MF8 datasheet(11/24 Pages) NSC

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10 Application Information (Continued)

fC1 and fC2 The filter’s lower and upper cutoff frequencies

These define the filter’s passband

fS1 and fS2 The boundaries of the filter’s stopband

BW The filter’s bandwidth BW e fC2 b fC1

SBW The width of the filter’s stopband SBW e fS2 b fS1

f0 The center frequency of the filter f0 is equal to the geo-

metric mean of fC1 and fC2 f0 e

0fC1fC2 f0 is also equal to

the geometric mean of fS1 and fS2

H0BP The nominal passband gain of the bandpass filter

This is normally taken to be the gain at f0

f0 BW The ratio of the center frequency to the bandwidth

For second-order filters this quantity is also known as ‘‘Q’’

SBWBW The ratio of stopband width to bandwidth This

quantity is also called ‘‘Omega’’ and may be represented by

the symbol ‘‘X’’

Amax The maximum allowable gain variation within the filter

passband This will depend on the system requirements but

typically ranges from a fraction of a dB to 3 dB

Amin The minimum allowable attenuation in the stopband

Again the required value will depend on system constraints

2) Choose a Butterworth or Chebyshev response charac-

teristic Butterworth bandpass filters are monotonic on ei-

ther side of the center frequency while Chebyshev filters

will have ‘‘ripple’’ in the passband but generally faster at-

tenuation outside the passband Chebyshev filters are spec-

ified according to the amount of ripple (in dB) within the

passband

3) Determine the filter order necessary to meet the re-

sponse requirements defined above This may be done with

the aid of the nomographs in

Figures 8 and 9 for Butter-

worth and Chebyshev filters To use the nomographs draw

a line through the desired values on the AMAX AMIN scales

to the left side of the graph Draw a horizontal line to the

right of this point and mark its intersection with the vertical

line corresponding to the required ratio SBWBW The re-

quired filter order will be equal to the number of the curve

falling on or just above the intersection of the two lines This

is illustrated in

Figure 10 for a Chebyshev filter with 1 dB

ripple 30 dB minimum attenuation in the stopband and

SBWBW e 3 From the

Figure the required filter order is

4) The design tables in section 20 can now be used to find

the component values that will yield the desired response

for filters of order 4 through 12 The ‘‘Kn’’ give the ratios of

resistors ‘‘Rn’’ to RF and KQ is Q divided by f0 BW

As an example of the Tables’ use consider a fourth-order

Chebyshev filter with 05 dB ripple and f0 BW e 6 Begin by

choosing a convenient value for RF such as 100 kX From

the ‘‘05 dB Chebyshev’’ filter table K0 e R0 RF e 13405

This gives R0 e RF c 1345 e 13405k In a similar man-

ner R2 is found to equal 20161k Q is found using the

column labeled KQ This gives Q e KQ c f0 BW e 84174

Table I shows the available Q values the nearest value is

85 which is programmed by tying pins 1 2 3 and 18 to Va

and pin 17 to Vb

Note that the resistor values obtained from the tables are

normalized for center frequency gain HOBP e 1 For differ-

ent gains simply divide R0 by the desired gain

5) Choose the clock-to-center-frequency ratio This will

nominally be 1001 when pin 10 is connected to pin 12(Va)

and 501 when pin 10 is connected to pin 11(Vb) 1001

generally gives a response curve nearer the ideal and fewer

(if any) problems with aliasing while 501 allows operation

over the highest octave of center frequencies (10 kHz to 20

kHz) Supply the MF8 with a clock signal of the appropriate

frequency to either the TTL or CMOS input depending on

the available clock logic levels

TABLE I Q and Clock-to-Center-Frequency Ratio

Versus Logic Levels on ‘‘Q-set’’ Pins

501 mode

1001 mode

ABCDE

FCLK Fo

QFCLK Fo

10000

437

045

940

047

11000

458

071

958

073

01000

468

096

968

098

10100

484

984

00100

487

987

01100

489

989

11100

492

992

01010

493

993

10010

494

994

10110

494

994

00010

495

995

11110

496

996

00110

496

106

996

106

11001

496

117

996

117

11010

497

125

997

125

11101

497

136

997

136

01001

497

147

997

147

10011

497

158

997

158

10101

497

165

997

165

01110

497

997

10001

498

998

10111

498

998

11011

498

998

11111

498

998

00101

498

998

01011

498

998

00111

498

998

00001

499

999

01101

499

999

00011

499

999

01111

499

999

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