2.0 Modes of Operation (Continued)
TABLE I. Summary of Modes. Realizable filter types (e.g. low-pass) denoted by asterisks.
Unless otherwise noted, gains of various filter outputs are inverting and adjustable by resistor ratios.
Number of
Resistors
Adjustable
/f
Mode
BP
LP
HP
N
AP
Notes
f
CLK
O
1
*
*
*
3
No
No
Yes (above f
(2)
May need input buffer.
Poor dynamics for
high Q.
e b
e a
a
1
1a
H
H
Q
1
H
2
OBP1
OLP
OBP2
/50
CLK
2
3
*
*
*
*
*
*
*
*
3
4
7
3
or f /100)
CLK
Universal State-Variable
Filter. Best general-purpose mode.
*
*
*
*
*
*
Yes
As above, but also includes
resistor-tuneable notch.
3a
4
Yes
No
Gives Allpass response with
e b
*
*
e b
H
1 and H
2.
OAP
OLP
Gives flatter allpass response
e
5
4
3
e
0.02R .
than above if R
Single pole.
R
2
1
4
6a
*
*
(2)
e a
6b
H
1
R3
2
Single Pole.
OLP1
b
e
H
OLP2
R2
3.0 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
filter. For the Chebyshev filter defined above, such a table
yields the following characteristics:
e
e
e
e
f
f
529 Hz
993 Hz
Q
Q
0.785
3.559
0A
A
(f
). By connecting pin 12 to the appropriate DC voltage,
CLK
the filter center frequency f can be made equal to either
0B
B
O
For unity gain at DC, we also specify:
f /100 or f /50. f can be very accurately set (within
CLK CLK O
e
e
H
H
1
1
g
6%) by using a crystal clock oscillator, or can be easily
varied over a wide frequency range by adjusting the clock
frequency. If desired, the f /f ratio can be altered by
0A
0B
CLK
O
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
external resistors as inFigures 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 inFigures 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.
f
CLK
to adjust
externally. From Table I, we see that Mode 3
f
0
can be used to produce a low-pass filter with resistor-adjust-
able center frequency.
3.1 DESIGN EXAMPLE
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 0.707. 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 (0.785) so it will be placed ahead of the
other stage.
In order to design a second-order filter section using the
MF10, we must define the necessary values of three param-
eters: f , the filter section’s center frequency; H , the pass-
0
0
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
For the first section, we begin the design by choosing a
e
list the characteristics (f and Q) of each of the second-or-
O
der filter sections needed to synthesize a given higher-order
convenient value for the input resistance: R
absolute value of the passband gain H
20k. The
is made equal
1A
OLPA
13
NSC [ National Semiconductor ]
