Oscillator Circuits 1 II. Oscillator Operation For self-sustaining oscillations: • the feedback signal must positive • the overall gain must be equal to one (unity gain) 2 If the feedback signal is not positive or the gain is less than one, then the oscillations will dampen out. If the overall gain is greater than one, then the oscillator will eventually saturate. 3 Types of Oscillator Circuits A. Phase-Shift Oscillator B. Wien Bridge Oscillator C. Tuned Oscillator Circuits D. Crystal Oscillators E. Unijunction Oscillator 4 A. Phase-Shift Oscillator 1 Frequency of the oscillator: f0 = (the frequency where the phase shift is 180º) 2πRC 6 Feedback gain β = 1/[1 – 5α2 –j (6α – α3) ] where α = 1/(2πfRC) Feedback gain at the frequency of the oscillator β = 1 / 29 The amplifier must supply enough gain to compensate for losses. The overall gain must be unity. Thus the gain of the amplifier stage must be greater than 1/β, i.e. A > 29 The RC networks provide the necessary phase shift for a positive feedback. They also determine the frequency of oscillation. 5 Example of a Phase-Shift Oscillator FET Phase-Shift Oscillator 6 Example 1 7 BJT Phase-Shift Oscillator R′ = R − hie RC R h fe > 23 + 29 + 4 R RC 8 Phase-shift oscillator using op-amp 9 B. Wien Bridge Oscillator Vi Vd −Vb Z2 R4 1 1 β = = = − = − R3 R1 C2 V V Z + Z R + R Z R β = 0 ⇒ = + o a 1 2 3 4 1 + 1 3 + 1 R4 R2 C1 Z2 R4 Z2 Z1 , i.e., should have zero phase at the oscillation frequency When R1 = R2 = R and C1 = C2 = C then Z + Z Z 1 2 2 1 R 1 f = , and 3 ≥ 2 So frequency of oscillation is f = 0 0 2πRC R4 2π ()R1C1R2C2 10 Example 2 Calculate the resonant frequency of the Wien bridge oscillator shown above 1 1 f0 = = = 3120.7 Hz 2πRC 2 π(51×103 )(1×10−9 ) 11 C. Tuned Oscillator Circuits Tuned Oscillators use a parallel LC resonant circuit (LC tank) to provide the oscillations. There are two common types: • Colpitts – The resonant circuit is an inductor and two capacitors. •Hartley– The resonant circuit is a tapped inductor or two inductors and one capacitor. 12 Colpitts Tuned Oscillator Circuit FET based Colpitts Oscillator 1 C1C2 Frequency of oscillations: f0 = , where Ceq = 2π LCeq C1 + C2 13 Transistor Colpitts oscillator. 14 Op-amp Colpitts oscillator. 15 Hartley Tuned Oscillator Circuit FET Hartley Oscillator 1 Frequency of oscillations: f0 = , where Leq = L1 + L2 + 2L12 2π LeqC 16 BJT based Hartley Oscillator 17 D. Crystal Oscillators The crystal appears to the rest of the circuit as a resonant circuit. 18 Crystal Resonant Frequencies The crystal has two resonant frequencies: Series resonant: RLC determine the resonant frequency. The crystal has a low impedance. Parallel resonant: RL and CM determine the resonant frequency. The crystal has a high impedance. The series and parallel resonant frequencies are very close, within 1% of each other. 19 Series Resonant Crystal Oscillator FET Crystal Oscillator 20 Parallel Resonant Crystal Oscillator BJT Crystal Oscillator 21 Crystal Oscillator using Op-amp 22 E. Unijunction Oscillator 1 Frequency of oscillations: f0 = RT CT ln[]1 (1 − η) where η = 0.4 to 0.6 η is a rating of the unijunction transistor. 23 Unijunction Oscillator Waveforms VBB = VB2 −VB1 VP = ηVBB +VB1 +VD The unijunction oscillator (or relaxation oscillator) produces a sawtooth waveform. 24 25 Unijunction transistor (UJT): basic construction. 26 UJT – Unijunction Transistor The UJT is also basically a switching device. Schematic Symbol: 27 UJT Basic Operation Even though the UJT is a switching device it works very differently from the SCR variety of devices. The equivalent circuit indicates that the UJT is like a diode and a resistive voltage divider circuit. The resistance exhibited by RB1 is variable; it is dependent on the value of current IE. 28 UJT Characteristic Curve A voltage is applied across the UJT (VBB) and to the Emitter input (VE). Once VE reaches a peak value (Vp) the UJT begins to conduct. At the point where VE = Vp, the current IE is at minimum. This is the threshold value of VE that puts the UJT into conduction. Once conducting, IE increases and VE decreases. This phenomenon occurs because the internal resistance labeled RB1 in the equivalent circuit decreases as the UJT conducts more and more. This is called negative resistance. 29.