Half wave rectifier | Electronics | Power supply

Half wave rectifier

Rectifier

• A device which is used to convert alternating current (or voltage) into direct current (or voltage) is known as rectifier
• The process of converting ac into dc is known as rectification.

Principle of rectifier

• A diode offers a low resistance in forward bias and a high resistance in reverse bias.
• It means a very small or practically a zero current flows through the circuit, when diode is reverse biased. This principle is used in the working of rectifier.

Half wave rectifier (HWR)

• A rectifier which converts only half cycle of input ac into dc is known as half wave rectifier.

• In this rectifier an alternating voltage E = E₀ sin ωt is applied at the primary coil of transformer.
• The output voltage is always positive, but it does not remain constant with respect to time.
• The output voltage obtained will be pulsating dc voltage.
• If R_f = forward dynamic resistance of diode, R_s = resistance of secondary coil of transformer, and R_L = load resistance, then
• Current flowing through R_L

Average value of output pulsating current/voltage

Average value of voltage across R_L

Root mean square value of pulsating current/voltage

• For a complete cycle of input, the square root of mean of square of current is root mean square (rms) value of current.

Root mean square value of output voltage

Power supplied to the circuit

• Input ac power = Power across R_s + Power across diode resistance R_f + Power across R_L

Average power supplied to the load

• Output dc power in load R_L

Efficiency of half wave rectifier

• It is defined as the ratio of the output dc power to the input ac power.
• η = (output dc power / input ac power) × 100 %

• By increasing the value of load resistor R_L, the value of rectifier efficiency increases.
• When R_L >> R, η_max = 40.6 %
• When R_L = R, η = 20.3 %

Ripple factor (r)

• The output voltage or current obtained from rectifier is unidirectional, but its value does not remain constant with time.
• The pulsation available in the output current or voltage is ripples.
• Ripple factor gives the measure of smoothing of output voltage or current of a rectifier.
• r = effective value of output ac component / Average of dc component of output current = I_ac / I_dc
• From ac circuit theory

• Thus half wave rectifier is a poor device for converting ac into dc

Voltage regulation (VR)

• The strength of maintaining a constant voltage by a rectifier on varying the load resistance is voltage regulation.
• VR = [(V_NL - V_FL) / V_FL ] × 100%
• V_NL = Output in the absence of load resistance (when R_L = ∞)
• V_FL = Output in the presence of load resistance
• For ideal power supply VR = 0
• It means in ideal power supply the output voltage should not depend on load.

• As the value of I_dc increases, the value of E_dc decreases linearly.

Peak inverse voltage (PIV)

• The maximum value of voltage which is withstand on the diode, when no current is flowing in the circuit.
• It is the maximum voltage on the diode in its non-conducting state.
• For half wave rectifier, PIV = - E₀

Frequency component of output voltage or current

• From Fourier analysis, the output current

• First term I₀ / π represents the dc or average value of current
• Frequency of second term is equal to the frequency of input ac voltage and its peak value is I₀ / 2
• The other terms represents the harmonics.

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