Chapter 16: Semiconductor Devices
In December 1947, in a laboratory at Bell Telephone Laboratories in the United States, two physicists named John Bardeen and Walter Brattain pressed two fine metal contacts onto a small piece of germanium. Germanium is a semiconductor — a material that conducts electricity far better than an insulator but far worse than a metal. When they applied a voltage, they found something remarkable: a very small signal fed into the device came out much larger. A tiny input was controlling a much bigger output.
The device was called a transistor. William Shockley, who led the group, went on to develop the junction transistor, the design that became the basis of almost all modern electronics. The three of them shared the Nobel Prize in Physics in 1956.
Before this, electronic amplification needed bulky glass vacuum tubes that grew hot, consumed a lot of power and burned out often. The transistor did the same job with a fingernail-sized piece of doped semiconductor. Today, the phone in your pocket contains billions of transistors, along with diodes that convert your wall socket’s AC into DC, LEDs that light your screen, and solar cells that turn sunlight into current. All of them are built on one idea you already met in Class XI — the p-n junction.
Diagram
Fig. 16.0 – A p-n junction chip at the centre with arrows radiating out to a mobile charger, a solar panel, an LED lamp and a logic circuit board.
As you work through this chapter, you will find the answer to each of these questions.
16.1 Introduction
The Diode as an Electrical Switch
In Class XI you studied the p-n junction diode. It is formed by joining a p-type semiconductor (which has holes as majority carriers) and an n-type semiconductor (which has free electrons as majority carriers). At the junction, a thin region called the depletion region is formed, and it opposes the flow of charge carriers across the junction.
When the diode is forward biased — that is, when the p-side is connected to the positive terminal of the supply and the n-side to the negative terminal — the depletion region becomes narrow. Once the applied voltage crosses a small value called the knee voltage, the diode conducts easily. In this state the diode behaves as a closed switch, and current flows in the diode circuit.
When the diode is reverse biased — the p-side connected to the negative terminal and the n-side to the positive terminal — the depletion region becomes wider. The diode now behaves as an open switch, and only a negligibly small current flows in the circuit. (If the reverse voltage is pushed far beyond a certain critical value, called the breakdown voltage, the behaviour changes completely; this is taken up in Section 16.3.)
This one-way switching action of a diode is the property that allows it to be used as a rectifier.
Why AC Must Be Converted into DC
Generation of AC at a power station is more cost effective than producing DC power. The transmission of AC power over long distances is also more economic than transmitting DC power. This is why the supply that reaches our homes is alternating.
This AC voltage varies sinusoidally, which means its magnitude keeps changing and its direction reverses in every cycle. In India, the mains supply is 230 V and has a frequency of 50 Hz. A frequency of 50 Hz means the voltage completes 50 full cycles in one second, reversing its direction 100 times in that second.
However, there are many electronic gadgets such as a TV, or a mobile charger, which require a DC supply. Transistors, integrated circuits and LEDs inside them work only with a steady, one-directional voltage. Therefore, it is necessary to convert AC voltage into a DC voltage.
The AC mains voltage is rectified by using junction diodes to obtain a DC voltage. In this chapter, we will study the use of diode as a rectifier and also different types of rectifiers. We will also study filters which remove the AC component from the rectified voltage, and voltage regulators which provide the required DC voltage.
Inside a DC Power Supply: Stage by Stage
The working of a simple rectifier circuit is shown as a block diagram in Fig. 16.1, along with the shape of the waveform obtained at the end of each stage.
Diagram
Fig. 16.1 – Block diagram of a simple rectifier circuit: AC mains (230 V rms, 50 Hz) → transformer → diode rectifier → filter → voltage regulator → load, with output waveforms (a) sinusoidal AC, (b) pulsating DC, (c) DC with small ripple, (d) steady pure DC shown below the respective blocks.
The AC mains supply is connected to the primary of a transformer, and its secondary is connected to a rectifier circuit. The transformer brings the high mains voltage down to the smaller voltage level that the circuit actually needs.
The AC voltage coming from the secondary of the transformer is a sinusoidal wave, shown as waveform (a) in Fig. 16.1. This is converted into a DC voltage by a diode rectifier. The result is shown next as a pulsating wave (b) — the current now flows in one direction only, but its value keeps rising and falling instead of staying steady.
The output of the rectifier therefore still contains some AC component. This AC component in the DC output of a rectifier is called ripple, and it is shown at the output of the rectifier in Fig. 16.1.
The ripple is removed by using a filter circuit. The output of the filter circuit, waveform (c), is almost a pure DC. (It can still contain some ripple — a filter reduces the fluctuation greatly but does not wipe it out completely.)
The voltage regulator circuit shown after the filter restricts the output voltage to the desired value, so that it does not drift when the input supply varies or when the load draws more current. The output voltage at this stage, waveform (d), is a steady, pure DC.
In examination questions, this block diagram is often given with one block left blank, or with the four waveforms shuffled, and you are asked to identify the missing stage or match each waveform to its block. It is therefore worth remembering not just the order of the blocks, but the reason each one is there — what defect in the signal that particular block is meant to correct.
16.2 p-n Junction Diode as a Rectifier
An AC voltage varies sinusoidally, that is, both its value and its direction change within one cycle. During one half of the cycle the current is driven one way round the circuit, and during the next half it is driven the opposite way. Such a voltage or current is called bidirectional.
A rectifier converts this bidirectional voltage or current into a unidirectional voltage or current — one that may still rise and fall in magnitude, but never reverses its direction.
The p-n junction diode is ideally suited for this job, because it conducts in one direction and blocks in the other. Placed in the path of an alternating voltage, it simply refuses to let the reversed half of the cycle through.
There are two types of rectifier circuits: 1) half wave rectifier and 2) full wave rectifier. They differ in how much of the input AC waveform they are able to make use of, and we study each of them in the following subsections.
16.2.1 Half Wave Rectifier
A simple half wave rectifier circuit using only one diode is shown in Fig. 16.2.
Diagram
Fig. 16.2 – Circuit diagram of a half wave rectifier: AC source feeding the primary of a transformer, secondary coil AB in series with diode D and load resistance R_L across output terminals X and Y.
The Circuit and the Role of the Transformer
The secondary coil AB of a transformer is connected in series with a diode D and the load resistance \(R_\text{L}\). The output DC voltage is taken across this load resistance.
The use of a transformer here has two advantages. First, it allows us to step up or step down the AC input voltage as per the requirement of the circuit — a circuit that needs only a few volts should not be fed the full mains voltage. Second, it isolates the rectifier circuit from the mains supply to reduce the risk of electric shock, since there is no direct metallic connection between the mains wiring and the circuit you touch; energy is transferred only through the magnetic field linking the two coils.
How the Diode Selects One Half Cycle
The AC voltage across the secondary coil AB changes its polarities after every half cycle. This means that the ends A and B take turns at being the higher-potential end.
When the positive half cycle begins, the voltage at the point A is at higher potential with respect to that at the point B. The diode D is therefore forward biased. It conducts, working as a closed switch, and current flows through the circuit and through the load resistance.
When the negative half cycle begins, the potential at the point A is lower with respect to that at the point B. The diode is now reverse biased, and therefore it does not conduct, working as an open switch. No current passes through the circuit during this half cycle, and so no voltage appears across \(R_\text{L}\).
Hence, the diode conducts only in the positive half cycles of the AC input. It blocks the current during the negative half cycles. The waveform for input and output voltages are shown in Fig. 16.3.
Diagram
Fig. 16.3 – Waveform of input and output signals for a half wave rectifier: full sinusoidal input above, and below it an output showing only the positive half cycles with gaps in place of the negative half cycles.
Notice in Fig. 16.3 that the output waveform is the input waveform with the negative humps simply missing. In this way, current always flows through the load \(R_\text{L}\) in the same direction for alternate positive half cycles.
Hence a DC output voltage obtained across \(R_\text{L}\) is in the form of alternate pulses. It is unidirectional, but for one half of every cycle it is zero — the circuit throws away half of the energy supplied to it.
16.2.2 Full Wave Rectifier
As discussed in the previous section, the output of a half wave rectifier is available only in alternate positive half cycles of the AC input. All negative half cycles are lost, and so the efficiency of a half wave rectifier is very poor. Half of the energy supplied by the transformer never reaches the load at all. Therefore, a rectifier circuit using two diodes is more useful.
In a full wave rectifier, current flows through the load in the same direction during both the half cycles of input AC voltage. This is because the full wave rectifier circuit consists of two diodes conducting alternately. When one diode is blocking, the other one is conducting, so the load is never left without current.
Figure 16.4 shows a typical circuit of a full wave rectifier. The circuit consists of a centre tapped transformer and diodes \(D_1\) and \(D_2\).
Diagram
Fig. 16.4 – Circuit diagram of a full wave rectifier: centre tapped transformer with terminals A and B and a centre tap, diode D1 connected from A and diode D2 connected from B, both joined to load resistance R_L returning to the centre tap.
A centre tapped transformer is a transformer whose secondary coil has an extra connection brought out from the exact middle of the winding. This centre point acts as the common return path for the circuit, and it divides the secondary into two equal halves whose voltages are always opposite in polarity to each other.
The Output Waveform
The input and output waveforms of a full wave rectifier are shown in Fig. 16.5. First waveform is input AC. The second waveform shows the output when the diode \(D_1\) conducts, and the third waveform shows the output when diode \(D_2\) conducts. The fourth waveform shows the total output waveform of the full wave rectifier.
Diagram
Fig. 16.5 – Four stacked waveforms for a full wave rectifier: sinusoidal input, output during D1 conduction, output during D2 conduction, and the combined output showing a continuous series of positive humps.
Notice in Fig. 16.5 that the second and third waveforms fit into each other’s gaps. Adding them gives an unbroken chain of positive humps, with no idle gaps in between.
Advantages of a Full Wave Rectifier
- Rectification takes place in both the cycles of the AC input.
- The ripple in a full wave rectifier is less than that in a half wave rectifier.
The second advantage follows directly from the first. Since the output humps come twice as often and there are no gaps between them, the output voltage does not fall as far before the next hump arrives, so the fluctuation left in it is smaller.
16.2.3 Ripple Factor
The output of a rectifier consists of a small fraction of an AC component along with DC, called the ripple. This ripple is undesirable and is responsible for the fluctuations in the rectifier output. Figure 16.6 (a) shows the ripple in the output of a rectifier.
Diagram
Fig. 16.6 (a) – Ripple in the output of a rectifier: a wavy output voltage plotted against time, with the steady level marked V_DC and the peak-to-peak fluctuation about it marked V_ripple.
As Fig. 16.6 (a) shows, the output can be thought of as two parts added together: a steady DC level \(V_\text{DC}\), and a small wavy AC part riding on top of it. It is this wavy part that we call the ripple, and it is what prevents the output from being pure DC.
The effectiveness of a rectifier depends upon the magnitude of the ripple component in its output. A smaller ripple means that the rectifier is more effective, because the output is then closer to a genuinely steady voltage.
To compare two rectifiers fairly, we need a number rather than a description. This number is obtained by comparing the size of the unwanted AC part with the size of the useful DC part.
The ratio of root mean square (rms) value of the AC component to the value of the DC component in the rectifier output is known as the ripple factor, i.e.,
\[\text{Ripple factor} = \frac{\text{r.m.s. value of AC component}}{\text{value of DC component}}\]
Here the rms value is used because the AC component keeps changing in magnitude and averages out to zero over a cycle; the rms value gives its effective size. Both quantities in the ratio are voltages measured in volt (V), so the ripple factor itself has no unit — it is a pure number.
Since a smaller ripple factor indicates a better rectifier, this quantity provides the numerical justification for the second advantage of the full wave rectifier listed in the previous subsection.
16.2.4 Filter Circuits
The output of a rectifier is in the form of pulses, as shown in the fourth waveform in Fig. 16.5. The output is unidirectional, but the output does not have a steady value. It keeps fluctuating due to the ripple component present in it.
