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Hartley Oscillator
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AIM

        To design and construct a Hartley oscillator and to measure its output frequency.


COMPONENTS


        Transistors, Bread board, resistors, capacitors, inductance coil, dc power supply, C.R.O, connection wires etc


THEORY

    

TANK CIRCUIT


         A circuit which produces electrical oscillations of any desired frequency is known as an oscillatory circuit. A simple oscillatory circuit is one which contains a capacitor C and inductor L placed in parallel as shown


         When the key K1 is closed, the capacitor C is charged with upper plate positive and lower plate negative. Now the key K1 is kept open. At this moment lower plate has an excess and upper plate a deficit of electrons. This gives rise to an electric field across the capacitor plates in the direction shown.


         When the key K is closed, the capacitor discharges itself through inductor and there is a flow of electrons as indicated by arrow head. The current flow sets up a magnetic field around the inductor coil. Due to inductive effect the current builds up slowly up to a maximum value which is attained when the capacitor is fully discharged. At that instant the electrostatic energy is zero but due to maximum current flow the magnetic field energy around the inductor coil is at maximum.


        As the capacitor is fully discharged the magnetic field starts decreasing. As the magnetic flux linked with circuit changes, an e.m.f is induced, which makes the current to flow. This current recharges the capacitor in opposite direction with its upper plate negative and lower plate positive.Finally the magnetic field fully collapses. At this stage the magnetic field energy is zero and electrostatic energy is again at maximum.


       As soon as the magnetic field is zero, the capacitor which is fully recharged begins to discharge, due to which the current flows in opposite direction and a magnetic field is again set up around the inductor coil. The magnetic field energy becomes a maximum when electric field energy is zero.


  HARTLEY OSCILLATOR


        Hartley Oscillator is a device that generates oscillatory output (sinusoidal). It consists of an amplifier linked to an oscillatory circuit, also called LC circuit or tank circuit. The function of tank circuit is to tune a certain frequency.


LC oscillators are designed to operate in the radio-frequency range. Its inductance will be in micro Henries. However they can also be designed to produce oscillations in the low audio-frequency range. But for the low-frequency operation, the inductors used will be very large in value, i.e of milli Henrie range and hence very large in physical size.


The circuit oscillates when the components are suitably selected to satisfy the Barkhausen criteria. 

i.e.βA=+1(feedback factor must be unity).


Also there must be a positive feedback, where A is the open loop gain and β is the feedback ratio.


 In Hartley oscillator the feedback voltage is across L2 and output voltage is across L1


Feedback ratio «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»§#946;«/mi»«mo»=«/mo»«mfrac»«msub»«mi»V«/mi»«mn»2«/mn»«/msub»«msub»«mi»V«/mi»«mn»1«/mn»«/msub»«/mfrac»«mo»=«/mo»«mfrac»«msub»«mi»X«/mi»«mrow»«mi»L«/mi»«mn»2«/mn»«/mrow»«/msub»«msub»«mi»X«/mi»«mrow»«mi»L«/mi»«mn»1«/mn»«/mrow»«/msub»«/mfrac»«mo»=«/mo»«mfrac»«mrow»«msub»«mi»L«/mi»«mn»2«/mn»«/msub»«mi»§#969;«/mi»«/mrow»«mrow»«msub»«mi»L«/mi»«mn»1«/mn»«/msub»«mi»§#969;«/mi»«/mrow»«/mfrac»«mo»=«/mo»«mfrac»«msub»«mi»L«/mi»«mn»2«/mn»«/msub»«msub»«mi»L«/mi»«mn»1«/mn»«/msub»«/mfrac»«/math»


 
The frequency of oscillation is given by«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«mo»=«/mo»«mfrac»«mn»1«/mn»«mrow»«mn»2«/mn»«mi»§#960;«/mi»«msqrt»«mrow»«msub»«mi»L«/mi»«mi»e«/mi»«/msub»«mi»C«/mi»«/mrow»«/msqrt»«/mrow»«/mfrac»«/math»  
Where Le is the effective inductance of the coil L1 and L2, given by
 Le =L1+L2
                                                                            

                                                                                  For faithful amplification, a transistor amplifier must satisfy three basic conditions, namely:            (i) proper zero signal collector current, (ii) proper base-emitter voltage at any instant and (iii) proper collector-emitter voltage at any instant.Fulfilment of these conditions is known as transistor biasing. One method of obtaining transistor biasing is by potential divider arrangement.

The circuit consists of a potential divider arrangement.R1 and R2 form a potential divider across Vcc. The voltage drop VR2 across R2 forward-biases the emitter whereas Vcc supply reverse biases the collector.


