oscillators-6p.pdf - Oscillators Contents Oscillators Oscillators How the feedback circuit provides operation as an oscillator is obtained by noting the

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Unformatted text preview: Oscillators Contents Oscillators Oscillators How the feedback circuit provides operation as an oscillator is obtained by noting the denominator in the basic negative feedback equation, Types of Oscillator Circuits Phase-Shift Oscillator FET Phase-Shift Oscillator Af (ω) = BJT Phase-Shift Oscillator Opamp Phase-Shift Oscillator A(ω) . 1 + β(ω)A(ω) When β(ω)A(ω) = −1 or magnitude 1 at a phase angle of 180◦ , the denominator becomes 0 and the gain with feedback, Af (ω), becomes innite. Thus, an innitesimal signal (noise voltage) can provide a measurable output voltage, and the circuit will be unstable and have oscillations. So, this criterion Wien-Bridge Oscillator Tuned Oscillator Circuits Colpitts Oscillator Circuits β(ω)A(ω) = −1 Hartley Oscillator Circuits is known as the Barkhausen criterion for oscillation. If we have the negative feedback loop-gain βA to be −1 only at a single frequency, i.e., Crystal Oscillator Unijunction Oscillator β(ω0 )A(ω0 ) = −1, then we will have oscillations only at ω = ω0 .Thus, this circuit will act as an oscillator even without an input signal (noise in the circuit acts as an input signal), will be called an oscillator circuit where it produces a signal only at the frequency of ω = ω0 . Dr. U. Sezen &amp; Dr. D. Gökçen (Hacettepe Uni.) ELE315 Electronics II 18-Nov-2016 1 / 31 Dr. U. Sezen &amp; Dr. D. Gökçen (Hacettepe Uni.) Oscillators ELE315 Electronics II 18-Nov-2016 2 / 31 Oscillators To understand how a feedback circuit performs as an oscillator, consider the positive feedback circuit below. In reality, no input signal is needed to start the oscillator going. Only the condition βA = 1 must be satised for self-sustained oscillations to result. In practice, βA is made greater than 1 and the system is started oscillating by amplifying noise voltage, which is always present. Saturation factors in the practical circuit provide an average value of βA = 1. The resulting waveforms are never exactly sinusoidal. However, the closer the value βA is to exactly 1, the more nearly sinusoidal is the waveform. The gure below shows how the noise signal results in a buildup of a steady-state oscillation condition. Consider that we have a ctitious voltage at the amplier input, vi . Thus, we have a feedback voltage vf = βAvi , where βA is referred to as the loop-gain. If the circuits of the base amplier and feedback network provide βA of a correct magnitude and phase, vf can be made equal to vi . Then, when the switch is closed and ctitious voltage vi is removed, the circuit will continue operating since the feedback voltage is sucient to drive the amplier and feedback circuits resulting in a proper input voltage to sustain the loop operation. The output waveform will still exist after the switch is closed if the condition βA = 1 is met. Dr. U. Sezen &amp; Dr. D. Gökçen (Hacettepe Uni.) ELE315 Electronics II 18-Nov-2016 3 / 31 Dr. U. Sezen &amp; Dr. D. Gökçen (Hacettepe Uni.) Oscillators Types of Oscillator Circuits ELE315 Electronics II 18-Nov-2016 4 / 31 Oscillators Phase-Shift Oscillator Types of Oscillator Circuits Phase-Shift