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AN-797
THE SV fiLTER IS USUALLY IMPLEMENTED WITH R4 = R6 = R JUMP ,
R8 = R13 = R AND C6 = C8 = C . SO, THE ABOVE EXPRESSIONS
SIMPLIFY TO
ω O = 1 / RC Q = 1 / 3 ( 1 + R JUMP1 / R5 )
H OHP = – 1 H OBP = Q H OLP = – 1
THE fiLTER IS TUNED AS FOLLOWS:
1. ADJUST R6 FOR DESIRED MAGNITUDE OF THE RESPONSE
OF INTEREST.
2. ADJUST R8 OR R13 TO TUNE  O .
3. ADJUST THE RATIO R JUMP1 /R5 TO TUNE Q .
THE BIQUAD FILTER
THIS PARTICULAR fiLTER IMPLEMENTATION CONSISTS OF TWO
INTEGRATORS. THE THIRD OP AMP IS A UNITY GAIN INVERTING
AMPLIfiER WHOSE SOLE PURPOSE IS TO PROVIDE POLARITY REVERSAL.
UNLIKE THE SV fiLTER, THE BIQUAD YIELDS ONLY TWO SIGNIfiCANT
RESPONSES; HOWEVER, SINCE ALL ITS OP AMPS ARE OPERATED IN
THE INVERTING MODE, THE CIRCUIT IS IMMUNE FROM COMMON-
MODE LIMITATIONS.
FROM THE CIRCUIT ABOVE WE HAVE:
H OBP = – R4 / R6 H OLP = R JUMP / R6
STATE VARIABLE FILTER (NONINVERTING)
ω O = 1 /
( R8 R JUMP C6 C4 )
Q = R4 C4 /
( R8 R JUMP C6 )
ANOTHER POPULAR TYPE OF STATE VARIABLE FILTER CAN BE
FORMED BY JUST MOVING THE INPUT SIGNAL FROM THE
INVERTING TO THE NONINVERTING SIDE OF A1, RESULTING IN THE
NONINVERTING STATE VARIABLE fiLTER. SEE FIGURE 2.
BY PROPERLY CHOOSING THE FOLLOWING COMPONENTS:
R4 = R6; R8 = R13 ; R5 = R JUMP ; C6 = C8
THE BIQUAD fiLTER IS USUALLY IMPLEMENTED WITH R8 = R JUMP = R
C4 = C6 = C , AFTER WHICH THE ABOVE EXPRESSIONS SIMPLIFY AS:
H OBP = – R4 / R6 H OLP = R / R6
ω O = 1 / RC Q = R4 / R
THIS fiLTER IS TUNED AS FOLLOWS:
IT CAN BE SHOWN THAT:
ω O = 1 / R8 C6
H OHP = 1 / Q
Q = 1 + R JUMP1 / R3
H OBP = – 1 H OLP = 1 / Q
R6
1. ADJUST R8 OR R JUMP TO TUNE  O .
2. ADJUST R4 TO TUNE Q .
3. ADJUST R6 FOR DESIRED VALUES H OBP OR OF H OLP .
JUMP –V IN A TO V OUT C
R4
V CC
R8
V CC
C6
R13
C8
V CC
2
3
V+
V–
A1
1
V HP = V OUT A
6
5
V+
V–
A2
7
V BP = V OUT B
9
10
V+
V–
A3
8
V LP = V OUT C
R5
V EE
R JUMP *
V EE
V EE
+V IN A
R3
*R JUMP IS AN EXTERNAL COMPONENT, NOT PROVIDED ON THE APPLICATION BOARD.
FIGURE 2. STATE VARIABLE FILTER (NONINVERTING)
R JUMP *
R4
C4
V CC
R8
V CC
C6
R13
R1 6
V CC
–V IN A
R6
2
3
V+
V–
A1
1
V HP = V OUT A
6
5
V+
V–
A2
7
V BP = V OUT B
9
10
V+
V–
A3
8
V LP = V OUT C
V EE
V EE
V EE
*R JUMP IS AN EXTERNAL COMPONENT, NOT PROVIDED ON THE APPLICATION BOARD.
FIGURE 3. BIQUAD FILTER
–2–
REV. 0
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