7 and 10), compares it to a de set-point reference, and feeds the amplified difference back to the load. At the wattmeter, X measures the voltage, Y measures the current in the 1 .S1 shunt, and the output of the ADS34 therefore measures the power. The AD741 is used as the servo ampli-fier , and an ADS80 bandgap reference provides the set point, which is compared with the power measured by the ADS34. Boosted power to heat the resistor is provided via Ql, which provides voltage gain, and the Darlington pair, Q2-Q3 , which provide current boost. Since Q 1 inverts the AD7 41's output, feedback is returned to the "+" input terminal. C 1 provides dynamic feedback for stability and noise reduction. The D l-Q4 contbination provides the SV nominal drive potential to the ADS 90 temperature transducers. The l11A/K current output of the ADS 90's is converted to voltage by RA and Rs, and the difference is amplified by the ADS 21 instrumentation amplifier, set for a gain of 1 OOV /V. Figure 13 is a plot of flow rate vs. the output voltage of the ADS 21 . The function is hyper-bolic (flow period is measured linearly) and may be converted to a linear measure of the flow rate by performing a division (Const/x) to obtain the reciprocal. The function could be

p e r f o r m e d i n a d i v i d e r - c o n n e c t e d g e n e r a l - p u r p o s e m u l t i p l i e r , l i k e t h e A D 5 3 2 o r t h e A D 5 3 4 ,

b u t f o r w i d e r d y n a m i c r a n g e a n d b e t t e r p e r f o r m a n c e a t l o w - l e v e l o u t p u t s f r o m t h e A D 5 2 1 , a

h i g h - a c c u r a c y d e d i c a t e d d i v i d e r , s u c h a s t h e 4 3 6 , c a n b e u s e d , a s s h o w n i n t h e f i g u r e .

2 4 0

2 1

1 8

1 5

0

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I

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I

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)

)

\

! ' \ . .

" I ' -

t - -

1 2 1 6 2 0 2 4 2 8 3 2 3 6 4 0

A D 5 2 1 O U T P U T X 1 0 0 m V

F i g u r e 1 3 . F l o w r a t e v s . o u t p u t v o l t a g e o f t h e A D 5 2 1 , s h o w i n g

i n v e r s e r e l a t i o n s h i p

T h e o u t p u t o f t h e d i v i d e r c a n b e c a l i b r a t e d t o r e a d ( f o r e x a m p l e ) 1 O V a t f u l l s c a l e . O t h e r

s c a l e f a c t o r s a r e p o s s i b l e b y c h a n g i n g t h e g a i n o f t h e A D S 2 1 o r o f t h e d i v i d e r . T h e t i m e r e -

s p o n s e o f t h e f l o w m e t e r i s s l o w - o f t h e o r d e r o f 1 0 - 1 5 s e c o n d s . I n m o s t l o w f l o w - r a t e a p p l i -

c a t i o n s , t h i s i s n o t a s e v e r e p e n a l t y , u n l e s s t h e f l o w r a t e c h a n g e s q u i c k l y o v e r a w i d e d y -

n a m t c r a n g e .

D E N S I T O M E T E R

I n t h i s a p p l i c a t i o n , a m a t h e m a t i c a l f u n c t i o n t h a t i s n o t e a s y t o a c h i e v e w i t h a s i n g l e m u l t i -

p l i e r i s n e e d e d f o r l i n e a r i z i n g . T h e p r o b l e m h a s b e e n r e s o l v e d b y t h e u s e o f a M o d e l 4 3 3

m u l t i f u n c t i o n c o m p o n e n t , w h i c h e m b o d i e s t h e m a t h e m a t i c a l r e l a t i o n s h i p Y ( Z / X )

1 1 1

I n F i g -

u r e 1 4 , t h e d e n s i t y o f a l i q u i d m o v i n g i n a p i p e i s c o m p u t e d b y m e a s u r i n g t h e d i f f e r e n c e b e -

t w e e n v e l o c i t y - p r o d u c e d p r e s s u r e a n d s t a t i c p r e s s u r e i n t h e p i p e . T h i s o u t p u t i s n o n l i n e a r l y

r e l a t e d t o d e n s i t y , a n d t h e 4 3 3 p e r f o r m s t h e l i n e a r i z a t i o n .

- . - - - - - - ,

-

-

m " ' 2

0 - 5 V

~VOLTAGE P R O P O R T I O N A L T O p~ z

_ . . , . . ; : V O L T A G E

~---+-~~ PROPOR~ONAL T O

y X

V O L T A G E

P R O P O R T I O N A L T O

p I D E N S I T Y )

S C A L E

F A C T O R

A D J U S T M E N T

P " 2~: (-~t F ) '

E

0

~ g V 6 P \ - - - - v : -

F i g u r e 1 4 . B l o c k d i a g r a m o f d e n s i t o m e t e r

T h e s t a t i c p r e s s u r e i n t h e p i p e i s t a k e n t h r o u g h a s i m p l e o r i f i c e i n t h e p i p e w a l l . T h e v e l o c i t y -

p r o d u c e d p r e s s u r e i s g e n e r a t e d b y a P i t o t t u b e . T h e p r e s s u r e p r o d u c e d i n t h e P i t o t t u b e i s

g o v e r n e d b y t h e r e l a t i o n s h i p ,

P o u t = P V

2

/ 2 + P o

9

10

The differential pressure at the output of the pressure sensor is: pV2

L':-P = Pout - Po = -2-

Therefore , the density , p, is

p = 2t:-P (~Y If L':-P and V are measured electrically, the analogous voltage corresponding top can be com-puted electrically using a 433 , withY analogous to L':-P , X analogous to V, Z a scale constant, and m = 2. The choice of flowmeter and pressure sensor depends upon the ranges of the variables and the conditions of measurement. In the case of the actual device illustrated here, a high-level-output LX-series pressure transducer was used, together with a flowmeter consisting of a

\

paddle wheel, which interrupted a light beam from a light-emitting diode, and a frequency-to-analog converter.

PHASE MEASUREMENT AND PHASE-SENSITIVE DETECTION Although there has been a vast increase in the use of square waves and pulses , in their various degrees of freedom (amplitude , frequency, phase, duty cycle, code), for conveying informa-tion, sine waves are still widely used. The analog multiplier is a simple and useful way of re-covering information from sine waves. Figure 15a shows the AD532 connected as a phasemeter. At a given frequency, if the phase reference signal is applied to one input of the multiplier, and the phase-shifted signal is ap-plied to the other input, and a further 90 phase shift is introduced between the inputs, then the average value of the product is proportional to the sine of the phase angle. Since the sine is approximately equal to the angle (in radians) for small angles, this circuit provides a good linear measure of phase for small angles (within 0.0025 radian for angles up to 0. 25 radian, or 14), and a sinusoidal measure for angles between 90 .

