廬
APPLICATION BULLETIN
by R. Mark Stitt (602) 746-7445
Mailing Address: PO Box 11400 鈥?Tucson, AZ 85734 鈥?Street Address: 6730 S. Tucson Blvd. 鈥?Tucson, AZ 85706
Tel: (602) 746-1111 鈥?Twx: 910-952-111 鈥?Telex: 066-6491 鈥?FAX (602) 889-1510 鈥?Immediate Product Info: (800) 548-6132
SIMPLE FILTER TURNS SQUARE WAVES INTO SINE WAVES
Many signals are digitally generated or transmitted as square
waves. It is often desirable to convert these signals into sine
waves. For example, the 350Hz, 440Hz, 480Hz, and 620Hz
telephone supervisory tones transmitted over fiber-optics
may appear at curb-side as square waves. To be used in
telephone equipment it is desirable to convert the square
waves into low-distortion sine waves. This can be done with
a simple filter.
According to its Fourier series, a 50% duty-cycle square
wave consists of odd order harmonic sine waves with the
fundamental at the same frequency as the square wave.
Fourier Series for a Square Wave
4k
sin x
+
1
sin 3x
+
1
sin 5x
+
L
3
5
蟺
where k = peak amplitude of the square wave
square wave. This is because the fundamental has an ampli-
tude of 4/蟺 times that of the square wave as shown by the
Fourier series. The bandpass filter will also filter out any DC
component of the square wave input as shown in Figure 1B.
The circuit for a 鈥渢uned-circuit鈥?bandpass filter using a Burr-
Brown UAF42 universal active filter chip is shown in Figure
2. The UAF42 contains op amps, gain-set resistors, and on-
chip precision (0.5%) 1000pF capacitors to form a time
continuous filter, free from the anomalies and switching
noise associated with switched-capacitor filters. The only
external components required are three 1% resistors to set
center frequency and Q. In this example, resistors are se-
lected to produce a 鈥渢uned-circuit鈥?bandpass filter simulat-
ing a tuned-circuit response with 350Hz center frequency
and Q = 10. A computer-aided design program, FilterPro, is
available free of charge from Burr-Brown to make it easy to
design all kinds of active filters using the UAF42.
To design a 鈥渢uned-circuit鈥?bandpass filter with Q = 10: load
FilterPro FILTER42, select Bandpass filter response, select
Order n = 2, set the desired center frequency (f
CENTER
), and
set the bandwidth to 1/10 the center frequency. You can plot
the filter response and print out component values.
A fourth, auxiliary, op amp in the UAF42 is available for use
in other circuitry. If the auxiliary op amp is not used, connect
it as a unity-gain follower with the input to ground (connect
鈥揑N to V
OUT
and +IN to ground).
(
)
A sine wave with the same frequency as the square wave can
be gleaned by filtering out the harmonics above the funda-
mental. A 鈥渢uned-circuit鈥?bandpass filter with a Q of 10
attenuates signals at three times the bandpass frequency by
28.4dB. Since the amplitude of the third harmonic is 1/3 that
of the fundamental, the total attenuation of the third har-
monic compared to the fundamental is nearly 40dB. The
result is a low distortion sine wave as shown in Figure 1A.
Notice that although the filter has unity gain, the amplitude
of the sine wave output signal is greater than that of the
+2V
+1V
0V
0V
鈥?V
1a. A square wave passed through a simple 鈥渢uned-
circuit鈥?bandpass filter produces a low distortion sine
wave.
1b. DC components of a square wave passed through
bandpass filter are eliminated to produce a low distortion
sine wave.
FIGURE 1. Low Distortion Sine Wave.
漏
1993 Burr-Brown Corporation
AB-058
Printed in U.S.A. December, 1993
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