Rainbow Electronics MAX7407 - Manual (Page 9)

MAX7400/MAX7403/MAX7404/MAX7407
8th-Order, Lowpass, Elliptic,
Switched-Capacitor Filters
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Detailed Description
The MAX7400/MAX7403/MAX7404/MAX7407 family of
8th-order, lowpass filters provides sharp rolloff with
good stopband rejection. All parts operate with a
100:1 clock-to-corner frequency ratio and a 10kHz
maximum corner frequency. These devices accept a
single +5V (MAX7400/MAX7403) or +3V (MAX7404/
MAX7407) supply. Figure 1 shows the functional dia-
gram.
Most switched-capacitor filters (SFCs) are designed
with biquadratic sections. Each section implements two
filtering poles, and the sections can be cascaded to
produce higher-order filters. The advantage of this
approach is ease of design. However, this type of
design is highly sensitive to component variations if any
section’s Q is high. The MAX7400 family uses an alter-
native approach, which is to emulate a passive network
using switched-capacitor integrators with summing and
scaling. The passive network can be synthesized using
CAD programs or can be found in many filter books.
Figure 2 shows a basic 8th-order ladder elliptic filter
structure.
A switched-capacitor filter that emulates a passive lad-
der filter retains many of the same advantages. The
component sensitivity of a passive ladder filter is low
when compared to a cascaded biquadratic design,
because each component affects the entire filter shape
rather than a single pole-zero pair. In other words, a
mismatched component in a biquadratic design has a
concentrated error on its respective poles, while the
same mismatch in a ladder filter design spreads its
error over all poles.
Elliptic Characteristics
Lowpass, elliptic filters such as the MAX7400/MAX7403/
MAX7404/MAX7407 provide the steepest possible rolloff
with frequency of the four most common filter types
(Butterworth, Bessel, Chebyshev, and Elliptic). Figure 3
shows the 8th-order elliptic filter response. The high Q
value of the poles near the passband edge combined
with the stopband zeros allows for the sharp attenua-
tion characteristic of elliptic filters, making these
devices ideal for anti-aliasing and post-DAC filtering in
single-supply systems (see the
Anti-Aliasing and Post-
DAC Filtering section).
In the frequency domain, the first transmission zero
causes the filter’s amplitude to drop to a minimum level.
Beyond this zero, the response rises as the frequency
increases until the next transmission zero. The stopband
begins at the stopband frequency, f
S . At frequencies
above f S , the filter’s gain does not exceed the gain at f S .
The corner frequency, f C , is defined as the point where
the filter output attenuation falls just below the passband
ripple. The transition ratio is defined as the ratio of the
stopband frequency to the corner frequency:
r = f S / f C
The MAX7400/MAX7404 have a transition ratio of 1.5
and a typical stopband rejection of 82dB. The
MAX7403/MAX7407 have a transition ratio of 1.2 (pro-
viding the steepest rolloff) and a typical stopband
rejection of 60dB.
2
INT
CLOCK
IN
1
COM
8
CLK SHDN
7
4
5
6
3
V DD
OUT
OS
GND
BIAS
SCF
LOGIC
OFFSET
ADJ
MAX7400
MAX7403
MAX7404
MAX7407
V DD
Figure 1. Functional Diagram
C10 C11 C9
L3 L5 L7
C8 R2 C4 C2 V IN
+
-
V
0
L1 R1
C6
Figure 2. 8th-Order Ladder Filter Network