Lab6 - L303.6.R3 Drexel University Electrical and Computer...

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L303.6.R3 6-1 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 op-amp 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 second-order experiments done in Lab II (ECEL-302). 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 second-order 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 second-order 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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L303.6.R3 6-2 Fig. 1a. Feedback Block Diagram Fig. 1b. Test Loop Diagram The system consists of three functions: a feed-forward 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 feed-forward 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 R-C filter, has a transfer function, B(s) = V f /V 2 . And it can be connected to the input to
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Lab6 - L303.6.R3 Drexel University Electrical and Computer...

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