Fundamentals of Linear Electronics Integrated & Discrete by L7kjV3

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```									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