EMT212 Analog Electronic II. Chapter 4. Oscillator
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1 EMT Analog Electronic II Chapter 4 Oscillator
2 Objectives Describe the basic concept of an oscillator Discuss the basic principles of operation of an oscillator Analyze the operation of RC, LC and crystal oscillators Describe the operation of the basic relaxation oscillator circuits
3 Introduction Oscillators are circuits that produce a continuous signal of some type without the need of an input. These signals serve a variety of purposes. Communications systems, digital systems (including computers), and test equipment make use of oscillators. 3
4 The Oscillator An oscillator is a circuit that produces a repetitive signal from a dc voltage. The feedback oscillator relies on a positive feedback of the output to maintain the oscillations. The relaxation oscillator makes use of an RC timing circuit to generate a nonsinusoidal signal such as square wave. 4
5 Types of Oscillator. RC Oscillator - Wien Bridge Oscillator - Phase Shift Oscillator. LC Oscillator - Hartley Oscillator - Colpitts Oscillator - Clapp Oscillator - Crystal Oscillator 3. Relaxation Oscillator 5
6 Feedback Oscillator Principles An oscillator is an amplifier with positive feedback. V e = V i + V f () V o = Av e () V f = βv o (3) From (), () and (3), we get V V o i A = β ( A) 6
7 Feedback Oscillator Principles Hence the closed loop gain, Vo/Vi = A/( - Aβ) The closed loop gain can be very large if ( - Aβ)= 0 A small signal value at the input can produce an output of reasonable magnitude. Thus the amplifier will be unstable when ( - Aβ) ) = 0, or when the loop gain Aβ A = In polar form, Aβ A = 0 or 360 7
8 Feedback Oscillator Principles The feedback oscillator is widely used for generation of sine wave signals. The positive (in phase) feedback arrangement maintains the oscillations. The feedback gain must be kept to unity to keep the output from distorting. 8
9 Design Criteria for oscillators ) Aβ equal to unity or slightly larger at the desired oscillation frequency. - Barkhaussen criterion, Aβ = = ) Total phase shift,φ of the loop gain must be 0 0 or
10 Factors that determine the frequency of oscillation Oscillators can be classified into many types depending on the feedback components, amplifiers and circuit topologies used. RC components generate a sinusoidal waveform at a few Hz to khz range. LC components generate a sin wave at frequencies of 00 khz to 00 MHz. Crystals generate a square or sin wave over a wide range,i.e. about 0 khz to 30 MHz. 0
11 Oscillators With Feedback Circuits. RC Oscillators
12 Oscillators With RC Feedback Circuits RC feedback oscillators are generally limited to frequencies of MHz or less. The types of RC oscillators that we will discuss are the Wien - bridge and the phase-shift.
13 Wien - Bridge Oscillator It is a low frequency oscillator which ranges from a few khz to MHz. Structure of this oscillator is 3
14 Wien - Bridge Oscillator 4
15 5 5 Wien Wien - Bridge Oscillator Bridge Oscillator ( )( ) R C j R C j C R j C R j V V o ω ω ω ω = = ω ω ω C R C R C R C R R C j C R C R R C j V V o Multiply the top and bottom by jωc, we get Divide the top and bottom by C R C R
16 Wien - Bridge Oscillator Now the amplifier gives K=A cl V 0 ' = V K Furthermore, for steady state oscillations, we want the feedback V to be exactly equal to the amplifier input, V. Thus ' V V = = V K o V o 6
17 7 7 Wien Wien - Bridge Oscillator Bridge Oscillator = ω ω ω C R C R C R C R R C j C R C R R C j K = ω ω ω C R C R C R C R R C j C R C R R C K j 0 = ω R C R C Hence Equating the real parts, R C R C R C R C K + + =
18 Wien - Bridge Oscillator If R = R = R and C = C = C K ω = = 3 RC f r = πrc - Gain > 3 : growing oscillations - Gain < 3 : decreasing oscillations 8
19 Wien - Bridge Oscillator The lead-lag circuit of a Wien -bridge oscillator reduces the input signal by /3 and yields a response curve as shown. The frequency of resonance can be determined by the formula below. f r = /πrc 9
20 Wien - Bridge Oscillator The lead-lag circuit is in the positive feedback loop of Wien -bridge oscillator. The voltage divider limits gain. The lead lag circuit is basically a band-pass with a narrow bandwidth. 0
21 Wien - Bridge Oscillator Since there is a loss of about /3 of the signal in the positive feedback loop, the voltage-divider ratio must be adjusted such that a positive feedback loop gain of is produced. This requires a closed-loop gain of 3. The ratio of R and R can be set to achieve this.
22 Wien - Bridge Oscillator To start the oscillations an initial gain greater than must be achieved. The back-to-back zener diode arrangement is one way of achieving this. When dc is first applied the zeners appear as opens. This allows the slight amount of positive feedback from turn on noise to pass.
23 Wien - Bridge Oscillator The lead-lag circuit narrows the feedback to allow just the desired frequency of these turn transients to pass. The higher gain allows reinforcement until the break over voltage for the zeners is reached. 3
24 Wien - Bridge Oscillator Automatic gain control is necessary to maintain a gain of exact unity. The zener arrangement for gain control is simple but produces distortion because of the nonlinearity of zener diodes. A JFET in the negative feedback loop can be used to precisely control the gain. After the initial startup and the output signal increases the JFET is biased such that the negative feedback keeps the gain at precisely. 4
25 Phase Shift Oscillator The phase shift oscillator utilizes three RC circuits to provide 80º phase shift that when coupled with the 80º of the opamp itself provides the necessary feedback to sustain oscillations. The gain must be at least 9 to maintain the oscillations. The frequency of resonance for the this type is similar to any RC circuit oscillator. f r = /π 6RC 5
26 Phase Shift Oscillator The transfer function of the RC network is 6
27 Phase Shift Oscillator If the gain around the loop equals, the circuit oscillates at this frequency. Thus for the oscillations we want, Putting s=jω and equating the real parts and imaginary parts, we obtain 7
28 Phase Shift Oscillator From equation () ; Substituting into equation () ; # The gain must be at least 9 to maintain the oscillations. 8
29 Phase Shift Oscillator Practical The last R has been incorporated into the summing resistors at the input of the inverting op-amp. f r π 6RC R f = K = = 9 R 3 9
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