Diode Circuits and Half-Wave Rectifiers

Chapter 2: Diode Circuits

• Diodes are used in rectifier circuits, which are the first stage of a DC power supply.
• DC voltage powers electronic devices like computers, televisions, and stereo systems.
• Battery chargers for devices like cell phones and laptops also use rectifier circuits.

Half Wave Rectifier with Ideal Diode

• Only the positive side of the input voltage reaches the load in a half-wave rectifier.
• The output voltage has a non-zero DC component.
• Rectification involves creating a DC voltage from an AC voltage.
• During the positive half cycle, the ideal diode is in forward bias.
• All the input voltage appears across the load resistor (RL).
• During the negative half cycle, the ideal diode is in reverse bias.
• There is no current flow, and the voltage across RL is zero.
• (V_{oavg} = V_{o,dc} = \frac{V_m}{\pi} )

Half Wave Rectifier with Ideal Diode and Filter Capacitor

• As the positive half cycle rises, the diode is in forward bias.
• The capacitor charges to ( V_m ) (peak voltage) very quickly through the diode.
• ( V_L(t) )follows ( v(t) ) during the charging phase.
• The capacitor charge equals to ( V_m )
• When ( v(t) ) passes its maximum point at ( T/4 ), the anode voltage becomes smaller than the cathode.
• The diode enters reverse bias.
• The capacitor discharges through ( R_L ) with a time constant of ( R_L C ).
• In the next cycle, when ( v(t) ) becomes larger than the capacitor voltage, the diode becomes forward biased again.
• Then, the capacitor recharges to ( V_m ).
• The output voltage ( v_L(t) ) is nearly a DC voltage close to ( V_m ), but contains fluctuations called 'ripple'.
• The ripple voltage and output DC voltage of a half-wave rectifier with an ideal diode and filter capacitor are:
  • ( v_r = \frac{V_m}{fR_LC} )
  • ( V_{dc} = V_m - \frac{1}{2}v_r )
• For a smoother DC voltage with reduced ripple, increase the value of the filter capacitor.
• For small ripple: ( V_{dc} \approx V_m )

Half Wave Rectifier with Real Diode

• The output voltage appears with a delay and goes to zero earlier compared to the ideal diode.
• The output voltage is smaller than the input voltage by the diode's forward voltage (0.7 V)
• The output DC voltage of a half-wave rectifier with a real diode and filter capacitor: ( V_{dc} = V_m - V_\gamma - \frac{1}{2}V_r )

Full Wave Rectifier with Ideal Diode

• Full-wave rectifiers invert the negative portions of the sine wave to generate a unipolar output signal during both halves of the input.
• A full wave rectifier uses 4 diodes in a bridge configuration.
• During the positive half cycle ( (0 < t < T/2) ), the output voltage ( v_L(t) = v(t) ).
• During the negative half cycle ( (T/2 < t < T) ), the output voltage ( v_L(t) = -v(t) ), making the cycle positive at the output.

Full Wave Rectifier with Ideal Diode and Filter Capacitor

• The ripple voltage and output DC voltage of a full-wave rectifier with an ideal diode and filter capacitor:
  • (V_r = \frac{V_m}{2fR_LC}), Ripple is halved compared to a half-wave rectifier.
  • (V_{dc} = V_m - \frac{1}{2}V_r ), Output DC voltage approximately equal to ( V_m).

Full Wave Rectifier with Real Diode

• The maximum output voltage for a full-wave rectifier with a real diode without a filter capacitor is: ( V_{o(max)} = V_m - 2V_\gamma )

Full Wave Rectifier with Real Diode and Filter Capacitor

• The ripple voltage and output DC voltage of full-wave rectifier with real diode and filter capacitor:
  • (v_r = \frac{V_m}{2fR_LC} ) (ripple has halved compared to half-wave rectifier)
  • (V_{dc} = V_m - 2V_\gamma - \frac{1}{2}V_r )

Clippers

• Clipper circuits are used to eliminate signal portions above or below a specified level.
• Half-wave rectifiers are a form of clipper circuit.
• Clippers can limit voltage at the input of an electronic circuit to prevent transistor breakdown.
• Clipper applications include shaping waveforms, converting signals to square waves, and frequency doubling.

