8th-Order, Lowpass, Elliptic,

Switched-Capacitor Filters

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9

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, fS. At frequencies

above fS, the filter’s gain does not exceed the gain at fS.

The corner frequency, fC, 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 = fS / fC

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

VDD

OUT

OS

GND

BIAS

SCF

LOGIC

OFFSET

ADJ

MAX7400

MAX7403

MAX7404

MAX7407

VDD

Figure 1. Functional Diagram

C10

C11

C9

L3

L5

L7

C8

R2

C4

C2

VIN

+

-

V0

L1

R1

C6

Figure 2. 8th-Order Ladder Filter Network