If the MF were set up for a cutoff frequency of 10 kHz the in-

put impedance would be:

In this example with a source impedance of 10K the overall

gain, if the MF4 had an ideal gain of 1 or 0 dB, would be:

Since the maximum overall gain error for the MF4 is

would be +0.06 dB to −0.24 dB.

1.4 CUTOFF FREQUENCY RANGE

The filter’s cutoff frequency (f

age currents through the internal switches draining the

charge stored on the capacitors. At lower clock frequencies

these leakage currents can cause millivolts of error, for ex-

ample:

The propagation delay in the logic and the settling time re-

quired to acquire a new voltage level on the capacitors limit

the filter’s accuracy at high clock frequencies. The amplitude

CLK

exceeds 750 kHz and then peak at about 0.5 dB at the cor-

ner frequency with a 1 MHz clock. As supply voltage drops to

noticeable when the clock frequency exceeds 250 kHz. The

response of the MF4 is still a good approximation of the ideal

Butterworth low-pass characteristic shown in

Figures 6, 7.

2.0 Designing With The MF4

Given any low-pass filter specification, two equations will

come in handy in trying to determine whether the MF4 will do

the job. The first equation determines the order of the

low-pass filter required to meet a given response specifica-

tion:

(3)

where n is the order of the filter, A

band attenuation (in dB) desired at frequency f

the passband ripple or attenuation (in dB) at cutoff frequency

f

single MF4 is required.

The attenuation at any frequency can be found by the follow-

ing equation:

Attn (f) = 10 log [1 + (10

(4)

where n = 4 for the MF4.

2.1 A LOW-PASS DESIGN EXAMPLE

Suppose the amplitude response specification in

Figure 8 is

given. Can the MF4 be used? The order of the Butterworth

approximation will have to be determined using

Equation (1):

Since n can only take on integer values, n = 4. Therefore the

MF4 can be used. In general, if n is 4 or less a single MF4

stage can be utilized.

Likewise, the attenuation at f

(4) with the above values and n = 4:

Attn (2 kHz) = 10 log [1 + 10

18.28 dB

This result also meets the design specification given in

Fig-

ure 8 again verifying that a single MF4 section will be ad-

equate.

Since the MF4’s cutoff frequency (f

a gain attenuation of −3.01 dB, was not specified in this ex-

ample, it needs to be calculated. Solving

Equation (4) where

f = f

where f

c

= f

implement this example for the

MF4-50 the clock frequency will have to be set to f

50(1.184 kHz) = 59.2 kHz, or for the MF4-100, f

(1.184 kHz) = 118.4 kHz.

2.2 CASCADING MF4s

When a steeper stopband attenuation rate is required, two

MF4s can be cascaded (

Figure 9) yielding an 8th order slope

of 48 dB per octave. Because the MF4 is a Butterworth filter

and therefore has no ripple in its passband when MF4s are

cascaded, the resulting filter also has no ripple in its pass-

band. Likewise the DC and passband gains will remain at

1V/V. The resulting response is shown in

Figure 10, Figure

11.

In determining whether the cascaded MF4s will yield a filter

that will meet a particular amplitude response specification,

as above,

Equations (5), (6) can be used, shown below.

(5)

(6)

where n = 4 (the order of each filter).

Equation (5) will determine whether the order of the filter is

adequate (n

≤ 4) while Equation (6) can determine the actual

stopband attenuation and cutoff frequency (f

obtain the desired frequency response. The design proce-

dure would be identical to the one shown in section 2.0.

www.national.com

8