Precision Rectifiers & Oscillators

Precision Rectifiers

The Super Diode (Precision Half-Wave Rectifier)

Eliminates the standard diode $0.7V$ forward voltage drop, allowing rectification of small signals (mV range).

Configuration: Diode placed inside the negative feedback loop.

Operation:

• When V_{in} > 0: Op-amp output drives positive, diode conducts, negative feedback active. $V_{out} = V_{in}$
• When V_{in} < 0: Diode reverse-biased, no feedback, output = 0V

Advantages:

• Eliminates 0.7V threshold
• Linear for millivolt signals
• Fast response (limited by op-amp SR)

Limitations:

• Slew rate limits high-frequency operation
• Output swings rail-to-rail during switching

Precision Full-Wave Rectifier

Provides absolute value: $V_{out} = |V_{in}|$

Configuration: Two-stage circuit 1. First stage: Precision half-wave with inverting amp 2. Second stage: Summing amplifier

Applications:

• AC-to-DC conversion for measurement
• RMS detection circuits
• Envelope detection
• Peak detection with hold capacitor

Sinusoidal Oscillators

Using Positive Feedback to generate stable sinusoidal signals.

Barkhausen Criteria for Oscillation

For sustained oscillation at frequency $f_0$:

1. Loop Gain Criterion: $|A\beta| = 1$ (unity magnitude) 2. Phase Criterion: Total phase shift = $0°$ or $360°$ ($2n\pi$ radians)

Where:

• $A$ = Amplifier gain
• $\beta$ = Feedback network attenuation

Stability Considerations:

• If |A\beta| < 1: Oscillations decay (damped)
• If $|A\beta| = 1$: Sustained oscillations (ideal)
• If |A\beta| > 1: Oscillations grow until limited by saturation (non-linear)

Practical Design: Start with |A\beta| > 1 slightly, use amplitude limiting (diodes, thermistor, FET) to stabilize at $|A\beta| = 1$.

Wien Bridge Oscillator

Most popular RC oscillator for audio frequencies (20 Hz - 20 kHz).

Feedback Network: Lead-lag RC network (Wien bridge)

Oscillation Frequency: $$f_0 = \frac{1}{2\pi RC}$$

Feedback Factor at $f_0$: $$\beta(f_0) = \frac{1}{3} \angle 0°$$

Required Amplifier Gain: $$A = \frac{1}{\beta} = 3$$

To satisfy Barkhausen: $A \times \beta = 3 \times (1/3) = 1$ ✓

Amplitude Stabilization Methods: 1. Tungsten lamp: Positive temperature coefficient resistor in feedback 2. Thermistor: Negative temperature coefficient 3. Diodes: Soft limiting with back-to-back diodes 4. FET/JFET: Voltage-controlled resistance

Advantages:

• Low distortion (<0.1% THD achievable)
• Stable frequency
• Easy frequency adjustment (vary R or C)

Applications:

• Audio signal generators
• Function generators
• Test equipment

RC Phase Shift Oscillator

Uses cascaded RC networks to provide 180° phase shift, combined with inverting amplifier (180°) = 360° total.

Three-Stage RC Network: Each RC stage contributes 60° phase shift at $f_0$.

Oscillation Frequency: $$f_0 = \frac{1}{2\pi RC\sqrt{6}}$$

Required Gain: $$A \geq 29$$

Characteristics:

• Simple design
• Higher gain requirement than Wien
• More sensitive to component variations

LC Oscillators (Hartley, Colpitts)

For high-frequency applications (MHz range) where RC becomes impractical.

Advantages:

• High frequency capability
• Better frequency stability
• Lower phase noise

Disadvantages:

• Requires inductors (bulky, expensive)
• Not suitable for IC integration