Unit– IV Oscillators Index

4.1 Types of feedback(Positive and Negative)

4.2 Principle of oscillation.

4.3 Oscillators: Hartley and Colpitts 4.1 Types of feedback(Positive and Negative)

Feedback in amplifier In amplifier circuit, when a small signal is taken from the output and given to the input. It is called feedback in amplifier. • Input voltage Vi is given to an amplifier having gain A. Output voltage is Vo. • Feedback V f = β Vo is given to the input.

• Β is the feedback factor. Value of the β is less than 1.

• Due to feedback , input to the amplifier changes from Vi to Vi’

• If the feedback is in phase opposition to the input signal it is called degenerative feedback or negative feedback. Vi’ = Vi – V f • If the feedback is in phase with the input signal it is called positive feedback. Vi’ = Vi + V f 4.2 Principle of oscillation. Oscillator An electronic device that generates sinusoidal oscillation of desired frequency is known as oscillator.

Oscillation are produced without any external signal source. The only input power to an oscillator is the d.c.power supply.In fact oscillator is the amplifier with positive feedback in which no input signal is given. Oscillators convert dc to ac.

Oscillator ac out dc in

Some possible output waveforms Damped oscillation in LC tuned circuit:

• A tank or oscillatory circuit is a parallel form of inductor and capacitor elements which produces the electrical oscillations of any desired frequency. • Both these elements are capable of storing energy. Whenever the potential difference exists across a capacitor plates, it stores energy in its electric field. • Similarly, whenever current flows thorough an inductor, energy is stored in its magnetic field. • The below figure shows a tank circuit in which inductor L and capacitor C are connected in parallel. • Consider that the capacitor is initially charged with a DC source having the polarities upper plate positive and lower plate negative as shown below. • This represents that the upper plate has of electrons deficiency , whereas the lower plate has excess of electrons. Therefore, potential differences exist between these two plates. • Consider that this charged capacitor is connected across the inductor through a switch S as shown in figure. • When the switch S is closed, the conventional current flow or electrons moves from plate A to B through the inductor coil. Therefore the energy stored or strength of the electric field in the capacitor decreases. • The current flowing through the inductor induces an EMF which opposes the electrons flow through it. • This current flow set up a magnetic field around the inductor thereby it starts storing the magnetic energy. When the capacitor is fully discharged, current or electron flow through the coil becomes zero. At this time magnetic field has maximum value and there is no electric field. • Once the capacitor is fully discharged, magnetic field around the inductor starts collapsing and produces the counter emf. • As per the Lenz’s law, this counter emf produces the current which begin to charge the capacitor with opposite polarity by making plate upper plate negative and lower plate positive as shown in figure below. • When the capacitor is fully charged in opposite direction, the entire magnetic energy is converted back into the electric energy in capacitor, i.e., magnetic energy is collapsed. • At this instant, capacitor starts discharging in the opposite direction as shown in figure. Once again the capacitor is fully discharged and this process will be continued. • This continuous charging and discharging process results an alternating motion of electrons which is nothing but an oscillating current. • But these oscillations of the capacitor are damped because every time transferring of energy from L to C and C to L dissipates energy in the form of heat in the resistance of the coil and in the connecting wires in the form of electromagnetic radiation.

• These losses decrease the amplitude of oscillating current gradually till it ceases. These are called as exponentially decaying oscillations or damped oscillations. Sustained(undamped) oscillation:

• The oscillation produced are damped oscillation because at every oscillation there is waste of energy in capacitor and inductor.

• If energy equal to the loss is supplied at every oscillation there is no decrease in the voltage and sustained oscillation are produced. Amplifier with positive feedback as oscillator: “the process of injecting a fraction of output energy of some device back to the input is known as feedback”.

There are two types: 1) Positive feedback 2) Negative feedback Amplifier with positive feedback as oscillator: • An amplifier with gain A is shown in figure(a).

• Positive feedback is given through β network taking signal from the output. Total gain is given by A f = A / 1-Aβ Aβ is called the loop gain.