A INPUT I VR sin wt 1kHz

""

10k

~B INPUT

< 1 > 1

V s i n w t

E o

E

0

= ~ s i n w t { s i n w t c o s + c o s w t s i n )

E

0

= ~ ( s i n

2

w t c o s + s i n w t c o s w t s i n )

E

0

= ~( [ 1 - c o s 2 w t ] c o s + s i n 2 w t s i n r p )

E a = ~cos =~ ( I N P H A S E )

-~ ( 1 8 0 O U T O F P H A S E )

OUT~

E o

R

F i g u r e 1 5 b . P h a s e - s e n s i t i v e d e t e c t o r f o r s i n u s o i d a l s i g n a l s . M e a s u r e s

m a g n i t u d e o f i n - p h a s e o r 1 8 0 " - o u t - o f - p h a s e i n p u t w i t h p r o p e r p o l a r i t y ,

d e p e n d i n g o n p h a s e r e l a t i o n s h i p t o r e f e r e n c e , w i t h l e s s t h a n 1 % n o m i n a l

e r r o r f o r p h a s e s h i f t b e t w e e n s i g n a l a n d r e f e r e n c e o f l e s s t h a n 0 . 1 4

r a d i a n ( 8 )

F i g u r e 1 5 c s h o w s a p h a s e - s e n s i t i v e d e t e c t o r i n w h i c h t h e r e f e r e n c e s i g n a l i s a s q u a r e w a v e . I f

t h e s i g n a l a n d t h e r e f e r e n c e a r e i n p h a s e , t h e o u t p u t i s p o s i t i v e ; i f t h e y a r e 1 8 0 o u t - o f - p h a s e ,

t h e o u t p u t w i l l b e n e g a t i v e . T h e o u t p u t m a g n i t u d e w i l l b e /

0

V V R I s i n w t I , a n d t h e a v e r -

a g e o u t p u t w i l l b e t h e a c a v e r a g e 0 . 6 3 6 Y i n Y r e f f o r s i n e w a v e s . T h e c i r c u i t w i l l t o l e r a t e s m a l l

p h a s e s h i f t s b e t w e e n t h e s i g n a l a n d t h e r e f e r e n c e .

r v

0

i l l -

I

I

I

I

I

I

I

I

I

m

S I G N A L

V s i n w t

V R E F

I X 1

D C O U T P U T ( F I L T E R

V A L U E S D E P E N D O N

I N P U T F R E Q U E N C Y )

O U T P U T

( S I G N A L A N D R E F E R E N C E

I N P H A S E )

+ V V R s i n w t D U R I N G P O S I T I V E H A L F - C Y C L E

( - V ) ( - V R ) s ; n w t D U R I N G N E G A T I V E H A L F - C Y C L E

P O S I T I V E - S I G N A L A N D R E F E R E N C E I N P H A S E

N E G A T I V E - S I G N A L A N D R E F E R E N C E 1 8 0 O U T O F P H A S E

F i g u r e 1 5 c . P h a s e - s e n s i t i v e d e t e c t o r , s q u a r e - w a v e r e f e r e n c e

A C O U S T I C T H E R M O M E T E R

A n o v e l a n d w i d e - r a n g e t e 1 ] 1 p e r a t u r e s e n s o r c a n b e c o n s t r u c t e d b y u s i n g t h e r e l a t i o n s h i p b e -

t w e e n t h e s p e e d o f s o u n d a n d a b s o l u t e t e m p e r a t u r e . A c o u s t i c t h e r m o m e t e r s r e l y o n t h e

p r i n c i p l e t h a t t h e s p e e d o f s o u n d v a r i e s p r e d i c t a b l y w i t h t e m p e r a t u r e i n a k n o w n m e d i u m .

T h e y a r e u s u a l l y i m p l e m e n t e d a s e i t h e r c l o c k e d ( p u l s e d ) s y s t e m s o r o s c i l l a t o r s . I n b o t h

m o d e s , t h e s e n s o r i s , i n e f f e c t , a t h e r m a l l y d e p e n d e n t d e l a y l i n e .

I n t h e o r y , t h e s p e e d o f s o u n d t h r o u g h a m e d i u m i s p r e d i c t a b l e a n d r e p r o d u c i b l e o v e r t e m p e r -

a t u r e r a n g e s f r o m c r y o g e n i c t o t h o u s a n d s o f d e g r e e s . A c o u s t i c t e c h n i q u e s w i l l f u n c t i o n a t

e x t r e m e s w h i c h o t h e r s e n s o r s c a n n o t t o l e r a t e . T h e r e l a t i o n s h i p b e t w e e n t h e s p e e d o f s o u n d

i n d r y a i r ( f o r e x a m p l e ) a n d t e m p e r a t u r e i s :

c = 331.5~ m / s .

T h u s , f o r a m e a s u r e d v a l u e o f c , t h e a b s o l u t e t e m p e r a t u r e i s

T =

2 7 3

3 3 1 . 5 2 c

2

I f c i s m e a s u r e d i n t e r m s o f t h e l e n g t h o f t i m e , 6 t , r e q u i r e d f o r a s o u n d i m p u l s e t o t r a v e l a

g i v e n d i s t a n c e , " A . , t h e a b s o l u t e t e m p e r a t u r e i s

- 2 7 3 ) \

2

( 1 )

2

T - 3 3 T S T 6 t

1 1

12

Thus, in addition to the physical hardware for implementing the measurement, a means of computing the inverse square is needed. It could be the 433, as used in Figure 14. However, in this case, a Model 436 high-accuracy dedicated divider was used for reciprocation, and an AD534 multiplier was used for squaring. A linearized temperature sensor using analog components is shown in Figure 16. Some of the critical waveforms are shown in Figure 17. The clock pulse (trace A) simultaneously sets the flip-flop, drives the piezoelectric 40kHz transducer, and triggers the 7 4121 one-shot into its output low state. This causes Q6 to turn off, allowing the AD812-AD820 current source to begin charging C4, the 0.04J.LF integrating capacitor (trace C).

