MAX7409/MAX7410/MAX7413/MAX7414
5th-Order, Lowpass,
Switched-Capacitor Filters
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The difference between Bessel and Butterworth filters
can be observed when a 1kHz square wave is applied
to the filter input (Figure 1, trace A). With the filter cutoff
frequencies set at 5kHz, trace B shows the Bessel filter
response and trace C shows the Butterworth filter
response.
Background Information
Most switched-capacitor filters (SCFs) are designed with
biquadratic sections. Each section implements two filter-
ing poles, and the sections are cascaded to produce
higher-order filters. The advantage to this approach is
ease of design. However, this type of design is highly
sensitive to component variations if any section’s Q is
high. An alternative approach is to emulate a passive net-
work using switched-capacitor integrators with summing
and scaling. Figure 2 shows a basic 5th-order ladder filter
structure.
A switched-capacitor filter such as the MAX7409/
MAX7410/MAX7413/MAX7414 emulates a passive ladder
filter. The filter’s component sensitivity is low when com-
pared to a cascaded biquad design, because each
component affects the entire filter shape, not just one
pole-zero pair. In other words, a mismatched component
in a biquad design will have a concentrated error on its
respective poles, while the same mismatch in a ladder
filter design results in an error distributed over all poles.
Clock Signal
External Clock
The MAX7409/MAX7410/MAX7413/MAX7414 family of
SCFs is designed for use with external clocks that have
a 50% ±10% duty cycle. When using an external clock
with these devices, drive CLK with a CMOS gate pow-
ered from 0 to V
DD
. Varying the rate of the external
clock adjusts the corner frequency of the filter as fol-
lows:
f
C
= f
CLK
/ 100
Internal Clock
When using the internal oscillator, connect a capacitor
(C
OSC
) between CLK and ground. The value of the
capacitor determines the oscillator frequency as follows:
f
OSC
(kHz) = 30 x 10
3
/ C
OSC
(pF)
Minimize the stray capacitance at CLK so that it does
not affect the internal oscillator frequency. Vary the rate
of the internal oscillator to adjust the filter’s corner fre-
quency by a 100:1 clock-to-corner frequency ratio. For
example, an internal oscillator frequency of 100kHz
produces a nominal corner frequency of 1kHz.
Input Impedance vs. Clock Frequencies
The MAX7409/MAX7410/MAX7413/MAX7414’s input
impedance is effectively that of a switched-capacitor
resistor (see the following equation), and is inversely
proportional to frequency. The input impedance values
determined below represent the average input imped-
ance, since the input current is not continuous. As a
rule, use a driver with an output impedance less than
10% of the filter’s input impedance. Estimate the input
impedance of the filter using the following formula:
Z
IN
= 1 / ( f
CLK
x 2.1pF)
For example, an f
CLK
of 100kHz results in an input
impedance of 4.8MΩ.
