Oscillators Study Notes

Oscillators Chapter Outline

  • 16–1 The Oscillator

  • 16–2 Feedback Oscillators

  • 16–3 Oscillators with RC Feedback Circuits

  • 16–4 Oscillators with LC Feedback Circuits

  • 16–5 Relaxation Oscillators

  • 16–6 The 555 Timer as an Oscillator

Chapter Objectives

  • Describe the operating principles of an oscillator.

  • Discuss the principle on which feedback oscillators are based.

  • Describe and analyze the operation of RC feedback oscillators.

  • Describe and analyze the operation of LC feedback oscillators.

  • Describe and analyze the operation of relaxation oscillators.

  • Discuss and analyze the 555 timer and use it in oscillator applications.

Key Terms

  • Oscillator: An electronic circuit that produces a periodic waveform on its output with only the DC supply voltage as an input.

  • Positive feedback: The return of a portion of the output signal to the input such that it reinforces and sustains the output.

  • Voltage-controlled oscillator (VCO): A type of relaxation oscillator whose frequency can be varied by a DC control voltage.

  • Astable: Characterized by having no stable states.

Application Activity Preview

  • The application in this chapter involves a circuit that produces an ASK signal for testing the RFID reader developed in the previous chapter.

  • The ASK test generator uses an oscillator, a 555 timer, and a JFET analog switch to produce a 125 kHz carrier signal modulated at 10 kHz by a digital signal.

  • The output amplitude is adjustable down to a low level to simulate the RFID tag signal.

Introduction to Oscillators

  • Definition: Oscillators are electronic circuits that generate an output signal without the necessity of an input signal and are used as signal sources in various applications.

  • Waveforms: Different types of oscillators produce outputs including sine waves, square waves, triangular waves, and sawtooth waves.

  • Components: Several types of basic oscillator circuits using discrete transistors and op-amps are introduced, along with the 555 timer and its applications.

  • Operating Principle: Sinusoidal oscillator operation is based on positive feedback, where a portion of the output signal is fed back to the input, reinforcing itself to sustain a continuous output signal.

  • Uses: Oscillators are widely used in communications systems, digital systems, and various test instruments.

The Oscillator

  • Basic Concept: An oscillator is a circuit producing periodic waveforms using only DC supply voltage as input.

  • Types of Outputs: Outputs can be sinusoidal or nonsinusoidal depending on the type of oscillator.

  • Classification: The two major classifications are:

    • Feedback oscillators

    • Relaxation oscillators.

Feedback Oscillators

  • Definition: Feedback oscillators return a fraction of the output signal to the input without net phase shift, reinforcing the output signal.

  • Operation: Loop gain is maintained at 1.0 to sustain oscillations. It involves an amplifier (transistor or op-amp) and a feedback circuit that produces phase shift and provides attenuation.

  • **Key Elements:

    • Amplifier for gain

    • Feedback circuit for phase shift and attenuation.

Relaxation Oscillators

  • Definition: Unlike feedback oscillators, relaxation oscillators utilize an RC timing circuit to generate a waveform typically a square wave or other nonsinusoidal waveform.

  • Components Used: Normally uses Schmitt trigger or devices that change states to charge and discharge a capacitor through a resistor.

Feedback Oscillator Principle

  • Positive Feedback: Characterized by a portion of the output voltage being fed back with no net phase shift, reinforcing the output signal.

  • Condition for Oscillation: For oscillation to occur, two conditions must be met:

    1. The phase shift around the feedback loop must equal 0° (in-phase).

    2. The voltage gain (loop gain) around the closed feedback loop must equal 1 (unity).

  • Effects of Gain:

    • A loop gain greater than 1 will cause output saturation, producing distortion, necessitating gain control.

    • Start-up requires the loop gain to initially exceed 1 to build output amplitude, then decrease to sustain oscillation at 1.

