INTRODUCTION convert dc energy to ac energy at a very high frequency. If the feedback signal is large enough and has correct phase, there will be an output signal even though there is no external input signal. The criterion is that the signal fed back to the input of the amplifier must be in phase. In-phase feedback is also called positive feedback, or regenerative feedback. It is an unstable amplifier.
Electronic oscillators are divided into: Sinusoidal (or harmonic) oscillators-which produce an output having sine waveform Non-sinusoidal (or relaxation) oscillator-the output is square, rectangular or saw-tooth or pulse shape. Oscillators are widely applied in many digital devices, Signal generator, Touch-tone telephone, musical instrument and radio/television transmitter and etc.
BLOCK DIAGRAM Closed loop transfer function with positive feedback: If, βA= 1 + j0 or βA = 1∠0o
Barkhausen criterion : The feedback factor or loop gain . The gain is infinite, this represent the condition for oscillation. The net phase shift around the loop 0 ˚ (or an ˚ integral multiple of 360 ). In other word, feedback should be positive. The amplifier gain must be greater than the loss in the feedback path.
OSCILLATOR CONDITION Aβ less than 1 AβVin is less than Vin the output signal will die out (Damped Oscillation). Aβ greater than 1 AβVin is greater than Vin the output signal will build up. Aβ equal to 1 AβVin is equal to Vin the output signal will steady, Undamped Oscillations (Stable oscillator).
TYPE OF OSCILLATOR LC Hartley Colpitt’s Crystal Amstrong RC Phase Shift (RC)
HARTLEY OSCILLATOR The configuration of the transistor amplifier is of a Common emitter amplifier with the output signal 180o out of phase with regards to the input signal These two inductances form an autotransformer action and gives the feedback with a phase reversal of 180°, thus the total phase shift becomes 360o to give the feedback positive or regenerative feedback. A Hartley oscillator uses an inductive (single tapped- coil) of L1 and L2. Voltage divider to determine the feedback ratio. If ignore Mutual inductance,
When the LC tank is resonant, the circulating current flows through L1 in series with L2. The equivalent L to use in equation is: L T = L1 + L2 +2M or L T ≅ L1 + L2 L1 ,is a primary L2 ,is the secondary M, Mutual inductance between the coils. The tuning capacitor CT allows the Hartley oscillator to be tuned over a wide range of frequency The lowest frequency is determined by the maximum capacitance of CT or otherwise. The frequency is determined by the tank’s resonant frequency: To start Oscillating, the circuit needs a minimum voltage gain or must be greater than 1/β , If ignore Mutual inductance
a) FET shunt-Fed Hartleyb)Transistor series-fed Hartley
R1 and R2 – provide the usual stabilizing DC bias for the bipolar transistor. C1 and C2 – as a dc- blocking capacitor that provides low impedance at the oscillator’s operating frequency while preventing the transistor’s dc operating point from being disturbed and less power is wasted when DC flow through inductive coil. The radio frequency choke (RFC) - in providing the amplifier with a steady dc supply while eliminating unwanted ac disturbances. RE,CE Fet and RS, CS Bipolar – to improve amplifier stability (temperature effect) and provide ac ground thereby preventing any signal degeneration.
The Colpitts oscillator is adaptable to a wide range of frequencies and has better stability than the Hartley. The configuration of the transistor amplifier is of a Common emitter amplifier with the output signal 180o out of phase with regards to the input signal. The additional 180o phase shift required for oscillation is achieved by the fact the two capacitors are connected together in series but parallel with the inductive coil resulting in overall phase shift of the circuit being zero or 360o. R1 and R2 stabilizing DC bias for the transistor. While C1 and C2 acts as DC-blocking capacitor To start-up and oscillate at the proper frequency, the voltage gain of the circuit must meet or exceed the Barkhausen criterion, to start. Aβ ≥ 1
The output voltage Vout, collector to ground, appears across C1, while feedback voltage Vf, base to ground, appears across C2, Therefore, the ratio of the voltage Vf/Vout, then, is the feedback ratio and is equal to the ratio of For oscillator start-up The resonant frequency for this Colpitts tank circuit occurs when XL = XC
PHASE SHIFT OSCILLATOR The amplifier (common emitter or inverting amplifier) produces 180° of phase shift because the signal drives the inverting input. Then the RC lag or lead circuit feedback network must produce an additional phase shift network of 180° to get a loop phase shift of 360o or 0°. The total phase shift of the three RC lag or lead circuits must equal to 180° (approximately 60° each). But the RC feedback also produces a significant loss of gain due to the nature of RC network. So the amplifier must produce sufficient gain to overcome this loss at the frequency of a.Phase shift oscillators with three lag operation. circuits
b) Phase shift oscillator with threelead circuits
The reactive term must be zero at To ensure oscillation, Gain must the frequency of oscillation fo, the exceed, from gain expression V1/V2 at 180° becomes
AMSTRONG OSCILLATOR(TUNED BASE) If we ignore the loading effect of the base, the feedback fraction is: M = mutual inductance of the autotransformer L = the primary inductance For the oscillator to start, the voltage gain must greater than 1/β. a)Amstrong (tuned base) Oscillator This oscillator uses transformer couplingThe common emitter with the output for the feedback signal and the smallsignal 180° phase shift with regards to secondary winding is sometimes called athe input signal. tickler coil.Therefore, the feedback signal is taken from •The resonant frequency isa small secondary winding and fed back tothe base, there is a phase shift of 180° in thetransformer, which means that the phaseshift around the loop is zero.