+15V ACOUSTIC MED IUM

+5V SPECIAL I

AD8 12

AD820

3.3k .J

100pF C4 = 0.04M F I. 02 03 06 = 2N708 V A L'L OT HER NPN = 2N2222A 04 = AD8 12 SON IC TRANSDUCERS- MASSA ELECTRONICS MODEL 109- (40kHz)

Figure 16. Acoustic-thermometer analog output

A 5V/DIV

B 5V/DIV

c 5V/DIV

Figure 11. Waveforms in acoustic thermometer

When the acoustic pulse reaches the receiver transducer, the output is amplified by the AD301A amplifiers, producing the damped pulse train of trace B- the output of the second AD30 1 A. The leading edge of the pulse train is used to reset the Q2-Q3 flip-flop, via the third

~

A D 3 0 1 A , w h i c h f u n c t i o n s a s a c o m p a r a t o r . W h e n t h e f l i p - f l o p r e s e t s , Q 6 i s t u r n e d o n , a n d

t h e c u r r e n t s o u r c e t u r n s o f f v e r y q u i c k l y , t y p i c a l l y i n 1 O n s .

T h e v o l t a g e o n C 4 a t t h i s t i m e i s a f u n c t i o n o f t h e l e n g t h o f t h e t u b e a n d i t s t e m p e r a t u r e .

T h e f u l l - s c a l e t r i m i s a d j u s t e d b y a l t e r i n g t h e s l o p e o f t h e r a m p a t t h e c u r r e n t s o u r c e w i t h

t h e S O k D . p o t e n t i o m e t e r i n t h e A D 8 1 2 c o l l e c t o r l i n e . T h e v o l t a g e a t C 4 i s u n l o a d e d b y t h e

f i r s t L M 3 1 0 f o l l o w e r , a n d t h e v a l u e i s s t o r e d i n t h e sa mple~hold f o r m e d b y s w i t c h Q 8 , t h e

0 . 0 3 J . 1 F c a p a c i t o r , a n d t h e s e c o n d L M 3 1 0 . T h e s t o r e d v o l t a g e i s p r o p o r t i o n a l t o t h e t r a n s i t

t i m e o f s o u n d i n t h e t u b e .

T o o b t a i n a n o u t p u t r e a d i n g p r o p o r t i o n a l t o t e m p e r a t u r e , t h e o u t p u t o f t h e s a m p l e - h o l d i s

a p p l i e d t o t h e d e n o m i n a t o r i n p u t o f t h e M o d e l 4 3 6 p r e c i s i o n d i v i d e r ; a c o n s t a n t d e r i v e d

f r o m t h e A D 5 8 1 r e f e r e n c e i s a p p l i e d t o t h e n u m e r a t o r . T h e o u t p u t o f t h e 4 3 6 i s s q u a r e d i n

a n A D 5 3 4 , t h u s o b t a i n i n g a n o u t p u t v o l t a g e w h i c h i s a m e a s u r e o f t h e a b s o l u t e t e m p e r a t u r e .

A v o l t a g e d e r i v e d f r o m t h e A D 5 8 1 m a y b e o p t i o n a l l y a p p l i e d t o i n p u t Z 2 o f t h e A D 5 3 4 t o

s u b t r a c t a c o n s t a n t . i f t h e a n a l o g r e a d o u t i s d e s i r e d i n d e g r e e s C e l s i u s . T h e A D 5 3 4 o u t p u t

w i l l b e r e l a t e d t o t h e t e m p e r a t u r e a t t h e t r a n s d u c e r t o a t y p i c a l a c c u r a c y o f b e t t e r t h a n 1 %

o v e r a 0 t o I 0 0 C r a n g e .

T h e p r o s p e c t i v e c o n s t r u c t o r o f t h i s c i r c u i t s h o u l d b e a w a r e o f t h e d i f f i c u l t y o f d e v e l o p i n g a

g o o d t r a n s d u c e r d e s i g n . T h e d e s i g n u s e d h e r e i s c r u d e i n c o m p a r i s o n t o w h a t c a n b e a c h i e v e d .

A c o u s t i c t h e r m o m e t e r s i n v o l v e a g r e a t d e a l o f e n g i n e e r i n g t o c o m p e n s a t e f o r e r r o r s i n t h e

s o n i c t r a n s d u c e r s , t h e r m a l e x p a n s i o n e f f e c t s i n t h e t u b e w a l l s , w a v e d i s p e r s i o n i n s i d e t h e t u b e ,

a n d s u n d r y o t h e r p o t e n t i a l p r o b l e m a r e a s . T h i s e x a m p l e , w h i l e c e r t a i n l y w o r k a b l e , i s p r i m a r -

i l y i n t e n d e d t o s h o w t h e k e y r o l e o f t h e a n a l o g m u l t i p l i e r a n d d i v i d e r i n o b t a i n i n g a n o u t p u t

t h a t l i n e a r l y r e p r e s e n t s t e m p e r a t u r e , o n c e a t i m e i n t e r v a l c a n b e m e a s u r e d .

S I G N A L G E N E R A T J O N A N D F I L T E R S

W I E N - B R I D G E O S C I L L A T O R

F i g u r e 1 8 i s a s c h e m a t i c d i a g r a m o f a s t a b i l i z e d W i e n - b r i d g e o s c i l l a t o r . T h e A D S 3 4 s e r v e s a s

a v a r i a b l e - g a i n a m p l i f i e r f o r t h e f e e d b a c k s i g n a l f r o m o u t p u t t o i n p u t , v i a t h e W i e n b r i d g e .

T h e p e a k - r e c t i f i e r & f i l t e r c o m b i n a t i o n a p p l i e s s u f f i c i e n t v o l t a g e t o t h e X ( d e n o m i n a t o r ) i n -

p u t t o s u p p o r t s t a b l e o s c i l l a t i o n w i t h a b o u t 0 . 2 % r i p p l e . T h e c i r c u i t h a Y n o s t a r t u p p r o b l e m s ,

x ,

+ V s

1Ml1~

I

X z

A D 5 3 4

= -

I

O U T P U T

1 9 k H z

S F

1 2 V P K .

Y z

-

F i g u r e 1 8 . S t a b i l i z e d W i e n - b r i d g e o s c i l l a t o r

1 3

14

since X is small and the gain very high, allowing rapid buildup of the oscillation. Tighter amplitude control is possible with other schemes at the expense of simplicity. This circuit will typically stay within 0.01 dB of am plitude over 1 0C temperature range and 1 V supply variation.

VOLT AGE-CONTROLLED SINE-WAVE OSCILLATOR Voltage-to-frequency converters using charge balancing and other techniques (for example, Models 456 , 454, 460, and the monolithi c AD537) are readily available and feature excel-lent performance at low cost . However , voltage-contro lled oscillators with sine-wave out-put are not so plentiful and constitute a non-trivial design task if reasonable performance is desired.