Clipping Circuits with Ideal Diodes

• If input voltage ( \lt V ), Diode is OFF, ( V_o = V_i )
• If input voltage ( \gt V ), Diode is ON, ( V_o = V )
• The circuit in this configuration clips the top of the waveform.
• The voltage can be either positive or negative.
• When the input voltage ( \lt -V ), the diode is ON, and ( V_o = -V )
• When the input voltage ( \gt -V ), the diode is OFF, and ( V_o = V_i )
• This configuration clips the bottom of the waveform.
• The voltage can be positive or negative.
• Dual Clipper: A circuit using two diodes to clip both the top and bottom of a waveform.
• In a dual diode clipper, ( V_1 ) and ( V_2 ) can be positive or negative, but ( V_1 > V_2 ).

Clipping Circuits with Real Diodes

• Consider the forward voltage of real diodes.

Clampers

• Clamping shifts the entire signal voltage by a DC level.
• At a steady state, the output waveform is an exact replica of the input, but shifted by a DC value.
• An electronic circuit that alters the DC level of a signal without changing its shape.
• It moves the entire signal up or down to set either the positive or negative peak to the desired level.
• Clamping adds or subtracts a DC component to the input signal.
• The basic difference between clipping and clamping:
  • Clippers remove unwanted signal portions.
  • Clampers shift the entire signal up or down.
• During the negative half cycle: the diode is forward biased, so no signal appears at the output.
• In the forward biased condition: the diode allows the electric current to flow to the capacitor, and charge it.
• The capacitor charged in inverse polarity with the input voltage.
• As input current or voltage decreases, the capacitor holds the charge until the diode remains forward biased.
• During the positive half cycle: the diode is reverse biased, so the signal appears at the output.
• In reverse biased condition: The diode does not allow electric current flow.
• Input current directly flows toward the output which is: ( V_o = V_m + V_m = 2V_m )
• A minimum discharge capacity is required: ( RC >> T )
• Peak-to-peak amplitudes of both the input/output signal are the same as total swing.

Clamping Circuits without a DC Voltage

• The circuit includes positive/negative clampers, ideal/real diode.

Clamping Circuits with a DC Voltage

• The circuit includes positive/negative clampers, ideal/real diodes.

Logic Gates

• Logic gates built using diodes, including OR and AND gates.

OR Gate

• If voltage at inputs A/B are either 0 V (Low, 0) , or ( V ) (High, 1)
• When one/both of the inputs are at ( V ): One/both diodes are forward, and the output is ( V ).
• Output is High if A OR B is High.

AND Gate

• When one/both of the inputs are at 0 V: One/both diodes are forward, and the output is 0 V
• If both inputs are at ( V ): There is no current flow in diodes, and the output equals ( V )
• Output is High only if both A AND B are High.

Other Types of Diodes

• Specialized diodes and their applications are introduced:

Diode Breakdown

• Zener diode is introduced
• the diode current in reverse bias ( reverse saturation current) in normal operation is very small and is usually neglected.
• At large reverse voltages, the diode cannot tolerate the strong filled and reaches to breakdown.
• Breakdown in lower voltages can be useful if the current is controlled.

Zener Diode

• Zener breakdown occurs when the depletion region is very narrow.
• Zener diodes are designed to be used in breakdown.
• After breakdown, Zener diodes provide a nearly constant reverse voltage.
• Zener diodes are used to regulate or stabilize a DC voltage and for clipping waveforms.
• Limit Current, prevents destructive breakdown.
• ( V_zI_z < P_{max} ) , which is the maximum power that the diode can tolerate (power rating).

Zener Limiter

• Zener diodes as voltage regulation in AC applications to limit voltage swings.
• Way#1: shows a Zener diode limits the positive peak, during the negative alternation, the Zener acts as a forward-biased diode, and limits the negative voltage.
• Way#2: Turn Zener diode: the negative peak is limited by Zener action and the positive voltage is limited to ( +0.7 V ).
• Way#3: The two-back-to back Zener diodes can limit both peaks by the Zener Voltage.