LMF60 datasheet(14/20 Pages) NSC

14 / 20 page

20 Designing with the LMF60

Given any lowpass filter specification two equations will

come in handy in trying to determine whether the LMF60 will

do the job The first equation determines the order of the

lowpass filter required

n e

log (1001AMin b 1) b log(1001AMax b 1)

2 log (fs fb)

(1)

where n is the order of the filter AMin is the minimum stop-

band attenuation (in dB) desired at frequency fs and AMax is

the passband ripple or attenuation (in dB) at frequency fb If

the result of this equation is greater than 6 then more than

a single LMF60 is required

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

lowing equation

Attn(f) e 10 log 1 a (1001AMax b 1) (ffb)2n dB

(2)

where n e 6 (the order of the filter)

21 A LOWPASS DESIGN EXAMPLE

Suppose the amplitude response specification in

Figure 8 is

given Can the LMF60 be used

The order of the Butter-

worth approximation will have to be determined using eq 1

AMin e 30 dB AMax e 10 dB fs e 2 kHz and fb e 1 kHz

n e

log(103 b 1) b log(1001 b 1)

2 log(2)

596

Since n can only take on integer values n e 6 Therefore

the LMF60 can be used In general if n is 6 or less a single

LMF60 stage can be utilized

Likewise the attenuation at fs can be found using equation

2 with the above values and n e 6 giving

Atten (2 kHz) e 10 log 1 a (1001 b 1) (21)12

3026 dB

This result also meets the design specification given in

Fig-

ure 8 again verifying that a single LMF60 section will be

adequate

TLH9294 – 21

FIGURE 8 Design Example Magnitude Response

Specification Where the Response of the Filter Design

Must Fall Within the Shaded Area of the Specification

Since the LMF60’s cutoff freqency fC which corresponds to

a gain attenuation of b301 dB was not specified in this

example it needs to be calculated Solving equation 2 where

f e fC as follows

fc e fb

1001(301 dB) b 1)

(1001AMax b 1)

(1(2n)

0301 b 1

1001 b 1

J112

1119 kHz

where fC e fCLK 50 or fCLK 100

To implement this example for the LMF60-50 the clock fre-

quency will have to be set to fCLK e 50(1119 kHz) e

5595 kHz or for the LMF60-100 fCLK e 100(1119 kHz) e

1119 kHz

22 CASCADING LMF60s

In the case where a steeper stopband attenuation rate is

required two LMF60’s can be cascaded

(Figure 9) yielding a

12th order slope of 72 dB per octave Because the LMF60

is a Butterworth filter and therefore has no ripple in its pass-

band when LMF60’s are cascaded the resulting filter also

has no ripple in its passband Likewise the DC and pass-

band gains will remain at 1VV The resulting response is

shown in

Figure 10

In determining whether the cascaded LMF60’s will yield a

filter that will meet a particular amplitude response specifi-

cation as above equations 3 and 4 can be used shown

below

n e

log (10005 Amin b 1) b log(10005 AMax b 1)

2 log (fs fb)

(3)

Attn(f) e 10 log 1 a (10005 AMax b 1) (ffb)2n dB

(4)

where n e 6 (the order of each filter)

Equation 3 will determine whether the order of the filter is

adequate (n s 6) while equation 4 can determine if the

required stopband attenuation is met and what actual cutoff

frequency (fC) is required to obtain the particular frequency

response desired The design procedure would be identical

to the one shown in Section 21

23 IMPLEMENTING A ‘‘NOTCH’’ FILTER WITH THE

LMF60

A ‘‘notch’’ filter with 60 dB of attenuation can be obtained by

using one of the Op-Amps available in the LMF60 and three

external resistors The circuit and amplitude response are

shown in

Figure 11

The frequency where the ‘‘notch’’ will occur is equal to the

frequency at which the output signal of the LMF60 will have

the same magnitude but be 180 degrees out of phase with

its input signal For a sixth order Butterworth filter 180

phase shift occurs where f e fn e 0742 fC The attenua-

tion at this frequency is 012 dB which must be compensat-

ed for by making R1 e 1014 c R2

Since R1 does not equal R2 there will be a gain inequality

above and below the notch frequency At frequencies below

the notch frequency (f m fn) the signal through the filter

has a gain of one and is non-inverting Summing this with

the input signal through the Op-Amp yields an overall gain

of two or a6 dB For f n fn the signal at the output of the

filter is greatly attenuated thus only the input signal will ap-

pear at the output of the Op-Amp With R3 e R1 e 1014

R2 the overall gain is 0986 or b012 dB at frequencies

above the notch

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