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oscillators oscillators Document Transcript

  • University of Geneva Oscillators TPA-Electronique OscillatorsContents1 Introduction 12 RC oscillators 1 2.1 Wien bridge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2.2 Phase-shift oscillator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.3 Double T-filter oscillator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 LC oscillators 4 3.1 Colpitts Oscillator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 Biliography 51 IntroductionOscillators are circuits that produce a repetitive waveform with only a DC voltage at theoutput. The output waveform can be sinusoidal, rectangular, triangular, etc. At the base ofalmost any oscillator there is an amplification stage with a positive feedback circuit that willproduce a phase shift and an attenuation. Positive feedback consist in the redirecting of the output signal to the input stage of theamplifier without a phase shift. This feedback signal is then amplified again generating theoutput signal, that produces the feedback signal. This phenomenon, in wich the output signal“takes care”of itself in order to generate continuum signal is called oscillation. Two conditions then should be fulfilled to have an stable oscillator: 1. The phase shift of the feedback loop should be 0 2. The overall gain of the feeddback loop should be 1 In order to arrive to the stable regime of the oscillator, during the starting period the gainof the feedback loop should be greater than one, to allow the amplitude of the output signalto achieve the desired level. Once this amplitude has been reached, the overall gain shouldgoes down again to one. The very first oscillations are generated by trasitory reactions andnoises once the power is switched on. The feedback circuit should be designed to amplifyjust a single frequency, and the relatively faint signal picked up from transitories and noise isthen used to startup the oscillator2 RC oscillatorsThis type of oscillators, use RC elements in the feedback branch. Useful to frequencies upto 1 MHz.E. Cortina Page 1
  • University of Geneva Oscillators TPA-Electronique Av Vout A fl = A v B B In Phase Figure 1: Positive feedback. Oscillator conditions2.1 Wien bridgeWien bridge is a sinusoidal oscillator based in so called RC lead-lag network, as shown inthe figure 2 R1 C2 Vin Vout C1 R2 Figure 2: Lead-lag network We can see this network as a pass-low filter (R1 and C1 ) together as a high-pass filter(R2 and C2 ). The transfer function of this setup is easily computed: vout R2 || − jXC2 H(jw) = = vin R1 − jXC1 + R2 || − jXC2 The most interesting case is when R1 = R2 and C1 = C2 then −jRX R−jX −jRX RX H(jw) = −jRX = 2 − jRX = (R − jX) + R−jX (R − jX) 3RX + j(R2 − X 2 ) 1 B= 9 + (X/R − R/X)2E. Cortina Page 2
  • University of Geneva Oscillators TPA-Electronique X/R − R/X φ = arctan 3 In figure 3 are shown both the gain in tension (B) as the phase shift (φ) as a function ofthe frequency. The oscillating frequency is 1 fr = 2πRCand for this frequency we have that B = 1/3 and φ = 0o . This means that the amplifiershould have a gain A = 3 and introduce a phase shift φ = 0o / Gain Phase shift 80 0.3 60 0.25 40 20 0.2 0 0.15 -20 0.1 -40 -60 0.05 -80 0 -2 -1 -2 -1 10 10 1 10 10 10 1 10 Frequency (au) Frequency (au) Figure 3: Lead-lag network gain and phase shift for RC = 1/2π In the figure 4 is shown the base schematics of a Wien oscillator, based in an opamp.The positive feedback is created by the lead-jag network, and the negative feedback createa non-inverting amplifer with gain R1 A=1+ =3 → R1 = 2R2 R2 In the beginning, the gain of the negative feedback should be greater than 3, and later,once the output amplitude has been achieved, go back to 3. There are various methods toaccomplish it in an automatic way. 1. The most easy and classical method is to use a low power incandescende lamp instead of R2 . When swicth on, the resistance of the lamp