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AN-733
THE ALGEBRAIC SUM OF THESE TWO COMPONENTS SHOULD BE
EQUAL TO V OUT . BY APPLYING THE PRINCIPLES EXPRESSED IN
THE OUTPUT VOLTAGE V OUT COMPONENTS, AND BY LETTING R4
= R2 AND R7 = R6, THEN:
V OUT 1 = V IN 1 R7/R2
V OUT 2 = –V IN 2 R7/R2
V OUT = V OUT 1 + V OUT 2 = ( V IN 1 – V IN 2) R7/R1
CURRENT-TO-VOLTAGE CONVERTER
CURRENT MAY BE MEASURED IN TWO WAYS WITH AN OPERA-
TIONAL AMPLIfi ER: IT CAN BE CONVERTED TO A VOLTAGE WITH A
RESISTOR AND THEN AMPLIfi ED, OR INJECTED DIRECTLY INTO A
SUMMING NODE.
??
DIFFERENCE AMPLIFIERS ARE COMMONLY USED IN HIGH
ACCURACY CIRCUITS TO IMPROVE THE COMMON-MODE REJEC-
? ?? ?
? ???
TION RATIO, TYPICALLY KNOWN AS CMRR.
FOR THIS TYPE OF APPLICATION, CMRR DEPENDS UPON HOW
TIGHTLY MATCHED RESISTORS ARE USED; POORLY MATCHED RESIS-
TORS RESULT IN A LOW VALUE OF CMRR.
TO SEE HOW THIS WORKS, CONSIDER A HYPOTHETICAL SOURCE
OF ERROR FOR RESISTOR R7 (1 – ERROR). USING THE SUPERPOSI-
TION PRINCIPLE AND LETTING R4 = R2 AND R7 = R6, THE OUTPUT
VOLTAGE WOULD BE AS FOLLOWS:
??
? ??? ? ? ?? ? ? ??
FIGURE 3. CURRENT-TO-VOLTAGE CONVERTER
FIGURE 3 IS A TYPICAL REPRESENTATION OF A CURRENT-TO-VOLTAGE
TRANSDUCER. THE INPUT CURRENT IS FED DIRECTLY INTO THE SUM-
MING NODE AND THE AMPLIfi ER OUTPUT VOLTAGE CHANGES TO
EXACTLY THE SAME CURRENT FROM THE SUMMING NODE THROUGH
R7. THE SCALE FACTOR OF THIS CIRCUIT IS R7 VOLTS PER AMPS.
? ? R 7 ? R 2 + 2 R 7 ? ERROR ? ?
R 2 ? ?
R 2 + R 7 ? ?
? ? 1 ? × ? ?
? ?
? ? ?
= ? ?
?
?
?
?
?
VD + ?
× ERROR ?
?
?
??
V OUT
? ? R 2 + R 7 ? ?
R 7
2
THE ONLY CONVERSION ERROR IN THIS CIRCUIT IS I BIAS , WHICH IS
SUMMED ALGEBRAICALLY WITH I IN .
??
??
V DD = V IN 2 ? V IN 1
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??
? ???
FROM THIS EQUATION, A CM AND A DM CAN BE DEfi NED AS
FOLLOWS:
A CM = R7/(R7 – R2) ERROR
A DM = R7/R2 [1 – [(R2+2R7/R2+R7) ERROR/2]]
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FIGURE 4. BISTABLE MULTIVIBRATOR
THESE EQUATIONS DEMONSTRATE THAT WHEN THERE IS NOT AN
ERROR IN THE RESISTOR VALUES, THE A CM = 0 AND THE AMPLIfi ER
RESPONDS ONLY TO THE DIFFERENTIAL VOLTAGE BEING APPLIED TO
ITS INPUTS; UNDER THESE CONDITIONS, THE CMRR OF THE CIRCUIT
BECOMES HIGHLY DEPENDENT ON THE CMRR OF THE AMPLIfi ER
SELECTED FOR THIS JOB.
AS MENTIONED ABOVE, ERRORS INTRODUCED BY RESISTOR
??
??? ? ? ??
MISMATCH CAN BE A BIG DRAWBACK OF DISCRETE DIFFERENTIAL
AMPLIfi ERS, BUT THERE ARE DIFFERENT WAYS TO OPTIMIZE THIS
CIRCUIT CONfi GURATION:
1. THE DIFFERENTIAL GAIN IS DIRECTLY RELATED TO THE RATIO
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??? ? ? ??
R7/R2; THEREFORE, ONE WAY TO OPTIMIZE THE PERFOR-
MANCE OF THIS CIRCUIT IS TO PLACE THE AMPLIfi ER IN A HIGH
GAIN CONfi GURATION. WHEN LARGER VALUES FOR RESISTORS
R7 AND R6 AND SMALLER VALUES FOR RESISTORS R2 AND R4
ARE SELECTED, THE HIGHER THE GAIN, THE HIGHER THE CMRR.
FOR EXAMPLE, WHEN R7 = R6 = 10 K , AND R2 = R4 = 1 K ,
AND ERROR = 0.1%, CMRR IMPROVES TO BETTER THAN 80 DB.
FOR HIGH GAIN CONfi GURATION, SELECT AMPLIfi ERS WITH
VERY LOW I BIAS AND VERY HIGH GAIN (SUCH AS THE AD8551,
AD8571, AD8603, AND AD8605) TO REDUCE ERRORS.
2. SELECT RESISTORS THAT HAVE MUCH TIGHTER TOLERANCE AND
ACCURACY. THE MORE CLOSELY THEY ARE MATCHED, THE BETTER
THE CMRR. FOR EXAMPLE, IF A CMRR OF 90 DB IS NEEDED,
THEN MATCH RESISTORS TO APPROXIMATELY 0.02%.
–2–
FIGURE 5. OUTPUT RESPONSE
GENERATION OF SQUARE WAVEFORMS USING A
BISTABLE MULTIVIBRATOR
A SQUARE WAVEFORM CAN BE SIMPLY GENERATED BY ARRANG-
ING THE AMPLIfi ER FOR A BISTABLE MULTIVIBRATOR TO SWITCH
STATES PERIODICALLY AS FIGURE 5 SHOWS.
ONCE THE OUTPUT OF THE AMPLIfi ER REACHES ONE OF TWO POS-
SIBLE LEVELS, SUCH AS L+, CAPACITOR C9 CHARGES TOWARD THIS
LEVEL THROUGH RESISTOR R7. THE VOLTAGE ACROSS C9, WHICH
IS APPLIED TO THE NEGATIVE INPUT TERMINAL OF THE AMPLI-
fi ER DENOTED AS V–, THEN RISES EXPONENTIALLY TOWARD L+
WITH A TIME CONSTANT = C9R7. MEANWHILE, THE VOLTAGE
REV. A
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