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Published byRafael Fairall Modified about 1 year ago

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Diode Applications Half wave rectifier and equivalent circuit with piece-wise linear model Ideal V c R f vivi vivi v i = V M sin ( t)

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Half Wave Rectifier We initially consider the diode to be ideal, such that V C =0 and R f =0

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Half Wave Rectifier The (ideal) diode conducts for v i >0 and since R f =0 v 0 v i For v i < 0 the (ideal) diode is an open circuit (it doesn’t conduct) and v 0 0.

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Half Wave Rectifier In this simplified (ideal diode) case the input and output waveforms are as shown The diode must withstand a peak inverse voltage of V M

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Half Wave Rectifier The average d.c. value of this half-wave- rectified sine wave is

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Half Wave Rectifier So far this rectifier is not very useful. Even though the output does not change polarity it has a lot of ripple, i.e. variations in output voltage about a steady value. To generate an output voltage that more closely resembles a true d.c. voltage we can use a reservoir or smoothing capacitor in parallel with the output (load) resistance.

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Smoothed Half Wave Rectifier Circuit with reservoir capacitor Output voltage The capacitor charges over the period t 1 to t2 when the diode is on and discharges from t2 to t3 when the diode is off.

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Smoothed Half Wave Rectifier When the supply voltage exceeds the output voltage the (ideal) diode conducts. During the charging period (t 1 < t< t 2 ) v o = V M sin ( t) (The resistance in the charging circuit is strictly R f which we have assumed to be zero. Even for a practical diode R f C will be very small)

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Smoothed Half Wave Rectifier When the supply voltage falls below the output voltage the diode switches off and the capacitor discharges through the load. During the discharge period (t 2 < t< t 3 ) and v o = V M exp {- t ’ /RC} where t’= t- t 2 At time t 3 the supply voltage once again exceeds the load voltage and the cycle repeats

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Smoothed Half Wave Rectifier The resistance in the discharge phase is the load resistance R. RC can be made large compared to the wave period. The change in output voltage (or ripple) can then be estimated using a linear approximation to the exponential discharge.

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Smoothed Half Wave Rectifier v o = V M exp {- t ’ /RC} V M [ 1- (t ’ /RC)] The change in voltage V is therefore approximately given by V M t ’ /RC For a the half wave rectifier this discharge occurs for a time (t 3 - t 2 ) close to the period T = 1/f, with f= frequency. Giving the required result:

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Smoothed Half Wave Rectifier We can define a ripple factor as where V d.c. = (V M - V/2) The lower the ripple factor the better

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Half Wave Rectifier If we don’t consider the diode to be ideal then from the equivalent circuit we obtain, for v i >V c: v i – V c – i R f - iR =0 i.e. Giving

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Non-Ideal Half Wave Rectifier VMVM

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A plot of v 0 against v i is known as the transfer characteristic VCVC vivi R/(R + R f )

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Non-Ideal Half Wave Rectifier We usually have R>> R f so that R f can be neglected in comparison to R. Often V M >> V c so V c can also be neglected. The transfer characteristic then reduces to v 0 v i

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Full-Wave (Bridge) Rectifier We initially consider the diodes to be ideal, such that V C =0 and R f =0 The four-diode bridge can be bought as a package vi

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Full-Wave (Bridge) Rectifier During positive half cycles v i is positive. Current is conducted through diodes D1, resistor R and diode D2 Meanwhile diodes D3 and D4 are reverse biased. vi

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Full-Wave (Bridge) Rectifier During negative half cycles v i is negative. Current is conducted through diodes D3, resistor R and diode D4 Meanwhile diodes D1 and D2 are reverse biased. vi

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Full-Wave (Bridge) Rectifier Current always flows the same way through the load R. Show for yourself that the average d.c. value of this full-wave-rectified sine wave is V AV = 2V M / (i.e. twice the half-wave value)

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Full-Wave (Bridge) Rectifier Two diodes are in the conduction path. Thus in the case of non-ideal diodes v o will be lower than v i by 2V C. As for the half-wave rectifier a reservoir capacitor can be used. In the full wave case the discharge time is T/2 and

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Diode Clipper Circuits These circuits clip off portions of signal voltages above or below certain limits, i.e. the circuits limit the range of the output signal. Such a circuit may be used to protect the input of a CMOS logic gate against static.

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Diode Clipper Circuits

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When the diode is off the output of these circuits resembles a voltage divider

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Diode Clipper Circuits If R S << R L The level at which the signal is clipped can be adjusted by adding a d.c. bias voltage in series with the diode. v0 viv0 vi

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For instance see example sheet 1, Q11

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Diode Clipper Circuits Let’s look at a few other examples of clipper circuits.

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Diode Clamper Circuits The following circuit acts as a d.c. restorer. see Q9, example sheet1.

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Diode Clamper Circuits A bias voltage can be added to pin the output to a level other than zero.

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