Diodes and Forward Bias

The Diode

• Diodes comprise semiconductive material, often silicon
• Half the diode is doped as a p-region, and the other half as an n-region
• The depletion region is present in between
• The p region is the anode, connected to a conductive terminal
• The n region is the cathode, connected to a second conductive terminal

Forward Bias

• To bias a diode, direct current (dc) voltage is applied
• Bias is an external voltage supply connected across the terminals of a device
• This extracts a device's response
• Forward bias allows current through the pn junction.
• The negative side of the bias voltage (VBIAS) is connected to the n region of the diode
• The positive side of VBIAS is connected to the p region
• The bias voltage, VBIAS, must exceed the barrier potential
• Because like charges repel, the negative side of the bias-voltage source "pushes" free electrons
• Free electrons are the majority carriers in the n region, toward the pn junction
• The bias-voltage source imparts energy to the free electrons
• Electrons overcome the barrier potential of the depletion region and move into the p region
• Once in the p region, conduction electrons have lost enough energy to combine with holes in the valence band
• The positive side of the bias-voltage source attracts valence electrons toward the left end of the p region
• Holes in the p region are the medium for valence electrons to move through the p region
• Valence electrons move from one hole to the next toward the left
• Holes effectively move to the right toward the junction, making up the hole current
• As electrons flow out of the p region through the external connection to the positive side of the bias-voltage source, they leave holes behind in the p region
• These electrons become conduction electrons in the metal conductor
• The energy electrons need to pass through the depletion region equals the barrier potential
• Electrons give up energy equivalent to the barrier potential when crossing the depletion region
• Energy loss results in a voltage drop across the pn junction equal to the barrier potential (0.7 V)
• Doped semiconductive material has dynamic resistance, which is an additional small voltage drop across the p and n regions; it is very small and usually negligible

Reverse Bias

• Reverse bias prevents current through the diode
• The positive side of the bias voltage (VBIAS) is connected to the n region of the diode
• The negative side of VBIAS is connected to the p region
• The depletion region is much wider than in forward bias or equilibrium
• Because unlike charges attract, the positive side of the bias-voltage source "pulls" the free electrons away from the pn junction
• As electrons flow toward the positive side of the voltage source, additional positive ions are created
• This results in both a widening of the depletion region and a depletion of majority carriers
• In the p region, electrons from the negative side of the voltage source enter as valence electrons
• Valence electrons move from hole to hole toward the depletion region, creating additional negative ions
• The flow of valence electrons can be viewed as holes being "pulled" toward the positive side
• The initial flow of charge carriers is transitional and lasts only a very short time after the reverse-bias voltage is applied
• As more of the n and p regions become depleted of majority carriers, the electric field increases until the potential across the depletion region equals the bias voltage, VBIAS
• The extremely small current in reverse bias is caused by minority carriers that are produced by thermally generated electron-hole pairs
• Free minority electrons in the p region are "pushed" toward the pn junction by the negative bias voltage
• They "fall down the energy hill" and combine with the minority holes in the n region as valence electrons, and flow toward the positive bias voltage, creating a small hole current

Reverse Breakdown

• If the external reverse-bias voltage is increased to the breakdown voltage, the reverse current increases drastically
• High reverse-bias voltage imparts energy to free minority electrons so that as they speed through the p region, they collide with atoms with enough energy to knock valence electrons out of orbit and into the conduction band
• Newly created conduction electrons are also high in energy and repeat the process
• The avalanche effect is the multiplication of conduction electrons; and reverse current can increase dramatically
• High heat will permanently damage the diode if the reverse current is not limited

Voltage-Current Characteristic of a Diode

• With 0 V across the diode, there is no forward current.
• When a forward-bias voltage is applied across a diode, there is forward current (IF)
• As the forward-bias voltage increases, the forward current and voltage across the diode gradually increase
• As the forward-bias voltage continues to increase, the current increases very rapidly, but the voltage across the diode increases only gradually above 0.7 V
• The forward current increases very little until the forward voltage reaches approximately 0.7 V
• After this point, the forward voltage remains nearly constant at approximately 0.7 V, but the forward current increases rapidly.
• Above 0.7 V, there is a slight increase in forward voltage as the current increases due mainly to the voltage drop across the dynamic resistance

