LTC1562 View Datasheet(PDF) - Linear Technology
Part Name
Description
MFG CO.
'LTC1562' PDF : 28 Pages View PDF
LTC1562
APPLICATIONS INFORMATION
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
bandpass 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:
( ) HBR(s)
=
s2
–HNs2 +
+ ωO / Q
ω
2
N
s
+
ω
2
O
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 = ƒO2
DC Gain
ƒN2
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 articles1 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:
RIN2 = RQ1
RFF2 RIN1
1Nello Sevastopoulos, et al. “How to Design High Order Filters with Stopband Notches Using the
LTC1562 Quad Operational Filter.” Attached to this data sheet, available on the LTC web site
(www.linear-tech.com).
CIN1
RIN1
VIN
RQ1 R21 RIN2
IO
RGAIN
INV V1 V2
2nd ORDER
VIRTUAL
–
GROUND
1/4 LTC1562
RFF2
+
VOUT
1562 F11
Figure 11. Feedforward Notch Configuration for fN ≥ fO
20
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