39CHAP. 2]RF OSCILLATORS, PLLs,AND FREQUENCY SYNTHESIZERSThe following is a list ofthe fourrequirements required for aself-sustaining oscillator towork.1.A dc power source.There mustbe asourceofelectrical power: either adc power supply orabattery.2.Frequency-determining components. There mustbe a component or componentswhich controlthe frequency ofoscillation. In somecases, the oscillator may operate atonly asingle frequency, whereasin other casesit mayneed tobe variable over agiven range of frequencies.3.Amplification. The oscillatorcircuit mustbecapable of amplification. The gain of the amplifiermustbe large enough toovercomethe losses in the feedbacknetwork. In other words, theAVB productmustequal 1.4. Positivefeedback. There mustbe apath forthe output signal tobe fedback totheinput. Thefeedbacksignal musthavethe correctphase andamplitude tosustain oscillations. Ifthe phase of thefeedback voltage is incorrect orif the feedback voltage is too small,oscillations will cease.The termpositive feedback refers tothe factthat thesignal fedback from output toinput aids orreinforcestheoriginal input signal.EXAMPLE 2.1. InFig. 2-1(6),assume thatthe feedback fraction Bequals 0.01.Calculate the required value ofAv inorder to sustainoscillations.Ans.The Barkhausencriterion statesthatin order foranoscillator tobe self-sustaining,the AVB product mustequal 1. Therefore,AVB =1Solving forAv gives us:1Ay——BInserting 0.01 forthe value of Bgives us:1Av--TT7"0.01=100This means that the voltage gainAv mustbe atleast 100in order tosustainoscillations. If Av shoulddecrease below100,then oscillationswill cease.EXAMPLE 2.2. In Fig. 2-1(6), assumethatAv =-100. Solve forthe value ofB.Ans.Again,recall that AVB mustequal 1. Insertingthe value of Av and solving for B gives us:1B =—Ay1-100=-0.01The negative quantity of -0.01 for Bindicates that a180° phase shift mustbe provided by the feedback network.2.2RF OSCILLATORCIRCUITSLet usapply ourknowledge ofoscillator fundamentals tosome commonly usedoscillator circuits.Figure 2-2(a) shows apopular circuit known as aHartleyoscillator. Itsidentifiable feature is the tappedcoilin the LCtank circuit.Notice that the coil’s tappoint is grounded.The amplifierportion oftheoscillator is acommon-emitter amplifier. Therefore, the acbase voltageand accollectorvoltage are180° outofphase. This meansthat the feedback network mustprovide anadditional180° phase shift sothat the feedbackvoltage is ofthe correctphase tosustain oscillations. Tohelp you understandthe circuit’s operation,it has been redrawn inFig. 2-2(6). Notice that Lx is in parallelwithLi and C3 inseries. At the resonantfrequency ofthe tank circuit,the netreactanceofthe L2C3 branch