Figure 19 shows two multipliers being used to form integrators with controllable time con-stants in a 2nd-order-differential-equation feedback loop. R2 and RS are connected for con-trolled current-output operation. The currents are integrated in capacitors C 1 and C3 , and the resulting voltages at high impedance are unloaded by the X inputs of the " next" ADS 34. The frequency-control input , Ein, connected to the Y inputs, varies the integrator gains, with a sensitivity of 1 OOHz/V , to 1 OV. C2 (proportional to C 1 and C3), R3, and R4 provide re-generative damping to start and maintain oscillation. The diode bridge, CR1-CR4 and Zener diode Z 1 provide economical temperature-compensated amplitude stabilization at 8.5V by degenerative damping. Figure 20 shows the VCO's response to a ramp input.

OUT 10Vsin wt

R3 X1 330k

X2 OUT R2 OUT

AD534 16k. AD534 R5 10V COS Wl EIN Z1 Z1 16k.

Y1 Z2 Y 1 Z2 C1 Y2 C3 w = 21Tf Y2 ~0.01 ~0.01.

f = 100E1NHz

PRECISION ELEMENT

Figure 19. Voltage-controlled sine-wave oscillator

10V DIV

10ms DIV

Figure 20. Ramp-modulated output of V.C.O.

CRYSTAL OSCILLATOR WITH AMPLITUDE-MODULATED OUTPUT Fast amplitude slewing and settling of a crystal-stabilized oscillator are provided by an AD534 in the circuit of Figure 21 . This arrangement was used to test 3 2. 768kHz clock crystals for Q vs. amplitude.

- 1 5 V

S O L I D

T A N T A L U M

C I R C U I T U S E D

T O O B T A I N

+ 1 5 V

W A V E F O R M S M O D U L A T I O N

I N F I G U R E 2 2 I N P U T

- - - - - - - - - . , \

+ 1 5 V I

A D 5 8 0 ( ) - - - - , : \

H . P .

2 1 4

P U L S E

G E N

Z

0

= s o n

I - 1

~r

I

I

I

I

I

I

2 . 7 k

A D 5 8 0

O U T P U T

F i g u r e 2 1 . C r y s t a l o s c i l l a t o r c i r c u i t , s h o w i n g h i g h - s p e e d g a i n a d j u s t m e n t .

T h e c i r c u i t a t t h e l o w e r l e f t w a s u s e d t o o b t a i n t h e t e s t w a v e f o r m s i n

F i g u r e 2 2 .

T h e " b l a c k - b o x " c r y s t a l o s c i l l a t o r ' s o u t p u t i s c o n v e r t e d t o d e b y t h e A D 5 3 6 r m s / d c c o n v e r -

t e r . T h e A D 5 3 6 o u t p u t i s s u m m e d i n a n A D 7 4 1 w i t h t h e d e r e f e r e n c e v o l t a g e o b t a i n e d b y

i n v e r t i n g a n d a m p l i f y i n g t h e o u t p u t o f a n A D 5 8 0 b a n d - g a p r e f e r e n c e . * T h e A D 7 4 1 d r i v e s

t h e 2 N 2 2 2 2 c o n t r o l t r a n s i s t o r t o c l o s e t h e f e e d b a c k l o o p a r o u n d t h e o s c i l l a t o r b y a d j u s t i n g

i t s s u p p l y v o l t a g e . T h e o p a m p r u n s a t a g a i n o f 3 5 V / V , a s d e t e r m i n e d b y i t s f e e d b a c k c i r c u i t .

T h e 1 5 0 0 p F c a p a c i t o r s t a b i l i z e s t h e l o o p .

A m p l i t u d e m o d u l a t i o n c o u l d b e o b t a i n e d b y c h a n g i n g t h e r e f e r e n c e v o l t a g e , b u t s e t t l i n g t i m e

w o u l d b e l o n g b e c a u s e o f t i m e c o n s t a n t s i n t h e A D 5 3 6 f i l t e r c i r c u i t , a s w e l l a s a n y u n k n o w n

p o l e s i n t h e " b l a c k - b o x " o s c i l l a t o r .

F a s t s e t t l i n g i s c o n v e n i e n t l y o b t a i n e d b y u s i n g a n A D 5 3 4 a s a n a m p l i t u d e m o d u l a t o r . T h e

o s c i l l o s c o p e p h o t o o f F i g u r e 2 2 s h o w s t h e 3 2 . 7 6 8 k H z w a v e f o r m b e i n g s w i t c h e d b y a f a s t s t e p

~ . . ~ ~ r a r . f i i I i i r i 1 . . r . ~.. i i 1 1 1

I I I I l 1 I

0 . 5 V I D

u u ~ ~~ ~ ~~~~

2 V I D I V

I I f 1

1

'l '

. . ~ . . ~ . . ~ . . ~ . . . . . ~ . . . ~ . . . . : ; . . ~ . . . . , , , ' l l . . ~,

1 V I D I V

O u s / 0

F i g u r e 2 2 . A m p l i t u d e m o d u l a t i o n o f c r y s t a l o s c i l l a t o r o u t p u t . U p p e r

t r a c e i s u n m o d u l a t e d o u t p u t , m i d d l e t r a c e i s m o d u l a t i n g w a v e f o r m ,

l o w e r t r a c e i s m o d u l a t e d o u t p u t .

* T h e n e w l y a v a i l a b l e A D 5 8 L c o u l d a l s o h a v e b e e n u s e d , i n i t s c o n n e c t i o n a s a t w o - t e r m i n a l - l O Y r e f e r e n c e .

1 5

16

from 0.3 to 2.2 volts peak-to-peak, with no ringing, overshoot , or other untoward dynamics. Since an nns-to-dc converter is used in th e co ntro l loop to measure th e output for setting the amplitude, the output of the circuit can be readily ca librated in rms volts, if desired .

LOW-DISTORTION OSCILLATOR A low-distortion (0.01 %) oscillator is depicted in F igure 23. Amplifier AI is connected as a non-inverting gain of about 3. The band-pass filt er , R 1, C 1, RS , C2, provides notched feed-back at 1kHz, causing the circuit to oscill ate at f0 = (2 1r RC)- 1 , where R 1 = R5 =Rand C1 = C2 =C. The output amplitude is measured and compared with the set-point voltage by R6 and R7 at the input of A2. Integrator A2 accumul ates the error and applies voltage to input Y 1 of the AD532 multiplier. This will increase or decrease the gain in the damping feedback loop around A 1. This loop can be visualized as a "smart" resistor , of large value , that parallel-trims R4 and adjusts the overall gain of A 1 to keep the oscillation stable.