Oscillator Main classes of oscillator circuits are given below 1. Phase-Shift Oscillator 2. Wien-Bridge Oscillator 3. Tuned Oscillator Circuits 4. Crystal Oscillator 5. Unijunction Oscillator I In this conguration (where A is negative), feedback gain is given by β(ω) = 1 1 − 5α2 − j (6α − α3 ) where α = 1/(ωRC). The oscillation occurs at a frequency ω0 where ∠β(ω0 ) = 180◦ . Thus, the oscillation frequency f0 which cancels the imaginary part is given by f0 = Dr. U. Sezen &amp; Dr. D. Gökçen (Hacettepe Uni.) ELE315 Electronics II 18-Nov-2016 5 / 31 Dr. U. Sezen &amp; Dr. D. Gökçen (Hacettepe Uni.) 1 √ 2πRC 6 ELE315 Electronics II 18-Nov-2016 6 / 31 Oscillators Phase-Shift Oscillator Oscillators Phase-Shift Oscillator FET Phase-Shift Oscillator β(ω) = I √ 1 1 − 5α2 − j (6α − α3 ) As α|ω0 = 6, feedback gain at the oscillation frequency is given by β(ω0 ) = − 1 29 The amplier must supply enough gain to compensate for losses. The overall gain must be unity. Thus, the absolute gain of the amplier stage must be greater than |1/β(ω0 )|, i.e., |A| &gt; 29. I The RC networks provide the necessary phase shift for a positive feedback. They also determine the frequency of oscillation. Dr. U. Sezen &amp; Dr. D. Gökçen (Hacettepe Uni.) ELE315 Electronics II 18-Nov-2016 7 / 31 Dr. U. Sezen &amp; Dr. D. Gökçen (Hacettepe Uni.) Oscillators Phase-Shift Oscillator an FET having gm = 5 mS, rds = 40 kΩ, and feedback circuit resistor value of R = 10 kΩ. Select the value of C for oscillator operation at 1 kHz and RD for A &gt; 29 to ensure oscillator operation. 1 √ 2πRC 6 18-Nov-2016 8 / 31 Oscillators Phase-Shift Oscillator Example 1: It is desired to design phase-shift oscillator (as in the previous slide) using Solution: Since f0 = ELE315 Electronics II BJT Phase-Shift Oscillator , we can solve for C as follows C= 1 1 √ = √ 2πf0 R 6 2π(1k)(10k) 6 = 6.5 nF. 0 = r ||R Next, we solve for where RD D to provide a gain of A = 40 (this allows for ds 0 and the feedback network input impedance): some loading between RD 0 RD 0 |A| = gm RD = 40 0 RD = |A| 40 = = 8 kΩ. gm 5 × 10−3 In the gure above: R0 = R − Ri = R − R1 ||R2 ||hie . For the loop-gain to be greater than unity, the requirement on the current gain of the transistor is found to be Finally, we solve for RD to be RD = Dr. U. Sezen &amp; Dr. D. Gökçen (Hacettepe Uni.) 0 rds RD = 10 kΩ. 0 rds − RD ELE315 Electronics II hf e &gt; 23 + 29 18-Nov-2016 9 / 31 Dr. U. Sezen &amp; Dr. D. Gökçen (Hacettepe Uni.) Oscillators Phase-Shift Oscillator ELE315 Electronics II 18-Nov-2016 10 / 31 Oscillators Wien-Bridge Oscillator Opamp Phase-Shift Oscillator Wien-Bridge Oscillator In the gure above, in order to sustain oscillation, i.e., β(ω0 )A(ω0 ) ≥ 1 we need to have Rf ≥ 29 R1 I Let us rst dene Z1 = R1 + ZC1 and Z2 = R2 ||ZC2 . Then, the positive feedback loop-gain is given as β(ω)A(ω) = .     