Datasheet

LTC1164
11
1164fa
Mode 3A
This is an extension of Mode 3 where the highpass and
lowpass output are summed through two external resis-
tors R
H
and R
L
to create a notch. This is shown in Figure
10. Mode 3A is more versatile than Mode 2 because the
notch frequency can be higher or lower than the center
frequency of the 2nd order section. The external op amp of
Figure 10 is not always required. When cascading the
sections of the LTC1164, 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.
Figure 9. Mode 2: 2nd Order Filter Providing Notch, Bandpass, Lowpass
ODES OF OPERATIO
U
W
LTC1164 • MOO04
R3
R4
R2
NS BPLP
R1
1/4 LTC1164
f
o
=
1 +
1 +
R3/R1;
; H
OLP
=
H
OBP
= –
H
OBP
= –
MODE 2 (100:1):
f
CLK
100
–
+
+
–
Σ
∫
∫
V
IN
R3
R2
R2
R4
; f
n
=
; Q =
; THEN CALCULATE R1 TO SET THE DESIRED GAIN
R3 =
R2
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:
f
CLK
50
; f
n
=
; Q =
f
CLK
50
R3/R1
1 – (R3/16R4)
+
1.005
Q
R2
R4
R2
16R4
f
o
=
1 +
MODE 2 (50:1):
f
CLK
50
R2
R4
1 +
R2
R4
; H
ON1
(f → 0) =
–R2/R1
1 + (R2/R4)
; H
OLP
=
–R2/R1
1 + (R2/R4)
–R2/R1
1 + (R2/R4)
H
ON1
(f → 0) =
–R2/R1
1 + (R2/R4)
1.005 (√1 + R2/R4)
(R2/R3) – (R2/16R4)
= – R2/R1
H
ON2
f →
f
CLK
2
()
= – R2/R1
; H
ON2
f →
f
CLK
2
()
Figure 10. Mode 3A: 2nd Order Filter Providing Highpass, Bandpass, Lowpass, Notch
LTC1164 • MOO05
H
OBP
= –
H
OLP
–
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:
; f
n
=
f
CLK
50
R3/R1
1 – (R3/16R4)
f
o
=
MODE 3A (50:1):
MODE 3A (100:1):
f
CLK
50
R2
R4
R4
R1
R
H
R
L
R
G
R
L
R
G
R
H
R
G
R
L
H
OHP
; THEN CALCULATE R1 TO SET
THE DESIRED GAIN
R3 =
R2
+
1.005
Q
R2
R4
R2
16R4
; H
OLP
(f = 0) = – R4/R1
R4/R1;
H
OLP
= –
H
ON
(f = f
o
) = Q
H
ON1
(f → 0) =
=
; H
ON2
f →
f
CLK
2
()
= –R2/R1
; H
OHP
f →
; f
n
=
f
CLK
100
f
o
=
f
CLK
100
R2
R4
R2
R4
R3
R2
R
H
R
L
; H
OHP
= – R2/R1; H
OBP
= –R3/R1
f
CLK
2
(
)
(
)
R3
R4
R2
HP S BP LP
NOTCH
EXTERNAL OP AMP OR
INPUT OP AMP OF THE
LTC1164, SIDE A, B, C, D
R1
AGND
1/4 LTC1164
–
+
+
–
Σ
∫
∫
V
IN
R
H
R
L
R
G
C
C
–
+
; Q =
; Q =
1.005 (√R2/R4)
(R2/R3) – (R2/16R4)
×
R2
R1
R
G
R
H
×