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Rectifier Half Wave Rectifier Full Wave Rectifier Centre ... · PDF file half wave rectifier works in the positive half cycles. Positive Half Cycle In the positive half cycles when

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  • Rectifiers

    A diode is used to pass current in a single direction. Alternating current is a current which flows

    in both directions. In some applications we need dc (direct current) power supply. A method to

    obtain dc supply is by using batteries. But it is not economical at all times. It is possible to obtain

    dc from ac supply .That process is known as rectification. Rectification is of two types:

    1. Half wave rectification

    2. Full wave rectification

    In a half wave rectifier only one half cycle of ac voltage is used. Unlike a half wave rectifier, a

    full wave rectifier conducts in both half cycles of ac voltage. A full wave rectifier can be

    implemented in two ways

    1. Full wave centre tap rectifier

    2. Full wave bridge rectifier

    Rectifier

    Half Wave Rectifier Full Wave Rectifier

    Centre Tap Rectifier Bridge Rectifier

  • Half Wave Rectifier

    The half rectifier consist a step down transformer, a diode connected to the transformer and a

    load resistance connected to the cathode end of the diode. The circuit diagram of half wave

    transformer is shown below:

    The main supply voltage is given to the transformer which will increase or decrease the voltage

    and give to the diode. In most of the cases we will decrease the supply voltage by using the step

    down transformer here also the output of the step down transformer will be in AC. This

    decreased AC voltage is given to the diode which is connected serial to the secondary winding of

    the transformer, diode is electronic component which will allow only the forward bias current

    and will not allow the reverse bias current. From the diode we will get the pulsating DC and give

    to the load resistance RL.

    Working of Half Wave Rectifier

    The input given to the rectifier will have both positive and negative cycles. The half rectifier will

    allow only the positive half cycles and omit the negative half cycles. So first we will see how

    half wave rectifier works in the positive half cycles.

    Positive Half Cycle

    ο‚· In the positive half cycles when the input AC power is given to the primary winding of

    the step down transformer, we will get the decreased voltage at the secondary winding

    which is given to the diode.

  • ο‚· The diode will allow current flowing in clock wise direction from anode to cathode in the

    forward bias (diode conduction will take place in forward bias) which will generate only

    the positive half cycle of the AC.

    ο‚· The diode will eliminate the variations in the supply and give the pulsating DC voltage to

    the load resistance RL. We can get the pulsating DC at the Load resistance.

    Negative Half Cycle

    ο‚· In the negative half cycle diode will go in to the reverse bias. In the reverse bias the diode

    will not conduct so, no current flow through diode from anode to cathode, and we cannot

    get any power at the load resistance.

    Half Wave Rectifier Circuit Analysis

    1. Peak Inverse Voltage (PIV)

    Peak Inverse Voltage (PIV) rating of a diode is important in its design stages. It is the maximum

    voltage that the rectifying diode has to withstand, during the reverse biased period.

    When the diode is reverse biased, during the negative half cycle, there will be no current flow

    through the load resistor RL. Hence, there will be no voltage drop through the load resistance RL

    which causes the entire input voltage to appear across the diode. Thus VSMAX, the peak secondary

    voltage, appears across the diode. Therefore,

    𝑃𝐼𝑉 = π‘‰π‘†π‘šπ‘Žπ‘₯

    2. Average and Peak Currents in the diode

    By assuming that the voltage across the transformer secondary be sinusoidal of peak values

    VSMAX, instantaneous value of the voltage given to the rectifier can be written as

    𝑉𝑆 = π‘‰π‘†π‘šπ‘Žπ‘₯ sin πœ”π‘‘

    For Instantaneous value of voltage applied to Half Wave Rectifier, assuming that the diode has a

    forward resistance of RF ohms and infinite reverse resistance value, the current flowing through

