Exp_5_fa09

Exp_5_fa09 - Physics 3330 Experiment #5 Fall 2009 Positive...

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Physics 3330 Experiment #5 Fall 2009 Positive Feedback and Oscillators Purpose In this experiment we will study how spontaneous oscillations may be caused by positive feedback. You will construct an active LC filter, add positive feedback to make it oscillate, and then remove the feedback to make a Schmitt trigger. Introduction By far the most common problem with op-amp circuits, and amplifiers in general, is unwanted spontaneous oscillations caused by positive feedback. Just as negative feedback reduces the gain of an amplifier, positive feedback can increase the gain, even to the point where the amplifier may produce an output with no input. Unwanted positive feedback is usually due to stray capacitive or inductive couplings, couplings through power supply lines, or poor feedback loop design. An understanding of the causes of spontaneous oscillation is essential for debugging circuits. On the other hand, positive feedback has its uses. Essentially all signal sources contain oscillators that use positive feedback. Examples include the quartz crystal oscillators used in computers, wrist watches, and electronic keyboards, traditional LC oscillator circuits like the Colpitts oscillator and the Wien bridge, and lasers. Positive feedback is also useful in trigger and logic circuits that must determine when a signal has crossed a threshold, even in the presence of noise. In this experiment we will try to understand quantitatively how positive feedback can cause oscillations in an active LC filter, and how much feedback is necessary before spontaneous oscillations occur. We will also construct a Schmitt trigger to see how positive feedback can be used to detect thresholds. Readings 1. Horowitz and Hill, Section 5.12 to 5.19. If you are designing a circuit and want to include an oscillator, look here for advice. Amplifier stability is discussed in Sections 4.33-4.34. 2. (Optional.) Bugg discusses the theory of spontaneous oscillations in Chapter 19. You may want to read Section 19.4 on the Nyquist diagram after you read the theory section below. Experiment #5 5.1 Fall 2009
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Theory LC ACTIVE BANDPASS FILTER The circuit for the active LC filter is shown in Figures 5.1 and 5.2. Recall from the theory section of Experiment #4 that the gain of an inverting amplifier is G = –R F /R when the open loop gain is large. The basic idea of this filter is to replace R F with a resonant circuit whose impedance becomes very large at the resonant frequency. Then there will be a sharp peak in the gain at the resonant frequency. If we replace R F with the impedance Z F shown in Fig. 5.2 and do a fair bit of algebra, we can show that G ( ω ) =− Z F R Z 0 R i 0 + 1 Q 2 0 2 + i 0 Q + 1 , where we have defined the resonant frequency ω 0 , the characteristic impedance Z 0 , and the Q: 0 = 1 LC , Z 0 = L C , Q= Z 0 r .
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Exp_5_fa09 - Physics 3330 Experiment #5 Fall 2009 Positive...

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