Half Wave Rectifiers

Table of Content

diode‘s ability to pass current in one direction and blocks current in another direction, that’s why they are used in circuits that convert AC voltage into DC voltage. these circuits are called a rectifier. a rectifier is an essential part of DC power supplies. the most basic type of rectifier is a halfwave rectifier and another is full wave rectifier. to understand, Rectifier introduction to DC power supplies and their uses is important.

The half wave DC Power Supply

The DC power supply converts the 110V,60Hz or 220V, 50Hz AC voltage into a constant DC voltage. nearly all electronic circuits are operated with a DC voltage source. Normally Electronic circuits need less supply voltage than utility AC Voltage. in power supplies step-down transformers are used to down-convert AC voltage to a required voltage level. then rectifier is used to convert AC voltage into pulsating DC Voltage. now we are required to convert pulsating DC into a smooth DC Voltage. So, a filter circuit is used to do this. The filter circuit may compose of capacitor, inductor, or resistor combinations. in filters capacitor stores energy in rising or peak voltage and releases energy during decreasing or no voltage cycles. After filtration voltage regulator is necessary for fragile electronic circuits, the regulator circuit provides a constant voltage to load which full-fil load requirements. A supply made of a half wave rectifier is called a half wave power supply which delivers a half portion of the input sinewave. Half wave power supply schematic diagram as shown under.

half wave power supply circuit diagram with output
Half wave power supply circuit with pulsating DC output

Working of Half Wave Rectifier

The Half Wave rectifier circuit is an addition of a diode in the series of AC source and load. Diode conduct for positive half cycle and acts as an open circuit for the negative half cycle of input AC voltage. as shown in the figure of the half wave rectifier waveform, negative half cycles are clipped off. Current flows throw a load in one direction only. as shown in the half wave rectifier circuit diagram diode anode is connected to the AC voltage source line and the cathode is connected to the load terminal. So, the diode will deliver only positive half cycles to load. this configuration is called a positive half wave rectifier. here is explained half wave rectifier with diagram.

half wave rectifier schematic and graph

Half wave rectifier graph

the above figure shows the output waveform of the half wave rectifier concerning input sinewave. A half wave rectifier circuit converts only one half cycle of the applied ac signal into pulsating dc. The other half of the applied signal gets wiped off as the diode allows conduction in one direction only. in a half wave rectifier output waveform area under the curve is half of the input waveform.

sinewave half wave graphical demonstration
half wave voltage graph

Half wave rectifier Voltage formula

when the input of the half wave rectifier is sinewave, then the average voltage of half wave rectifier is determined by the (ea#1) equation. VRL is instantaneous voltage of input wave. here Vm is peak-peak Voltage of input sinewave. Vavg is average voltage or DC voltage output of HW rectifier. In ideal condition a average value of half wave rectifier is mean value of output. area under positive and negative half cycle is equal in sinewave. but sum of both half cycle is equal to zero or negate each other. so we consider absolute value. In half wave rectifier we acquire only one half cycle. So Vavg of half wave rectified sine wave is equal to average voltage of half sine wave cycle.

average voltage of half wave rectifier equation
(Eq#1) Average voltage of half wave rectifier (Vm is Vp-p)

RMS voltage of half wave rectifier

RMS is the square root of the mean value square. in general equation of RMS value T is the period of one complete cycle of a given periodic wave. Vac is the function of the signal. In sinewave’s case, the RMS value is determined by equation (eq#2). If a rectifier rectifies only half of one complete sinewave cycle. Then we can simply divide it by 2. in the sinewave RMS equation, we find the area under the curve of the sinusoidal wave. This equation applies only in ideal conditions, assuming zero voltage drops on the diode in forward bias. in practice, we negate junction barrier voltage from peak voltage before using the RMS equation, as described in equ#3.

Vrms of sinewave
Vrms general equation
half wave rectifier rms voltage equation
(eq#2) sine wave half wave rectifier RMS voltage (Vm is Vp-p)

silicon diode also exhibits junction barrier voltage in forward bias. for silicon diode junction barrier voltage is 0.7V and 0.3V for germanium diode. to evaluate Vrms and Vavg we have to negate junction barrier voltage first from Vp as in (eq#3)

Vm = Vp – 0.7 (eq#3)

Half wave rectifier Ripple Factor

Ripple factor of half wave rectifier
ripple factor of half wave rectifier valu
Eq#4 Ripple factor of half wave rectifier without filtration when input is pure sinewave

Half wave rectifier Efficiency

The efficiency of half wave rectifier is defined by a ratio of load power dissipation and input AC power. rf is diode forward bias resistance which ratio of junction barrier voltage and load current.

power efficiency of half wave rectifier
Eq#5 Rectifier Efficiency
half wave rectifier power efficiency equation
Eq#6 half wave rectifier efficiency

if we assume rf is negligible against RL. Then 𝜂 is nearly equal to 0.4053 or 40.53%. This value is the maximum efficiency of a half wave rectifier. Adding diode forward bias voltage efficiency becomes lower than 40.53%.