    the output load resistance RL is

  • 𝑖 = πΌπ‘šπ‘Žπ‘₯ sin πœ”π‘‘ π‘“π‘œπ‘Ÿ 0 ≀ πœ”π‘‘ ≀ πœ‹

    𝑖 = 0 π‘“π‘œπ‘Ÿ πœ‹ ≀ πœ”π‘‘ ≀ 2πœ‹

    Maximum current flowing through the diode

    πΌπ‘šπ‘Žπ‘₯ = π‘‰π‘†π‘šπ‘Žπ‘₯

    𝑅𝐹 + 𝑅𝐿

    3. DC Output Current

    The dc output current is given as

    𝐼𝑑𝑐 = 1

    2πœ‹ 𝑖 𝑑 πœ”π‘‘

    2πœ‹

    0

    𝐼𝑑𝑐 = 1

    2πœ‹ 𝑖 𝑑 πœ”π‘‘

    πœ‹

    0 + 𝑖 𝑑 πœ”π‘‘

    2πœ‹

    πœ‹

    𝐼𝑑𝑐 = 1

    2πœ‹ 𝑖 𝑑 πœ”π‘‘

    πœ‹

    0 + 0

    𝐼𝑑𝑐 = 1

    2πœ‹ πΌπ‘šπ‘Žπ‘₯ sin πœ”π‘‘ 𝑑 πœ”π‘‘

    2πœ‹

    0

    𝐼𝑑𝑐 = πΌπ‘šπ‘Žπ‘₯

    2πœ‹ sin πœ”π‘‘ 𝑑 πœ”π‘‘

    2πœ‹

    0

    𝐼𝑑𝑐 = πΌπ‘šπ‘Žπ‘₯

    2πœ‹ βˆ’ βˆ’1 βˆ’ 1

    𝐼𝑑𝑐 = πΌπ‘šπ‘Žπ‘₯

    πœ‹

    𝐼𝑑𝑐 = 0.318πΌπ‘šπ‘Žπ‘₯

    Substituting the value of IMAX for the equation IMAX = VSMAX/(RF + RL), we have

    𝐼𝑑𝑐 = π‘‰π‘†π‘šπ‘Žπ‘₯

    𝑅𝐹+𝑅𝐿 πœ‹

    if RL >> RF 𝐼𝑑𝑐 = π‘‰π‘†π‘šπ‘Žπ‘₯

    πœ‹π‘…πΏ

    4. DC Output Voltage

    Dc value of voltage across the load is given by

  • 𝑉𝑑𝑐 = 𝐼𝑑𝑐𝑅𝐿

    𝑉𝑑𝑐 = π‘‰π‘†π‘šπ‘Žπ‘₯

    𝑅𝐹+𝑅𝐿 πœ‹ 𝑅𝐿

    𝑉𝑑𝑐 = π‘‰π‘†π‘šπ‘Žπ‘₯

    𝑅𝐿 𝑅𝐹 𝑅𝐿

    +1 πœ‹ 𝑅𝐿

    𝑉𝑑𝑐 = π‘‰π‘†π‘šπ‘Žπ‘₯

    𝑅𝐹 𝑅𝐿

    +1 πœ‹

    if RL >> RF

    𝑉𝑑𝑐 = π‘‰π‘†π‘šπ‘Žπ‘₯

    πœ‹

    5. Root Mean Square (RMS) Value of Current

    RMS value of current flowing through the diode is given as

    πΌπ‘Ÿπ‘šπ‘  = 1

    2πœ‹ 𝑖2 𝑑 πœ”π‘‘

    2πœ‹

    0

    πΌπ‘Ÿπ‘šπ‘  = 1

    2πœ‹ 𝑖2 𝑑 πœ”π‘‘

    πœ‹

    0 + 𝑖2 𝑑 πœ”π‘‘

    2πœ‹

    πœ‹

    πΌπ‘Ÿπ‘šπ‘  = 1

    2πœ‹ 𝑖2 𝑑 πœ”π‘‘

    πœ‹

    0 + 0

    πΌπ‘Ÿπ‘šπ‘  = 1

    2πœ‹ πΌπ‘šπ‘Žπ‘₯2 sin2 πœ”π‘‘ 𝑑 πœ”π‘‘

    πœ‹

    0

    πΌπ‘Ÿπ‘šπ‘  = πΌπ‘šπ‘Žπ‘₯

    2

    2πœ‹ sin2 πœ”π‘‘ 𝑑 πœ”π‘‘

    πœ‹

    0

    πΌπ‘Ÿπ‘šπ‘  = πΌπ‘šπ‘Žπ‘₯

    2

    2πœ‹

    1βˆ’cos 2πœ”π‘‘

    2 𝑑 πœ”π‘‘

    πœ‹

    0

    πΌπ‘Ÿπ‘šπ‘  = πΌπ‘šπ‘Žπ‘₯