• There are three possibilities. Amplifier with positive feedback as oscillator: 1) Aβ<1 If the value of loop gain Aβ is less than i.e. Aβ<1, the output voltage will be decreasing with the passage of time.(fig.(b)).

2) Aβ>1 If Aβ>1, the voltage will be increasing with time.(fig(c))

3) Aβ=1 If Aβ=1, A f = 1/0 = ∞ means there is output even if there is no input. Value of the output voltage remains constant and sustained oscillations are produced. Thus amplifier works as oscillator. This condition is called “ Barkhausen criterian ” Requirement of oscillator:

• Active device: It works as amplifier. for this transistor or FET are used. • power supply: Power supply is necessary for biasing the active device and to compensate for energy loss. • Frequency determining network: It determines the frequency of oscillation. In LC oscillator frequency of oscillation depends upon the tuned circuit. • Positive feedback: Positive type feedback is essential. Hartley oscillator • The Hartley oscillator is designed for generation of sinusoidal oscillations in the R.F range (20 KHz - 30 MHz). • It is very popular and used in radio receivers as a local oscillator. • The circuit diagram of Hartley oscillator (parallel or shunt- fed) using BJT is shown in Figure. • It consists of an R-C coupled amplifier using an n-p-n transistor in CE configuration. • R1 and R2 are two resistors which form a voltage divider bias to the transistor. • A resistor RE is connected in the circuit which stabilizes the circuit against temperature variations. • A capacitor CE is connected in parallel with RE, acts as a bypass capacitor and provides a low reactive path to the amplified ac signal. • The coupling capacitor CC blocks dc and provides an ac path from the collector to the tank circuit. • The L-C feedback network (tank circuit) consists of two inductors L1, and L2 (in series) which are placed across a common capacitor C1 and the centre of the two inductors is tapped as shown in fig. • The feedback network (L1, L2 and C1) determines the frequency of oscillation of the oscillator. Colpitt oscillator • Colpitts oscillator is generally used in RF applications and the typical operating range is 20KHz to 300MHz. • In Colpitts oscillator, the capacitive voltage divider setup in the tank circuit works as the feed back source and this arrangement gives better frequency stability when compared to the Hartley oscillator which uses an inductive voltage divider setup for feedback. • The circuit diagram of a typical Colpitts oscillator using transistor is shown in the figure as shown. • In the circuit diagram resistors R1 and R2 gives a voltage divider biasing to the transistor. • Resistor R4 limits the collector current of the transistor. Cin is the input DC decoupling capacitor while Cout is the output decoupling capacitor. • Re is the emitter resistor and its meant for thermal stability. Ce is the emitter by-pass capacitor. • Job of the emitter by-pass capacitor is to by-pass the amplified AC signals from dropping across Re. • The the emitter by-pass capacitor is not there, the amplified AC signal will drop across Re and it will alter the DC biasing conditions of the transistor and the result will be reduced gain. • Capacitors C1, C2 and inductor L1 forms the tank circuit. Feedback to the base of transistor is taken from the junction of Capacitor C2 and inductor L1 in the tank circuit. Uses of LC oscillator: • Radio Frequency generator • As carrier in radio and T.V. Transmitters and receivers • Radio telephony • Radio telegraphy • Carrier telephony : Several signal are transmitted over a single pair of wire • Radio & TV receiver • Induction heating: to harden the surface of the shaft,gears etc. • Di electric heating: heating of insulating material. • Remote control • Clock in digital signal • Generation of ultrasonic wave Examples (based on above two oscillator):

For Hartley oscillator c=250 pF , l1=1.5mH , l2=1.5mH .determine the operating frequency.

For Hartley oscillator c=20 pF , l1=1000uH , l2=100uH .determine the operating frequency.

For colpitt oscillator c1=750 pF , c2=2500pF , l=40uH .determine the operating frequency.

For colpitt oscillator c1=0.1uF , c2=1uF , l=470uH .determine the operating frequency. Any Question

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