An oscillator is a circuit that generates a periodic waveform using only a DC supply voltage as input.

No repetitive input signal is required, except for synchronization in certain applications.

The output can be either:

• Sinusoidal: e.g., sine wave.

• Nonsinusoidal: e.g., square, sawtooth waves.

Two major types of oscillators:

• Feedback Oscillators.

• Relaxation Oscillators.

Feedback Oscillators:

• Utilize positive feedback to return a fraction of the output signal to the input.

• Maintain loop gain = 1, ensuring no net phase shift.

Relaxation Oscillators:

• Use an \(RC\) timing circuit combined with a switching device (e.g., Schmitt Trigger).

• Generate nonsinusoidal waveforms, typically square waves.

Based on positive feedback: A portion of the output is fed back in-phase to reinforce the signal.

Consist of an amplifier (e.g., transistor or op-amp) and a feedback circuit that provides phase shift and attenuation.

Conditions for oscillation:

1. Phase shift around the feedback loop must be \(0^\circ\).

2. The closed-loop gain, \(A_{cl} = A_v B\), must equal 1.

Initial condition for oscillation: The loop gain, \(A_v B\), must be greater than 1 to build up the output amplitude.

Once oscillation begins, the gain reduces to 1 to sustain stable oscillation without distortion.

The initial feedback signal typically originates from noise or power supply transients.

Used for frequencies up to 1 MHz.

Common types include:

• Wien-bridge oscillator

• Phase-shift oscillator

• Twin-T oscillator

Produce sinusoidal outputs using \(RC\) circuits in the feedback loop.

The Wien-bridge oscillator generates sine waves.

It uses an operational amplifier in a positive feedback configuration with a lead-lag network.

Theoretically developed by Max Wien in 1891.

Practical implementation achieved by William Hewlett in 1939.

The Wien-bridge oscillator consists of two RC networks:

• \(R_1\) and \(C_1\) form the lag portion.

• \(R_2\) and \(C_2\) form the lead portion.

At low frequencies, the lead circuit dominates.

At high frequencies, the lag circuit dominates.

The circuit peaks at the resonant frequency, \(f_r\), with a phase shift of \(0^\circ\).

At resonant frequency, \(f_r\):

• Phase shift = \(0^\circ\)

• Attenuation, \(\frac{V_{out}}{V_{in}} = \frac{1}{3}\) (when \(R_1 = R_2\) and \(X_{C1} = X_{C2}\))

The resonant frequency formula is:

Below \(f_r\): output leads input.

Above \(f_r\): output lags input.

Lead-lag circuit in positive feedback loop.

Voltage divider in negative feedback loop.

Can be viewed as a noninverting amplifier configuration.

In the bridge configuration, the op-amp is connected across the lead-lag circuit and voltage divider.

Positive feedback requirements:

• Phase shift around loop = \(0^\circ\) (achieved at \(f_r\))

• Gain around loop = 1

Closed-loop gain must be 3 to offset 1/3 attenuation:

Initially need \(A_{cl} > 3\) to build up oscillation

Then gain must decrease to 3 to sustain oscillation

Methods to achieve this:

• Zener diode arrangement

• JFET as voltage-controlled resistor

Modified voltage divider with \(R_3\) and back-to-back zeners

Initially zeners appear as opens - higher gain

When output reaches zener voltage, zeners conduct - gain reduces to 3

Simple but can cause distortion

Better method using JFET as voltage-controlled resistor

JFET operates in ohmic region

Gate voltage controls drain-source resistance

Negative feedback automatically adjusts gain

Produces excellent sinusoidal waveform

Uses three \(RC\) sections, each providing up to \(90^\circ\) phase shift (total \(180^\circ\)).

Op-amp inversion provides additional \(180^\circ\) for \(0^\circ\) net phase shift.

Attenuation: \(B = 1/29\), requiring amplifier gain \(A_v > 29\).

Frequency: \(f_r = \dfrac{1}{2 \pi \sqrt{6} R C}\).

Uses two T-type \(RC\) filters (low-pass and high-pass) forming a band-stop response.

Oscillates at the center frequency (\(f_r\)) where negative feedback is minimal.

Positive feedback through a voltage divider enables oscillation.