Half wave rectifier form factor

Ratio between RMS output voltage and average output voltage of rectifier is form factor. form factor of half wave rectifier is 1.571 when input AC voltage is pure sinewave. Purpose of calculating form factor of half wave rectifier is digitally measurement RMS value of rectified signal. RMS voltage is evaluate by average voltage of output signal measured by an Analog to digital converter then multiply by form factor. It is easy way to measure average value then convert into RMS value by digital circuits due to massive quantization is required to attain a good RMS value.

form factor of half wave rectifier
eq#7 form factor of half wave rectifier

Crest factor of half wave rectifier

Crest or peak factor is ratio of peak voltage to RMS voltage. To analyze of balance between transient and sustained elements in the output of a rectifier we use crest factor. Peak voltage and RMS voltage both are measured at output of rectifier. according to eq#8 crest or peak factor is equal to 2 with a sine wave input.

eq#8 crest factor of half wave rectifier (sine wave)

Peak Inverse voltage of half wave rectifier

Peak Inverse Voltage (PIV) is refer to the maximum voltage a diode can withstand in the reverse-biased direction without having a breakdown. Similar to diode Reverse Breakdown Voltage. The peak inverse voltage of the half wave rectifier is equal to Vm or input peak voltage. Peak inverse voltage is also called Peak Reverse Voltage (PRV).

Negative half wave rectifier

(a) negative half wave rectifier circuit diagram (b) negative half wave graph

Another type of half wave rectification is a negative half wave rectifier. in which the diode cathode is connected to the AC voltage source terminal. and the anode is connected to the load terminal. in this configuration, the diode passes only negative half cycles of input AC Voltage waveform. voltage appears at load terminal to ground terminal negative pulsating DC voltage.

half wave rectifier with capacitor filter

Circuit diagram of half wave rectifier with smoothing capacitor filter , wave form of half wave rectifier with filter capacitor
(a)Circuit diagram of half wave rectifier with smoothing capacitor filter (b) wave form of half wave rectifier with filter capacitor

half wave rectifier with smoothing capacitor example circuit is given in above figure with output. As we can observe in the circuit diagram of a half wave rectifier with capacitor filter, the diode not only rectifies positive half cycles of input sinewave but also blocks the drainage of stored energy in the capacitor towards the AC voltage source. During the negative half-cycle, or AC voltage is declined by capacitor voltage. Then Capacitor starts to deliver DC voltage to the load until the next positive half cycle of AC voltage begins and rises to capacitor voltage. when the input voltage is greater than the capacitor voltage then the diode goes into the forward bias mode. thus capacitor is again charged by the AC source and the load current also drains from the AC source. New Ripple factor can be determined by eq#9.

Ripple Factor formula of Half wave rectifier with smoothing capacitor
eq#9 Ripple Factor formula of Half wave rectifier with smoothing capacitor

The ripple factor is the ratio of ripple RMS voltage and output DC voltage or average voltage. when we have known DC voltage then we can calculate ripple voltage by multiplying ripple factor with DC voltage or average voltage. the result will be ripple component voltage.

Advantages and Disadvantages of half wave rectifier

  • Advantages
    • only a Single diode is required to perform half wave rectification
    • cheap and easy to build
    • Transformer heat induction due to copper losses is half as compare to full wave rectifier
    • some application do not require full wave or pure DC, half wave is simply best. for example LED indicator on a panel is required only one diode and a current limiting resistor to indicate AC power.
  • Disadvantages
    • lower efficiency than full wave rectification
    • utilization of input source is half.
    • High ripple factor
    • input and ripple frequency is equal

Uses of half wave rectifier

A single diode as a rectifier is used for low-power applications where pure DC is not mandatory. For example rechargeable torch, and mosquito repellent. A half wave rectifier is also used to limit soldering iron temperature using half the efficiency of a half-wave rectifier. the half-wave rectifier is used as an amplitude demodulator in AM radio receivers using a high-speed diode. Half wave rectifier is also used in circuits in which frequency measurement and phase identification of AC signals is done.

One response to “Half Wave Rectifiers”

  1. […] half wave rectifier always skips one-half cycle. so its power efficiency is half that of full wave rectifier power efficiency. full wave rectifier output ripple frequency is double the input frequency. in the case of a half-wave rectifier, the ripple frequency is equal to the input frequency. Due to the double ripple frequency, the half-wave rectifier needs a big filter capacitor. half-wave rectifiers are not used fully for supply-sensitive electronic circuits. how ever simple resistive loads with reduced duty cycle are a major application of single diode rectifiers. […]

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