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Feedback Amplifierssampled and the feedback output signalfrom the feedback network is connectedin shunt across input signal. Thecurrent gain of the current amplifierdecreases by a factor (1 Aiβ)Aii.e. Aif 1 A iβAlso the input impedance decrease &output impedance of the amplifierincreases by a factor (1 Aiβ)Rii.e. R if 1 A iβand R of R o (1 Aiβ)Note:1) The gain of the amplifier can be writtenas A dAWhere, A is gain of the amplifier and d Ais absolute change in gain2) The gain of the amplifier can also bewritten as A %dAWhere, A is gain of the amplifier and% dA is percentage change in gain3) If absolute gain is know, the % changecan be calculated asdA% dA 100%A4) The percentage change in gain withfeedback is given by%dA% dAf 1 Aβ5) If D is harmonic distortion in theamplifier without feedback, theharmonic distortion with feedback isDDf 1 AβExampleThe overall gain of a multistage amplifier is140. When negative voltage feedback isapplied, the gain is reduced to 17.5. Findthe fraction of the output that is feedbackto the input.SolutionGiven A v 140 , A vf 17.5We know that, Av1 A vβ14017.5 1 140β1 140β 8β 0.05 5%A vf Therefore 5% of the output is feedback tothe input.ExampleAn amplifier has a voltage gain of 250 and abandwidth of 400 KHz without feedback. Ifnegative feedback (β 0.01) is applied, whatis the bandwidth of the amplifier?SolutionGain bandwidth product for an amplifier isalways constant & we know that withnegative the voltage gain of amplifierdecreases b (1 Aβ) , hence the bandwidthincreases by (1 Aβ)BWf BW(1 Aβ) BWf 400 1 250 0.01 1.4MHzExampleCalculate the closed-loop gain for thenegative feedback amplifier withAv 100,000and β 1/100 .Also calculate the closed-loop gain whenthe open-loop gain is changed by 50%.SolutionThe closed loop gain isAv100000A vf 1 A vβ 1 100000 0.01A vf 99.9 %dANow, %dA f 1 Aβ50 %dAf 1 100000 0.01%dAf 0.05% Therefore the gain with feedback is99.9 0.05% Copyright Reserved by Inspiring Creativity & Endeavour Gate Institute. No part of this material should be copied or reproduced without permission.65

Feedback Amplifiers7.4 OSCILLATORSMany electronic devices require a source ofenergy at a specific frequency which mayrange from a few Hz to several MHz. This isachieved by an electronic device called anoscillator. Oscillators are extensively usedin electronic equipment. For example, inradio and television receivers, oscillatorsare used to generate high frequency wave(called carrier wave) in the tuning stages.Audio frequency and radio frequencysignals are required for the repair of radio,television and other electronic equipment.Oscillators are also widely used in radar,electronic computers and other electronicdevices. Oscillators can produce sinusoidalor non-sinusoidal (e.g. square wave) waves.In this chapter, we shall confine ourattention to sinusoidal oscillators i.e. thosewhich produce sine-wave signals. Anelectronic device that generates sinusoidaloscillations of desired frequency is knownas a sinusoidal oscillator.Although we speak of an oscillator as“generating” a frequency, it should benoted that it does not create energy, butmerely acts as an energy converter. Itreceives DC energy and changes it into ACenergy of desired frequency. The frequencyof oscillations depends upon the constantsof the device.undamped oscillations can be obtainedat the output immediately afterconnecting the necessary power supplies7.5 AUDIO FREQUENCY OSCILLATORSAn oscillator is composed of an amplifier anda frequency selective element, a filter. Anoscillator circuit which uses an RC network,a combination of resistors and capacitors,for its frequency selective part is calledan RC oscillator & it generates oscillation inaudio frequency range. There are two typesof audio frequency oscillators:7.5.1 RC PHASE SHIFT OSCILLATORThis circuit uses the property of RC filtersto cause a phase shift, and by usingmultiple filters, a feedback circuit withexactly 180 phase shift can be produced.When used with a common emitteramplifier, which also has a phase shift of180 between base and collector, the filtersproduce positive feedback to causeoscillation to take place. The RC networkcommonly used is that of a high pass filter,which produces a phase shift of between 0 and 90 depending on the frequency of thesignal used, although low pass filters canalso be used.7.4.1 BARKHAUSEN’S CRITERIONBarkhausen criterion is that in order toproduce continuous undamped oscillationsat the output of an amplifier, the positivefeedback should be such that:1) The total gain provided to the signal inloop must be equal to unity. Aβ 12) The total phase around the loop mustbe integral multiple of 360o . Aβ n 360oWhere,n 0,1, 2,3, 4.Once these conditions are set in thepositive feedback amplifier, continuousThe frequency of oscillation for a BJT RCphase shift oscillator is1fo R 2πRC 6 4 C R The minimum value of h fe required forsustained oscillations is h femin 44.5 and ifh fe is less than the said value the circuitwon’t oscillate. Copyright Reserved by Inspiring Creativity & Endeavour Gate Institute. No part of this material should be copied or reproduced without permission.66