Z2 R3 1 R3 1+ = 1+ Z1 + Z2 R4 1 + Z1 /Z2 R4 | {z } | {z } β(ω) A(ω) In order to have the loop-gain to be 1, the Z1 /Z2 needs to have zero phase, i.e., imaginary part needs to be zero. Thus, the oscillation frequency f0 is found to be f0 = Dr. U. Sezen &amp; Dr. D. Gökçen (Hacettepe Uni.) R RC +4 . RC R ELE315 Electronics II 18-Nov-2016 11 / 31 Dr. U. Sezen &amp; Dr. D. Gökçen (Hacettepe Uni.) 1 √ 2π R1 C1 R2 C2 ELE315 Electronics II 18-Nov-2016 12 / 31 Oscillators Wien-Bridge Oscillator I Oscillators Wien-Bridge Oscillator Hence, the positive feedback loop-gain at the oscillation frequency f0 becomes  1 β(ω0 )A(ω0 ) = 1+  R1 R2 + C2 C1  1+ R3 R4  In order to sustain the oscillation, i.e., β(ω0 )A(ω0 ) ≥ 1, Example 2: Calculate the resonant frequency of the Wien bridge oscillator shown above. Solution: Oscillation frequency is given by R3 R1 C2 ≥ + R4 R2 C1 I f0 = Thus, when R1 = R2 = R and C1 = C2 = C , then f0 = 1 1 = = 3120.7 Hz. 2πRC 2π(51k)(1n) 1 2πRC R3 ≥ 2. R4 Dr. U. Sezen &amp; Dr. D. Gökçen (Hacettepe Uni.) ELE315 Electronics II 18-Nov-2016 13 / 31 Oscillators Wien-Bridge Oscillator Dr. U. Sezen &amp; Dr. D. Gökçen (Hacettepe Uni.) ELE315 Electronics II 18-Nov-2016 14 / 31 Oscillators Tuned Oscillator Circuits Tuned Oscillator Circuits Example 3: Design the RC elements of a Wien bridge oscillator for operation at f0 = 10 kHz. Solution:Using equal values of R and C , we can select R = 100 kΩ and calculate the required value of C as C= 1 1 = = 159 pF. 2πf0 R 2π(10k)(100k) We can use R3 = 300 kΩ and R4 = 100 kΩ to provide a ratio R3 /R4 greater than 2 for oscillation to take place. 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. Dr. U. Sezen &amp; Dr. D. Gökçen (Hacettepe Uni.) ELE315 Electronics II 18-Nov-2016 15 / 31 Oscillators Tuned Oscillator Circuits Dr. U. Sezen &amp; Dr. D. Gökçen (Hacettepe Uni.) ELE315 Electronics II 18-Nov-2016 16 / 31 18-Nov-2016 18 / 31 Oscillators Tuned Oscillator Circuits Colpitts Oscillator Circuits BJT Colpitts Oscillator FET Colpitts Oscillator Oscillator frequency f0 = where Ceq = 2π 1 p LCeq C1 C2 . C1 + C2 Dr. U. Sezen &amp; Dr. D. Gökçen (Hacettepe Uni.) ELE315 Electronics II 18-Nov-2016 17 / 31 Dr. U. Sezen &amp; Dr. D. Gökçen (Hacettepe Uni.) ELE315 Electronics II Oscillators Tuned Oscillator Circuits Oscillators Tuned Oscillator Circuits Hartley Oscillator Circuits Opamp Colpitts Oscillator FET Hartley Oscillator Oscillator frequency f0 = 2π 1 p Leq C where Leq = L1 + L2 + 2M with M denoting the mutual inductance. Dr. U. Sezen &amp; Dr. D. Gökçen (Hacettepe Uni.) ELE315 Electronics II 18-Nov-2016 19 / 31 Dr. U. Sezen &amp; Dr. D. Gökçen (Hacettepe Uni.) Oscillators Tuned Oscillator Circuits ELE315 Electronics II 18-Nov-2016 20 / 31 Oscillators Crystal Oscillator Crystal Oscillator BJT Hartley Oscillator A crystal oscillator is basically a tuned-circuit oscillator using a piezoelectric crystal as a resonant tank circuit. The crystal (usually quartz) has a greater stability in holding constant at whatever frequency the crystal is originally cut to operate. Crystal oscillators are used whenever great stability is required, such as in communication transmitters and receivers. A quartz crystal (one of a number of crystal types) exhibits the property that when mechanical stress is applied across the faces of the crystal, a dierence of potential develops across opposite faces of the crystal. This property of a crystal is called the piezoelectric eect. Similarly, a voltage applied across one set of faces of the crystal causes mechanical distortion in the crystal shape. When alternating voltage is applied to a crystal, mechanical vibrations are set up. These vibrations having a natural resonant frequency dependent on the crystal. Although the crystal has electromechanical resonance, we can