Rectifiers & Regulators
Converting AC to DC with diode rectifiers, then regulating the output with linear regulators — the foundation of every power supply.
1. Diode Rectifiers
A rectifier converts AC to pulsating DC by allowing current to flow only in one direction using diodes. The half-wave rectifier uses one diode; the full-wave bridge uses four.
Half-Wave Rectifier
\[ V_{dc} = \frac{V_p}{\pi} \approx 0.318\,V_p \]
Uses one diode. Ripple frequency = \(f_{ac}\). Poor efficiency — only conducts on positive half-cycle.
Full-Wave Bridge
\[ V_{dc} = \frac{2V_p}{\pi} \approx 0.637\,V_p \]
Four diodes, both half-cycles used. Ripple at \(2f_{ac}\). Two diode drops (\(2 \times 0.7\) V) subtracted from output.
Bridge Rectifier Circuit
2. Ripple Voltage & Filter Capacitor
After rectification, a filter capacitor \(C\) is placed across the load to reduce ripple. During non-conducting intervals, \(C\) discharges through the load. The peak-to-peak ripple is:
\[ V_r \approx \frac{I_{load}}{f \cdot C} \]
For full-wave: \(f = 2f_{ac}\). For half-wave: \(f = f_{ac}\).
To select the capacitor for a desired ripple: \(C = I_{load}/(f \cdot V_{r,max})\). For \(I_{load} = 500\) mA, \(V_{r} = 1\) V, full-wave 50 Hz: \(C = 0.5/(100 \times 1) = 5000\;\mu\text{F}\).
In practice, electrolytic capacitors have ESR (equivalent series resistance) which contributes additional ripple: \(V_{ESR} = I_{peak} \times ESR\). Low-ESR capacitors are preferred for high-current supplies.
3. Linear Regulators
A linear regulator maintains a stable output voltage by varying the resistance of a series pass transistor. It works like a variable resistor in series — dissipating the excess as heat:
\[ P_{diss} = (V_{in} - V_{out}) \times I_{load} \qquad \eta = \frac{V_{out}}{V_{in}} \]
Standard Linear Regulator
Requires \(V_{in} \geq V_{out} + V_{dropout}\) (typically 2–3 V). Common ICs: 78xx series (7805 = 5 V out, min 7 V in). Simple, stable, low noise.
Good for: low-noise analog circuits, small voltage drops.
LDO (Low Dropout)
PMOS pass transistor reduces dropout to 100–300 mV. Essential when\(V_{in}\) is close to \(V_{out}\) — e.g., 3.3 V out from a single Li-ion cell (3.7 V). Common: AMS1117, LP2985.
Good for: battery-powered systems, low-margin voltage rails.
Thermal Design
Junction temperature: \(T_j = T_a + P_{diss} \times \theta_{ja}\) where \(\theta_{ja}\)is thermal resistance (junction to ambient, °C/W). Absolute max \(T_j\) is typically 125–150 °C. For a 5 V to 3.3 V regulator at 1 A: \(P_{diss} = 1.7\) W. With \(\theta_{ja} = 50\) °C/W, heatsink is mandatory above \(T_a = 40\) °C.
Python Simulation
Half-wave and full-wave bridge rectifier outputs, ripple vs capacitance (theory and simulation), LDO regulator efficiency and dissipation vs input voltage, and ripple frequency spectrum.
Click Run to execute the Python code
Code will be executed with Python 3 on the server