+15V (REF)

AMPLITUDE CONTR OL

RZ 9.76k

DAMPI NG

R3 301k 1%

R4 20k

L---'V\11...--.~ OUT AD532

21

R7 C3 + 499k 1%

3.3)J F RB R6

lOOk 1% 10k

CR1 IN4148

X2

Y1

Y2

R5 15.9k 1%

A1 "' R5 "' R c, 0 c, 0 c

fo = 2 rr ~C-

OUTPUT

Figure 23. Low-distortion sine-wave oscillator

Since the multiplier is linear, and its output is attenuated to provide a "vernier" gain adjust-ment on the oscillator amplifier, its distortion has negligible effect upon the output. The distortion is due primarily to the nonlinearity of the op amp. An AD540J provides 0.01 % distortion at the frequency in this exam ple, 1kHz. F igure 24 shows the output waveform in trace A and th e crossover distortion, greatly amplified ( from the output of a distortion ana-lyzer) in trace B.

A

B 5V/DIV (0.005% DISTORTION/DIV)

Figure 24. Waveforms in /ow-distortion oscillator- output and distortion

~

V O L T A G E - C O N T R O L L E D L O W - P A S S F I L T E R

F i g u r e 2 5 i s t h e c i r c u i t o f a c o n t r o l l e d l o w - p a s s f i l t e r , a n d F i g u r e 2 6 s h o w s i t s r e s p o n s e t o a

s q u a r e - w a v e i n p u t , a s t h e c o n t r o l i n p u t r a m p s t h e t i m e c o n s t a n t f r o m v e r y s l o w t o q u i t e

f a s t r e s p o n s e .

d B

C O N T R O L

I N P U T

E c

x ,

+ V s

o r

O U T P U T B

S I G N A

I N P U T

E ,

x ,

S F

v ,

v ,

A D 5 3 4

O U T P U T

z ,

z ,

- V s

R

_ r

O U T P U T B = 1 + T

1

P

1 + T z P

1

O U T P U T A = 1 + T 2 P

T 1 = d . , = R C

T 2 = _ 1 _ = ! _ ( ) _ R C

w z E c

F i g u r e 2 5 . V o l t a g e - c o n t r o l l e d l o w - p a s s f i l t e r

. . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

I I

~

l l

' l 1

G

. l ' . .

~ . . .

0 0 0 0

~

O O u s / 0

2 V / D I V

F i g u r e 2 6 . R e s p o n s e o f ! o w - p a s s f i l t e r t o s q u a r e w a v e a s c u t o f f f r e q u e n c y

i s l i n e a r l y i n c r e a s e d

T h e v o l t a g e a t o u t p u t A , w h i c h s h o u l d b e u n l o a d e d b y a f o l l o w e r , r e s p o n d s a s t h o u g h t h e

i n p u t s i g n a l , E s , w e r e a p p l i e d d i r e c t l y t o t h e f i l t e r , b u t i t s b r e a k f r e q u e n c y i s m o d u l a t e d b y

E c , t h e c o n t r o l i n p u t . T h e b r e a k f r e q u e n c y , f

2

, i s e q u a l t o E c / ( 2 0 7 1 " R C ) , a n d t h e r o l l o f f i s a t

- 6 d B p e r o c t a v e .

O u t p u t B , t h e d i r e c t o u t p u t o f t h e A D 5 3 4 , h a s t h e s a m e r e s p o n s e u p t o f r e q u e n c y f

1

, t h e

" n a t u r a l " b r e a k p o i n t o f t h e R C f i l t e r ( l / ( 2 7 r R C ) ) , t h e n l e v e l s o f f a t a c o n s t a n t a t t e n u a t i o n

o f f

2

/ f

1

= E c / 1 0 .

F o r e x a m p l e , i f R = 8 H 2 , C = 0 . 0 0 2 1 1 F , O u t p u t A h a s a p o l e a t f r e q u e n c i e s f r o m 1 0 0 H z t o

1 0 k H z , f o r E c r a n g i n g f r o m l O O m V t o l O Y . O u t p u t B h a s a n a d d i t i o n a l z e r o a t 1 0 k H z ( a n d

c a n b e l o a d e d , s i n c e i t ' s t h e l o w - i m p e d a n c e m u l t i p l i e r o u t p u t ) . T h e c i r c u i t c a n b e c o n v e r t e d

t o h i g h p a s s b y i n t e r c h a n g i n g C a n d R .

D E R I V A T I V E - C O N T R O L L E D L O W - P A S S F I L T E R

F i g u r e 2 7 s h o w s a n i n t e r e s t i n g v a r i a t i o n o f t h e v o l t a g e - c o n t r o l l e d l o w - p a s s f i l t e r . A w e l l -

k n o w n d i f f i c u l t y w i t h c o n v e n t i o n a l l i n e a r f i l t e r s i s t h a t l o n g t i m e c o n s t a n t s p r o v i d e e x c e l l e n t

f i l t e r i n g , b u t t h e y a l s o r e q u i r e a g r e a t d e a l o f t i m e t o s e t t l e . T h e f i l t e r d e s c r i b e d h e r e s e t t l e s

r a p i d l y i n r e s p o n s e t o s t e p c h a n g e s , t h e n a s s u m e s a l o n g t i m e c o n s t a n t f o r f i l t e r i n g ( s m a l l

a m o u n t s o f ) n o i s e .

1 7

18

R1 10k

X1

R2 3.3k X2

A D534

Y1

Y2

OUT

Z1

Z2

R3

Bk

o1 : 2N2907 0 1 "" 1N4148

OUTPUT

Figure 27. Deriva tive-controlled low-pass filter

In the circuit of Figure 27, a controllable low-pass filter , like that of Figure 25 , has its con-trol input driven from a high-pass filt er (i.e. , a differentiator) , consisting of Rl , R2, and C 1. When a step voltage is applied to the input, the time constant is immediately determined by the voltage applied to X 1, the amplitude of the step ; then the control voltage exponentially decays until it is about 25% of the step, (the divider ratio R2 /(R 1 + R 2 ) , which increases the filter time constant fourfold.

Figure 28 shows salient waveforms in the circuit Trace A is the input step, trace B is the control input, showing the immediate jump in cutoff frequency , and the decay to a cutoff frequency of about :4. Trace Cis the signal output, showing a rapid response - faster , in fact, than that of the control input, followed by a long tail, indicating the low steady-state cutoff frequency .

.... .... . ... .... ....

....

