Datasheet

8
LTC1562
1562fa
APPLICATIONS INFORMATION
WUU
U
tolerance (by a factor of 2 incrementally), but it also
implies that R2 has a wider range than f
O
. (R
Q
and R
IN
also
tend to scale with R2.) At high f
O
these resistors fall below
5k, heavily loading the outputs of the LTC1562 and leading
to increased THD and other effects. At the other extreme,
a lower f
O
limit of 10kHz reflects an arbitrary upper
resistor limit of 1MΩ. The LTC1562’s MOS input circuitry
can accommodate higher resistor values than this, but
junc tion leakage current from the input protection cir-
cuitry may cause DC errors.
The 2nd order transfer functions H
LP
(s), H
BP
(s) and
H
HP
(s) (below) are all inverting so that, for example, at DC
the lowpass gain is –H
L
. If two such sections are cas-
caded, these phase inversions cancel. Thus, the filter in the
application schematic on the first page of this data sheet
is a dual DC preserving, noninverting, rail-to-rail lowpass
filter, approximating two “straight wires with frequency
selectivity.”
Figure 4 shows further details of 2nd order lowpass,
bandpass and highpass responses. Configurations to
obtain these responses appear in the next three sections.
Basic Lowpass
When Z
IN
of Figure 3 is a resistor of value R
IN
, a standard
2nd order lowpass transfer function results from V
IN
to V2
(Figure 5):
Vs
Vs
Hs
H
sQs
IN
LP
LO
OO
2
2
2
2
()
()
()
–
/
==
+
()
+
ω
ωω
The DC gain magnitude is H
L
= R2/R
IN
. (Note that the
transfer function includes a sign inversion.) Parameters
ω
O
(= 2πf
O
) and Q are set by R2 and R
Q
as above. For a 2nd
order lowpass response the gain magnitude becomes QH
L
INV V1
2nd ORDER
1/4 LTC1562
V2
1562 F05
R2R
Q
R
IN
V
IN
V
OUT
f
L
GAIN (V/V)
0.707 H
B
H
B
f
O
f (LOG SCALE)
BANDPASS RESPONSE
f
H
GAIN (V/V)
0.707 H
L
H
P
H
L
H
H
f
P
f (LOG SCALE)
LOWPASS RESPONSE
f
C
f
C
GAIN (V/V)
0.707 H
H
H
P
f
P
f (LOG SCALE)
HIGHPASS RESPONSE
Q
f
ff
fff
ff
QQ
ff
QQ
O
HL
OLH
L
O
HO
==
=
+






+










=+






+










–
;
–1
2
1
2
1
1
2
1
2
1
2
2
ff
QQ
ff
Q
HH
Q
Q
CO
PO
PL
=






+






+
=
=














1
1
2
1
1
2
1
1
1
2
1
1
1
1
4
22
2
2
2
––
–
–
ff
QQ
ff
Q
HH
Q
Q
CO
PO
PH
=






+






+










=






=














1
1
2
1
1
2
1
1
1
2
1
1
1
1
4
22
2
1
2
1
2
––
–
–
–
–
Figure 4. Characteristics of Standard 2nd Order Filter Responses
Figure 5. Basic Lowpass Configuration