LTC1064_09 Datasheet, PDF (10/20 Pages) Linear Technology – Low Noise, Fast, Quad Universal Filter Building Block

LTC1064
W
U
ODES OF OPERATIO
R1
V_IN
R4
R3
R2
–
+
AGND
N
S
+
–
Σ
∫
1/4 LTC1064
R2
√ √ ^{MODE 2 (100:1):}
f_O
=
f_CLK
100
1+
R2
R4
; f_n =
f_CLK
50
;
Q
=
R3
R2
1+
R2
R4
;
H_OLP
=
–
1
R1
+ ^R2
;
BP
LP
( ) ^R2
H_OBP = –
R3
R1
;
H_ON1(f→
0)
=
–
1
R1
+ ^R2
; H_ON2
f→
f_CL=K
2
–
R4
R2
R1
R4
∫
MODE 2 (50:1):
√ ^{√ fO}
=
f_CLK
50
1+
R2
R4
;
f_n
=
f_CLK
50
;
Q
1.005
=
R2
R3
1 + ^R2
R4
–
R2
16R4
; H_OLP = –
R2
R1
1 + ^R2
R4
;
1064 F08
( ) ^R3
R2
H_OBP
=
–
1
R1
–
R3
16R4
;
H_ON1(f→
0)
=
–
1
R1
+ ^R2
R4
;
H_ON2
=
f→ ^fC₂^L=^K
–
R2
R1
NOTE: THE 50:1 EQUATIONS FOR MODE 2 ARE DIFFERENT FROM THE EQUATIONS
FOR MODE 2 OPERATION OF THE LTC1059, LTC1060 AND LTC1061. START WITH
f_O, CALCULATE R2/R4, SET R4; FROM THE Q VALUE, CALCULATE R3:
R3 =
R2
; THEN CALCULATE R1 TO SET THE DESIRED GAIN.
√ ^{1.005 1 + R2 + R2}
Q
R4 16R4
1064 F08Eq
Figure 8. Mode 2: 2nd Order Filter Providing Notch, Bandpass and Lowpass
Mode 3a
This is an extension of Mode 3 where the highpass and
lowpass outputs are summed through two external resis-
tors R_H and R_L to create a notch. This is shown in Figure 9.
Mode 3a is more versatile than Mode 2 because the notch
frequency can be higher or lower than the center fre-
quency of the 2nd order section. The external op amp of
Figure 9 is not always required. When cascading the
sections of the LTC1064, the highpass and lowpass
outputs can be summed directly into the inverting input of
the next section. The topology of Mode 3a is useful for
elliptic highpass and notch filters with clock-to-cutoff
frequency ratios higher than 100:1. This is often required
to extend the allowed input signal frequency range and to
avoid premature aliasing.
When the internal clock-to-center frequency ratio is set at
50:1, the design equations for Q and bandpass gain are
different from the 100:1 case.
R1
V_IN
R4
R3
R2
–
+
AGND
10
C_C
HP S
BP
+–
Σ∫
∫
1/4 LTC1064
R_H
MODE 3a (100:1):
MODE 3a (50:1):
LP
R_G
R_L
–
+
NOTCH
EXTERNAL OP AMP OR INPUT
OP AMP OF THE LTC1064,
SIDE A, B, C, D
1064 F09
√ √ ^fO
=
f_CLK
100
R2
R4
;
f_n
=
f_CLK
100
R_H
R_L
;
H_OHP
=
–
R2 _;
R1
HOBP
=
–
R3
R1
;
( )( ) ( ) ( )( ) ^HOLP ^{= –}
R4
R1
;
H_ON1(f→
0)
=
R_G
R_L
R4
R1
;
H_ON2
f→
f_CL=K
2
R_G
R_H
;
R2
R1
( ) _√ ^HON^(f=fO^{) = Q}
RR_{GL HOLP –}
R_G
R_H
H_OHP
;
Q=
R3
R2
R2
R4
√ √ ^{( ) fO}
=
f_CLK
50
1+
R2
R4
; f_n =
f_CLK
50
R_H
R_L
; H_OHP
f→
f_C2L=K
–
R2
R1
;
R3
H_OBP
=
–
1
–
R1
R3
; H_OLP(f = 0) =
–
R4
R1
;Q
=
16R4
√ ^1.005
R2
R4
R2
R3
–
R2
16R4
NOTE: THE 50:1 EQUATIONS FOR MODE 3A ARE DIFFERENT FROM
THE EQUATIONS FOR MODE 3A OPERATION OF THE LTC1059,
LTC1060 AND LTC1061. START WITH f_O, CALCULATE R2/R4, SET R4;
FROM THE Q VALUE, CALCULATE R3:
R3 =
R2
; THEN CALCULATE R1 TO
√ 1.005 R2 + R2 SET THE DESIRED GAIN.
Q R4 16R4
1064 F09Eq
Figure 9. Mode 3a: 2nd Order Filter Providing Highpass, Bandpass, Lowpass and Notch
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