PRODUCT SPECIFICATION

RC4156/RC4157

8

REV. 1.0.1 6/13/01

characteristics. The values shown for C1, C2, R4, R5 and R6

are arbitrary. Pre-selecting their values will simplify the filter

tuning procedures, but other values can be used if necessary.

The generalized transfer function for the state-variable active

filter is:

Filter response is conventionally described in terms of a nat-

ural frequency

complex pole pair. The filter parameters

the coefficients in T(s) as:

and

Ts

()

a

2

a

++

s

2

b

++

------------------------------------

=

ω

0

b

0

=

Q

ω

0

b

0

------

=

The input configuration determines the polarity (inverting or

non-inverting), and the output selection determines the type

of filter response (lowpass, bandpass, or highpass).

Notch and all-pass configurations can be implemented by

adding another summing amplifier.

Bandpass filters are of particular importance in audio and

telecommunication equipment. A design approach to band-

pass filters will be shown as an example of the state-variable

configuration.

Design Example Bandpass Filter

For the bandpass active filter (Figure 16) the input signal is

applied through R3 to the inverting input of the summing

amplifier and the output is taken from the first integrator

the inverting and non-inverting inputs (see Equation 1).

Figure 15. 2-Pole State-Variable Active Filter

65-0751

C2

1000 pF

V

Lowpass

Output

LP

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C

R2**

C1

1000 pF

R5

100K

R4

10K

R1**

R6

100K

V

Highpass

Ouput

HP

V

Bandpass

Output

BP

V1

R3*

R8*

R7*

* Input connections are chosen for inverting or non-inverting response. Values of

R3,R7,R8 determine gain and Q.

** Values of R1 and R2 determine natural frequency.

4156/57

B

4156/57

A

10

9

8

5

6

7

3

2

1

Equation 1.

R3R5

R3

R5

+

---------------------

R4

R3R5

R3

R5

+

---------------------

+

-----------------------------------V

()

R3R4

R3

R4

+

---------------------

R5

R3R4

R3

R4

+

---------------------

+

-----------------------------------V

()

R4R5

R4

R5

+

---------------------

R3

R4R5

R4

R5

+

---------------------

+

-----------------------------------V

()

R7

R6

R7

+

---------------------V

()

++

+