As per voltage divider theorem (fig 1),

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«msub»«mi»V«/mi»«mrow»«mi»R«/mi»«mn»2«/mn»«/mrow»«/msub»«mo»=«/mo»«mfrac»«mrow»«msub»«mi»V«/mi»«mrow»«mi»C«/mi»«mi»C«/mi»«/mrow»«/msub»«msub»«mi»R«/mi»«mn»2«/mn»«/msub»«/mrow»«mfenced»«mrow»«msub»«mi»R«/mi»«mn»1«/mn»«/msub»«mo»+«/mo»«msub»«mi»R«/mi»«mn»2«/mn»«/msub»«/mrow»«/mfenced»«/mfrac»«/math»



       As seen, «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi»V«/mi»«mi»E«/mi»«/msub»«mo»=«/mo»«msub»«mi»V«/mi»«mrow»«mi»R«/mi»«mn»2«/mn»«/mrow»«/msub»«mo»-«/mo»«msub»«mi»V«/mi»«mrow»«mi»B«/mi»«mi»E«/mi»«/mrow»«/msub»«/math»
       So,«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi»I«/mi»«mi»B«/mi»«/msub»«mo»=«/mo»«mfrac»«mrow»«msub»«mi»V«/mi»«mrow»«mi»R«/mi»«mn»2«/mn»«/mrow»«/msub»«mo»-«/mo»«msub»«mi»V«/mi»«mrow»«mi»B«/mi»«mi»E«/mi»«/mrow»«/msub»«/mrow»«mrow»«msub»«mi»R«/mi»«mi»B«/mi»«/msub»«mo»+«/mo»«mo»(«/mo»«mn»1«/mn»«mo»+«/mo»«mi»§#946;«/mi»«mo»)«/mo»«msub»«mi»R«/mi»«mi»E«/mi»«/msub»«/mrow»«/mfrac»«/math»  

       «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi»I«/mi»«mi»C«/mi»«/msub»«mo»=«/mo»«mi»§#946;«/mi»«msub»«mi»I«/mi»«mi»B«/mi»«/msub»«/math» and «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi»I«/mi»«mi»E«/mi»«/msub»«mo»=«/mo»«mo»(«/mo»«mn»1«/mn»«mo»+«/mo»«mi»§#946;«/mi»«mo»)«/mo»«msub»«mi»I«/mi»«mi»B«/mi»«/msub»«/math»


       Also,  «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi»V«/mi»«mi»C«/mi»«/msub»«mo»=«/mo»«msub»«mi»V«/mi»«mrow»«mi»C«/mi»«mi»C«/mi»«/mrow»«/msub»«mo»-«/mo»«msub»«mi»I«/mi»«mi»C«/mi»«/msub»«msub»«mi»R«/mi»«mi»C«/mi»«/msub»«/math»  

      «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi»V«/mi»«mrow»«mi»C«/mi»«mi»E«/mi»«/mrow»«/msub»«mo»=«/mo»«msub»«mi»V«/mi»«mi»C«/mi»«/msub»«mo»-«/mo»«msub»«mi»V«/mi»«mi»E«/mi»«/msub»«mo»=«/mo»«msub»«mi»V«/mi»«mrow»«mi»C«/mi»«mi»C«/mi»«/mrow»«/msub»«mo»-«/mo»«msub»«mi»I«/mi»«mi»C«/mi»«/msub»«msub»«mi»R«/mi»«mi»C«/mi»«/msub»«mo»-«/mo»«msub»«mi»I«/mi»«mi»E«/mi»«/msub»«msub»«mi»R«/mi»«mi»E«/mi»«/msub»«/math»


  
This value of IC and VCE gives the Q point, also called dc operating point or working point. It is called operating point because the variations of IC and VCE takes place about this point when signal is applied. It is also called quiescent (silent) point or Q point because it is point on the IC-VCE characteristics when the transistor is silent i.e.  in the absence of signal.

 

 



WORKING


When the supply is switched–on, a voltage V1 is developed across L1 and V2 across L2.V1 is the oscillator output. There is a phase difference of 1800 between the voltage of L1 and L2.The voltage across L2 (V2) is given as the feedback signal. Since the amplifier is in CE configuration, it produces a phase difference of 1800.Therfore amplifier and the feedback network together produces a phase difference of 3600.i.e, a positive feedback is achieved and circuit work as an oscillator.
                  

                                                                                                     Once energy is supplied to the tank circuit, cycle begins. The capacitor stores energy in its electric field whenever there is a potential difference across its plates. As the current begins to flow out of the capacitor and into the inductor, a magnetic field builds up around the coil. Capacitor loses its energy and current will continue to flow in the inductor caused by the effect of the energy in the magnetic field. This current will start to send current back into the capacitor, in reverse direction. The cycle then repeats, over and over, at a period (frequency) that is determined by the values of the inductor, the capacitor.The frequency of oscillation is given by

     «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«mo»=«/mo»«mfrac»«mn»1«/mn»«mrow»«mn»2«/mn»«mi»§#960;«/mi»«msqrt»«mrow»«mi»L«/mi»«mi»C«/mi»«/mrow»«/msqrt»«/mrow»«/mfrac»«/math»



This is our output wave form.

 

 

 


 


RESULT


     Amplitude and frequency of sine wave from Hartley Oscillator =……V...Hz.
 

Cite this Simulator:

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