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LTC1562CN#PBF

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7
LTC1562
1562fa
APPLICATIONS INFORMATION
WUU
U
Functional Description
The LTC1562 contains four matched, 2nd order, 3-termi-
nal universal continuous-time filter blocks, each with a
virtual-ground input node (INV) and two rail-to-rail out-
puts (V1, V2). In the most basic applications, one such
block and three external resistors provide 2nd order
lowpass and bandpass responses simultaneously (Figure
3, with a resistor for Z
IN
). The three external resistors set
standard 2nd order filter parameters f
O
, Q and gain. A
combination of internal precision components and exter-
nal resistor R2 sets the center frequency f
O
of each 2nd
order block. The LTC1562 is trimmed at manufacture so
that f
O
will be 100kHz ±0.5% (±0.6% typical for PDIP
package) if the external resistor R2 is exactly 10k.
However, lowpass/bandpass filtering is only one specific
application for the 2nd order building blocks in the LTC1562.
Highpass response results if the external impedance Z
IN
in
Figure 3 becomes a capacitor C
IN
(whose value sets only
gain, not critical frequencies) as described below.
Responses with zeroes are available through other con-
nections (see Notches and Elliptic Responses). Moreover,
the virtual-ground input gives each 2nd order section the
built-in capability for analog operations such as gain
(preamplification), summing and weighting of multiple
inputs, handling input voltages beyond the power supplies
or accepting current or charge signals directly. These
Operational Filter
TM
frequency-selective building blocks
are nearly as versatile as op amps.
The user who is not copying exactly one of the Typical
Applications schematics shown later in this data sheet is
urged to read carefully the next few sections through at
least Signal Swings, for orientation about the LTC1562,
before attempting to design custom application circuits.
Also available free from LTC, and recommended for de-
signing custom filters, is the general-purpose analog filter
design software FilterCAD
TM
for Windows
®
. This software
includes tools for finding the necessary f
0
, Q and gain
parameters to meet target filter specifications such as
frequency response.
Setting f
O
and Q
Each of the four 2nd order sections in the LTC1562 can be
programmed for a standard filter function (lowpass, band-
pass or highpass) when configured as in Figure 3 with a
resistor or capacitor for Z
IN
. These transfer functions all
have the same denominator, a complex pole pair with
center frequency ω
O
= 2πf
O
and quality parameter Q. (The
numerators depend on the response type as described
below.) External resistors R2 and R
Q
set f
O
and Q as
follows:
f
CRR
k
R
kHz
O
==
()
1
212
10
2
100
π ()
Ω
Q
R
RR
R
kR
R
R
kHz
f
QQQ
O
== =
() ( )1 2 10 2
2
100
Ω
R1 = 10k and C = 159pF are internal to the LTC1562 while
R2 and R
Q
are external.
A typical design procedure proceeds from the desired f
O
and Q as follows, using finite-tolerance fixed resistors.
First find the ideal R2 value for the desired f
O
:
R Ideal
kHz
f
k
O
2
100
10
2
()
=
(
)
Ω
Then select a practical R2 value from the available finite-
tolerance resistors. Use the actual R2 value to find the
desired R
Q
, which also will be approximated with finite
tolerance:
RQ kR
Q
= ()10 2Ω
The f
O
range is approximately 10kHz to 150kHz, limited
mainly by the magnitudes of the external resistors
required. As shown above, R2 varies with the inverse
square of f
O
. This relationship desensitizes f
O
to R2’s
Operational Filter and FilterCAD are trademarks of Linear Technology Corporation.
Windows is a registered trademark of Microsoft Corporation.
8
LTC1562
1562fa
APPLICATIONS INFORMATION
WUU
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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
9
LTC1562
1562fa
APPLICATIONS INFORMATION
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U
Parameters ω
O
= 2πf
O
and Q are set by R2 and R
Q
as
above. The highpass gain parameter is H
H
= C
IN
/159pF.
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.
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
OO
()
–/
/
=
()
+
()
+
ω
ωω
2
2
ω
O
= 2πf
O
and Q are set by R2 and R
Q
as described previ-
ously in Setting f
O
and Q. 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
/10kΩ)(C
IN
/159pF). 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 band-
pass function, as illustrated in Figure 4.
INV V1
2nd ORDER
1/4 LTC1562
(b) Capacitive Input(a) Resistive Input
V2
1562 F06
R2R
Q
C
IN
V
IN
V
OUT
INV V1
2nd ORDER
1/4 LTC1562
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
OO
1
2
2
2
()
()
()
–
/
==
+
()
+ωω
INV V1
2nd ORDER
1/4 LTC1562
V2
1562 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 can
still be used with high performance in such situations as
long as this constraint is followed.
For an LTC1562 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
100ω
ω
=
regardless of the details of Z
IN
. Therefore, an input fre-
quency above or below 100kHz 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 section.
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LTC1562CN#PBF

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Manufacturer:
Analog Devices Inc.
Description:
Active Filter Active RC Quad Universal Filter
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