= !!J L! = A

I~ ~ B ~ II

= !!J . .... .... .... .... .... .... . . e

= c

Figure 28. Waveforms in derivative-controlled low-pass filter

Since the spike produced by the R 1, R2, C 1 network will go in the wrong direction, tending to greatly lengthen the time constant, when the square-wave returns, a clamping circuit, con-sisting of Q 1 and D 1 rapidly resets C 1 to zero . If derivative control of the falling edge were de-sired, an absolute value amplifier could be inserted between the X 1 input and R l-R2 junction.

In this example, the ultimate time constant is determined by the height of the step and/or the ratio of the resistors Rl-R2. If there are to be other influences on the time constant, ap-propriate additional voltages could be summed in at the X2 input. It is important to note that this circuit will function properly only if the noise is relatively small and has lower-fre-quency components than the initial step.

This kind of approach to filtering has proven useful in electronic weighing applications, where long time-constants are undesirable when weighing an object, yet "floor noise" has to be filtered out.

. .

I n d e f e r e n c e t o o b j e c t i v i t y , a n o t h e r n o n l i n e a r a p p r o x i m a t i o n , u s i n g s i m p l e c i r c u i t r y b u t n o t

a s f a s t - s e t t l i n g , c a n e x h i b i t r e l a t e d b e h a v i o r . F i g u r e 2 9 s h o w s a p a i r o f d i o d e s a n d a n R - C

f i l t e r . T h i s c i r c u i t w i l l o n l y e x h i b i t l o w - p a s s c h a r a c t e r i s t i c s a f t e r t h e c a p a c i t o r h a s c h a r g e d t o

w i t h i n 0 . 6 V o f t h e a p p l i e d s i g n a l . F u r t h e r , t h e d i o d e c o u l d b e r e p l a c e d b y a c o m p u t e r - c o n -

t r o l l e d s w i t c h , a l l o w i n g t h e " b r e a k d o w n v o l t a g e " t o b e a n y d e s i r e d v a l u e .

I N

~

; .

- ' -

~

*

F i g u r e 2 9 . D i o d e - c o n t r o l l e d / o w - p a s s f i l t e r

M I S C E L L A N E O U S M U L T I P L I E R A P P L I C A T I O N S

% D E V I A T I O N - R A T I O C O M P U T E R

F i g u r e 3 0 s h o w s a c i r c u i t t h a t c o m p u t e s t h e p e r c e n t d e v i a t i o n b e t w e e n i t s t w o i n p u t s . T h e

s c a l e f a c t o r i n t h i s a r r a n g e m e n t i s 1 % p e r v o l t , b u t o t h e r s c a l e f a c t o r s c a n b e o b t a i n e d b y a l -

t e r i n g t h e r e s i s t o r r a t i o s . T h e p e r c e n t a g e d e v i a t i o n f u n c t i o n i s o f p r a c t i c a l v a l u e f o r m a n y

a p p l i c a t i o n s i n m e a s u r e m e n t , t e s t i n g , a n d c o n t r o l . F o r e x a m p l e , t h e o u t p u t o f t h i s c i r c u i t

m i g h t b e a p p l i e d t o a p a i r o f b i a s e d c o m p a r a t o r s t o s t i m u l a t e p a r t i c u l a r a c t i o n s o r d i s p l a y s

d e p e n d i n g o n w h e t h e r t h e g a i n o f a c i r c u i t u n d e r t e s t w e r e w i t h i n l i m i t s , o r d e v i a t i n g b y a

p r e s e t a m o u n t i n e i t h e r d i r e c t i o n .

C O M P O N E N T S O R T E R

9 k l 1

1 k l 1

B I N P U T

( P O S I T I V E

O N L Y )

A I N P U T

x ,

+ V s

X z

A D 5 3 4

O U T P U T

S F

z ,

- V s

E o u T

I - ; ' a E o u r I I B I

1 0 = B - A

E o u r = 100~

B

( 1 % P E R V O L T )

F i g u r e 3 0 . 6 % r a t i o c o m p u t e r

T h e c i r c u i t o f F i g u r e 3 0 f o r m s t h e b a s i s f o r t h e c o m p o n e n t s o r t e r s h o w n i n F i g u r e 3 1 . T h i s

c i r c u i t w i l l g r a d e c a p a c i t o r s , r e s i s t o r s , o r Z e n e r d i o d e s b y p e r c e n t a g e d e v i a t i o n f r o m a s e t -

t a b l e v a l u e . T h e c i r c u i t c o m p r i s e s a s w i t c h a b l e c u r r e n t s o u r c e , a c l o c k , a s a m p l e - h o l d n e t w o r k ,

a n d s o m e t i m i n g l o g i c . W a v e f o r m s a r e s h o w n i n F i g u r e 3 2 .

1 9

20

03 AD7510

A

B

c

D

OUT

FOR CAPACITORS

VeA L- ~ 100 _-:7C_c_,_,- = 100 [c VeAL _ 1]

lilt lilt c;

CONNECT { REF TO Z2 A2 TO Y1

FOR RESISTORS AND ZENERS

100 I Ax - VeAL = 100 [~ - 1 J VeAL VeAL

100 v, - VeAL = 100 [~ - 1] VeA L VeA L

CONNECT [ REF TO Y1 l A2 TO Z2

Figure 31. Capacitor, resistor, and Zener-diode sorter

.... .... . . .... ....

=::1 = .......::: II ~ ... ~ I I

=il = li 5V/DIV I 1':1 ;;'1 = ~- ..

ALL 20011s/DIV

Figure 32. Waveforms inC, R, Zener sorter

The "A" portion of the AD821 functions as the current-source transistor, and the "B'' por-tion provides temperature compensation. The AD812B prevents the AD821 pair from conducting in the reverse direction whenever the voltage across the component under test (C.U .T.) exceeds the AD821 B emitter voltage (when Q 1 is on). The adjustable 1 Ok.Q resistor, RA, sets the output of the current source. The 1kHz square-wave clock (trace A) is applied to Ql , turning the current source on and off. The capacitor under test, in this case O.Ol,uF, is allowed to charge until the clock goes high, turning off the current source (trace B). The voltage the capacitor sits at is inversely proportional to its absolute value .

The AD506 follows this potential and feeds the simple sample-hold circuit, Q4, C2 , A2. The sample-hold is enabled by the one-shot "A" for 200,us when the clock goes high (trace C). After this time , "A" goes low, triggering one-shot "B" on for lOO,us. This pulse drives Q3 on (trace D) and discharges the C.U.T. The output of the sample-hold is applied to the percent deviation circuit. In practice, a 0.0 l,uF standard capacitor is put into the fixture , and the reference voltage is adjusted so that the AD534 output reads zero. The circuit is now ready for use at a scale factor of 1 V/%

I

d e v i a t i o n . W h e n c a p a c i t o r s a r e m e a s u r e d , t h e u n k n o w n i s a p p l i e d t o i n p u t Y l , a n d t h e

c a l i b r a t i o n i n p u t t o Z 2 .

