Datasheet

9
LTC1562-2
15622fa
APPLICATIONS INFORMATION
WUU
U
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
at frequency f
O
, and for Q > 0.707, a gain peak occurs at
a frequency below f
O
, as shown in Figure 4.
Basic Bandpass
There are two different ways to obtain a bandpass function
in Figure 3, both of which give the following transfer
function form:
Hs
HQs
sQs
BP
BO
O
O
()
–/
/
=
()
+
()
+
ω
ωω
22
The value of the gain parameter H
B
depends on the circuit
configuration as follows. When Z
IN
is a resistor of value
R
IN
, a bandpass response results at the V1 output (Figure
6a) with a gain parameter H
B
= R
Q
/R
IN
. Alternatively, a
capacitor of value C
IN
gives a bandpass response at the V2
output (Figure 6b), with the same H
BP
(s) expression, and
the gain parameter now H
B
= (R
Q
/7958Ω)(C
IN
/100pF). This
transfer function has a gain magnitude of H
B
(its peak value)
when the frequency equals f
O
and has a phase shift of 180°
at that frequency. Q measures the sharpness of the peak
(the ratio of f
O
to – 3dB bandwidth) in a 2nd order bandpass
function, as illustrated in Figure 4. ω
O
= 2πf
O
and Q are set
by R2 and R
Q
as described previously in Setting f
O
and Q.
H
H
= C
IN
/100pF is the highpass gain parameter. Param-
eters ω
O
= 2πf
O
and Q are set by R2 and R
Q
as above. For
a 2nd order highpass response the gain magnitude at
frequency f
O
is QH
H
, and approaches H
H
at high frequen-
cies (f >> f
O
). For Q > 0.707, a gain peak occurs at a
frequency above f
O
as shown in Figure 4. The transfer
function includes a sign inversion.
INV V1
2nd ORDER
1/4 LTC1562-2
(b) Capacitive Input(a) Resistive Input
V2
1562-2 F06
R2R
Q
C
IN
V
IN
V
OUT
INV V1
2nd ORDER
1/4 LTC1562-2
V2
R2
R
Q
R
IN
V
IN
V
OUT
Figure 6. Basic Bandpass Configurations
Basic Highpass
When Z
IN
of Figure 3 is a capacitor of value C
IN
, a highpass
response appears at the V1 output (Figure 7).
Vs
Vs
Hs
Hs
sQs
IN
HP
H
O
O
1
2
22
()
()
()
–
/
==
+
()
+ωω
INV V1
2nd ORDER
1/4 LTC1562-2
V2
1562-2 F07
R2R
Q
C
IN
V
IN
V
OUT
Figure 7. Basic Highpass Configuration
Signal Swings
The V1 and V2 outputs are capable of swinging to within
roughly 100mV of each power supply rail. As with any
analog filter, the signal swings in each 2nd order section
must be scaled so that no output overloads (saturates),
even if it is not used as a signal output. (Filter literature
often calls this the “dynamics” issue.) When an unused
output has a larger swing than the output of interest, the
section’s gain or input amplitude must be scaled down to
avoid overdriving the unused output. The LTC1562-2 can
still be used with high performance in such situations as
long as this constraint is followed.
For an LTC1562-2 section as in Figure 3, the magnitudes
of the two outputs V2 and V1, at a frequency ω = 2πf, have
the ratio,
|()|
|()|
()Vj
Vj
kHz
f
2
1
200ω
ω
=
regardless of the details of Z
IN
. Therefore, an input fre-
quency above or below 200kHz produces larger output
amplitude at V1 or V2, respectively. This relationship can
guide the choice of filter design for maximum dynamic
range in situations (such as bandpass responses) where
there is more than one way to achieve the desired fre-
quency response with an LTC1562-2 section.