6.1 Sinusoidal Oscillators

An oscillator is an electronic circuit that generates a periodic signal, effectively converting DC energy from a power supply into AC energy in the form of a repeating waveform. A sinusoidal oscillator specifically produces a sine wave output. The operation of any feedback-based oscillator is governed by the Barkhausen criteria, which state the two conditions necessary for sustained oscillations:

1. The magnitude of the loop gain (the product of the amplifier gain, A_v, and the feedback network gain, \beta) must be greater than or equal to unity: |A_v\beta| \geq 1.
2. The total phase shift around the feedback loop must be exactly 0° or an integer multiple of 360°.

RC Phase Shift Oscillator

The RC phase shift oscillator uses an inverting amplifier and a feedback network composed of three cascaded RC sections to generate a sinusoidal output.

Principle of Operation:

• The inverting amplifier provides a phase shift of 180°.
• To satisfy the Barkhausen criteria, the feedback network must provide the remaining 180° of phase shift. Each of the three RC sections contributes 60° of phase shift at a specific frequency.
• The frequency of oscillation is determined by the values of R and C in the feedback network: f=\frac{1}{2\Pi RC\sqrt[]{6}}
• For oscillations to be sustained, the gain of the inverting amplifier must be large enough to overcome the attenuation of the RC network. The condition for the amplifier gain is: \frac{R_f}{R_1}\geq29

Wien Bridge Oscillator

The Wien bridge oscillator uses a non-inverting amplifier and a frequency-selective feedback network (the Wien bridge) to produce a very stable, low-distortion sine wave.

Principle of Operation:

• The non-inverting amplifier provides a 0° phase shift.
• Therefore, the feedback network must also provide a 0° phase shift at the desired frequency of oscillation. The Wien bridge network achieves this at a specific resonant frequency.
• The frequency of oscillation is given by: f=\frac{1}{2\Pi RC}
• For sustained oscillations, the gain of the non-inverting amplifier must be at least 3. This leads to the following condition: 1+\frac{R_f}{R_1}\geq3 \quad \implies \quad R_{f}\geq2R_{1}

6.2 Waveform Generators

A waveform generator is a circuit designed to produce standard, non-sinusoidal waveforms, such as square waves and triangular waves. These are fundamental building blocks in digital electronics, timing circuits, and testing equipment.

Square Wave Generator

An op-amp based square wave generator, also known as an astable multivibrator, produces a continuous square wave output. The circuit cleverly uses both positive feedback (to create switching behavior) and negative feedback (to control timing).

Operation: The circuit’s operation relies on the charging and discharging of capacitor C through the negative feedback resistor R_1. The positive feedback network, composed of resistors R_2 and R_3, sets the upper and lower voltage thresholds at which the output switches states.

1. Assume the output is at positive saturation, +V_{sat}. The positive feedback network sets an Upper Threshold Voltage (V_{UT}) at the non-inverting terminal, given by V_{UT} = +V_{sat} \frac{R_3}{R_2+R_3}.
2. The capacitor C begins charging towards +V_{sat} through resistor R_1.
3. When the capacitor voltage at the inverting terminal just exceeds V_{UT}, the op-amp’s output rapidly switches to negative saturation, -V_{sat}.
4. Now, the feedback network sets a Lower Threshold Voltage (V_{LT}) at the non-inverting terminal, given by V_{LT} = -V_{sat} \frac{R_3}{R_2+R_3}.
5. The capacitor begins to discharge and then charge towards -V_{sat}. When its voltage drops just below V_{LT}, the output switches back to +V_{sat}, and the cycle repeats.

Triangular Wave Generator

A triangular wave generator produces a continuous triangular waveform. It is constructed by cascading a square wave generator and an integrator circuit.

Principle of Operation:

1. The first stage is a square wave generator, which produces a high/low output as described above.
2. The output of this square wave generator is fed directly into the input of an integrator circuit.
3. The integrator performs the mathematical operation of integration on its input. The integral of a constant positive voltage (the high state of the square wave) is a positive-sloping ramp. The integral of a constant negative voltage (the low state) is a negative-sloping ramp.
4. As the square wave switches between its positive and negative levels, the integrator’s output ramps up and down, creating a continuous triangular waveform.