Most electronic circuits cannot work properly on such a supply. A radio would hum, a measuring instrument would give unsteady readings, and a digital circuit could misread its own logic levels. A filter circuit is therefore used to remove the ripple from the output of a rectifier.
A filter circuit is a circuit which removes the AC component or the ripple from a rectifier output and allows only the DC component.
A Capacitor Filter
The simplest and most common filter uses a single capacitor connected in parallel with the load, as shown in Fig. 16.6 (b).
Diagram
Fig. 16.6 (b) – Filter circuit with capacitor: AC input feeding a block marked “Rectifier”, with capacitor C connected in parallel with load resistance R_L across the output terminals X and Y, giving DC output.
As shown in Fig. 16.6 (b), the pulsating DC voltage of a rectifier output is applied across the capacitor. Recall that a capacitor stores charge when the voltage across it rises and returns that charge to the circuit when the voltage across it tries to fall. It therefore behaves rather like a small reservoir placed across the load.
As the voltage across the capacitor rises, the capacitor gets charged to point A and supplies current to the load resistance. At the end of quarter cycle, the capacitor gets charged to the peak voltage shown as \(V_\text{p}\) in Fig. 16.6 (c) of the rectified output voltage.
Diagram
Fig. 16.6 (c) – Output waveform after filtration: the rectified humps shown dotted, with the actual output following the peak value V_p and dipping only slightly between successive peaks, marking points A and B.
Now, the rectifier voltage begins to decrease, so that the capacitor starts discharging through the load resistance and the voltage across it begins to drop. Voltage across the load decreases only slightly, up to the point B, because the next voltage peak recharges the capacitor immediately.
The reason the drop is small is a matter of timing. The rectifier delivers a fresh peak every half cycle, which for a 50 Hz supply is only a few milliseconds later, whereas the capacitor discharges through the load resistance much more slowly than that. So the capacitor barely begins to empty before it is topped up again.
This process is repeated again and again and the output voltage waveform takes the form shown in Fig. 16.6 (c). Comparing this waveform with the deep humps of Fig. 16.5, it is clear that the fluctuation left in the output is now only a small ripple riding on a nearly steady voltage.
Regulated and Unregulated Power Supplies
This output is an unregulated DC waveform. Voltage regulator circuits are used to obtain a regulated DC supply.
The capacitor filter circuit is widely used because of its low cost, small size and light weight. This type of filter is preferred for small load currents. It is commonly used in battery eliminators.
When a power supply is connected to a load, it is noticed that there is a drop in the output voltage. This happens because the load now draws current, and the capacitor is being emptied faster than before.
A power supply whose output changes when a load is connected across it is called an unregulated power supply. When the output of a power supply remains steady even after connecting a load across it, it is called a regulated power supply.
There are many ways in which a power supply can be regulated. A commonly used voltage regulator circuit uses a Zener diode. We will now discuss a Zener diode first, and then try to understand how it can be used as a voltage regulator.
16.3 Special Purpose Junction Diodes
So far we have used the p-n junction diode only as a switch that conducts one way. By altering the doping levels, the choice of semiconductor material or the packaging, the same junction can be made to do quite different jobs.
In this section we will study some of the common special purpose junction diodes such as,
- Zener diode, 2) Photo diode, 3) Solar cell, 4) Light Emitting Diode (LED).
16.3.1 Zener Diode
A Zener diode works on the principle of junction breakdown. The other diodes mentioned above make use of photosensitivity, a very important and useful property of semiconductors. We take up the Zener diode first, because it is the device that completes the power supply we began building in Section 16.2.
Junction Breakdown
In Class XI we have studied that when reverse bias voltage of an ordinary junction diode is increased beyond a critical voltage, the reverse current increases sharply to a high value. This critical voltage is called reverse breakdown voltage. The diode is damaged at this stage.
The damage in an ordinary diode is not caused by the breakdown itself but by the heat produced. Once a large current flows while a large reverse voltage is still present across the junction, the power dissipated at the junction becomes very high and the diode is destroyed. We will now discuss what happens when there is a junction breakdown.
Electrical breakdown of any material (metal, semiconductor or even insulator) can be due to 1) Avalanche breakdown or 2) Zener breakdown. We will discuss only the Zener breakdown in some details.
Zener Breakdown
When the reverse voltage across a p-n junction diode is increased, the electric field across the junction increases. This results in a force of attraction on the negatively charged electrons at the junction.
Covalent bonds which hold the semiconductor together are broken due to this force, and electrons are removed from the bonds. These free electrons are then available for electrical conduction and result in a large current.
When the applied voltage is increased, the electric field across the junction also increases, and more and more electrons are removed from their covalent bonds. Thus, a net current is developed which increases rapidly with increase in the applied voltage.
Zener breakdown occurs in diodes which are heavily doped. The depletion layer is narrow in such diodes. Zener breakdown does not result in damage of a diode.
The reason a narrow depletion layer matters is that the electric field is the voltage divided by the width over which it acts. If the same reverse voltage is squeezed across a much thinner depletion layer, the field strength becomes very large, and the bonds break at a comparatively low applied voltage. Because this voltage is low, the power dissipated at the junction stays within safe limits, and the diode survives the breakdown.
Zener Diode Characteristic
A Zener diode is a p-n junction diode designed to work in the breakdown region. It is used as a voltage regulator or a voltage stabiliser. Figure 16.7 (a) shows the circuit symbol of a Zener diode.
Diagram
Fig. 16.7 (a) – Circuit symbol of a Zener diode: the usual diode triangle and bar, with the bar bent at both ends to form a shape like the letter Z.
Its I-V characteristic is shown in Fig. 16.7 (b).
Diagram
Fig. 16.7 (b) – I-V characteristic curve of a Zener diode: forward characteristic in the first quadrant like an ordinary diode; in the third quadrant, a small reverse current until the breakdown voltage V_Z, where the curve turns almost vertically downwards.
As can be seen from the characteristic, a Zener diode behaves like a normal diode when forward biased. When reverse biased, it shows a breakdown. This breakdown, discussed previously, occurs at a voltage called the Zener voltage \(V_\text{Z}\), measured in volt (V).
The current suddenly increases if the applied voltage is increased beyond the Zener voltage. It is interesting to note that the voltage remains constant at \(V_\text{Z}\), for increasing current, once the Zener breakdown occurs.
This is the single most important feature of the device, and it is worth reading the graph carefully. Beyond breakdown, the curve in Fig. 16.7 (b) runs almost vertically. A vertical portion on an I-V graph means that a large change along the current axis corresponds to almost no change along the voltage axis. In other words, the diode will accept whatever current the circuit sends through it while holding the voltage across itself fixed at \(V_\text{Z}\).
This property of the Zener diode is used in a voltage regulator. The Zener voltage \(V_\text{Z}\) depends upon the amount of doping. For a heavily doped diode, the depletion layer is thin and the breakdown occurs at a lower reverse voltage. A lightly doped diode has higher breakdown voltage.
This is how manufacturers produce Zener diodes of different rated voltages — by controlling the doping level during fabrication, a diode can be given a breakdown voltage of 3.3 V, 5.1 V, 12 V and so on, and the user simply picks the value needed.
The Zener diodes with breakdown voltage of less than 6 V operate mainly at Zener breakdown region. Those with voltage greater than 6 V operate mainly in avalanche breakdown region (not discussed here), but both are called Zener diode.
Zener Diode as a Voltage Regulator
When a Zener diode is operated in the breakdown region (reverse bias), voltage across it remains almost constant even if the current through it changes by a large amount. A voltage regulator maintains a constant voltage across a load regardless of variations in the applied input voltage and variations in the load current.
Figure 16.8 shows a typical circuit diagram of a voltage regulator using a Zener diode.
Diagram
Fig. 16.8 – Voltage regulator using a Zener diode: input source V_in in series with resistance R_S, the Zener diode connected in reverse bias across the output, and load resistance R_L connected in parallel with the Zener diode.
A Zener diode of breakdown voltage \(V_\text{Z}\) is connected in reverse bias to an input voltage source \(V_\text{in}\) (with \(V_\text{in} > V_\text{Z}\)). The resistor \(R_\text{S}\) connected in series with the Zener diode limits the current flow through the diode.
The load resistance \(R_\text{L}\) is connected in parallel with the Zener diode, so that the voltage across \(R_\text{L}\) is always the same as the Zener voltage, (\(V_\text{R} = V_\text{Z}\)). This follows from the fact that components in parallel always have the same potential difference across them. So if the Zener holds its own voltage constant, the load voltage is automatically held constant as well.
We will try to understand how voltage is regulated using such a circuit by looking at three separate situations.
- When the input voltage changes. If the input voltage increases, the current through \(R_\text{S}\) and the Zener diode also increases. This results in an increase in the voltage across the resistance \(R_\text{S}\), but the voltage across the Zener diode does not change.
The series resistance \(R_\text{S}\) absorbs the output voltage fluctuations and maintains a constant voltage across the load resistance. This is because the Zener voltage remains constant even though the current through the Zener diode changes when it is in the breakdown region.
Hence the output voltage remains constant irrespective of the change in the input voltage. Thus, the Zener diode acts as a voltage regulator.
Think of it as a sharing arrangement. The input voltage is divided between \(R_\text{S}\) and the Zener diode. Since the Zener refuses to take more than \(V_\text{Z}\), every extra volt at the input has to appear across \(R_\text{S}\), and the load never sees it.
- When the load changes. When the input voltage is constant but the load resistance \(R_\text{L}\) decreases, the load current increases. This extra current cannot come from the source, because the drop across \(R_\text{S}\) will not change as the Zener is within its regulating range. The additional load current is due to a decrease in the Zener current \(I_\text{Z}\).
In other words, the Zener diode acts as a reservoir of spare current. The total current arriving through \(R_\text{S}\) stays the same, and the Zener simply gives up a part of its own share to the load whenever the load asks for more.
- When there is no load. When there is no load in the circuit, \((R_\text{L} = \infty)\), the load current will be zero, \((I_\text{L} = 0)\), and all the circuit current passes through the Zener diode. This results in maximum dissipation of power across the Zener diode.
Similarly, a small value of the series resistor \(R_\text{S}\) results in a larger diode current when a load resistance \(R_\text{L}\) of a large value is connected across it. This will increase the power dissipation requirement of the diode.
The value of the series resistance \(R_\text{S}\) is so selected that the maximum power rating of the Zener diode is not exceeded when there is no load or when the load is very high.
The voltage across the Zener diode remains constant at its breakdown voltage \(V_\text{Z}\) for all the values of Zener current \(I_\text{Z}\) as long as the current persists in the breakdown region. Hence, a regulated DC output voltage \(V_\text{O} = V_\text{Z}\) is obtained across \(R_\text{L}\) whenever the input voltage remains within a minimum and a maximum voltage.
The maximum power rating \((P_\text{Z})\) of a Zener diode is given by
\[P_\text{Z} = I_\text{Z(max)} V_\text{Z}\]
where \(P_\text{Z}\) is the maximum power the diode can dissipate, measured in watt (W); \(I_\text{Z(max)}\) is the maximum permissible Zener current in ampere (A); and \(V_\text{Z}\) is the Zener voltage in volt (V). This is simply the familiar relation \(P = VI\) applied to the diode, and it is the equation that tells a designer how much current the diode may safely be allowed to carry.
While designing a Zener regulator, the value of series resistance is determined by considering the specification of the Zener diode.
Applications of Zener Diode
The Zener diode is used when a constant voltage is required. It has a number of applications such as: voltage regulator, fixed reference voltage provider in transistor biasing circuits, peak clipper or limiter in a wave shaping circuit, protector against meter damage from accidental fluctuations, etc.
16.3.2 Photo Diode
A photodiode is a special type of a p-n junction diode which converts light energy into electrical energy. It generates current when exposed to light. It is also called as photodetector or a photosensor. It operates in reverse biased mode.
Figure 16.9 (a) shows the circuit symbol of a photodiode. Note the two arrows drawn pointing towards the symbol — they indicate light falling on the device.
Diagram
Fig. 16.9 (a) – Circuit symbol of a photodiode: ordinary diode symbol with anode and cathode marked, and two arrows pointing inwards towards the junction to represent incident light.
Only minority current flows through a photodiode. This single statement explains why the device is always used in reverse bias, as we shall see shortly. Figure 16.9 (b) shows a schematic of the structure of a photodiode.
Diagram
Fig. 16.9 (b) – Schematic structure of a photodiode: an n-region below with a shallow p-region above it, a diffusion mask of SiO2 and a silicon nitride coating on the top surface, with arrows showing light entering the exposed window.
The p-n junction of a photodiode is placed inside a glass material so that only the junction of a photodiode is exposed to light. Other part of the diode is generally painted with an opaque colour or covered. This ensures that the electrical effect produced is caused only by the light meant to be measured, and not by stray light striking other parts of the device. Figure 16.9 (c) shows a typical photodiode.
Diagram
Fig. 16.9 (c) – Photograph-style illustration of a typical photodiode: a small metal can package with a square transparent window on top and two leads below.
Working Principle of Photodiode
When a p-n junction diode is reverse biased, a reverse saturation current flows through the junction. The magnitude of this current is constant for a certain range of reverse bias voltages.
This current is due to the minority carriers on its either side. Electrons are minority carriers in the p-region, and holes are minority carriers in the n-region of a diode. Although they are few in number, the reverse bias field sweeps every one of them across the junction as soon as it appears there.
The reverse current depends only on the concentration of the minority carriers and not on the applied voltage. This is the key point. Increasing the reverse voltage does not increase this current, because the voltage is already collecting every available minority carrier; the only way to change the current is to change how many minority carriers there are.
This current is called the dark current in a photodiode, because it flows even when the photodiode is not illuminated. Figure 16.10 schematically shows working of a photodiode.
Diagram
Fig. 16.10 – Working of a photodiode: p-type and n-type regions with the depletion region between them, incident light arrows falling on the depletion region, electron-hole pairs being generated and swept in opposite directions, connected to a reverse bias battery.
What Light Does to the Junction
When a p-n junction is illuminated, electron-hole pairs are generated in the depletion region. The energy of the incident photons should be larger than the band gap of the semiconductor material used to fabricate the photodiode.
A photon of light of frequency \(\nu\) carries energy \(E = h\nu\), where \(h\) is Planck’s constant. The band gap is the minimum energy needed to lift an electron out of a covalent bond and into the conduction band. If a photon carries less than this, it cannot break a bond and simply passes through without producing any carriers, however bright the light may be.
The electrons and the holes are separated due to the intrinsic electric field present in the depletion region. This field already exists across the depletion region of every p-n junction and is strengthened by the reverse bias, so no external effort is needed to pull the new carriers apart.
The electrons are attracted towards the anode and the holes are attracted towards the cathode. More carriers are available for conduction and the reverse current is increased.
The reverse current of a photodiode depends on the intensity of the incident light. Thus, the reverse current can be controlled by controlling the concentration of the minority carriers in the junction — and light is exactly the tool that controls that concentration. A brighter light means more photons per second, which means more electron-hole pairs per second, which means a larger reverse current.
Figure 16.11 shows the I-V characteristic of a photodiode. It clearly shows the relation between intensity of illumination and the reverse current of a photodiode.
Diagram
Fig. 16.11 – I-V characteristic of a photodiode: reverse bias voltage on the negative V-axis, reverse current in microampere downwards, with a set of nearly horizontal curves, one for each level of illumination, the dark current curve lying closest to the axis.
Notice in Fig. 16.11 how each curve is almost flat. Moving along a curve means changing the reverse voltage, and it changes the current hardly at all. Moving from one curve to the next means changing the illumination, and it changes the current a great deal. The photodiode is therefore a device whose current is set by light, not by voltage.
The total current passing through a photodiode is the sum of the photocurrent and the dark current. Figure 16.12 shows the graphical relation between the reverse current of a photodiode and the intensity of illumination incident on the photodiode. The sensitivity of the device can be increased by minimizing the dark current, since the dark current is an unwanted background reading that is present even with no light at all.
Diagram
Fig. 16.12 – Relation between the reverse current of a photodiode and the intensity of illumination: reverse current I_R on the vertical axis against light intensity in mW/cm2, rising from the dark current value I_D and levelling off at the saturation current I_S, for a constant reverse voltage V_R.
As you can see from the curve, reverse current increases initially with increase in the intensity of illumination. It reaches a constant value after certain voltage is reached. This constant value is called the saturation current of the photodiode.
Dark Resistance
One more term associated with a photodiode is its dark resistance \(R_\text{d}\). It is the resistance of a photodiode when it is not illuminated.
Dark resistance of a photodiode \((R_\text{d})\) is defined as the ratio of the maximum reverse voltage and its dark current.
\[R_\text{d} = \frac{\text{Maximum reverse voltage}}{\text{Dark current}}\]
Here the maximum reverse voltage is measured in volt (V) and the dark current in ampere (A), so the dark resistance is in ohm (\(\Omega\)). Since the dark current is extremely small, the dark resistance of a good photodiode is very large — which is another way of saying that in darkness, the device is very nearly an open switch.
Advantages of Photodiode
- Quick response when exposed to light.
- Linear response. The reverse current is linearly proportional to intensity of incident light.
- High speed of operations.
- Light weight and compact size.
- Wide spectral response. For example, photodiodes made from Si respond to radiation of wavelengths from 190 nm (UV) to 1100 nm (IR).
- Relatively low cost.
The second point is the one that makes the photodiode a measuring instrument rather than a mere switch. Because the current is proportional to the intensity, reading the current tells you how bright the light is, and not merely whether light is present.
Disadvantages of Photodiode
- Its properties are temperature dependent, similar to many other semiconductor devices.
- Low reverse current for low illumination levels.
Applications of Photodiode
A photodiode has many applications in a number of fields, ranging from domestic applications to industrial applications, due to its linear response. The basic concept used in almost all these devices and applications is that a photodiode conducts whenever light strikes it and it stops conducting the moment light stops. Some applications of a photodiode are:
- Counters and switches.
- Burglar alarm systems.
- Detection of visible and invisible radiations.
- Circuits in which fast switching and high-speed operations are required.
- Fiber optic communication systems.
- Optocouplers, used to provide an electric isolation between two electronic circuits.
- Photo sensors/detectors, for accurate measurement of light intensity.
- Safety electronics like fire and smoke detectors.
16.3.3 Solar Cell or Photovoltaic Cell
Solar energy can be used in many ways. It is pollution free and available free of cost. Two major types of devices converting solar energy in usable form are:
Photo thermal devices, which convert the solar energy into heat energy. These are mostly used for providing hot water.
Photo voltaic devices, which convert solar energy into electrical energy using solar cells.
The distinction is worth fixing in the mind. A photo thermal device is satisfied with the heating effect of sunlight, whereas a photovoltaic device must produce charge carriers and drive them round a circuit. Only the second kind involves a p-n junction, and it is the second kind that we will discuss in some details. It is also known as photovoltaic cell.
Light incident on a solar cell produces both a current and a voltage to generate electric power. A solar cell thus works as a source of DC power. Solar cells can supply power for electric equipment at remote places on earth or aboard a satellite or a space station.
Structure of a Solar Cell
Figure 16.13 (a) shows the schematic structure of a solar cell.
Diagram
Fig. 16.13 (a) – Schematic structure of a solar cell: sunlight falling on the top surface, antireflection coating and front contact on the thin n-side (emitter), the thick p-side (base) below it, rear contact at the bottom, with load resistance R_L connected across the two contacts.
It consists of a p-n junction. The n-side of the junction faces the solar radiation. The p-side is relatively thick and is at the back of the solar cell.
Both the p-side and the n-side are coated with a conducting material, since the current generated inside must be led out to the external circuit. The n-side is coated with antireflection coating which allows visible light to pass through it.
The main function of this coating is to reflect the IR (heat) radiations and protect the solar cell from heat. This is necessary, because the electronic properties of semiconductors are sensitive to fluctuations in temperature. This coating works as the electrical contact of the solar cell.
The contact on the n-side is called the front contact, and that at the p-side is called the back contact or the rear contact.
The n-side of a solar cell is thin so that the light incident on it reaches the depletion region where the electron-hole pairs are generated. If this layer were thick, most of the light would be absorbed well before reaching the junction, the carriers produced there would simply recombine, and no useful current would result.
Choosing the Material
Material used for fabricating a solar cell should fulfil two important requirements.
Firstly, it must be a photosensitive material which absorbs light and raises electrons to a higher energy state.
Secondly, the higher energy electrons thus generated should be taken from the solar cell into an external circuit. The electrons then dissipate their energy while passing through the external circuit and return to the solar cell.
This second requirement is easy to overlook, but it is what turns a light-absorbing material into a power source. Absorbing light is of no use unless the excited electrons can be led out, made to do work in an external circuit, and returned. Almost all photovoltaic devices use semiconductor materials in the form of a p-n junction, because such a junction provides both the absorption and the built-in field needed to collect the carriers.
Working of a Solar Cell
When light is incident on a solar cell, the following sequence of events takes place.
- Electron-hole pairs are generated in the depletion region of the p-n junction. These are photo-generated carriers.
- The electrons and holes are separated and collected at the cathode and the anode respectively.
- The carriers are accumulated and generate a voltage across the solar cell.
- Power thus produced is dissipated (utilised) in the load resistance or in the circuit connected across the solar cell.
Current produced in a solar cell is called the ‘light-generated current’, or ‘photo-generated current’. This is a two-step process.
The first step is the absorption of incident photons to generate electron-hole pairs. Electron-hole pairs will be generated in the solar cell provided that the incident photon has energy greater than that of the band gap. A photon carrying less energy than the band gap cannot break a bond at all, and passes through the material without contributing anything.
Normally, the electrons and holes thus produced recombine and will be lost. There will be no generation of current or power. An ordinary illuminated piece of semiconductor therefore produces no voltage — the carriers it creates simply fall back into their bonds within a very short time.
However, the photo-generated electrons (in the p-type material), and the photo-generated holes (in the n-type material) are spatially separated and prevented from recombination in a solar cell. This separation is the second step, and it is the whole reason a junction is needed.
How the Carriers Are Separated
This separation of carriers is possible due to the intrinsic electric field of the depletion region. Figure 16.13 (b) shows this schematically.
Diagram
Fig. 16.13 (b) – Separation of carriers in a solar cell: p-region and n-region with the depletion region between them, a light-generated electron in the p-region being swept across the junction into the n-region, and a light-generated hole being swept the other way into the p-region.
When the light-generated electron in the p-type region reaches the p-n junction, it is swept across the junction by the electric field at the junction. It reaches the n-type region, where it is now a majority carrier.
Similarly, the light generated hole reaches the p-type region and becomes a majority carrier in it. Once a carrier has crossed over, it is among its own kind and is comparatively safe from recombination, which is exactly why the separation makes the current possible.
The positive and negative charges are thus accumulated on the p-region and the n-region of the solar cell, which can be used as a voltage source. When the solar cell is connected to an external circuit, the light-generated carriers flow through the external circuit.
V-I Characteristic of Solar Cell or Photovoltaic Cell
Figure 16.14 shows the I-V characteristic of solar cell when illuminated. This is drawn in the fourth quadrant because a solar cell supplies current to the load.
Diagram
Fig. 16.14 – V-I characteristic of a solar cell drawn in the fourth quadrant: the curve meeting the current axis at the short-circuit current I_sc and the voltage axis at the open circuit voltage V_oc, with the maximum power point marked on the curve between them.
The fourth quadrant is used because voltage and current have opposite signs here. In every device studied so far, current was pushed into the device by an external source; a solar cell instead pushes current out into the circuit. It is a source, not a load, and the sign convention records that fact.
The power delivered to the load is zero when the load is short-circuited. The intersection of the curve with the I-axis is the short-circuit current, \(I_\text{sc}\), corresponding to a given light intensity. Here the current is largest, but the voltage across the cell has been reduced to zero, and the product \(VI\) is therefore zero.
The intersection of the curve with the V-axis is the open circuit voltage, \(V_\text{oc}\), corresponding to given light intensity. Again, power delivered to the load is zero when the load is open — this time the voltage is largest but no current flows.
However, there is a point on the curve where power delivered
\[P_\text{L} = V_\text{oL} \cdot I_\text{sc}\]
is maximum. Somewhere between the two extremes, the product of voltage and current reaches its greatest value, and a well-designed solar installation always tries to operate the panel near this point.
Criteria for Selection of Material for Solar Cell
- Its band gap should be between 1.0 eV to 1.8 eV.
- It should have high optical absorption (conversion of light into electrical energy).
- It should have good electrical conductivity.
- Material should be easily available.
The first condition is a compromise. If the band gap is too large, only the most energetic photons in sunlight can create carriers and most of the light is wasted. If it is too small, many photons can create carriers but each carrier is produced with very little energy, so the voltage obtained is small.
Most materials used for fabrication of solar cells have a band gap of about 1.5 eV. These include: Si (\(E_g\) = 1.1 eV), GaAs (\(E_g\) = 1.43 eV), CdTe (\(E_g\) = 1.45 eV), CuInSe (\(E_g\) = 1.04 eV).
Solar cells used in domestic and space applications are mostly Si based solar cells. Solar cells are non-polluting, they require less maintenance and last longer. They have a higher cost of installation, and are low in efficiency.
Use of Solar Cell
Solar cells are used for charging batteries during day time so that batteries can supply power during night. They are useful at remote places, for supplying power to various electronic equipment from calculators to satellites and space stations, to supply power to traffic signals, in communication stations, and in Lux meter to measure intensity of light.
16.3.4 Light Emitting Diode / LED
The Light Emitting Diode, or LED as it is more commonly called, is a diode which emits light when large forward current passes through it.
Notice at once that this device works in forward bias, unlike the photodiode and the solar cell of the previous subsections. An LED is not a detector of light but a source of it, and the energy it radiates is supplied by the external circuit.
Figure 16.15 (a) shows the circuit symbol of LED, and Fig. 16.15 (b) shows a schematic construction of a typical LED.
Diagram
Fig. 16.15 (a) – Circuit symbol of an LED: ordinary diode symbol with anode A and cathode K marked, and two arrows pointing away from the junction to represent emitted light.
Construction of an LED
The construction of a LED is different from that of a normal diode. The n-region is heavily doped than the p-region of the p-n junction, so that a large number of electrons is available to be injected across the junction.
The LED p-n junction is encased in a dome-shaped transparent case, so that light is emitted uniformly in all directions and internal reflections are minimized. Light that is reflected back into the device would be absorbed and wasted, so the shape of the case is a matter of efficiency and not merely of appearance.
Metal electrodes attached on either side of the p-n junction serve as contacts for external electrical connection. The larger leg of a LED is the positive electrode or anode. This is a practical detail worth remembering, because an LED connected the wrong way round simply does not light.
Diagram
Fig. 16.15 (b) – Schematic structure of an LED: the p-n junction sitting in a reflecting cavity on the cathode lead, connected by a fine wire bond to the anode lead, the whole enclosed in a dome-shaped epoxy lens, with anode (+) and cathode (–) legs below.
LEDs with more than 2 pins are also available, such as 3, 4 and 6 pin configurations, to obtain multi-colours in the same LED package. Surface mounted LED displays are available that can be mounted on PCBs.
LED is fabricated in such a way that light emitted is not reabsorbed into the material. It is ensured that the electron-hole recombination takes place on the surface for maximum light output. If recombination occurred deep inside the crystal, the light produced would have to travel through the material to escape, and much of it would be absorbed on the way.
Working of a LED
Figure 16.16 schematically shows the emission of light when an electron-hole pair combines.
Diagram
Fig. 16.16 – Emission of light from an LED: p-type and n-type regions with the depletion region between them under forward bias, free electrons entering from the n-side, recombining with holes near the junction, and light emerging upwards from the recombination region.
When the diode is forward biased, electrons from the semiconductor’s conduction band recombine with holes from the valence band, releasing sufficient energy to produce photons which emit a monochromatic (single colour) light.
It is worth being clear about where the energy comes from. An electron in the conduction band possesses more energy than one sitting in a valence bond. When it falls into a hole, it must give up the difference, which is roughly the band gap energy of the material. In an ordinary silicon diode this energy is released mostly as heat; in an LED, made of a suitable material, it is released as a photon instead.
Because of the thin layer, a reasonable number of these photons can leave the junction and emit coloured light.
The amount of light output is directly proportional to the forward current. Thus, higher the forward current, higher is the light output. This is easy to see physically: a larger current means more electrons crossing the junction every second, hence more recombination events every second, hence more photons.
Colour and the Choice of Material
LEDs are fabricated by using compound semiconductors made with elements such as gallium, phosphorus and arsenic. By varying the proportions of these elements in the semiconducting materials, it is possible to produce light of different wavelengths.
For example, when LED is manufactured using aluminium gallium arsenide (AlGaAs), it emits infrared radiations. LED made using gallium arsenic phosphide (GaAsP) produces either red or yellow light, whereas LED made by using aluminium gallium phosphide (AlGaP) emits red or green light, and zinc selenide (ZnSe) produces blue light.
The reason the material decides the colour is that the photon carries away an energy set by the band gap, and the energy of a photon fixes its frequency and hence its wavelength. A wider band gap gives a more energetic photon, which means a shorter wavelength, moving the colour from infrared towards red, then green, then blue. Changing the applied voltage cannot change the colour; only changing the material can.
I-V Characteristics of Light Emitting Diodes
Figure 16.17 shows the I-V characteristic of LED. It is similar to the forward characteristic of an ordinary diode. The LED starts conducting after its cut-in voltage is reached.
Diagram
Fig. 16.17 – Light Emitting Diode (LED) I-V characteristic curve: forward current in mA plotted against forward voltage V, showing negligible current up to the cut-in voltage and then a steeply rising curve.
Notice in Fig. 16.17 how sharply the curve rises once the cut-in voltage is passed. A small further increase in voltage produces a very large increase in current. This steepness is precisely why an LED must never be connected directly across a supply — a slightly higher voltage than intended would drive a destructive current through it.
Advantages of LED
LED is a solid state light source.
- Energy efficient: More light output for lesser electrical power. LEDs are now capable of producing 135 lumens/watt.
- Long Lifetime: 50,000 hours or more if properly manufactured.
- Rugged: LEDs are also called Solid State Lights (SSL), as they are made of solid material with no filament or tube or bulb to break.
- Almost no warm up period. LEDs start emitting light in nanoseconds.
- Excellent colour rendering: Colours produced by LED do not fade out, making them perfect for displays and retail applications.
- Environment friendly: LEDs do not contain mercury or other hazardous substances.
- Controllable: Brightness and colour of light emitted by LEDs can be controlled.
LED lamps, bulbs and street lighting are becoming very popular these days because of the very high efficiency of LEDs in terms of light output per unit input power (in milli Watts), as compared to the incandescent bulbs. So for general purpose lightings, white light is preferred.
Commercially available white LEDs are normally manufactured by using the technique of wavelength conversion. It is a process which partly or completely converts the radiation of a LED into white light. There are many ways of wavelength conversion. One of these methods uses blue LED and yellow phosphor. In this method of wavelength conversion, a LED which emits blue colour is used to excite a yellow colour phosphor. This results in the emission of yellow and blue light, and this mixture of blue and yellow light gives the appearance of white light. This method is the least expensive method for producing white light.
Disadvantages of LED
Hazardous blue light quality, temperature dependence, voltage sensitivity, high initial cost.
Application of LED
An LED is used in a variety of ways, such as burglar alarm system, counters, optical communication, indicator lamps in electric equipment, display screen of a cell phone handset, LED television, vehicle head lamps, domestic and decorative illumination, and street lighting.
16.4 Bipolar Junction Transistor (BJT)
A junction transistor is a semiconductor device having two junctions and three terminals. The current in a transistor is carried by both the electrons and the holes. Hence, it is called a bipolar junction transistor.
A transistor has three doped regions which form a structure with two back to back p-n junctions. There are two types of transistors, namely, (a) n-p-n transistor and (b) p-n-p transistor. The circuit symbols and schematic representation of the two types of transistors are shown in Fig. 16.18 (a).
Diagram
Fig. 16.18 (a) – Circuit symbols of a BJT: p-n-p symbol on the left with the emitter arrow pointing inwards towards the base, and n-p-n symbol on the right with the emitter arrow pointing outwards, both with emitter, base and collector terminals labelled.
In the circuit symbol, the emitter and collector are differentiated by drawing an arrow. Emitter has an arrow either pointing inwards or outwards. The direction of the arrow indicates the direction of the conventional current in the transistor.
For a n-p-n transistor, the arrow points away from the base to the emitter, and for a p-n-p transistor, it points away from the emitter, towards the base. This is shown in Fig. 16.18 (a). The arrow is therefore not a decoration — it is the quickest way of telling, from a circuit diagram alone, which type of transistor is being used and which way the current flows.
Structure of the Two Types
In an n-p-n transistor, a p-type semiconductor (base) layer separates two layers of the n-type semiconductor (emitter and collector). It is obtained by growing a thin layer of p-type semiconductor in between two relatively thick layers of n type semiconductor.
Similarly, for a p-n-p transistor, an n-type semiconductor (base) layer separates two layers of p-type semiconductor (emitter and collector). It is obtained by growing a thin layer of n-type semiconductor in between two relatively thick layers of p type semiconductor.
The three layers of a transistor are the Emitter (E), the Base (B) and the Collector (C), as shown in Fig. 16.18 (b).
Diagram
Fig. 16.18 (b) – Structure of a BJT: an n-p-n block with a thin p-type base between two thicker n-type regions marked emitter and collector, and below it a p-n-p block with a thin n-type base between two p-type regions.
A transistor can be thought to be two junction diodes connected back to back. This two-diode analogy is shown in Fig. 16.18 (c).
Diagram
Fig. 16.18 (c) – Two-diode analogy of a BJT: two diodes joined at the base terminal B, drawn for p-n-p and for n-p-n, with terminals E and C at the two outer ends.
The Three Regions and Why They Differ
Emitter: It is a thick heavily doped layer. This supplies a large number of majority carriers for the current flow through the transistor. Heavy doping is essential, because the whole current through the device begins here.
Base: It is the thin, central layer which is lightly doped compared to the emitter. Being thin and lightly doped means it contains few carriers of the opposite kind, so very few of the carriers passing through it are lost to recombination.
Collector: It is on the other side of the base. It is also a lightly doped layer. Its doping is about ten times lighter than that of the base. Its area is larger than that of the emitter and the base. This layer collects a major portion of the majority carriers supplied by the emitter. The collector also helps dissipation of any small amount of heat generated. The larger area serves both purposes — it catches carriers that have spread out while crossing the base, and it provides more surface from which heat can escape.
Depletion region: The depletion regions are formed at the emitter-base junction and the base-collector junction.
Current: The emitter current \(I_\text{E}\), the base current \(I_\text{B}\) and the collector current \(I_\text{C}\) are as indicated in Fig. 16.19 (d).
Resistance: The emitter-base junction has low resistance, while the base-collector junction has a high resistance. This difference between a low-resistance input and a high-resistance output turns out to be the key to the transistor’s usefulness as an amplifier, as we shall see in Section 16.4.2.
Biasing the Two Junctions
There are two p-n junctions in a transistor, the emitter-base (E-B) junction and the collector-base (C-B) junction, and they can be biased in different ways.
In the most common method of biasing a transistor, the emitter base junction is forward biased and the collector base junction is reverse biased. This helps an easy flow of the majority carriers supplied by the emitter through the transistor.
Working of a n-p-n Transistor
Electrons are the majority carriers in the emitter of a n-p-n transistor. The emitter current \(I_\text{E}\) is due to electrons.
The current flowing through the E-B junction is large because it is forward biased. The current flowing through the B-C junction is also large, though the junction is reverse biased. It is interesting to know how this is possible, because a reverse biased junction on its own carries almost no current at all.
Figure 16.19 (a) shows a typical biasing circuit of a n-p-n transistor.
Diagram
Fig. 16.19 (a) – Biasing of an n-p-n transistor: battery V_EB forward biasing the emitter-base junction on the left and battery V_CB reverse biasing the collector-base junction on the right, with “many electrons” marked in the emitter and collector regions and “few electrons” in the thin base.
At the instant the forward bias is applied to the E-B junction, electrons in the emitter region (n-type) have not entered the base region (p-type), as shown in Fig. 16.19 (b).
Diagram
Fig. 16.19 (b) – Majority carriers in emitter: n-p-n block with electrons shown crowded in the emitter region only, none yet in the base, with V_EB and V_CB connected.
When the biasing voltage \(V_\text{BE}\) is greater than the barrier potential (0.6–0.7 V for silicon transistors, which are commonly used), many electrons enter the base region and form the emitter current \(I_\text{E}\), as shown in Fig. 16.19 (c).
Diagram
Fig. 16.19 (c) – Injection of majority carriers into base: electrons from the emitter now crossing into the thin base region of the n-p-n structure under the applied bias.
Why Most of the Current Reaches the Collector
These electrons can now flow in two directions. They can either flow through the base circuit and constitute the base current \((I_\text{B})\), or they can also flow through the collector circuit and contribute towards the collector current \((I_\text{C})\).
The base current is small (about 5% of \(I_\text{E}\)) because the base is thin and also, it is lightly doped compared to the emitter. Being lightly doped, the base offers few holes with which the arriving electrons could recombine, and being thin, it gives them very little time in which to do so.
The base of a transistor plays a crucial role in its action. Electrons injected from the emitter into the base diffuse into the collector-base depletion region due to the thin base region.
When the electrons enter the collector-base depletion region, they are pushed into the collector region by the electric field at the collector-base depletion region. This is the point that answers the puzzle raised earlier. The reverse bias at the collector junction opposes the flow of the collector’s own majority carriers, but for an electron arriving from the base it is an accelerating field, so the electron is swept across rather than turned back.
The collector current \((I_\text{C})\) flows through the external circuit as shown in Fig. 16.19 (d). The collector current \(I_\text{C}\) is about 95% of \(I_\text{E}\).
Diagram
Fig. 16.19 (d) – Electron flow through a transistor: emitter current I_E entering, small base current I_B leaving from the base terminal and collector current I_C leaving through the collector, with supplies V_EB and V_CB in place.
Majority of the electrons injected by the emitter into the base are thus collected by the collector and flow through the collector circuit.
A p-n-p transistor works exactly the same way, except that the majority carriers are now holes. The directions of the currents are reversed accordingly, but the reasoning is unchanged.
From the schematic working shown in Fig. 16.19, we can write
\[I_\text{E} = I_\text{B} + I_\text{C}\]
where \(I_\text{E}\) is the emitter current, \(I_\text{B}\) is the base current and \(I_\text{C}\) is the collector current, all measured in ampere (A). This is nothing more than a statement of conservation of charge: whatever enters the transistor at the emitter must leave it, either at the base or at the collector.
Since the base current \(I_\text{B}\) is very small, we can write
\[I_\text{C} \approx I_\text{E}\]
Transistor Configuration
A transistor has three terminals, but a circuit needs two terminals for the input and two for the output. One terminal must therefore be shared between the input side and the output side, and the choice of which terminal is shared gives rise to three possible arrangements.
The possible configurations of transistor in a circuit are, (a) Common Emitter, CE, (b) Common Base, CB, and (c) Common Collector, CC.
Common Emitter configuration: The emitter of the transistor is common to both the input and the output, Fig. 16.20 (a).
Diagram
Fig. 16.20 (a) – Common emitter configuration: p-n-p and n-p-n transistors drawn with base as input terminal, collector as output terminal and the emitter grounded and shared by both.
Common Base configuration: The base of the transistor is common to both the input and the output, Fig. 16.20 (b).
Diagram
Fig. 16.20 (b) – Common base configuration: p-n-p and n-p-n transistors drawn with emitter as input terminal, collector as output terminal and the base grounded and shared by both.
Common Collector configuration: The collector of the transistor is common to both the input and the output, Fig. 16.20 (c).
Diagram
Fig. 16.20 (c) – Common collector configuration: p-n-p and n-p-n transistors drawn with base as input terminal, emitter as output terminal and the collector grounded and shared by both.
16.4.1 The Common Emitter (CE) Configuration
We will discuss the common emitter configuration in some details, because it is the most commonly used configuration.
In the Common Emitter or grounded emitter configuration, the input signal is applied between the base and the emitter, while the output is obtained between the collector and the emitter, as shown in Fig. 16.21. The emitter terminal is thus shared by the input side and the output side, which is what gives the arrangement its name.
Diagram
Fig. 16.21 – The Common Emitter configuration: n-p-n transistor with the input signal applied between base and emitter, the output taken between collector and emitter, and the emitter terminal common to both loops.
Why a Small Base Current Matters
Since the electrical relationship between these three currents \(I_\text{B}\), \(I_\text{C}\) and \(I_\text{E}\) is determined by the physical construction of the transistor itself, any small change in the base current \((I_\text{B})\) will result in a much larger change in the collector current \((I_\text{C})\).
The phrase “determined by the physical construction” is important. The proportion in which the injected carriers divide between the base and the collector is fixed once the transistor has been manufactured — it depends on how thin the base is and how the three regions are doped. The circuit cannot alter that proportion; it can only alter how many carriers are injected in the first place.
Thus, a small change in current flowing in the base will control the current in the emitter-collector circuit. The base acts as a control terminal, rather like a tap that governs a large flow while itself passing very little.
Typical value of \(\beta_\text{DC}\) is between 20 and 200 for most general purpose transistors. Here \(\beta_\text{DC}\) is the current amplification factor of the transistor in this configuration, and it is defined formally in the next subsection.
So if a transistor has a \(\beta_\text{DC} = 100\), then one electron will flow from the base terminal for every 100 electrons flowing between the emitter-collector terminal.
16.4.2 The Common Emitter (CE) Characteristic
A typical circuit used to study the common emitter (CE) characteristic is shown in Fig. 16.22.
Diagram
Fig. 16.22 – Circuit to study Common Emitter (CE) characteristic: input voltage V_in applied across the base-emitter junction giving base-emitter voltage V_BE and base current I_B, load resistance R_L in the collector circuit carrying collector current I_C, output voltage V_out taken across collector and emitter as V_CE, with emitter current I_E in the common lead.
The circuit allows two independent studies to be made. By varying the input side while holding the output voltage fixed, we obtain the input characteristic; by varying the output side while holding the base current fixed, we obtain the output characteristic. Together these two curves describe the behaviour of the transistor completely.
The common emitter amplifier configuration, to be discussed in Section 16.4.3, produces the highest current and power gain of all the three bipolar transistor configurations. This is mainly because the input impedance is low, as it is connected to a forward biased p-n junction, while the output impedance is high, as it is taken from a reverse biased p-n junction.
The Three Currents and the Two Current Gains
In this type of configuration, the current flowing out of the transistor must be equal to the currents flowing into the transistor, as the emitter current is given by
\[I_\text{E} = I_\text{C} + I_\text{B} \qquad \text{...(16.1)}\]
where \(I_\text{E}\), \(I_\text{C}\) and \(I_\text{B}\) are the emitter, collector and base currents respectively, all in ampere (A).
As the load resistance \((R_\text{L})\) is connected in series with the collector, the current gain of the common emitter transistor configuration is quite large. The current gain is called the current amplification factor and is defined as the ratio
\[\beta_\text{DC} = \frac{I_\text{C}}{I_\text{B}} \qquad \text{...(16.2)}\]
Since both quantities in the ratio are currents, \(\beta_\text{DC}\) has no unit. It is a pure number, and as noted earlier it usually lies between 20 and 200.
Similarly, the ratio of the collector current and the emitter current is defined as
\[\alpha_\text{DC} = \frac{I_\text{C}}{I_\text{E}} \qquad \text{...(16.3)}\]
This ratio is also a pure number, and it is always slightly less than one, because the collector receives only that part of the emitter current which is not lost as base current.
Relation Between the Two Factors
The ratios \(\alpha_\text{DC}\) and \(\beta_\text{DC}\) are related. From Eq. (16.1) and Eq. (16.2) we have,
\[I_\text{C} = \alpha I_\text{E} = \beta I_\text{B} \qquad \text{...(16.4)}\]
\[\beta = \frac{\alpha}{1 - \alpha} \qquad \text{...(16.5)}\]
and
\[\alpha = \frac{\beta}{\beta + 1} \qquad \text{...(16.6)}\]
These two relations are simply two ways of writing the same fact, and they can be obtained from Eq. (16.1) by dividing throughout by \(I_\text{C}\). They are worth examining for what they reveal physically. If \(\alpha\) is close to 1 — that is, if nearly all the emitter current reaches the collector — then \(1 - \alpha\) in Eq. (16.5) becomes very small, and \(\beta\) becomes very large. A transistor is a good amplifier precisely because very little of the emitter current is lost in the base.
The Input Characteristics
The variation of base current \(I_\text{B}\) with base-emitter voltage, \(V_\text{BE}\), is called input characteristic. While studying the dependence of \(I_\text{B}\) on \(V_\text{BE}\), the collector-emitter voltage \(V_\text{CE}\) is kept fixed. This is necessary because two quantities cannot be varied at once if the effect of either is to be understood. The characteristic is shown in Fig. 16.23.
Diagram
Fig. 16.23 – The input characteristics of a transistor in CE configuration: base current I_B in microampere plotted against base-emitter voltage V_BE, showing negligible current until the barrier potential is crossed and then a steeply rising curve, drawn for a fixed value of V_CE.
As we can see from the figure, initially, the current is very small till the barrier potential is overcome. When the voltage \(V_\text{BE}\) is more than the barrier potential, the characteristic is similar to that of a forward biased diode.
This resemblance is not accidental. The input side of the transistor is the emitter-base junction, and it is forward biased, so it behaves exactly like the forward biased diode studied in Class XI.
The input dynamic resistance \(r_\text{i}\) of a transistor is defined as the ratio of the change in the base-emitter voltage and the resulting change in the base current at a constant collector-base voltage.
\[r_\text{i} = \frac{\Delta V_\text{BE}}{\Delta I_\text{B}} \qquad \text{...(16.7)}\]
for \(V_\text{CE}\) constant. Here \(\Delta V_\text{BE}\) is measured in volt (V) and \(\Delta I_\text{B}\) in ampere (A), so \(r_\text{i}\) is in ohm (\(\Omega\)).
Note the word “dynamic”. This is not the ratio of voltage to current at a point, but the ratio of a small change in voltage to the small change in current it produces. Graphically, it is the reciprocal of the slope of the input characteristic at the chosen operating point. Since the curve rises steeply once conduction begins, the slope is large and \(r_\text{i}\) is small — which is the low input impedance referred to earlier.
The Output Characteristics
The output characteristic of a transistor is shown in Fig. 16.24.
Diagram
Fig. 16.24 – The output characteristics of a transistor in CE configuration: collector current I_C plotted against collector-emitter voltage V_CE, showing a family of nearly horizontal curves, one for each fixed value of base current I_B, with higher curves corresponding to larger I_B.
The variation of the collector current \(I_\text{C}\) with variation in the collector-emitter voltage is called the output characteristic of a transistor. The base current \(I_\text{B}\) is constant at this time.
From the curve we can see that the collector current \(I_\text{C}\) is independent of \(V_\text{CE}\) as long as the collector-emitter junction is reverse biased. Once the collector junction has enough reverse voltage to sweep up every carrier that arrives from the base, increasing that voltage further cannot produce any more current, because there are no more carriers to collect.
Also, the collector current \(I_\text{C}\) is large for large values of the base current \(I_\text{B}\) when \(V_\text{CE}\) is constant. Reading Fig. 16.24 in this way — moving from one curve to the next at a fixed value of \(V_\text{CE}\) — shows the control action of the base directly.
The output dynamic resistance \(r_\text{o}\) of a transistor is defined as the ratio of the change in the collector-emitter voltage \(V_\text{CE}\) and the change in the collector current \(I_\text{C}\) for constant base current \(I_\text{B}\).
\[r_\text{o} = \frac{\Delta V_\text{CE}}{\Delta I_\text{C}} \qquad \text{...(16.8)}\]
Because the output curves are nearly horizontal, a large change in \(V_\text{CE}\) produces only a tiny change in \(I_\text{C}\). The denominator of Eq. (16.8) is therefore very small, making \(r_\text{o}\) very large. This is the high output impedance mentioned at the beginning of this subsection, and the contrast between the small \(r_\text{i}\) and the large \(r_\text{o}\) is what the amplifier of the next subsection exploits.
In examinations, both dynamic resistances are commonly asked as graph-reading problems: you are given a characteristic curve and two marked points on it, and you must read off the changes in voltage and current between those points before applying Eq. (16.7) or Eq. (16.8). Take care to convert microampere and milliampere to ampere before dividing.
16.4.3 Transistor as an Amplifier
Amplifier is a device which is used for increasing the amplitude of the alternating signal (voltage, current or power).
We will discuss an amplifier using an n-p-n transistor in common emitter configuration. Figure 16.25 shows a typical circuit used for transistor amplifier.
Diagram
Fig. 16.25 – Typical transistor amplifier circuit: n-p-n transistor in CE configuration with base bias supply V_BB through resistance R_B, AC input signal v_i in series with the base circuit, collector supply V_CC through load resistance R_L, and output taken across the collector-emitter terminals through a coupling capacitor.
The Idea Behind the Circuit
A small sinusoidal input signal is superimposed on the DC bias, as shown in Fig. 16.25.
The DC bias is what keeps both junctions correctly biased so that the transistor is always working — the emitter-base junction forward biased and the collector-base junction reverse biased. The AC signal is then added on top of this steady setting, so that it makes the operating point move slightly to and fro instead of switching the transistor on and off.
The base current \(I_\text{B}\) and the collector current \(I_\text{C}\) will have these sinusoidal variations superimposed on them. This causes the output voltage \(V_\text{O}\) also to change sinusoidally.
A capacitor is connected in the output circuit to block the DC component. Only the varying part of the collector voltage is wanted at the output; the steady part is merely the bias, and the capacitor keeps it out of the next stage.
A load resistance \(R_\text{L}\) is connected in the collector circuit. Output is obtained across this resistance.
Working of the Amplifier
Let us discuss the working of the amplifier when the input signal \(v_\text{i}\) is not applied. Consider the output loop. We have, from Kirchhoff’s law,
\[V_\text{CC} = V_\text{CE} + I_\text{C} R_\text{L} \qquad \text{...(16.9)}\]
Here \(V_\text{CC}\) is the fixed collector supply voltage in volt (V), \(V_\text{CE}\) is the collector-emitter voltage in volt (V), \(I_\text{C}\) is the collector current in ampere (A), and \(R_\text{L}\) is the load resistance in ohm (\(\Omega\)). The equation simply says that the supply voltage divides itself between the transistor and the load resistance.
Similarly, for the input loop we have,
\[V_\text{BB} = V_\text{BE} + I_\text{B} R_\text{B} \qquad \text{...(16.10)}\]
where \(V_\text{BB}\) is the base bias supply and \(R_\text{B}\) is the resistance in the base circuit.
When AC signal voltage \(v_\text{i}\) is applied at the input, there will be a change in the emitter-base voltage and hence the emitter current. As the emitter current changes, collector current also changes.
In Eq. (16.9), as the collector current \(I_\text{C}\) changes, the collector voltage \(V_\text{CE}\) changes accordingly, because \(V_\text{CC}\) is fixed. This change in the collector voltage \(V_\text{CE}\) appears as amplified output of the input variation.
This is the heart of the matter, and it is worth restating in one line: the signal makes a small current change, the current change is multiplied inside the transistor, and the multiplied current change is turned back into a voltage change by the load resistance.
AC Current Gain
Changes in the base current cause changes in the collector current. We will now define the AC current gain \(\beta_\text{AC}\).
\[\beta_\text{AC} = \frac{i_\text{C}}{i_\text{B}}\]
Here \(i_\text{C}\) and \(i_\text{B}\) are the changing (AC) parts of the collector and base currents. Like \(\beta_\text{DC}\), this quantity is a pure number with no unit.
The AC current gain \(\beta_\text{AC}\) is almost the same as the DC current gain \(\beta_\text{DC}\) for normal operating voltages. The distinction is that \(\beta_\text{DC}\) compares the total steady currents, while \(\beta_\text{AC}\) compares the changes in them.
Voltage Gain and Power Gain
The changes in the base current \(I_\text{B}\) cause changes in the collector current \(I_\text{C}\). This changes the voltage drop across the load resistance, because \(V_\text{CC}\) is constant. We can write,
\[\Delta V_\text{CC} = \Delta V_\text{CE} + R_\text{L}\, \Delta I_\text{C} = 0\]
The left-hand side is zero because the supply voltage is fixed and therefore cannot change. Therefore,
\[\Delta V_\text{CE} = - R_\text{L}\, \Delta I_\text{C}\]
The minus sign here carries a physical meaning. When the collector current increases, more voltage is dropped across \(R_\text{L}\), so less is left across the transistor and \(V_\text{CE}\) falls. The output moves in the direction opposite to the input.
The change in the output voltage \(\Delta V_\text{CE}\) is the output voltage \(V_\text{o}\), hence we can write,
\[V_\text{o} = \Delta V_\text{CE} = \beta_\text{AC} R_\text{L}\, \Delta I_\text{B}\]
We now define the voltage gain \(A_\text{v}\) of the amplifier as,
\[A_\text{v} = \frac{v_\text{o}}{v_\text{i}} = \frac{\Delta V_\text{CE}}{r_\text{i}\, \Delta I_\text{B}}\]
The denominator uses the input dynamic resistance \(r_\text{i}\) defined in Eq. (16.7), because the input voltage needed to produce a base current change \(\Delta I_\text{B}\) is \(r_\text{i}\, \Delta I_\text{B}\).
The voltage gain is hence given by,
\[A_\text{v} = -\frac{\beta_\text{AC} R_\text{L}}{r_\text{i}}\]
The negative sign indicates that the output voltage and the input voltage are out of phase.
Read as a design rule, this expression says that a large voltage gain calls for a transistor of high \(\beta_\text{AC}\), a large load resistance, and a small input dynamic resistance. The last of these is supplied automatically by the forward biased input junction, which is one reason the common emitter configuration is preferred.
We know that there is also a current gain \(\beta_\text{AC}\) in the common emitter configuration. We can therefore write the power gain \(A_\text{p}\) as,
\[A_\text{p} = \beta_\text{AC} A_\text{v}\]
We have ignored the negative sign for the voltage gain to write the magnitude. A transistor can be used to gain power because \(\beta_\text{AC} > 1\). Since both the voltage and the current are increased, the power gain is the product of the two, and it can be very large.
16.5 Logic Gates
In Class XI we studied continuously varying signals (voltage or current). These are called analog signals. For example, a sinusoidal voltage is an analog signal, shown in Fig. 16.26 (a). In an analog electronic circuit, the output signal varies continuously according to the input signal.
A signal (voltage or current) which can have only two discrete values is called a digital signal. For example, a square wave is a digital signal, shown in Fig. 16.26 (b).
Diagram
Fig. 16.26 – (a) Analogue signal: a smooth sinusoidal voltage plotted against time. (b) Digital signal: a square wave switching abruptly between two fixed voltage levels against time.
Compare the two waveforms in Fig. 16.26. The analog signal glides through every value on its way from one level to another. The digital signal jumps, and spends its time at only two levels — it is either at one value or at the other, never in between.
In a digital circuit, the output voltage can have only two states (i.e. values), either low (0 V) or high (+5 V) value.
An electronic circuit that handles only a digital signal is called a digital circuit, and the branch of electronics which deals with digital circuits is called digital electronics.
What a Logic Gate Is
A digital circuit with one or more input signals but only one output signal is called a logic gate.
It is a switching circuit that follows a certain logical relationship between the input and output voltages. Therefore, they are generally known as logic gates — gates, because they control the flow of signal or information, in much the same way that a gate controls who may pass through it.
The output of a logic gate can have only one of the two possible states, i.e., either a high voltage or low voltage.
Whether the output voltage of a logic gate is high (1) or low (0) will depend upon the condition at its input. Notice that the gate does not measure its inputs; it only tests them. This is what makes it possible to describe the entire behaviour of a gate in a small table, since there are only a finite number of input combinations to consider.
Symbols, Truth Tables and Boolean Expressions
There are five common logic gates, viz., the NOT gate, the AND gate, the OR gate, the NAND gate, and the NOR gate.
Each logic gate is indicated by a symbol, and its function is defined by a truth table. A truth table shows all possible combinations of the input and corresponding outputs.
The truth table defines the function of a logic gate. Truth tables help understand the behaviour of a logic gate. All logic gates can be analysed by constructing a truth table. Since a gate with two inputs has only four possible input combinations, and one with three inputs only eight, the table is always short enough to write out completely — something that could never be done for an analog circuit.
The mathematical statement that provides the relationship between the input and the output of a logic gate is called a Boolean expression.
We will study these basic logic gates at an elementary level.
16.5.1 NOT Gate
This is the most basic logic gate. It has one input and one output.
It produces a ‘high’ output, or output ‘1’, if the input is ‘0’. When the input is ‘high’ or ‘1’, its output is ‘low’ or ‘0’. That is, it produces a negated version of the input at its output. This is why it is also known as an inverter.
The symbol and the truth table for a NOT gate are shown in Fig. 16.27.
Diagram
Fig. 16.27 – NOT gate symbol and its truth table: a triangle with a small circle at its output tip, input X on the left and output Y on the right.
| Input X | Output Y |
|---|---|
| 0 | 1 |
| 1 | 0 |
The small circle at the tip of the symbol is worth noticing, since it stands for inversion wherever it appears. The same circle will be seen again on the NAND and NOR gates later in this section.
The Boolean equation of a NOT gate is:
\[Y = \bar{X}\]
The bar drawn over a symbol means “not”, so the expression is read as “Y equals X bar”, or “Y is the complement of X”.
16.5.2 OR Gate
An OR gate has two or more inputs and one output. It is also called logical addition.
The output Y is 1 or high when either input A or input B or both are 1. That is, if any one of the inputs is high, or both inputs are high, the output is ‘1’ or high. The output is low only in the single case where every input is low.
The symbol and the truth table for an OR gate are shown in Fig. 16.28.
Diagram
Fig. 16.28 – OR gate symbol and its truth table: a curved shield-shaped symbol with two inputs A and B on the left and output Y on the right.
| Input A | Input B | Output Y |
|---|---|---|
| 0 | 0 | 0 |
| 1 | 0 | 1 |
| 0 | 1 | 1 |
| 1 | 1 | 1 |
The Boolean expression for an OR gate is:
\[Y = A + B\]
The plus sign here is read as “or”, not as ordinary addition, and the expression is read as “Y equals A or B”.
16.5.3 AND Gate
An AND gate has two or more inputs and one output. The AND operation represents a logical multiplication.
The output Y of an AND gate is high or 1 only when input A and input B are both 1, or both are high simultaneously. If even one input is low, the output is low. In this respect the AND gate is the exact opposite of the OR gate, which needed only one high input to give a high output.
The logic symbol and truth table for this gate are given in Fig. 16.29.
Diagram
Fig. 16.29 – AND gate symbol and its truth table: a D-shaped symbol with a flat left edge and rounded right edge, inputs A and B on the left and output Y on the right.
| Input A | Input B | Output Y |
|---|---|---|
| 0 | 0 | 0 |
| 0 | 1 | 0 |
| 1 | 0 | 0 |
| 1 | 1 | 1 |
The Boolean expression for an AND gate is:
\[Y = A \cdot B\]
The dot is read as “and”, so the expression is read as “Y equals A and B”.
16.5.4 NAND Gate
The NAND gate is formed by connecting the output of an AND gate to the input of a NOT gate, so that whatever the AND gate produces is inverted before it appears at the output.
The output of a NAND gate is exactly opposite to that of an AND gate. If the inputs A and B are both high or ‘1’, the output Y is the negation of that, i.e., the output is low or ‘0’. For every other combination of inputs the output is high.
The gate derives its name from this NOT-AND behaviour. Figure 16.30 shows the symbol and the truth table of a NAND gate.
Diagram
Fig. 16.30 – NAND gate symbol and its truth table: the D-shaped AND gate symbol with a small circle at its output, inputs A and B on the left and output Y on the right.
| Input A | Input B | Output Y |
|---|---|---|
| 0 | 0 | 1 |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 1 | 1 | 0 |
The Boolean expression for a NAND gate is:
\[Y = \overline{A \cdot B}\]
Note carefully that the bar extends over the whole product. The gate performs the AND operation first and inverts the result afterwards; it does not invert the two inputs separately.
16.5.5 NOR Gate
The NOR gate is formed by connecting the output of an OR gate to the input of a NOT gate, so that the result of the OR operation is inverted before it reaches the output.
The output of a NOR gate is exactly opposite to that of an OR gate. The output Y of a NOR gate is high or 1 only when both the inputs are low or 0. If even one input is high, the output is low.
The symbol and truth table for a NOR gate is given in Fig. 16.31.
Diagram
Fig. 16.31 – NOR gate symbol and its truth table: the curved OR gate symbol with a small circle at its output, inputs A and B on the left and output Y on the right.
| Input A | Input B | Output Y |
|---|---|---|
| 0 | 0 | 1 |
| 0 | 1 | 0 |
| 1 | 0 | 0 |
| 1 | 1 | 0 |
The Boolean expression for a NOR gate is:
\[Y = \overline{A + B}\]
As with the NAND gate, the bar covers the entire expression, showing that the OR operation is carried out first and the result inverted afterwards.
Universal Gates
NAND gate and NOR gate are called Universal Gates, because any gate can be implemented by the combination of NAND gates or NOR gates.
This is a result of considerable practical importance. A manufacturer need not fabricate five different kinds of gate on a chip; a large number of identical NAND gates, suitably interconnected, can perform any logical function required.
16.5.6 Exclusive OR / X-OR Gate
The Exclusive-OR logic function is a very useful circuit that can be used in many different types of computational circuits. The ability of the Exclusive-OR gate to compare two logic levels and produce an output value dependent upon the input condition is very useful in computational logic circuits.
The word “compare” is the key to this gate. The output of an Exclusive-OR gate goes ‘HIGH’ only when its two input terminals are at different logic levels with respect to each other. In other words, the gate answers the question “are these two inputs unlike each other?”
An odd number of high or ‘1’ at its input gives high or ‘1’ at the output. These two inputs can be at high level (‘1’) or at low level (‘0’), giving us the Boolean expression:
\[C = (A \oplus B) = \bar{A} \cdot B + A \cdot \bar{B}\]
The right-hand side states the same rule in the language of the earlier gates. The first term is high when A is low and B is high; the second is high when A is high and B is low. Since the two terms are joined by an OR operation, the output is high in either of these unlike cases, and low otherwise.
Figure 16.32 shows the symbol and truth table of a two input X-OR gate.
Diagram
Fig. 16.32 – Two input X-OR gate symbol and its truth table: the OR gate shield shape with an extra curved line across its input side, inputs A and B on the left and output C on the right.
| A | B | C |
|---|---|---|
| 0 | 0 | 0 |
| 1 | 0 | 1 |
| 0 | 1 | 1 |
| 1 | 1 | 0 |
The output is ‘high’ when either of the inputs A or B is high, but not if both A and B are high.
16.6 Summary
Rectifiers and Power Supplies
A p-n junction diode acts as a closed switch when forward biased and as an open switch when reverse biased. This one-way switching action allows it to be used as a rectifier.
The mains supply in India is 230 V at a frequency of 50 Hz. Many electronic gadgets need DC, so the AC mains voltage must be rectified.
A complete DC power supply has four stages: transformer, diode rectifier, filter and voltage regulator.
The conversion of AC voltage into a DC voltage is called rectification, and the circuit which does it is called a rectifier.
In a half wave rectifier, a single diode conducts only during the positive half cycles of the AC input and blocks the negative half cycles. The output is a series of alternate pulses across \(R_\text{L}\).
The transformer used in a rectifier serves two purposes: it steps the input voltage up or down as required, and it isolates the circuit from the mains supply, reducing the risk of electric shock.
In a full wave rectifier, a centre tapped transformer and two diodes \(D_1\) and \(D_2\) are used. \(D_1\) conducts during the positive half cycle and \(D_2\) during the negative half cycle, so current flows through the load in the same direction during both half cycles.
The maximum efficiency of a full wave rectifier is 81.2% and that of a half wave rectifier is 40.6% — the full wave value is twice the half wave value.
For a 50 Hz input, the output frequency is 50 Hz for a half wave rectifier and 100 Hz for a full wave rectifier.
The AC component present along with the DC in a rectifier output is called ripple.
\[\text{Ripple factor} = \frac{\text{r.m.s. value of AC component}}{\text{value of DC component}}\]
A smaller ripple factor means a more effective rectifier. The ripple in a full wave rectifier is less than that in a half wave rectifier.
A filter circuit removes the AC component or ripple from the rectifier output and allows only the DC component to pass. In a capacitor filter, the capacitor charges to the peak voltage \(V_\text{p}\) and then supplies the load while the rectifier voltage falls, so the output dips only slightly before the next peak recharges it.
A power supply whose output voltage changes when a load is connected is an unregulated power supply; one whose output stays steady is a regulated power supply.
Zener Diode
Electrical breakdown may occur by avalanche breakdown or by Zener breakdown.
In Zener breakdown, the strong electric field across a reverse biased junction breaks covalent bonds directly, releasing electrons and producing a large reverse current.
Zener breakdown occurs in heavily doped diodes, in which the depletion layer is narrow. It does not damage the diode. The field strength at breakdown is approximately \(3 \times 10^7\) V/m.
A Zener diode is a p-n junction diode designed to work in the breakdown region, and is used as a voltage regulator or voltage stabiliser.
Once breakdown occurs, the voltage across the diode remains constant at the Zener voltage \(V_\text{Z}\) even though the current through it changes by a large amount.
\(V_\text{Z}\) depends on the doping: heavier doping gives a lower breakdown voltage. Zener diodes below 6 V work mainly by Zener breakdown, those above 6 V mainly by avalanche breakdown, but both are called Zener diodes.
In the regulator circuit, the series resistance \(R_\text{S}\) limits the diode current and absorbs the fluctuations of the input voltage, while the load \(R_\text{L}\) is in parallel with the diode so that \(V_\text{R} = V_\text{Z}\). A regulated output \(V_\text{O} = V_\text{Z}\) is obtained.
Maximum power rating of a Zener diode:
\[P_\text{Z} = I_\text{Z(max)} V_\text{Z}\]
- Applications: voltage regulator, fixed reference voltage in transistor biasing, peak clipper or limiter in wave shaping circuits, protection of meters against accidental fluctuations.
Photodiode
A photodiode converts light energy into electrical energy and operates in reverse biased mode. Only minority current flows through it.
The reverse current flowing in the absence of light is called the dark current. It depends only on the concentration of minority carriers and not on the applied voltage.
When the junction is illuminated by photons of energy greater than the band gap, electron-hole pairs are generated in the depletion region and are separated by the intrinsic electric field, increasing the reverse current.
The reverse current of a photodiode depends on the intensity of the incident light. The total current is the sum of the photocurrent and the dark current.
The constant value reached by the reverse current is called the saturation current.
\[R_\text{d} = \frac{\text{Maximum reverse voltage}}{\text{Dark current}}\]
- Advantages include quick and linear response, high speed, small size, wide spectral response (Si: 190 nm to 1100 nm) and low cost. Its properties are temperature dependent.
Solar Cell
Photo thermal devices convert solar energy into heat; photovoltaic devices convert it into electrical energy. A solar cell is a photovoltaic device and acts as a source of DC power.
Its structure is a p-n junction with a thin n-side facing the radiation, an antireflection coating that reflects IR radiation, a front contact on the n-side and a rear contact on the p-side.
Working: electron-hole pairs are generated in the depletion region, separated and collected at the cathode and anode, a voltage builds up across the cell, and power is delivered to the load.
The separation of carriers by the intrinsic field of the depletion region prevents recombination and makes the light-generated current possible.
In the I-V characteristic, drawn in the fourth quadrant, the intercept on the I-axis is the short-circuit current \(I_\text{sc}\) and that on the V-axis is the open circuit voltage \(V_\text{oc}\). Power delivered is zero at both, and is maximum at an intermediate point:
\[P_\text{L} = V_\text{oL} \cdot I_\text{sc}\]
- Material requirements: band gap between 1.0 eV and 1.8 eV, high optical absorption, good electrical conductivity and easy availability. Common materials are Si (\(E_g\) = 1.1 eV), GaAs (\(E_g\) = 1.43 eV), CdTe (\(E_g\) = 1.45 eV) and CuInSe (\(E_g\) = 1.04 eV).
Light Emitting Diode
An LED is a diode which emits light when a large forward current passes through it. Its n-region is more heavily doped than its p-region, and the junction is enclosed in a dome-shaped transparent case.
On forward bias, electrons from the conduction band recombine with holes in the valence band, releasing energy as photons of monochromatic light.
The light output is directly proportional to the forward current.
The colour depends on the material: AlGaAs gives infrared, GaAsP gives red or yellow, AlGaP gives red or green, and ZnSe gives blue light.
The I-V characteristic is like the forward characteristic of an ordinary diode; the LED conducts after its cut-in voltage is reached. Its forward voltage drop is about 1.5 to 3.5 V and its current rating is a few tens of milliampere, so a series resistance is necessary.
Advantages: high efficiency (up to 135 lumens/watt), long life (50,000 hours or more), rugged solid state construction, no warm-up period, excellent colour rendering, environment friendly and controllable.
Bipolar Junction Transistor
A BJT has two junctions and three terminals, and its current is carried by both electrons and holes. The two types are n-p-n and p-n-p.
The emitter is thick and heavily doped, the base is thin and lightly doped, and the collector is lightly doped with a larger area.
For normal transistor action the emitter-base junction is forward biased and the collector-base junction is reverse biased.
The base current is about 5% of the emitter current and the collector current about 95%, because the thin, lightly doped base allows little recombination.
\[I_\text{E} = I_\text{C} + I_\text{B} \qquad \text{...(16.1)}\]
\[\beta_\text{DC} = \frac{I_\text{C}}{I_\text{B}} \qquad \text{...(16.2)} \qquad\qquad \alpha_\text{DC} = \frac{I_\text{C}}{I_\text{E}} \qquad \text{...(16.3)}\]
\[I_\text{C} = \alpha I_\text{E} = \beta I_\text{B} \qquad \text{...(16.4)}\]
\[\beta = \frac{\alpha}{1 - \alpha} \qquad \text{...(16.5)} \qquad\qquad \alpha = \frac{\beta}{\beta + 1} \qquad \text{...(16.6)}\]
The three configurations are common emitter (CE), common base (CB) and common collector (CC). The CE configuration is the most commonly used, and gives the highest current and power gain, because its input impedance is low and its output impedance is high. Typical \(\beta_\text{DC}\) lies between 20 and 200.
