TABLE I Summary of Modes Realizable filter types (eg low-pass) denoted by asterisks

Unless otherwise noted gains of various filter outputs are inverting and adjustable by resistor ratios

Mode

BP

LP

HP

N

AP

Number of

Adjustable

Notes

Resistors

1

3No

(2)

May need input buffer

1a

2

No

Poor dynamics for

high Q

2

3

3

4

Yes

Universal State-Variable

Filter Best general-purpose mode

3a

7

Yes

As above but also includes

resistor-tuneable notch

4

3No

Gives Allpass response with

5

4

Gives flatter allpass response

6a

3

Single pole

(2)

6b

2

Single Pole

b

R3

R2

30 Applications Information

The MF10 is a general-purpose dual second-order state

variable filter whose center frequency is proportional to the

frequency of the square wave applied to the clock input

g

6%) by using a crystal clock oscillator or can be easily

varied over a wide frequency range by adjusting the clock

external resistors as in

Figures 9 10 11 13 14 and 15 The

filter Q and gain are determined by external resistors

All of the five second-order filter types can be built using

either section of the MF10 These are illustrated in

Figures 1

through

5 along with their transfer functions and some relat-

ed equations

Figure 6 shows the effect of Q on the shapes

of these curves When filter orders greater than two are

desired two or more MF10 sections can be cascaded

31 DESIGN EXAMPLE

In order to design a second-order filter section using the

MF10 we must define the necessary values of three param-

band gain and the filter’s Q These are determined by the

characteristics required of the filter being designed

As an example let’s assume that a system requires a

fourth-order Chebyshev low-pass filter with 1 dB ripple unity

gain at DC and 1000 Hz cutoff frequency As the system

order is four it is realizable using both second-order sec-

tions of an MF10 Many filter design texts include tables that

der filter sections needed to synthesize a given higher-order

filter For the Chebyshev filter defined above such a table

yields the following characteristics

For unity gain at DC we also specify

The desired clock-to-cutoff-frequency ratio for the overall

filter of this example is 100 and a 100 kHz clock signal is

available Note that the required center frequencies for the

two second-order sections will not be obtainable with clock-

to-center-frequency ratios of 50 or 100 It will be necessary

to adjust

externally From Table I we see that Mode 3

can be used to produce a low-pass filter with resistor-adjust-

able center frequency

In most filter designs involving multiple second-order

stages it is best to place the stages with lower Q values

ahead of stages with higher Q especially when the higher Q

is greater than 0707 This is due to the higher relative gain

at the center frequency of a higher-Q stage Placing a stage

with lower Q ahead of a higher-Q stage will provide some

attenuation at the center frequency and thus help avoid clip-

ping of signals near this frequency For this example stage

A has the lower Q (0785) so it will be placed ahead of the

other stage

For the first section we begin the design by choosing a

13