very pure low distortion sine wave. However, the frequency
is fixed at the point where each RC section produces a 60
degree phase shift. That approximate frequency is:
f = 1/2.6RC
In the circuit of Figure 2, the frequency should be
about 3. 85 kHz.
Colpitts Crystal Oscillator
Quartz crystals are often used to set the frequency
of an oscillator because of their precise frequency of
oscillation and stability. The equivalent circuit of a crystal
is a series or parallel LC circuit. Figure 3 is a very popular
sine wave oscillator of the Colpitts type, as identified by
the two-capacitor feedback network. This is another widely
used circuit because it’s easy to implement and very stable.
Its useful frequency range is approximately 100 kHz to 40
MHz. The output is a sine wave with a slight distortion.
By the way, if you need a crystal oscillator with a sine
wave out, you can usually buy a commercial circuit. They
are widely available for almost any desired frequency. They
are packaged in a metal can and are the size of a typical
IC. The DC supply is usually five volts.
Square Wave and Filter
An interesting way to produce a sine wave is to select
it with a filter. The idea is to generate a square wave first.
As it turns out, it’s often easier to generate a square wave
or rectangular wave than a sine wave. According to Fourier
theory, the square wave is made up of a fundamental sine
wave and an infinite number of odd harmonics.
For example, a 10 kHz square wave contains a 10
kHz sine wave, and sine waves at the 3rd, 5th, 7th, etc.,
harmonics of 30 kHz, 50 kHz, 70 kHz, and so on. The idea
is to connect the square wave to a filter that selects the
Figure 4 shows one example. A CMOS 555 timer
IC produces a 50% duty cycle square wave. Its output is
sent to a low pass RC filter that filters out the harmonics,
leaving only the fundamental sine wave. Some distortion
is common as it’s difficult to completely eliminate the
harmonics. A more selective LC filter can be used to
improve sine wave quality. Keep in mind that you can
also use a selective band pass filter to pick out one of the
harmonic sine waves.
This circuit is designed for a frequency of 1,600 Hz.
Direct Digital Synthesis
An interesting way to produce a sine wave is to do
it digitally. Refer to Figure 5. It begins with a read-only
memory (ROM) that stores a series of binary values that
represent values that follow the trigonometry equation for
a sine wave. These values are then read out of the ROM
one at a time and applied to a digital-to-analog converter
(DAC). A clock signal steps an address counter that then
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Figure 4. The CMOS version of the 555 is recommended, but
you can make this work with a standard 555 by eliminating
the 100K resistor. Figure 5. Direct digital synthesis.
THE LATEST IN NETWORKING AND WIRELESS TECHNOLOGIES
86 May/June 2018