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CAPÍTULO 8. OSCILADORES SENOSOIDALES Since is real,for to be real 90 must be real. This is satisfied for a frequency At this frequency, and . Thus the magnitude of the loop gain is , which should be greater than 1 for sustained oscilations, and Since we neglected , another condition the must be satisfied is that 8.4. Practice Problems From chapter 12: problems 3, 9, 10, 13, 14, 21 and 22. 8.4.1. Extra Practice Problems 1. The following diagram shows a Wein-Bridge oscillator using an amplifoer with a nonzero output resistance . The opamp is ideal. Derive expresions for the frequency of oscillation and the conditions that must satisfy for sustained oscillations. R1 R2 Rout − vout + R C R C 2. The following circuit is used as the phase-shifting network for a two-stage FET oscilla. Determine the frequency of oscillation and the gain tor. Find the circuit’s beta, required from the amplifier. (30 points) R + vo - C C R + vf - CAPÍTULO 8. OSCILADORES SENOSOIDALES 91 3. Design a 680kHz Wein-bridge oscillator. Use an ideal op-amp as your active element. 4. For the oscilator circuit shown below, the two transistors have below is 5 points. . Each part a) Draw a diagram of the phase shift network. b) Find from the diagram drawn in part (a). c) Determine the loop gain, SHIFT NETWORK. . HINT: THE GAIN WILL DEPEND ON THE PHASE d) Apply the Barkhausen Criterion to find the frequency of oscillation. e) Find the minimum value of that would satisfy the Barkhausen Criterion. VCC RD RD vO vi M1 M2 L=25mH C=0.1µF R=1MΩ 5. For the oscillator shown below, derive an expression for the frequency of oscillation in is required for oscillations to be maintained? terms of and . What minimum value of R1 R2 − vO + C R R C 6. For the Colpitts oscillator shown below, find values for duce sustained oscillations at if . Use , and . appropriate to pro- CAPÍTULO 8. OSCILADORES SENOSOIDALES 92 vO L2 C1 RD C3 CAPÍTULO 8. OSCILADORES SENOSOIDALES Solutions 1. 93 CAPÍTULO 8. OSCILADORES SENOSOIDALES 2. Let be defined as follows 94 CAPÍTULO 8. OSCILADORES SENOSOIDALES R 95 VA C + vo - + C R vf - Zeq Then Applying the voltage divider rule, To satisfy the Barkhausen Criterion, or At , ; thus the amplifier gain should be grater or equal than 3. 3. From your lecture notes, and and . You can set the gain to . The resulting circuit is the following: . So for by selecting , select , or and CAPÍTULO 8. OSCILADORES SENOSOIDALES 96 1k 9k − vOUT + 234nF 1k 234nF 4. 1k a) The phase-shift network is 0.1µF vo vf 25mH b) Find 1MΩ from the diagram drawn in part (a). c) The impedance seen looking into the phase-shift network is so that the impedance connected to the drain is d) The frequency of oscillation is CAPÍTULO 8. OSCILADORES SENOSOIDALES 97 e) The minimum value of that would satisfy the Barkhausen Criterion should be found from the gain at . For minimum , From this the second order equation is obtained. The solution is . 5. The feedback network is identical to the one shown in problem 1. Thus 6. The phase-shift network is The impedance at the drain is The Barkhausen Criterion requires that which leads to the following expression for the frequency of oscillation: CAPÍTULO 8. OSCILADORES SENOSOIDALES Selecting and leads to or To select , apply the magnitude criterion which requires that For the component values chosen, A good selection would be . 98