20
LTC1562
1562fa
APPLICATIONS INFORMATION
WU
U
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 fN. 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
sQ s
BR
N
O
()
–
/
=
+
()
+
() +
22
ω
ωω
with parameters
ωN = 2πfN and HN set by component
values as described below. (
ω0 = 2πf0 and Q are set for the
Operational Filter block by its R2 and RQ resistors as
described earlier in Setting f0 and Q). Characteristically,
the gain magnitude |HBR(j2πf)| has the value HN(fN2/f02) at
DC (f = 0) and HN at high frequencies (f >> fN), so in
addition to the notch, the gain changes by a factor:
High Frequency Gain
DC Gain
O
N
=
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
fN. The two signals then cancel out at frequency fN. 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 fN 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 fO (Figure 11, with CIN1 = 0), so that fN = fO. The
bandpass section of Figure 6a, at its center frequency fO,
has a phase shift of 180
° and a gain magnitude of HB =
RQ/RIN. A notch results in Figure 11 if the paths summed
into virtual ground have the same gains at the 180
°
frequency (then IO = 0). This requires a constraint on the
resistor values:
R
IN
FF
Q
IN
2
1
=
INV
V1
2nd ORDER
1/4 LTC1562
V2
R21
RQ1
RIN1
RIN2
RGAIN
IO
RFF2
CIN1
VIN
VOUT
1562 F11
VIRTUAL
GROUND
–
+
Figure 11. Feedforward Notch Configuration for fN ≥ fO