Conditions for Oscillation

  1. Phase Shift Condition: Phase shift must be 0° at the desired oscillation frequency (ex: through lead-lag circuit).

  2. Closed Loop Gain: The amplified signals must maintain a closed loop gain at unity (1) after initial startup (which requires gain > 1 for startup conditions).

  3. Synergistic Interaction: Feedback signal for oscillation initiation arises from thermal noise or transient events, building up through the feedback loop.

Section 16–3: Oscillators with RC Feedback Circuits

  • **Types of RC Feedback Oscillators:

    1. Wien-bridge oscillator

    2. Phase-shift oscillator

    3. Twin-T oscillator**.

  • Frequency Range: RC feedback oscillators typically operate for frequencies up to about 1 MHz.

The Wien-Bridge Oscillator

  • Basic Feature: Utilizes a lead-lag circuit within the feedback for positive reinforcement to achieve oscillations at a resonant frequency where the response is maximized.

  • Attenuation and Resonance: Attenuation at resonance is derived via a voltage divider and feedback loop adjustments around a specified attenuation factor.

  • Mathematical Modeling: Resonant frequency is given by fr=rac12extπimesRCf_r = rac{1}{2{ ext{π}} imes RC} where R and C are components of the feedback circuit.

The Phase-Shift Oscillator

  • Functionality: Each RC circuit provides up to a 90° phase shift, with oscillation achieved when the total phase shift equals 180° to reinforce the cycle.

  • Operational Gain: Requires a closed-loop gain of 3 to sustain oscillations.

Section 16–4: Oscillators with LC Feedback Circuits

  • Usage: Preferred for applications requiring higher frequency oscillations.

  • Types of LC Feedback Oscillators:

    • Colpitts, Clapp, Hartley, Armstrong, and crystal-controlled oscillators.

The Colpitts Oscillator

  • Basic Structure: Uses an LC circuit whose resonant frequency is determined by the values of L and C, providing feedback for oscillation.

Loading Effects in Colpitts Oscillator

  • Component Impact: Loading effects alter oscillation frequency by affecting the quality factor (Q) of the LC circuit, which reduces oscillatory response at higher frequencies due to lower Q.

Relaxation Oscillators

  • Definition: Utilize RC timing devices with state-changing elements to generate outputs (e.g., triangular, square-form wave outputs).

Triangular-Wave Oscillator

  • Implementation: An op-amp integrator can create triangular waveforms through switching circuits.

Square-Wave Oscillator

  • Methodology: Based on charging and discharging capacitors through feedback regulation to generate square wave forms at predetermined frequencies.

The 555 Timer as an Oscillator

  • Versatility: The 555 timer can operate in various configurations, including astable and VCO states.

  • Astable Configuration: Functions as a free-running multivibrator, with output oscillations defined by RC timing components.

  • Voltage-Controlled Option: Applied as a VCO, with frequency adjustable by varying external control voltage.

Application Activity: ASK Test Generator

  • Purpose: Develops a signal source for testing RFID systems via ASK modulation circuitry.

  • Simulator Usage: Multisim is employed for circuit simulation, comparing calculated versus actual performance.

Summary

  • Key Concepts: Oscillators differentiate from amplifiers through output characteristics, with understanding positive feedback principles key.

  • Concept Integration: Understanding varied oscillator types introduces breadth of applications in electronics, from waveform generation to communication technologies.

Key Formulas

  • Resonant Frequencies:

    • Wien-bridge: fr=rac12extπRCf_r = rac{1}{2 ext{π}RC}

    • Phase-shift: frextdependentonconfigurationsf_r ext{ dependent on configurations}

    • Colpitts, Hartley: fr=rac12extπext√(LC)f_r = rac{1}{2 ext{π} ext{√(LC)}}

Circuit-Action Quiz Answers

  1. (b)

  2. (c)

  3. (a)
    …

Problems

  1. Describe conditions for oscillation onset.

  2. Calculate resonant frequency for given R and C values in specific configurations.

  3. Explain oscillatory behavior changes with component value adjustments.