CRYSTAL The main substances that produce the piezoelectric effect are quartz (RF oscillator and filters), Rochelle salts and tourmaline. If a high degree of oscillator stability is needed such as communication and computer systems, the crystal oscillator are used to generate the timing signal because the Crystal-controlled oscillators will typically have a minimum frequency drift of 0.0001%. a)Mounting Capacitance A crystal is used as a frequency determining device b) Ac equivalent circuit of vibrating and can act in both series and parallel tuned circuit. Crystal used in oscillator circuits are thin sheet, or wafer, cut from natural or synthetic quartz and ground to a specific thickness to obtain the desired resonant frequency. When it not vibrating, it is equivalent to a capacitance Cm because it has two metal plates separated by a dielectric. And known as the mounting capacitance. When it vibrating, it acts like a tuned circuit. The ac equivalent circuits of a crystal are L in Henry, CS in fractions of a picofarad, R in hundreds of ohm and Cm in picofarad. The extremely high Q-factor of crystal means the crystal oscillators have very stable frequency. When approach infinity, the resonant frequency approaches the ideal value determined by the values of L and C. which precisely in a crystal.
The parallel lower series resonance frequency fs which occurs when XL=XCS, in that case Z = R. The resonance frequency fp which occurs when reactance of the series leg equal to the reactance of Cm. At this frequency, the crystal offers very high impedance to the external circuit. Crystal oscillator a) Colpitts (Crystal controlled oscillator operating in parallel-resonant) b) Variation of Colpitts (Crystal controlled oscillator operating in series-resonant)
SERIES AND PARALLELRESONANCE The circuit has two resonant frequencies: In any crystal, CS is much smaller The series resonance frequency fS of a than Cm, Because of this FP is only crystal is the resonant frequency of the slightly greater than FS. LCR branch and the branch current reaches a maximum value because L The oscillation frequency will lie resonates with Cs. between FS and FP. In Colpitts crystal oscillator, The capacitive voltage divider produces the feedback voltage for the base of The Parallel resonant frequency fP of the transistor. the crystal is the frequency at which the circulating/loop current reaches a The crystal acts like an inductor that maximum value. Thus the current flow resonant with C1 and C2. true the series combination of Cs and Cm, the equivalent parallel capacitance The oscillation frequency is between is: the series and parallel resonant frequencies of the crystal. In the variation of the Colpitts crystal oscillator. The feedback signal And the parallel resonant frequency is: applied to the emitter instead of the base.
Example:A crystal has these values L = 3 H, CS = 0.05pF, R = 2 kΩ, and Cm = 10pF.Determine the series and parallel resonant frequencies of the crystal.i) The series resonant Frequencyii) The equivalent parallel capacitance:iii) The Parallel resonant frequency
MULTIPLE CHOICE QUESTIONS1. An oscillator’s circuit 3. Which of the LC oscillator basically converts type makes use of a tunedi) Ac to dc transformer?ii) Dc to ac i) Hartley oscillatoriii) Ac to ac ii) Colpitts oscillatoriv) Dc to dc iii) Armstrong oscillator2. To oscillate, a tuned circuit iv) Clapp oscillator. will need an amplifier with 4. Which LC oscillator typei) Regenerative feedback makes use of a tapped in the tuned circuit?ii) Degenerative feedback i) Hartley oscillatoriii) Negative feedback ii) Colpitts oscillatoriv)Both (a) and (c) are true iii) Armstrong oscillator iv)Clapp oscillator.