represent the crystal action by an equivalent electrical resonant circuit. Dr. U. Sezen &amp; Dr. D. Gökçen (Hacettepe Uni.) ELE315 Electronics II 18-Nov-2016 21 / 31 Oscillators Crystal Oscillator ELE315 Electronics II ELE315 Electronics II 18-Nov-2016 22 / 31 18-Nov-2016 24 / 31 Oscillators Crystal Oscillator The crystal has two resonant frequencies as shown below: ◦ 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. Dr. U. Sezen &amp; Dr. D. Gökçen (Hacettepe Uni.) Dr. U. Sezen &amp; Dr. D. Gökçen (Hacettepe Uni.) 18-Nov-2016 23 / 31 Series-Resonant Crystal Oscillator Series-Resonant Crystal FET Oscillator Dr. U. Sezen &amp; Dr. D. Gökçen (Hacettepe Uni.) ELE315 Electronics II Oscillators Crystal Oscillator Oscillators Crystal Oscillator Parallel-Resonant Crystal Oscillator Series-Resonant Crystal Opamp Oscillator Dr. U. Sezen &amp; Dr. D. Gökçen (Hacettepe Uni.) ELE315 Electronics II Parallel-Resonant Crystal BJT Oscillator 18-Nov-2016 25 / 31 Oscillators Unijunction Oscillator Dr. U. Sezen &amp; Dr. D. Gökçen (Hacettepe Uni.) ELE315 Electronics II 18-Nov-2016 26 / 31 Oscillators Unijunction Oscillator Unijunction Oscillator Unijunction transistor (UJT) can be used in a single-stage oscillator circuit to provide a pulse signal suitable for digital-circuit applications. The unijunction transistor can be used in what is called a relaxation oscillator as shown by the basic circuit above. Resistor RT and capacitor CT are the timing components that set the circuit oscillating rate. The oscillating frequency may be calculated as f0 = 1 RT CT ln  1 1−η ELE315 Electronics II 18-Nov-2016 27 / 31 Oscillators Unijunction Oscillator ELE315 Electronics II 1.5 RT CT Capacitor CT is charged through resistor RT toward supply voltage VBB . As long as the capacitor voltage VE is below a stand-o voltage (VP ) given by  VP = η VB2 − VB1 + VB1 + VD(ON ) ∼ = ηVBB + VD(ON ) Dr. U. Sezen &amp; Dr. D. Gökçen (Hacettepe Uni.) ELE315 Electronics II 18-Nov-2016 28 / 31 Oscillators Unijunction Oscillator When the unijunction res, a voltage rise is developed across R1 and a voltage drop is developed across R2 as shown above. The signal at the emitter is a sawtooth voltage waveform that at B1 is a positive-going pulse and at B2 is a negative-going pulse. Dr. U. Sezen &amp; Dr. D. Gökçen (Hacettepe Uni.) f0 ∼ = the unijunction emitter lead appears as an open circuit. When the emitter voltage across capacitor CT exceeds this value (VP ), the unijunction circuit res, discharging the capacitor, after which a new charge cycle begins.  where η is the unijunction transistor intrinsic stand-o ratio. Dr. U. Sezen &amp; Dr. D. Gökçen (Hacettepe Uni.) Typically, a unijunction transistor has a stand-o ratio from 0.4 to 0.6, i.e., 0.4 ≤ η ≤ 0.6. Using a value of η = 0.5 gives us 18-Nov-2016 29 / 31 A few circuit variations of the unijunction oscillator are provided in the gure above. Dr. U. Sezen &amp; Dr. D. Gökçen (Hacettepe Uni.) ELE315 Electronics II 18-Nov-2016 30 / 31 Oscillators Unijunction Oscillator Basic construction and equivalent circuit representation of the UJT is given in the gure above. Dr. U. Sezen &amp; Dr. D. Gökçen (Hacettepe Uni.) ELE315 Electronics II 18-Nov-2016 31 / 31 ...
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• Umut Sezen

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