Feedback AmplifiersThe frequency of oscillation for an OP-AMPRC phase shift oscillator is1fo 2πRC 6For sustained oscillation, the gain of theamplifier must be atleast 29 A 29We know that for an oscillator Aβ 11 β 29In the oscillator shown in the figure, theamplifier used in inverting mode & its gain isRRAnd A fA fR1R1We know that, A 29RfR f 29R1 29R17.5.2 WIEN BRIDGE OSCILLATORcircuit. The Wien Bridge Oscillator is a twostage RC coupled amplifier circuit that hasgood stability at its resonant frequency,low distortion and is very easy to tunemaking it a popular circuit as an audiofrequency oscillator but the phase shift ofthe output signal is considerably differentfrom the previous phase shift RC Oscillator.The Wien Bridge Oscillator uses a feedbackcircuit consisting of a series RC circuitconnected with a parallel RC of the samecomponent values producing a phase delayor phase advance circuit depending uponthefrequency.Attheresonantfrequency f o the phase shift is 0 hence theamplifier is used in non-inverting mode.The frequency of oscillation is given by1fo 2πRCFor sustained oscillation, the gain of theamplifier must be atleast 3 A 3We know that for an oscillator Aβ 11 β 3In the Wien bridge oscillator shown in thefigure, the amplifier is used in noninverting mode & its gain isRRandA 1 fA 1 fR1R1We know that, A 3R 1 f 3R1R f 2R1 7.6 RADIO FREQUENCY OSCILLATORSThe Wien Bridge Oscillator is so calledbecause the circuit is based on a frequencyselective form of the Whetstone bridgeA circuit which produces electricaloscillations of any desired frequency isknown as an oscillatory circuit or tankcircuit. A simple oscillatory circuit consistsof a capacitor (C) and inductance coil (L) inparallel as shown in Fig. This electricalsystem can produce electrical oscillationsof frequency determined by the values of Land C. To understand how this comes about, Copyright Reserved by Inspiring Creativity & Endeavour Gate Institute. No part of this material should be copied or reproduced without permission.67

Feedback Amplifierssuppose the capacitor is charged from aD.C. source with a polarity as shown in Fig.1) In the position shown in Fig.1, theupper plate of capacitor has deficit ofelectrons and the lower plate has excessof electrons. Therefore, there is avoltage across the capacitor and thecapacitor has electrostatic energy.2) When switch S is closed as shown inFig.2, the capacitor will dischargethrough inductance and the electronflow will be in the direction indicatedby the arrow. This current flow sets upmagnetic field around the coil. Due tothe inductive effect, the current buildsup slowly towards a maximum value.The current in the circuit will bemaximum when the capacitor is fullydischarged. At this instant, electrostaticenergy is zero but because electronmotion is greatest (i.e. maximumcurrent), the magnetic field energyaround the coil is maximum. This isshown in Fig.2. Obviously, theelectrostatic energy across the capacitoris completely converted into magneticfield energy around the coil.3) Once the capacitor is discharged, themagnetic field will begin to collapse andproduce counter e.m.f. According toLenz's law, the counter e.m.f. will keepthe current flowing in the samedirection. The result is that the capacitoris now charged with opposite polarity,making upper plate of capacitor negative& lower plate positive as shown in Fig.3.4) After the collapsing field has rechargedthe capacitor, the capacitor now beginsto discharge; current now flowing in theopposite direction. Fig.4 shows capacitorfully discharged and maximum currentflowing. The sequence of charge anddischarge results in alternating motionof electrons or an oscillating current.The energy is alternately stored in theelectric field of the capacitor (C) and themagnetic field of the inductance coil (L).This interchange of energy between Land C is repeated over and again resultingin the production of oscillations.7.6.1 COLPITT’s OSCILLATORFigure below shows a Colpitt's oscillator. Ituses two capacitors and placed across acommon inductor L and the centre of thetwo capacitors is tapped. The tank circuit ismade up of C1 , C 2 and L. The frequency ofoscillations is determined by the values ofC1 , C 2 and L and is given by;1fo 2π LCCCWhere,C 1 2C1 C2Circuit operation:When the circuit is turned ON, thecapacitors C1 & C 2 are charged. Thecapacitors discharge through L, setting uposcillations of frequency determined by expgiven above. The output voltage of theamplifier appears across C1 and feedbackvoltage is developed across C 2 . The voltageacross it is 180 out of phase with thevoltage developed across C1 (Vout ) as shownin Fig. Copyright Reserved by Inspiring Creativity & Endeavour Gate Institute. No part of this material should be copied or reproduced without permission.68

