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LTC1562CG-2#PBF

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7
LTC1562-2
15622fa
APPLICATIONS INFORMATION
WUU
U
The LTC1562-2 contains four matched, 2nd order,
3-terminal universal continuous-time filter blocks, each
with a virtual-ground input node (INV) and two rail-to-rail
outputs (V1, V2). In the most basic application, 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
program f
O
, Q and gain. A combination of internal preci-
sion components and external resistor R2 sets the center
frequency f
O
of each 2nd order block. The LTC1562-2 is
trimmed at manufacture so that f
O
will be 200kHz ±0.5%
if the external resistor R2 is exactly 7958Ω. The LTC1562-
2 is a higher frequency, pin compatible variant of the
LTC1562, with different internal R and C values and higher
speed amplifiers.
However, lowpass/bandpass filtering is only one specific
application for the 2nd order building blocks in the
LTC1562-2. 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 (e.g, elliptic or notch
responses) are available by feedforward connections with
multiple 2nd order blocks (see Typical Applicatons). More-
over, the virtual-ground input gives each 2nd order sec-
tion the built-in capability for analog operations such as
gain (preamplification), summing and weighting of mul-
tiple inputs, or accepting current or charge signals di-
rectly. 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 LTC1562-2,
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 LTC1562-2 can
be programmed for a standard filter function (lowpass,
bandpass or highpass) when configured as in Figure 3
with a resistor or capacitor for Z
IN
. These transfer func-
tions 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 de-
scribed below.) External resistors R2 and R
Q
set f
O
and Q
as follows:
f
CRR
R
kHz
Q
R
RR
R
R
R
R
kHz
f
O
QQQ
O
==
Ω
()
==
Ω
()
=
1
212
7958
2
200
12
7958 2
2
200
π ()
()
R1 = 7958Ω and C = 100pF are internal to the LTC1562-2
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
O
2
200
7958
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 R
Q
= ()7958 2Ω
The f
O
range is approximately 20kHz to 300kHz, 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
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
Operational Filter and FilterCAD are trademarks of Linear Technology Corporation.
Windows is a registered trademark of Microsoft Corporation.
8
LTC1562-2
15622fa
tend to scale with R2.)
At high f
O
these resistors fall below
4k, heavily loading the outputs of the LTC1562-2 and
leading to increased THD and other effects. At the other
extreme, a lower f
O
limit of 20kHz reflects an arbitrary
upper resistor limit of 1MΩ. The LTC1562-2’s MOS input
circuitry can accommodate higher resistor values than
this, but junc
tion leakage current from the input protection
circuitry 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
L
O
O
O
2
2
22
()
()
()
–
/
==
+
()
+
ω
ωω
H
L
= R2/R
IN
is the DC gain magnitude. (Note that the
transfer function includes a sign inversion.) Parameters
APPLICATIONS INFORMATION
WUU
U
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
1562-2 F04
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
INV V1
2nd ORDER
1/4 LTC1562-2
V2
1562 F05
R2R
Q
R
IN
V
IN
V
OUT
Figure 5. Basic Lowpass Configuration
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.
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LTC1562CG-2#PBF

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