T h e 3 . 3 k D - 1 0 0 p F n e t w o r k p r e v e n t s t h e s a m p l e - h o l d f r o m c a t c h i n g a n y p o r t i o n o f t h e d i s -

c h a r g e o f t h e c . u . t . a t t h e b e g i n n i n g o f h o l d b y i n t r o d u c i n g a s l i g h t d e l a y i n t o A I ' s r e s p o n s e .

T h e Z e n e r - d i o d e - b r i d g e c l a m p p r o v i d e s p r o t e c t i o n f o r t h e t e s t e r i n t h e e v e n t a c h a r g e d c a p a -

c i t o r i s p l a c e d i n t h e t e s t f i x t u r e . T h e d i s c r e t e - c o m p o n e n t c u r r e n t - s o u r c e f a c i l i t a t e s a g r o u n d -

r e f e r e n c e d t w o - t e r m i n a l , h i g h - n o i s e - r e j e c t i o n t e s t f i x t u r e .

T h e s a m e t w o - t e r m i n a l f i x t u r e m a y b e u s e d t o c h e c k r e s i s t o r s a n d Z e n e r d i o d e s , b y c l o s i n g

S 1 . T h i s a l l o w s t h e c u r r e - n t s o u r c e t o r u n a l l t h e t i m e ( n e c e s s a r y , s i n c e r e s i s t o r s a n d d i o d e s

h a v e n o " m e m o r y " ) . B e c a u s e t h e t e s t v o l t a g e w i l l b e p r o p o r t i o n a l t o t h e r e s i s t a n c e o r t h e

Z e n e r v o l t a g e , t h e c o n n e c t i o r . s t o t h e 6 % c i r c u i t a r e r e v e r s e d , t h e c a l i b r a t i o n r e f e r e n c e i s

c o n n e c t e d t o Y 1 , a n d t h e t e s t v o l t a g e i s c o n n e c t e d t o Z 2 .

B R I D G E L I N E A R I Z A T I O N

I f o n e a r m o f W h e a t s t o n e b r i d g e v a r i e s f r o m i t s n o m i n a l v a l u e b y a f a c t o r , ( 1 + 2 w ) , t h e v o l t -

a g e o r c u r r e n t o u t p u t o f t h e b r i d g e w i l l b e ( w i t h a p p r o p r i a t e p o l a r i t i e s a n d s c a l e f a c t o r s ) :

w ~ -~

y = - T + w

L i n e a r r e s p o n s e r e q u i r e s v e r y s m a l l v a l u e s o f w ( t o m a k e t h e d e n o m i n a t o r e s s e n t i a l l y i n d e -

p e n d e n t o f w ) a n d , a s a c o n s e q u e n c e , p r e a m p l i f i c a t i o n .

T h e c i r c u i t s h o w n i n F i g u r e 3 3 e n a b l e s l a r g e - d e v i a t i o n b r i d g e s t o b e u s e d w i t h o u t l o s i n g l i n -

e a r i t y o r r e s o r t i n g t o h i g h a t t e n u a t i o n . T h e c i r c u i t c o m p u t e s t h e i n v e r s e o f t h e b r i d g e f u n c -

t i o n , i . e . ,

w = _ _ y _ _

1 - y

D e p e n d i n g o n w h i c h a r m o f t h e b r i d g e v a r i e s , i t m a y b e n e c e s s a r y t o r e v e r s e t h e p o l a r i t y o f

t h e X c o n n e c t i o n s .

F L O A T E D

S U P P L Y

O R

I N S T R U M E N T A T I O N

A M P L I F I E R

+ E

I E , u , l l V I = y - E a u t

- , - 0.

[

y J = y

E o u t 1 w

Eout "' 10~

y

W H E R E Y = ( 1 0 V )

F i g u r e 3 3 . B r i d g e - l i n e a r i z a t i o n c i r c u i t

E a u t

S i n c e t h e i n p u t t o t h i s c i r c u i t i s s i n g l e - e n d e d , t h e b r i d g e m u s t e i t h e r f l o a t w i t h r e s p e c t t o

g r o u n d , o r a n i n s t r u m e n t a t i o n a m p l i f i e r m a y b e u s e d t o t r a n s l a t e t h e b r i d g e o u t p u t t o t h e

A D S 3 4 ' s c o m m o n . A n y r e s i s t i v e , l i n e a r l y r e s p o n d i n g t r a n s d u c e r ( i . e . , o n e o r m o r e l e g s o f

t h e b r i d g e p r o p o r t i o n a l t o t h e p h e n o m e n o n b e i n g m e a s u r e d ) m a y p r o f i t f r o m t h e a p p l i -

c a t i o n o f t h i s c i r c u i t . E x a m p l e s i n c l u d e p o s i t i o n s e r v o s , l i n e a r t h e r m i s t o r s , p l a t i n u m - r e s i s t -

a n c e - w i r e s e n s o r s ( n e a r l y l i n e a r o v e r w i d e r a n g e s ) , p r e s s u r e t r a n s d u c e r s , s t r a i n g a g e s , e t c .

H I G H - P E R F O R M A N C E R M S - T O - D C C O N V E R S I O N C I R C U I T

F o r a p p l i c a t i o n s c a l l i n g f o r g r e a t e r a c c u r a c y a n d b a n d w i d t h , b u t w i t h l e s s e r d y n a m i c r a n g e

2 1

22

than the AD536 rms-to-dc converter can easily handle, the circuit of Figure 34, employing the AD534, will be found useful.

MATCHED TO 0.025% 20k 10k ' 10k '

+V s C1

AD534 10k E IN ---1>-----i

(+5V PEAK)

OUTP UT f--....-'\NY--.------!

RMS + DC

AC 9 RMS j_

20k

z,

-Vs -15V ----'I/VIr- +15V

ZERO ADJ.

Figure 34. Wideband, high crest, rms-to-dc converter

The balance equation of this circuit is:

-CE;n + E0 )(Ein - E0 ) = -1 ORC ~f..o For steady state (or very slowly varying) values of E0 , the right-hand term approaches zero , the average value of Ein 2 is equal to E0 2 , and hence E0 measures the rms value of Ein .

After calibration, error < 0.1 % is maintained for frequencies up to 1OOkHz ; it increases to 0.5% at lMHz at 4V rms. Crest factors up to 10 have little effect on accuracy. To calibrate , with the mode switch at " RMS +DC", apply an input of (say) l.OOV de. Adjust the zero until the output reads the same as the input. Check for inputs of 5V.