is small, giving an amplification greater that 3. Once the oscillations grows in amplitude the resistance also goes up, arriving to a value R in the desired amplitude. If the feedback resistance is chosen to be R1 = 2R , we will obtain automatically a gain A = 3, giving the stable oscillations. See figure 5 2. Another method consist is adding a third resistor R3 in parallel with two zener diodes conected back to back as shown in figure ??. When switch on, the zener diodes are in open circuit, giving then the value of the gain as: R1 + R3 R3 A=1+ =3+ R2 R2 Once the output arrives to the zener voltage, the diodes short circuit the resistor restor- ing the gain A = 3 and the output signal becomes stable.E. Cortina Page 3
  • University of Geneva Oscillators TPA-Electronique R1 − + Vout R2 C R R C Figure 4: Wien-bridge, base setup2.2 Phase-shift oscillatorFigure ?? shows the two configurations of the phase-shift oscillators, a phase shift oscillator.Each of the RC circuits in the positive feedback introduces a phase shift that depend of theactual values of R and C. Only the frequency that produces a pahse shift on each sectorequal to 90o , will be stable, so the pahse shift of is 180o , then the op-amp should work in aninverting configuration with gain 1. The frequency that fullfill this condition is: 1 fr = √ 2πRC 62.3 Double T-filter oscillator3 LC oscillatorsRC oscillators are good for frequencies up to 1 MHz, but for higher frequencies, LC oscilla-tors are better. Due to the limited bandwidth of most of opamps the amplification is basedon discrete BJT transistors.3.1 Colpitts OscillatorThe resonance frequence of this circuit (see figure 7-a) is the resonance frequence of theLC circuit: 1 C1 C2 fr ≈ √ → CT = 2π LCT C1 + C2E. Cortina Page 4
  • University of Geneva Oscillators TPA-Electronique 2R’ R1 R3 − − + Vout + Vout R2 R’ C R C R R C R C (a) (b) Figure 5: Wien-bridge (a) with lamp, (b) The gain of the feedback circuit depend of the values of the capacitors, (see figure 7-b) Vr IXC1 XC1 1/2πfr C1 C2 B= = = = = Vout IXC 2 XC 2 1/2πfr C2 C1 Then the amplifier gain should be C2 A= C1In the common emitter configuration shown in the example, the gain is rC A= reBut this expression is valid only for low frequencies, with higher frequencies the lag networksin base and collector can distort, and even kill the oscillation. Indeed the actual value of Adepend on the bandwidth of the transistor. If the cut frequencies of these networks arebigger than oscillation frequency, the gain is the quoted in the previous expression. If theoscillation frequency is larger than the cut frequency then the gain is significantly lower thatrC /re that togheter with the phase shifts introduced will kill the oscillation. Another thing to take into account is the effect of the input impedance of the the am-plification. Input impedance is part of the load of the resonant circuit, and can reduce theQ factor of this circuit, then the resonant frequency change accordingly with the followingexpression: 1 Q2 fr = √ 2π LCT Q2 + 1In case ofQ > 10 (most of the cases) the effect is less than 1%, and this effect can beignored, but in order to minimize the effect of the input impedance, we can replace BJTtransistor by a FET, with input impedance much larger than in BJT . In case that the load ofthe circuit is too low, the Q factor can be also reduced. To avoid this a transformer couplingthat will increase the load impedance is adviced.4 Biliography 1 Electronique, Thomas L. Floyd, Ed. Reynald Goulet (1999)E. Cortina Page 5
  • University of Geneva Oscillators TPA-Electronique C C C − + Vout R R R (a) R R R − + Vout C C C (b) Figure 6: Phase shift oscillators (a) lead network and (b) lag network 2 The Art of Electronics,E. Cortina Page 6
  • University of Geneva Oscillators TPA-Electronique Vcc (a) (b) R1 R1 C2 Vout Vout L R1 R1 C2 I C2 C2 L Vr Vout C2 C2 Figure 7: Colpitts oscillator (a) base circuit and (b) Resonant circuit attenuationE. Cortina Page 7