Feedback AmplifiersIt is easy to see that voltage feedback(voltage across C 2 ) to the transistorprovides positive feedback. A phase shift of180 is produced by the transistor and afurther phase shift of 180 is produced byC1 C2 voltage divider. In this way,feedback is properly phased to producecontinuous undamped oscillation.The amount of feedback voltage in Colpitt’soscillator depends upon feedback factor βof the circuit. For this circuit,XCVCβ f 2 1Vout X C1 C27.6.2 HARTLEY’S OSCILLATORThe Hartley oscillator is similar to Colpitt’soscillator with minor modifications. Insteadof using tapped capacitors, two inductorsL1 and L 2 are placed across a commoncapacitor C and the centre of the inductorsis tapped as shown in Fig. The tank circuitis made up of L1 , L 2 and C. The frequencyof oscillations is determined by the valuesof L1 , L 2 and C and is given by:1fo 2π LCWhere, L L1 L2 2Macross L1 and feedback voltage acrossL2 .The voltage across L 2 is 180 out of phasewith the voltage developed across L1 (Vout )as shown in Fig.It is easy to see that voltage feedback (i.e.,voltage across L 2 ) to the transistorprovides positive feedback. A phase shift of180 is produced by the transistor and afurther phase shift of 180 is produced byL1 L2 voltage divider. In this way,feedback is properly phased to producecontinuous undamped oscillations. Theamount of feedback voltage in Colpitt’soscillator depends upon feedback factor βof the circuit. For this circuit,XLVLβ f 2 2Vout X L1 L1ExampleIn the Wien bridge oscillator shown infigure, R1 R 2 220kΩ & C1 C2 250pF .Determine the frequency of oscillations.M mutual inductance between L1 and L 2Circuit operation:When the circuit is turned on, the capacitoris charged. When this capacitor is fullycharged, it discharges through coils L1 andL 2 setting up oscillations of frequencydetermined by above expression. Theoutput voltage of the amplifier appearsSolutionThe frequency of oscillations is1 fo 2πRC1fo 2.893KHz2π 220 103 250 10 127.6.3 CRYSTAL OSCILLATOR Copyright Reserved by Inspiring Creativity & Endeavour Gate Institute. No part of this material should be copied or reproduced without permission.69

Feedback AmplifiersIn order to use crystal in an electroniccircuit, it is placed between two metalplates. The arrangement then forms acapacitor with crystal as the dielectric asshown in figure.crystal will start vibrating at the frequencyof applied voltage. However, if thefrequency of the applied voltage is madeequal to the natural frequency of thecrystal, resonance takes place and crystalvibrations reach a maximum value. Thisnatural frequency is almost constant.Effects of temperature change can beeliminated by mounting the crystal in atemperature-controlled oven as in radioand television transmitters. The naturalfrequency f of a crystal is inverselyproportional to crystal thickness & is givenby:Kf tWhere, K is a constant that depends uponthe cut and t is the thickness of the crystal.Resonant frequencies:1) The frequency at which the vibratingcrystal behaves as a ency f s . Its value is given by:1fs 2π LC2) The frequency at which the vibratingcrystal behaves as a parallel-resonantcircuit is called parallel-resonantfrequency f p .fp 12π LCTC CmC CmFigure shows the transistor crystaloscillator. Note that it is a Colpitt’soscillator modified to act as a crystaloscillator. The only change is theaddition of the crystal (Y) in thefeedback network. The crystal will actas a parallel-tuned circuit. As you cansee in this circuit that instead ofresonance caused by L and C1 C2 , weWhere,CT have the parallel resonance of thecrystal.Equivalent circuit:When the crystal is not vibrating, it isequivalent to capacitance Cm because itplates separated by a dielectric. Thiscapacitance is known as mountingcapacitance.When the crystal is vibrating, its equivalentelectrical circuit is as shown in figure. L isthe electrical equivalent of crystal mass, Cis the electrical equivalent of elasticity andR is electrical equivalent of mechanicalfriction. has two metalA phase shift of 180 is produced by thetransistor. A further phase shift of 180 is produced by the capacitor voltagedivider. This oscillator will oscillateonly at f p . Even the smallest deviationfrom f p will cause the oscillator to act asan effective short. Copyright Reserved by Inspiring Creativity & Endeavour Gate Institute. No part of this material should be copied or reproduced without permission.70

2.4 Clamper 24 2.5 Voltage Doubler 25 2.6 Voltage Regulator 26 3. BJT BIASING 3.1 Introduction 30 3.2 Operating Regions of Transistor 30 3.3 Modes of Operation of BJT 33 3.4 Load Line 34 3.5 Biasing 35 4. SMALL SIGNAL ANALYSIS OF BJT 4.1 Introduction 39 4.2 Transistors at Low Frequency 39 CONTENTS