Suitable for frequencies above 1 MHz.

Use discrete transistors (BJT or FET) due to op-amp frequency limitations.

Types: Colpitts, Clapp, Hartley, Armstrong, and Crystal-Controlled oscillators.

Uses an \(LC\) tank circuit with capacitors \(C_1\) and \(C_2\) and inductor \(L\).

Resonant frequency: \(f_r \approx \dfrac{1}{2 \pi \sqrt{L C_{\text{T}}}}\), where \(C_{\text{T}} = \dfrac{C_1 C_2}{C_1 + C_2}\).

Attenuation: \(B = C_2 / C_1\), requiring \(A_v > C_1 / C_2\) for start-up.

Loading reduces \(Q\), affecting \(f_r\).

A variation of Colpitts with an additional capacitor \(C_3\) in series with the inductor.

Total capacitance: \(C_{\text{T}} = \dfrac{1}{\dfrac{1}{C_1} + \dfrac{1}{C_2} + \dfrac{1}{C_3}}\).

If \(C_3 \ll C_1, C_2\), then \(f_r \approx \dfrac{1}{2 \pi \sqrt{L C_3}}\), improving frequency stability.

Uses two series inductors (\(L_1, L_2\)) and a parallel capacitor.

Frequency: \(f_r \approx \dfrac{1}{2 \pi \sqrt{L_{\text{T}} C}}\), where \(L_{\text{T}} = L_1 + L_2\).

Attenuation: \(B \approx L_1 / L_2\), requiring \(A_v > L_2 / L_1\) for start-up.

Uses transformer coupling ("tickler coil") for feedback.

Frequency: \(f_r = \dfrac{1}{2 \pi \sqrt{L_{\text{pri}} C_1}}\).

Less common due to transformer size and cost.

Use a piezoelectric quartz crystal for high stability and \(Q\) (several thousand).

Operates in series or parallel resonance modes.

The fundamental frequency is limited to 20 MHz, with higher frequencies utilizing overtone modes. These overtones are roughly integer multiples of the fundamental frequency.

Use an \(RC\) timing circuit and a switching device to produce non-sinusoidal waveforms (e.g., triangular, sawtooth, square).

Common types of relaxation oscillators:

• Triangular-wave oscillator

• Sawtooth VCO (Voltage-Controlled Oscillator)

• Square-wave oscillator

Uses an op-amp integrator and a comparator with hysteresis.

Output: Triangular wave from integrator, square wave from comparator.

Frequency: \(f_r = \dfrac{1}{4 R_1 C} \left( \dfrac{R_2}{R_3} \right)\).

UTP and LTP set by \(R_2\) and \(R_3\):

Uses an op-amp integrator and a Programmable Unijunction Transistor (PUT) switch.

Frequency: \(f = \dfrac{|V_{\text{IN}}|}{R_i C} \left( \dfrac{1}{V_p - V_{\text{F}}} \right)\).

PUT controls peak voltage, triggering capacitor discharge.

Uses an op-amp with an \(RC\) circuit and hysteresis.

Capacitor charges/discharges between feedback voltages, producing a square wave.

Versatile IC with two comparators, a flip-flop, a discharge transistor, and a resistive voltage divider.

Used as an astable multivibrator (free-running oscillator) or VCO.

Produces a square-wave output.

Frequency: \(f_r = \dfrac{1.44}{(R_1 + 2 R_2) C_{\text{ext}}}\).

Duty cycle: \(\left( \dfrac{R_1 + R_2}{R_1 + 2 R_2} \right) 100\%\).

Diode addition allows duty cycles below 50%.

Control voltage on pin 5 varies threshold levels, changing frequency.

Frequency decreases with increasing control voltage.

Applications: Phase-locked loops for communication receivers.

Oscillators are essential for generating periodic signals in communication, digital, and test systems.

Feedback oscillators use positive feedback to generate sinusoidal outputs.

Relaxation oscillators produce nonsinusoidal waveforms using \(RC\) timing circuits.

\(LC\) oscillators and crystal-controlled oscillators are used for generating higher frequencies.

The 555 timer is a versatile IC used in astable and VCO (Voltage-Controlled Oscillator) applications.