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L303.6.R3
61
Drexel University
Electrical and Computer Engr. Dept.
Electrical Engineering Laboratory III, ECEL 303
E. L. Gerber
SINE
WAVE
GENERATOR
Object
The object of this experiment is to learn the basics of electronic sine wave
generation.
Oscillation and feedback circuits will be introduced and practical electronic
oscillators will be studied.
Introduction
The generation of a sine wave is easily obtained.
Based on Faraday’s principle; a
rotating coil, at a constant speed, in a constant magnetic field, will induce a pure sine
voltage whose frequency is proportional to the speed of rotation.
This is how the electric
companies generate electric power at a low frequency, 60 Hz.
In the electronics laboratory we require signals over a very wide range of
frequencies and of different types.
For example: sine, square, pulse, triangle, and, ramps
are needed in the laboratory.
In practice the sine wave oscillator can be built using one
opamp and several resistors and capacitors.
The other functions can be obtained from
specially designed integrated circuits.
Theory
• Sine Wave Oscillators
A simple RLC circuit can be made to oscillate by the appropriate selection of the
element values.
Recall the two secondorder experiments done in Lab II (ECEL302).
The
circuit equations had the following denominator polynomials,
s
2
+ as + b
or
s
2
+ 2
ω
0
ζ
s +
ω
0
2
(1
When the poles (s
1
and s
2
) the roots of Eq. 1 of the secondorder circuit are complex
conjugates, that is,
ζ
< 1, the system response is
y(t) = A e

α
t
sin
ω
0
t
(2
The frequency,
ω
0
is determined by L and C and the decay factor
α
is proportional to the
resistance R.
If R = 0 then
α
= 0 and the response is a pure sine wave.
However, it is not
practical to achieve zero resistance in a coil (except for a superconducting coil at
T ~ 100° K).
It is possible to obtain a secondorder system with a = 0 in Eq. 1
by employing a
positive feedback amplifier. Consider the feedback block diagram in Fig. 1a.
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View Full DocumentL303.6.R3
62
Fig. 1a.
Feedback Block Diagram
Fig. 1b.
Test Loop Diagram
The system consists of three functions: a feedforward circuit
(A(s)), a feedback
circuit
(B(s)), and a summing junction where the input signal (V
1
) and the feedback signal
(V
f
) are summed.
The feedback may be additive (positive feedback) or subtractive
(negative feedback).
The
feedforward
circuit is
an
amplifier with
adjustable
gain, its
frequency
dependent forward voltage transfer function is expressed as A(s) = V
2
/V
e
.
Where, V
e
is
the “error” signal after the summing junction.
The feedback circuit, which is typically an
RC filter, has a transfer function, B(s) = V
f
/V
2
. And it can be connected to the input to
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 Spring '10
 GERBER

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