FREQUENCY DOUBLING By use of trigonometric identities that can be found in any mathematical formulary , cir-cuits can be assembled that accept sinusoidal inputs and generate outputs at two , three, four , and five-or-more times the input frequency. Frequency doubling, in its simplest form , makes use of the identity,

cos 2 e = 1 - sin 2 e

Since, for a sine wave, e = wt,

cos 2wt = 1 - sin 2 wt

If an input E sin wt, is applied to a multiplier, connected as a squarer, the output will be

E = _l_ E2 (1 - cos 2wt) 0 20

The de term may be eliminated from the output by capacitive coupling, or by applying a bias voltage (which can be done conveniently with the AD534). Figure 35 shows a circuit which accepts a sinusoidal signal with a 1 OV amplitude and produces a double-frequency signal also having a 1 OV amplitude with no de offse t.

SINE OUT AT DOUBLE FREQUENCY .-------i X1 OUT r-,.---- 10 sin 2wt- 10V +10V

10V SINE IN = 10 sin 2wt

ru 10 sin w t

AD534 Z1

10k

10k } 5 sin 2wt - 5V '-------1 Y2 Z2

+10.0V

Figure 35. Frequency doubler

A n o b v i o u s p r o b l e m i s t h a t v a r i a t i o n s o f i n p u t a m p l i t u d e r e s u l t i n d e e r r o r s a t t h e o u t p u t .

I f t h e o u t p u t i s a c - c o u p l e d , a b r u p t c h a n g e s o f i n p u t l e v e l c a u s e t h e o u t p u t t o b o u n c e , w h i c h

i n s o m e a p p l i c a t i o n s i s t r o u b l e s o m e . F i g u r e 3 6 s h o w s a c i r c u i t , u s i n g a d i f f e r e n t t r i g o n o m e t r i c

i d e n t i t y , w h i c h p r o d u c e s f r e q u e n c y d o u b l i n g , a t a g i v e n f r e q u e n c y , w i t h n o d e o f f s e t , h e n c e

n o b o u n c e . I t u s e s t h e i d e n t i t y :

c o s w t s i n w t = Y z s i n 2 w t

F i g u r e 3 6 . " N o - b o u n c e " f r e q u e n c y d o u b l e r

T h e X i n p u t l e a d s t h e i n p u t s i g n a l , E s i n w t , b y 4 5 ( a n d i s a t t e n u a t e d b y y 2 ) , a n d t h e Y

i n p u t l a g s t h e i n p u t b y 4 5 , a n d i s a l s o a t t e n u a t e d b y y 2 . S i n c e t h e X a n d Y i n p u t a r e 9 0

o u t o f p h a s e ( a t t h e f r e q u e n c y f = ( 2 n - R C ) - - 1 ) , t h e r e s p o n s e e q u a t i o n o f t h e c i r c u i t w i l l b e

1 E E . E

2

.

2

1 E

- - - = - - c o s w t - = - s 1 n w t = - s m w t = -

1 0 y 2 y 2 4 0 4

T h e r i g h t - h a n d s i d e r e f l e c t s t h e a t t e n u a t i o n o f t h e o u t p u t a t t h e Z i n p u t . H e n c e ,

E 2 .

E = - s m 2 w t

0

1 0

W h i l e t h i s c i r c u i t i s n o t w i d e b a n d ( a s F i g u r e 3 5 i s ) , c o n s i d e r a b l e f r e q u e n c y d e v i a t i o n c a n b e

t o l e r a t e d w i t h o u t c a u s i n g a p p r e c i a b l e c h a n g e i n o u t p u t a m p l i t u d e . A 1 0 % f r e q u e n c y e r r o r

c a u s e s a 0 . 5 % a m p l i t u d e e r r o r . O b v i o u s l y , f r e q u e n c y q u a d r u p l i n g c a n b e e f f e c t e d b y c a s -

c a d i n g d o u b l e r s . T h e w a v e f o r m s o f F i g u r e 3 7 s h o w a s i n e w a v e t h a t i s d o u b l e d a n d t h e n

d o u b l e d a g a i n b y r e p e a t i n g t h e c i r c u i t o f F i g u r e 3 5 .

1 0 V / D I V

1 0 V / D I V

1 0 V / D I V

1 0 0 1 1 s D I V

F i g u r e 3 7 . S i n e w a v e - d o u b l e d a n d r e d o u b l e d ( a n d n o t v u l n e r a b l e )

I n f r e q u e n c y - d o u b l i n g a p p l i c a t i o n s , a m p l i t u d e i s u s u a l l y n o t c r i t i c a l . T h i s i s f o r t u n a t e ,

b e c a u s e t h e s q u a r i n g o f t h e i n p u t a m p l i t u d e d o u b l e s t h e s e n s i t i v i t y t o a m p l i t u d e e r r o r s , a n d

d i s t o r t s t h e m o d u l a t i o n e n v e l o p e . A c i r c u i t t h a t u s e s f e e d b a c k o f t h e f i l t e r e d o u t p u t t o t h e

s c a l e - f a c t o r i n p u t o f t h e A D 5 3 1 t o p r o d u c e f r e q u e n c y d o u b l i n g w i t h p r o p o r t i o n a l a m p l i t u d e

i s s h o w n i n F i g u r e 3 8 . A d i s c u s s i o n o f t h i s c i r c u i t m a y b e f o u n d o n p a g e 5 0 2 o f t h e N O N -

L I N E A R C I R C U I T S H A N D B O O K .

2 3

24

Eo f-o_u_T ----o-- -? ~ --+

- 15kl1 _.f~-_V\___,-...__-___,-_ :2kE , E1 2 - E1 2 cos2wt

Eo "' 2 Eo

E0 = KE 1 - KE 1 cos2wt

Figure 38. Frequency doubler with linear amplitude response

FILTER TESTER USING WIDEBAND MULTIPLIER The high-speed testing of high frequency filters can pose some knotty problems. A circuit for testing a "black box" lMHz bandpass filter for insertion loss (gain) vs. input amplitude is shown in Figure 39. The test is performed by sweeping the amplitude of the input signal and comparing the envelopes of the input and output signals.

+15V - 15V

SOLID TANTALUM$ S"F S" F SOLID TANTALUM$

fL 008 ~-~

10V- 1kHz RAMP

1M Hz SINE WAVE

OUTPUT TO COMPUTER; COMPARATORS, ETC.

R2 R4 22k 22k

10k 0.6V

0,01

Figure 39. 1 MHz bandpass filter insertion-loss tester

AD580