The V-I Characteristic Curve

• A corresponds to a zero-bias condition.
• B corresponds to forward voltage that is less than the barrier potential of 0.7 V.
• C corresponds to forward voltage approximately equals the barrier potential.
• The resistance of the forward-biased diode is not constant over the entire curve
• Resistance is called dynamic or ac resistance (r'd), because resistance changes as you move along the V-I curve
• Below the knee of the curve, the resistance is greatest because the current increases very little for a change in voltage
• Above the knee, the resistance becomes smallest where the current has a large change for a given change in voltage
• The resistance begins to decrease in the region of the knee of the curve
• When reverse-bias voltage is applied across a diode, there is only a very small reverse current (IR) through the pn junction
• With 0 V across the diode, there is no reverse current
• As reverse-bias voltage increases, there is a small reverse current and the voltage increases.
• When bias voltage is increased to a value where the reverse voltage across the diode (VR) reaches the breakdown value, the reverse current begins to increase rapidly
• Breakdown is not a normal mode of operation for most pn junction devices
• The breakdown voltage for a diode depending on the doping level set by the manufacturer
• A typical rectifier diode has a 50V breakdown voltage, though some specialized diodes have a 5V breakdown voltage
• As temperature increases, the forward current increases for a given value of forward voltage
• The forward voltage decreases due to temperature for a given value of forward current
• Barrier potential decreases by 2 mV for each degree increase in temperature
• As temperature increases, the reverse-biased diode's reverse current increases, but remains extremely small
• Reverse current below breakdown current is typically negligible

Ideal Diode Model

• The ideal model is the least accurate diode approximation
• The ideal model can be represented by a simple switch
• The barrier potential, the forward dynamic resistance, and the reverse current are all neglected
• It is used when troubleshooting or when trying to figure out the operation of a circuit; it isn't concerned with more exact values of voltage or current

Practical Diode Model

• The practical model includes the barrier potential and is useful when designing basic diode circuits
• When forward-biased, the diode is equivalent to a closed switch in series with a small equivalent voltage source (VF) equal to the barrier potential (0.7 V) with the positive side toward the anode
• This equivalent voltage source represents the barrier potential that must be exceeded by the bias voltage before the diode will conduct and is not an active source of voltage
• When reverse-biased, the diode is equivalent to an open switch just as in the ideal model
• The barrier potential does not affect reverse bias
• Since the barrier potential is included and the dynamic resistance is neglected, the diode is assumed to have a voltage across it when forward-biased
• This is indicated by the portion of the curve to the right of the origin

Complete Diode Model

• The complete model of a diode is the most accurate approximation
• It includes the barrier potential, the small forward dynamic resistance and the large internal reverse resistance
• It is suited to design problems using a computer for simulation
• When forward-biased, it acts as a closed switch in series with the equivalent barrier potential voltage (VB) and the small forward dynamic resistance r'd
• When the diode is reverse-biased, it acts as an open switch in parallel with the large internal reverse resistance
• The reverse resistance is taken into account because it provides a path for the reverse current, which is included in this diode model
• The diode is assumed to have a voltage across it when forward-biased, since both the barrier potential and forward dynamic resistance are included
• This voltage consists of the barrier potential voltage plus the small voltage drop across the dynamic resistance
• This is indicated by the portion of the curve to the right of the origin
• The curve slopes because the voltage drop due to dynamic resistance increases as current increases

The Basic DC Power Supply

• All active electronic devices need a constant dc
• A power supply or battery typically provides this
• The dc power supply converts the standard 220V, 60 Hz ac voltage available at wall outlets into a constant dc voltage
• The ac input line voltage is stepped down to a lower ac voltage by a transformer
• A transformer changes ac voltages based on the turns ratio between the primary and secondary
• If the secondary has more turns than the primary, the output voltage will be higher and the current will be smaller
• If the secondary has fewer turns than the primary, the output voltage will be lower and the current will be higher
• The rectifier converts the ac input voltage to a pulsating de voltage, called a half-wave rectified voltage
• The filter eliminates the fluctuations in the rectified voltage and produces a relatively smooth de voltage
• The regulator is a circuit that maintains a constant de voltage for variations in the input line voltage or in the load (from a single semiconductor device - complex integrated circuits)
• The load is a circuit or device connected to the output of the power supply that operates from the power supply voltage and current

Half-Wave Rectifiers

• When the sinusoidal input voltage (Vin) goes positive, the diode is forward-biased, conducting current through the load resistor
• The current produces an output voltage across the load resistor (RL), with the same shape as the positive half-cycle of the input voltage
• When the input voltage goes negative, the diode is reverse-biased, and there is no current, so the voltage across the load resistor is 0 V
• Only the positive half-cycles of the ac input voltage appear across the load
• The output is a pulsating dc voltage with a frequency of 60 Hz
• The average value of the half-wave rectified output voltage is the value measured on a dc voltmeter
• The average value mathematically is determined by finding the area under the curve over a full cycle
• When the practical diode model is used, during the positive half-cycle, the input voltage must overcome 0.7 V
• This results in a half-wave output with a peak value that is 0.7 V less than the peak value of the input.
• Peak inverse voltage (PIV) equals the peak value of the input voltage
• The diode must be capable of withstanding this amount of repetitive reverse voltage.
• The maximum value of reverse voltage, designated as PIV, occurs at the peak of each negative alternation when the diode is reverse-biased
• A diode should be rated at least 20% higher than the PIV
• Transformer coupling allows the source voltage to be stepped down as needed
• Transformer coupling electrically isolates the ac source from the rectifier, thus, preventing a shock hazard
• The amount that the voltage is stepped down is determined by the turns ratio of the transformer

Full-Wave Rectifiers

• A full-wave rectifier allows unidirectional current through the load during the entire 360° of the input cycle, whereas a half-wave rectifier allows current through the load only during one-half
• The number of positive alternations that make up the full-wave rectified voltage is twice that of the half-wave voltage for the same time interval

Center-Tapped Full-Wave Rectifiers

• A center-tapped rectifier uses two diodes connected to the secondary of a center-tapped transformer.
• The input voltage is coupled through the transformer to the center-tapped secondary
• Half of the total secondary voltage appears between the center tap and each end of the secondary winding
• During the negative half-cycles, D2 is forward-biased and D1 is reverse-biased
• This equation is used for Peak Inverse Voltage, VD=-Vpsec + 0.7

Bridge Full-Wave Rectifiers

• A bridge full-wave rectifier has four diodes
• During the positive half-cycle of the input, D1 and D2 are forward-biased and conduct current. D3 and D4 are reverse-biased
• Vp(out) = Vp(sec - 1.4 V
• During the negative half-cycle of the input, D3 and D4 are forward-biased and conduct current. D1 and D2 are reverse-biased

Power Supply Filters

• A power supply filter eliminates the fluctuations in the output voltage of a half- or full-wave rectifier, and produces a constant-level dc voltage
• Filtering is necessary because electronic circuits require a constant source of dc voltage and current to provide power and biasing for proper operation
• Filters are implemented with capacitors
• During the positive first quarter-cycle of the input, the diode is forward-biased, allowing the capacitor to charge to within 0.7 V of the input peak
• When the input begins to decrease below its peak, the capacitor retains its charge and the diode becomes reverse-biased
• During the remaining part of the cycle, the capacitor can only discharge through the load resistance at a rate determined by the RLC time constant
• The RLC time constant is normally long compared to the period of the input
• During the first quarter of the next cycle, the diode will again become forward-biased the input voltage exceeds the capacitor voltage by approximately 0.7 V
• The variation in the capacitor voltage due to the charging and discharging is called the ripple voltage

Ripple

• The capacitor quickly charges at the beginning of a cycle and slowly discharges through RL after the positive peak of the input voltage
• Ripple is generally undesirable; thus, the smaller the ripple is more advantageous
• For a given input frequency, the output frequency of a full-wave rectifier is twice that of a half-wave rectifier, making a full-wave rectifier easier to filter because of the shorter time between peaks
• When filtered, the full-wave rectified voltage has a smaller ripple than does a half-wave voltage for the same load resistance and capacitor values
• The capacitor discharges less during the shorter interval between full-wave pulses
• Ripple factor (r) is an indication of the effectiveness of the filter
• The lower the ripple factor, the better the filter, and it can be lowered by increasing the value of the filter capacitor or increasing the load resistance

Voltage Regulators

• While filters can reduce the ripple from power supplies to low value, the most effective approach is a combination of a capacitor-input filter and a voltage regulator
• A voltage regulator, connected to the output of a rectifier, maintains a constant output voltage or current despite changes in the input, load current, or the temperature
• Regulations can be specified in terms of input and load regulation
• Line regulation specifies how much change in output for change in input
• Load regulation specifies how much change occurs in output over a certain range of load current values

Diode Limiters

• Limiters, or clippers, clip off portions of signal voltages above or below levels
• The level to which an ac voltage is limited can be adjusted by adding a bias voltage, VBIAS, in series with the diode

Diode Clampers

• A clamper adds a dc level to an ac voltage, and is also known as dc restorers
• Just after the negative peak, the diode is reverse-biased
• If the capacitor discharges during the period of the input wave, the clamping action is affected
• If the RC time constant is 100 times the period, the clamping action is excellent
• The net effect of the clamping action is that the capacitor retains a charge approximately equal to the peak value of the input less the diode drop
• The capacitor voltage acts essentially as a battery in series with the input voltage
• The dc voltage of the capacitor adds to the input voltage by superposition

Voltage Multipliers

• A voltage doubler is a voltage multiplier with a multiplication factor of two
• During the positive half-cycle of the secondary voltage, diode D1 is forward-biased and diode D2 is reverse-biased
• Capacitor C1 is charged to the peak of the secondary voltage (Vp) less the diode drop.
• During the negative half-cycle, diode D2 is forward-biased and D1 is reverse-biased
• Since C1 can't discharge, the peak voltage on C1 adds to the secondary voltage to charge C2
• When secondary voltage is positive, D1 is forward-biased and C1 charges to approximately Vp
• During the negative half-cycle, D2 is forward-biased and C2 charges to approximately Vp
• An additional diode-capacitor section to the half-wave voltage doubler creates a voltage tripler
• Adding still another diode-capacitor section produces an output four times the peak secondary voltage
• The output of voltage multipliers is a DC voltage approximately equal to the multiples of the peak value of the AC input voltage