CHAPTER 13 Sine Wave Oscillator Circuits Objectives Describe and Analyze: • Feedback oscillator theory • RC phase-shifting oscillators • LC resonant oscillators • Crystal oscillators • Troubleshooting Introduction • Oscillators use feedback to produce periodic AC output with DC power as the only input. • In contrast, function generators produce periodic outputs by joining pieces of wave-forms together. A Bit of Theory • We know that with negative feedback in an op-amp, the equation for closed-loop gain in terms of open-loop gain is: ACL = AOL / (1 + B AOL) where B is the feedback ratio set by external resistors. Now, if there is an additional 180° phase shift in B, we can express it mathematically as: ACL = AOL / (1 – B AOL) In that case, what happens when B AOL = 1? • Mathematically, ACL “goes to infinity” (whatever that means). Physically, the circuit oscillates: it takes no Vin to get a Vout. The trick is to get that 180° shift in B, the feedback network. RC Oscillators • As a group, RC oscillators use an RC network inserted into the feedback loop of an amplifier to produce positive feedback at exactly one frequency. As we just saw, that’s the recipe for oscillation. • One type of RC oscillator is the Wien-Bridge oscillator. Another is simply called the Phase-Shift oscillator. Wien-Bridge Oscillator Feedback to the (+) input > feedback to (–) input at fOSC Starting and Running • A problem with the Wien-Bridge (and with all feedback oscillators) is that the feedback necessary to start oscillating is slightly more than the feedback to maintain a pure sine wave. If the gain is left too high, the sinewave amplitude will increase until it hits the rails and is clipped. • The cure is to include a means for the circuit to lower its gain a bit once it starts oscillating. This is a type of negative feedback based on amplitude. Phase-Shift Oscillator • The RC phase-shift oscillator is the simplest of its type. A minimum of three RC LPF sections are put in the feedback loop of an inverting amplifier. Each RC stage causes an amount of phase shift that changes with frequency. At one specific frequency, the phase shifts of the network add up to 180°. • Since the inverting amplifier has a 180° phase shift, the total phase shift is 360°, which means it has become positive feedback. The circuit oscillates. Phase-Shift Oscillator Oscillations in Amplifiers The old joke is that, when you’re testing them, oscillators don’t oscillate but amplifiers do. If there’s an accidental feedback path from the output to the input, then it’s a good bet a high-gain amplifier will oscillate. Such feedback paths can be: • Through the power rails. • Through magnetic coupling of signal leads. • Through capacitive coupling of adjacent components. • Through unshielded input cables. • Through putting a microphone too close to a speaker. LC Oscillators Pulsing an LC “tank circuit” will make it “ring”. But the oscillations die off due to I2R losses in the circuit. If energy could be pumped back into the tank as fast as it were being dissipated, it would ring forever. That is the basic idea of an LC resonant oscillator. Colpitts Oscillator A common type of LC oscillator. Hartley Oscillator Another type of LC oscillator. Crystal Oscillators • Piezoelectric crystals behave like extremely high-Q resonant circuits. • A crystal’s frequency depends on its physical dimensions, which can be tightly controlled by grinding. • LC resonant oscillators can be “crystal stabilized”. • A crystal can take the place of an LC tank circuit. XTAL Oscillator Examples Since you’re stuck with it anyway, the Pierce oscillator (b) utilizes stray capacitance for feedback. Troubleshooting • Use a frequency counter to check frequency. You can use an oscilloscope, but your readings will be off by ±5%. • Use a X10 probe to minimize loading (they work on counters too). • At very high frequencies, you don’t have to touch the probe to the circuit, just get it close. • There can be high voltage in a transmitter’s tank circuit even if it uses a 12 Volt DC supply.
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