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Learn about half-wave and filtered rectifiers, battery charging circuits, and peak rectifiers with smoothing capacitors. Explore the operation of diodes in AC to DC conversion and the design equations for ripple voltage and capacitor capacitance.
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1- The Half-Wave Rectifier • This diode application changes ac into dc. • The voltage is most often a sinusoidal and diode is ideal.
During Positive half-cycle • Diode conduct (“ON”) • VD=0 • Vo=VS During Negative half-cycle • Diode conduct (“OFF”) • VD=VS • Vo=0, iD=0
2- A Typical Battery Charging Circuit In the Figure • VBATTRY represents the battery to be charged
Rtotal includes all resistance (wiring, diode, battery) reflected to the transformer secondary winding. Charging current flows only when Vm sin ωt >VBATTRY. Inertia of meter movement allows indication of average current
3- The Filtered Half-Wave Rectifier • Also called a peak rectifier, a half-wave rectifier with smoothing capacitor, or a half-wave rectifier with a capacitor-input filter. In this figure
In this figure • When Vs> VL, the diode is on, and the voltage source charges the capacitor. • When Vs< VL, the diode is off, and C discharge exponentially through RL. • We define peak to peak ripple voltage Vr, as the total change in VL over one cycle.
Relating Capacitance to Ripple Voltage • Because the diode is off for nearly the entire period, T, the capacitor must supply the “dc” load current during this interval. • The charge taken from the capacitor in this interval is: • The capacitor voltage decreases by Vr in this interval, which requires a decrease in the charge stored in the capacitor
Equating these equations and solving for C gives us a design equation that valid only for small Vr:
4- The Filtered Half-Wave Rectifier • During Positive half-cycle Diode 1 is ON and diode 2 is OFF • During Negative half-cycle • Diode 1 is OFF and Diode 2 is ON
Full wave rectifier The load voltage in this case is represented as: