Half-Wave Rectifier
Single diode — V_out = max(0, V_in − 0.7) with live oscilloscope trace.
Key Notes
Half-wave rectifier: a single diode in series with a load lets only one HALF of the AC cycle pass.
During the positive half of input AC: diode forward-biased, current flows.
During the negative half: diode reverse-biased, blocks current (output = 0).
Output is a series of positive pulses, not smooth DC.
Average (DC) output voltage: V_dc = V_m/π ≈ 0.318 V_m, where V_m is the input peak.
RMS output: V_rms = V_m/2 (over the full cycle).
Ripple factor (RMS of AC component / DC) for half-wave: ~1.21 — very poor; needs heavy filtering.
PIV (Peak Inverse Voltage) the diode must withstand: V_m.
Efficiency: ~40.6% — poor. Half-wave is used only when simplicity matters and load draws little current.
Formulas
DC output (no filter)
Time-average of V_m·sin(ωt) over a full cycle, accepting only positive half.
RMS output (no filter)
Half of the full-cycle RMS.
Ripple factor
Ratio of AC ripple to DC component.
Efficiency
Theoretical max for ideal half-wave with resistive load.
PIV
Maximum reverse voltage across the diode.
Important Points
Half-wave is the simplest rectifier — but inefficient. Used for AC-DC adapters drawing < 100 mA.
Output frequency = input frequency (50 Hz from 50 Hz mains).
Filter capacitor smooths the pulses but ripple remains worse than for full-wave.
Half-wave wastes the negative half of the cycle — only one pulse per period, vs two for full-wave.
Common pitfall: confusing V_dc (average) with V_rms — they are different things, both important.
Real diode drops ~0.7 V — so for low-voltage rectification, peak output is V_m − 0.7 V, not V_m.
Half-Wave Rectifier notes from sciphylab (also known as SciPhy, SciPhy Lab, SciPhy Labs, Physics Lab). Class 12 physics revision for JEE Mains, JEE Advanced, NEET UG, AP Physics 1/2/C, SAT, and CUET-UG.