5th-Order, Lowpass, Elliptic,

Switched-Capacitor Filters

8

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Detailed Description

The MAX7408/MAX7411/MAX7412/MAX7415 family of

5th-order, elliptic, lowpass filters provides sharp rolloff

with good stopband rejection. All parts operate with a

100:1 clock-to-corner frequency ratio and a 15kHz

maximum corner frequency.

Most switched-capacitor filters (SCFs) are designed

with biquadratic sections. Each section implements two

pole-zero pairs, and the sections can be 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. The MAX7408/MAX7411/

MAX7412/MAX7415 use an alternative approach, which

is to emulate a passive network using switched-capaci-

tor integrators with summing and scaling. The passive

network may be synthesized using CAD programs, or

may be found in many filter books. Figure 1 shows a

basic 5th-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 MAX7408/MAX7411/

MAX7412/MAX7415 provide the steepest possible

rolloff with frequency of the four most common filter

types (Butterworth, Bessel, Chebyshev, and elliptic).

The high Q value of the poles near the passband edge

combined with the stopband zeros allows for the sharp

attenuation 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 stop-

where the filter output attenuation falls just below the

passband ripple. The transition ratio (r) is defined as

the ratio of the stopband frequency to the corner fre-

quency:

The MAX7408/MAX7412 have a translation ratio of 1.6

and typically 53dB of stopband rejection. The

MAX7411/MAX7415 have a transition ratio of 1.25 (pro-

viding a steeper rolloff) and typically 37dB of stopband

rejection.

C4

C2

L4

C5

C3

C1

+

-

L2

Figure 1. 5th-Order Ladder Elliptic Filter Network

NAME

FUNCTION

1

COM

Common Input Pin. Biased internally at mid-supply. Bypass externally to GND with 0.1µF capacitor. To

override internal biasing, drive with an external supply.

2

IN

Filter Input

PIN

3

GND

Ground

4

Positive Supply Input, +5V for MAX7408/MAX7411 or +3V for MAX7412/MAX7415

8

CLK

frequency. To override the internal oscillator, connect to an external clock.

7

SHDN

6

OS

Offset Adjust Input. To adjust output offset, bias OS with a resistive voltage-divider between an external

supply and ground. Connect OS to COM if no offset adjustment is needed.

5

OUT

Filter Output

Pin Description