    2

    4πœ‹ 1 𝑑 πœ”π‘‘ βˆ’ cos 2πœ”π‘‘ 𝑑 πœ”π‘‘

    πœ‹

    0

    πœ‹

    0

    πΌπ‘Ÿπ‘šπ‘  = πΌπ‘šπ‘Žπ‘₯

    2

    4πœ‹ πœ‹ βˆ’ 0

  • πΌπ‘Ÿπ‘šπ‘  = πΌπ‘šπ‘Žπ‘₯

    2

    2

    πΌπ‘Ÿπ‘šπ‘  = πΌπ‘šπ‘Žπ‘₯

    2

    Substituting the value of Imax

    πΌπ‘Ÿπ‘šπ‘  = π‘‰π‘†π‘šπ‘Žπ‘₯

    2 𝑅𝐹+𝑅𝐿

    6. Root Mean Square (RMS) Value of Output Voltage

    RMS value of voltage across the load is given as

    π‘‰πΏπ‘Ÿπ‘šπ‘  = πΌπ‘Ÿπ‘šπ‘  𝑅𝐿

    π‘‰πΏπ‘Ÿπ‘šπ‘  = π‘‰π‘†π‘šπ‘Žπ‘₯

    2 𝑅𝐹+𝑅𝐿 𝑅𝐿

    π‘‰πΏπ‘Ÿπ‘šπ‘  = π‘‰π‘†π‘šπ‘Žπ‘₯

    2 𝑅𝐹 𝑅𝐿

    +1 𝑅𝐿 𝑅𝐿

    if RL >> RF

    π‘‰πΏπ‘Ÿπ‘šπ‘  = π‘‰π‘†π‘šπ‘Žπ‘₯

    2

    7. Rectification Efficiency

    Rectification efficiency is defined as the ratio between the output power to the ac input power.

    πœ‚ = DC power delivered to the load

    AC input power from the transformer =

    𝑃𝑑𝑐 π‘ƒπ‘Žπ‘

    DC power delivered to the load,

    𝑃𝑑𝑐 = 𝐼𝑑𝑐 2 𝑅𝐿

    𝑃𝑑𝑐 = πΌπ‘šπ‘Žπ‘₯

    πœ‹

    2

    𝑅𝐿

    AC power input to the transformer,

  • π‘ƒπ‘Žπ‘ = Power dissipated in diode junction + Power dissipated in load resistance RL

    π‘ƒπ‘Žπ‘ = πΌπ‘Ÿπ‘šπ‘  2 RF + Irms

    2 RL

    π‘ƒπ‘Žπ‘ = πΌπ‘šπ‘Žπ‘₯

    2

    2

    RF + πΌπ‘šπ‘Žπ‘₯

    2

    2

    RL

    π‘ƒπ‘Žπ‘ = πΌπ‘šπ‘Žπ‘₯

    2

    4 𝑅𝐹 + 𝑅𝐿

    So, Rectification Efficiency,

    πœ‚ = 𝑃𝑑𝑐

    π‘ƒπ‘Žπ‘

    πœ‚ = πΌπ‘šπ‘Žπ‘₯ 2

    πœ‹2 𝑅𝐿

    πΌπ‘šπ‘Žπ‘₯ 2

    4 𝑅𝐹+𝑅𝐿

    πœ‚ = 4

    πœ‹2 𝑅𝐿

    𝑅𝐹+𝑅𝐿

    πœ‚ = 0.406

    1+ 𝑅𝐹 𝑅𝐿

    if RL >> RF

    πœ‚ = 0.406

    πœ‚ = 40.6%

    The maximum efficiency that can be obtained by the half wave rectifier is 40.6%. This is

    obtained if RF is neglected.

    8. Ripple Factor

    Ripple factor is a measure of the remaining alternating components in a

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