20
LTC1562
1562fa
APPLICATIONS INFORMATION
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Notches and Elliptic Responses
The basic (essentially all-pole) LTC1562 circuit tech-
niques described so far will serve many applications.
However, the sharpest-cutoff lowpass, highpass and band-
pass filters include notches (imaginary zero pairs) in the
stopbands. A notch, or band-reject, filter has zero gain at
a frequency f
N
. Notches are also occasionally used by
themselves to reject a narrow band of frequencies. A
number of circuit methods will give notch responses from
an Operational Filter block. Each method exhibits an input-
output transfer function that is a standard 2nd order band-
reject response:
Hs
Hs
sQs
BR
N
N
O
O
()
–
/
=
+
()
+
()
+
22
22
ω
ωω
with parameters ω
N
= 2πf
N
and H
N
set by component
values as described below. (ω
0
= 2πf
0
and Q are set for the
Operational Filter block by its R2 and R
Q
resistors as
described earlier in Setting f
0
and Q). Characteristically,
the gain magnitude |H
BR
(j2πf)| has the value H
N
(f
N
2
/f
0
2
) at
DC (f = 0) and H
N
at high frequencies (f >> f
N
), so in
addition to the notch, the gain changes by a factor:
HighFrequency Gain
DC Gain
O
N
=
ƒ
ƒ
2
2
The common principle in the following circuit methods is
to add a signal to a filtered replica of itself having equal gain
and 180° phase difference at the desired notch frequency
f
N
. The two signals then cancel out at frequency f
N
. The
notch depth (the completeness of cancellation) will be
infinite to the extent that the two paths have matching
gains. Three practical circuit methods are presented here,
with different features and advantages.
Examples and design procedures for practical filters using
these techniques appear in a series of articles attached to
this data sheet on the Linear Technology web site
(www.linear-tech.com). Also available free is the analog
filter design software, FilterCAD for Windows, recom-
mended for designing filters not shown in the Typical
Applications schematics in this data sheet.
Elementary Feedforward Notches
A “textbook” method to get a 180° phase difference at
frequency f
N
for a notch is to dedicate a bandpass 2nd
order section (described earlier under Basic Bandpass),
which gives 180° phase shift at the section’s center
frequency f
O
(Figure 11, with C
IN1
= 0), so that f
N
= f
O
. The
bandpass section of Figure 6a, at its center frequency f
O
,
has a phase shift of 180° and a gain magnitude of H
B
=
R
Q
/R
IN
. A notch results in Figure 11 if the paths summed
into virtual ground have the same gains at the 180°
frequency (then I
O
= 0). This requires a constraint on the
resistor values:
R
R
R
R
IN
FF
Q
IN
2
2
1
1
=
INV V1
2nd ORDER
1/4 LTC1562
V2
R21R
Q1
R
IN1
R
IN2
R
GAIN
I
O
R
FF2
C
IN1
V
IN
V
OUT
1562 F11
VIRTUAL
GROUND
–
+
Figure 11. Feedforward Notch Configuration for f
N
≥ f
O