Input characteristic: variation of \(I_\text{B}\) with \(V_\text{BE}\) at constant \(V_\text{CE}\); it resembles the forward characteristic of a diode.
\[r_\text{i} = \frac{\Delta V_\text{BE}}{\Delta I_\text{B}} \qquad \text{...(16.7)} \quad (V_\text{CE} \text{ constant})\]
- Output characteristic: variation of \(I_\text{C}\) with \(V_\text{CE}\) at constant \(I_\text{B}\); \(I_\text{C}\) is nearly independent of \(V_\text{CE}\) while the collector junction is reverse biased.
\[r_\text{o} = \frac{\Delta V_\text{CE}}{\Delta I_\text{C}} \qquad \text{...(16.8)}\]
Transistor as an Amplifier
- An amplifier increases the amplitude of an alternating signal. A small AC signal is superimposed on the DC bias; a capacitor blocks the DC component at the output, and the output is taken across the load resistance \(R_\text{L}\).
\[V_\text{CC} = V_\text{CE} + I_\text{C} R_\text{L} \qquad \text{...(16.9)}\]
\[V_\text{BB} = V_\text{BE} + I_\text{B} R_\text{B} \qquad \text{...(16.10)}\]
\[\beta_\text{AC} = \frac{i_\text{C}}{i_\text{B}}, \qquad \Delta V_\text{CE} = - R_\text{L}\, \Delta I_\text{C}\]
\[A_\text{v} = \frac{v_\text{o}}{v_\text{i}} = -\frac{\beta_\text{AC} R_\text{L}}{r_\text{i}}, \qquad A_\text{p} = \beta_\text{AC} A_\text{v}\]
- The negative sign in \(A_\text{v}\) shows that the output and input voltages are out of phase. Power gain is possible because \(\beta_\text{AC} > 1\); the energy comes from the collector supply, not from the signal.
Logic Gates
An analog signal varies continuously; a digital signal has only two discrete values, low (0 V) and high (+5 V).
A logic gate is a digital circuit with one or more inputs and only one output, whose output depends on the inputs through a fixed logical relationship. Its behaviour is defined by a truth table, and the mathematical relation between its inputs and output is a Boolean expression.
Boolean expressions of the basic gates:
- NOT: \(Y = \bar{X}\) — output is the inverse of the input.
- OR: \(Y = A + B\) — output is high if any input is high.
- AND: \(Y = A \cdot B\) — output is high only if all inputs are high.
- NAND: \(Y = \overline{A \cdot B}\) — output is low only if all inputs are high.
- NOR: \(Y = \overline{A + B}\) — output is high only if all inputs are low.
- X-OR: \(C = (A \oplus B) = \bar{A} \cdot B + A \cdot \bar{B}\) — output is high only when the two inputs are different.
- NAND and NOR are called universal gates, because any gate can be built from combinations of NAND gates alone or NOR gates alone.
16.7 Objective Questions
- Choose the correct option.
- In a BJT, largest current flow occurs
- in the emitter
- in the collector
- in the base
- through CB junction
- A series resistance is connected in the Zener diode circuit to
- Properly reverse bias the Zener
- Protect the Zener
- Properly forward bias the Zener
- Protect the load resistance
- A LED emits visible light when its
- junction is reverse biased
- depletion region widens
- holes and electrons recombine
- junction becomes hot
- Solar cell operates on the principle of:
- diffusion
- recombination
- photo voltaic action
- carrier flow
- A logic gate is an electronic circuit which:
- makes logical decisions
- allows electron flow only in one direction
- works using binary algebra
- alternates between 0 and 1 value
16.8 Check Your Concepts
A half wave rectifier and a full wave rectifier are supplied from the same transformer. Explain why the half wave rectifier delivers far less power to the load, even though both use the same input.
Why is a centre tapped transformer essential in the two-diode full wave rectifier circuit? What would happen if an ordinary secondary coil were used instead?
The ripple frequency at the output of a full wave rectifier is twice that of the input. Explain the reason, using the shape of the output waveform.
A student connects the filter capacitor between the transformer and the rectifier instead of after the rectifier. Explain what the output will look like and why the circuit fails to work as intended.
The output of a capacitor-filtered power supply falls when a heavier load (smaller \(R_\text{L}\)) is connected across it. Explain this observation in terms of the charging and discharging of the capacitor.
An ordinary diode is destroyed when reverse breakdown occurs, but a Zener diode operates in breakdown continuously without damage. Explain the reason for this difference.
In a Zener voltage regulator, what happens to the regulation if the series resistance \(R_\text{S}\) is made (a) far too large and (b) far too small? Give reasons for both cases.
Why must the supply voltage in a Zener regulator always be greater than the Zener voltage \(V_\text{Z}\)? What happens to the output if it falls below \(V_\text{Z}\)?
Explain why the no-load condition, when the load is disconnected, is the most severe condition for the Zener diode in a regulator circuit.
Two Zener diodes are made of the same material, but one is more heavily doped than the other. Which of them will break down at the lower reverse voltage, and why?
A photodiode is operated in reverse bias, while a solar cell is used without any external bias at all. Explain the reason for this difference in the way the two devices are used.
Increasing the reverse voltage across a photodiode kept in the dark hardly changes the current through it, but increasing the illumination changes it a great deal. Explain why.
A photodiode is illuminated by a very bright source of red light, but produces no photocurrent at all. What can you conclude about the band gap of the material used, and why does increasing the brightness not help?
Why is the n-side of a solar cell made very thin, while the p-side is relatively thick?
Why is the I-V characteristic of an illuminated solar cell drawn in the fourth quadrant, unlike the characteristics of all the other diodes studied in this chapter?
Silicon is the most widely used semiconductor, yet LEDs are not made from it. Give two reasons.
An LED is connected directly across a 5 V supply without a series resistance. Explain, with reference to its I-V characteristic, what is likely to happen.
What would happen to the transistor action if the base region were made thick and heavily doped? Explain your answer in terms of the paths available to the injected carriers.
The collector-base junction of a transistor is reverse biased, and yet a large current flows through it. Explain how this is possible.
Two ordinary diodes are soldered together to form a p-n-p arrangement. Explain why this combination will not work as a transistor.
Explain why the output voltage of a common emitter amplifier is out of phase with its input voltage.
The common emitter configuration gives the highest power gain of the three configurations. Explain how this follows from the biasing of its input and output junctions.
Why are NAND and NOR gates called universal gates? Show how a NAND gate alone can be used to obtain the NOT function.
An OR gate and an X-OR gate are given the same four combinations of inputs. In how many rows do their outputs agree, and in which row do they differ? Explain the reason for the difference.
Digital signals can be sent over long distances and copied repeatedly without loss of quality, while analog signals deteriorate. Explain why, using the idea of two discrete levels.
Answer in brief.
- Why is the base of a transistor made thin and is lightly doped?
- How is a Zener diode different than an ordinary diode?
- On which factors does the wavelength of light emitted by a LED depend?
- Why should a photodiode be operated in reverse biased mode?
- State the principle and uses of a solar cell.
Draw the circuit diagram of a half wave rectifier. Explain its working. What is the frequency of ripple in its output?
Why do we need filters in a power supply?
Draw a neat diagram of a full wave rectifier and explain its working.
Explain how a Zener diode maintains constant voltage across a load.
Explain the forward and the reverse characteristic of a Zener diode.
Explain the working of a LED.
Explain the construction and working of a solar cell.
Explain the principle of operation of a photodiode.
What do you mean by a logic gate, a truth table and a Boolean expression?
What is a logic gate? Write down the truth table and Boolean expression for the ‘AND’ gate.
What are the uses of logic gates? Why is a NOT gate known as an inverter?
Write the Boolean expression for (i) OR gate, (ii) AND gate, and (iii) NAND gate.
Why are the emitter, the base and the collector of a BJT doped differently?
Which method of biasing is used for operating a transistor as an amplifier?
Define \(\alpha\) and \(\beta\). Derive the relation between them.
16.9 Practice with Numericals
An AC supply of frequency 400 Hz, used on board an aircraft, is applied to (a) a half wave rectifier and (b) a full wave rectifier. Find the output frequency in each case and the time interval between two successive output pulses in case (b).
The output of a rectifier is found to have a DC component of 12 V together with an AC component of rms value 0.36 V. Calculate the ripple factor of the rectifier.
A filtered power supply has a ripple factor of 0.02 and a DC output of 15 V. Calculate the rms value of the ripple voltage present in its output.
A Zener diode has a Zener voltage of 9.0 V and a power rating of 1.5 W. Calculate (a) the maximum current it can safely carry, and (b) the minimum series resistance required if it is operated from a 15 V DC supply.
In a Zener regulator circuit, the input voltage is 12 V, the Zener voltage is 6.0 V, the series resistance is 100 \(\Omega\) and the load resistance is 1.2 k\(\Omega\). Calculate (a) the current through the series resistance, (b) the load current, and (c) the current through the Zener diode.
In a Zener regulator, the current supplied through the series resistance is 60 mA and the Zener voltage is 5.0 V. Calculate the power dissipated in the Zener diode when the load is disconnected.
A photodiode can withstand a maximum reverse voltage of 10 V. The dark current measured under this condition is 5.0 nA. Calculate its dark resistance and express the answer in megaohm.
An LED has a forward voltage drop of 1.8 V and is to be operated at a forward current of 15 mA from a 6.0 V supply. Calculate (a) the value of the series resistance required, and (b) the power dissipated in that resistance.
Gallium arsenide has a band gap of 1.43 eV. Calculate the longest wavelength of light that a solar cell made of this material can absorb to produce an electron-hole pair. (Take \(1\ \text{eV} = 1.6 \times 10^{-19}\) J, \(h = 6.63 \times 10^{-34}\) J s and \(c = 3 \times 10^{8}\) m/s.)
A solar panel is made of 40 identical silicon solar cells connected in series, each developing an open circuit voltage of 0.55 V in bright sunlight. Calculate the open circuit voltage of the panel.
A transistor has a common base DC current gain of 0.96. If the emitter current is 5.0 mA, calculate the collector current, the base current and the value of \(\beta_\text{DC}\).
A transistor in the common emitter configuration has \(\beta_\text{DC} = 60\). If the base current is 30 \(\mu\)A, calculate the collector current and the emitter current.
In the input characteristic of a transistor, a change of 0.02 V in the base-emitter voltage produces a change of 20 \(\mu\)A in the base current, the collector-emitter voltage being held constant. Calculate the input dynamic resistance.
In the output characteristic of a transistor, a change of 4.0 V in the collector-emitter voltage produces a change of 0.05 mA in the collector current at constant base current. Calculate the output dynamic resistance.
In a common emitter amplifier, \(\beta_\text{AC} = 80\), the load resistance in the collector circuit is 5.0 k\(\Omega\) and the input dynamic resistance is 1.25 k\(\Omega\). Calculate the magnitude of the voltage gain and the power gain.
In the output loop of a transistor amplifier, the collector supply voltage is 12 V and the load resistance is 2.0 k\(\Omega\). If the collector current is 3.0 mA, calculate the collector-emitter voltage.
The common-base DC current gain of a transistor is 0.967. If the emitter current is 10 mA, what is the value of the base current?
In a common-base connection, a certain transistor has an emitter current of 10 mA and a collector current of 9.8 mA. Calculate the value of the base current.
In a common-base connection, the emitter current is 6.28 mA and the collector current is 6.20 mA. Determine the common base DC current gain.