#### CHAPTER 11 SEMICONDUCTORS

TYPES OF SUBSTANCES ON THE BASIS OF CONDUCTIVITY

Metals on the basis of conductivity

Conductors are those substances through which electricity can pass easily, e.g., all metals are conductors. They possess very low resistivity (or high conductivity).

ρ ~ 10–2 – 10–8 Ωm

σ ~ 102 – 108 Sm–1

Semiconductors on the basis of conductivity

Semiconductors are those substances whose conductivity lies between conductors and insulators, e.g., germanium, silicon, carbon etc. They have resistivity or conductivity intermediate to metals and insulators.

ρ ~ 10–5 – 106 Ωm

σ ~ 105 – 10–6 Sm–1

Insulators on the basis of conductivity

Insulators are those substances through which electricity cannot pass, e.g., wood, rubber, mica etc. They have high resistivity (or low conductivity).

ρ ~ 1011 – 1019 Ω m

σ ~ 10–11 – 10–19 S m–1

Energy bands in solids

The collection of closely spaced energy levels is called an energy band. In a crystal due to inter-atomic interaction valence electrons of one atom are shared by more than one atom in the crystal and splitting of energy levels takes place.

1. Valence band: This energy band contains valence electrons. This band may be partially or completely filled with electrons but never be empty. The electrons in this band are not capable of gaining energy from external electric field to take part in conduction of current.

2. Conduction band: This band contains conduction electrons. This band is either empty or partially filled with electrons. Electrons present in this band take part in the conduction of current.

3. Forbidden band: This band is completely empty. The minimum energy required to shift an electron from valence band to conduction band is called band gap (Eg).

TYPES OF SUBSTANCES ON THE BASIS OF ENERGY BANDS

Metals on the basis of energy bands

A substance is a metal either when the conduction band is partially filled and the balanced band is partially empty or when the conduction and valance bands overlap. When there is overlap electrons from valence band can easily move into the conduction band.

This situation makes a large number of electrons available for electrical conduction. When the valence band is partially empty, electrons from its lower level can move to higher level making conduction possible. Therefore, the resistance of such materials is low or the conductivity is high.

Semiconductors on the basis of energy bands

In this case a finite but small band gap (Eg < 3 eV) exists. Because of the small band gap, at room temperature some electrons from valence band can acquire enough energy to cross the energy gap and enter the conduction band. These electrons (though small in numbers) can move in the conduction band. Hence, the resistance of semiconductors is not as high as that of the insulators.

Insulators on the basis of energy bands

In this case, a large band gap Eg exists (Eg > 3 eV). There are no electrons in the conduction band, and therefore no electrical conduction is possible. Note that the energy gap is so large that electrons cannot be excited from the valence band to the conduction band by thermal excitation. This is the case of insulators.

TYPES OF SEMICONDUCTORS

Elemental semiconductors: Si and Ge

Compound semiconductors:

• Inorganic: CdS, GaAs, CdSe, InP, etc.

• Organic: anthracene, doped pthalocyanines, etc.

• Organic polymers: polypyrrole, polyaniline, polythiophene, etc.

TYPES OF SEMICONDUCTORS BASED ON PURITY

Intrinsic semiconductor

A semiconductor in its pure state is called intrinsic semiconductor.

In its crystalline structure, every Si or Ge atom tends to share one of its four valence electrons with each of its four nearest neighbour atoms, and also to take share of one electron from each such neighbour.

Effect of temperature on conductivity of semiconductors

As the temperature increases, more thermal energy becomes available to these electrons and some of these electrons may break away (becoming free electrons contributing to conduction).

The thermal energy ionises only a few atoms in the crystalline lattice and creates a vacancy in the bond. The neighbourhood, from which the free electron (with charge –q) has come out leaves a vacancy with an effective charge (+q ). This vacancy with the effective positive electronic charge is called a hole.

An intrinsic semiconductor will behave like an insulator at T = 0 K.

At higher temperatures (T > 0K), some electrons are excited and move from the valence band to the conduction band.

In intrinsic semiconductors, the number of free electrons, ne is equal to the number of holes, nh. That is,

Where, ni is called intrinsic carrier concentration.

Both electrons and holes move to conduct.

Also, I = Ie + Ih, where Ie is the current due to movement of free electrons and Ih is the current due to movement of holes.

Extrinsic semiconductor

A semiconductor doped with suitable impurity, is called extrinsic semiconductor. The deliberate addition of a desirable impurity is called doping and the impurity atoms are called dopants.

On the basis of doped impurity extrinsic semiconductors are of two types, i.e., m-type and p-type.

n-type semiconductor

Extrinsic semiconductor doped with penta-valent impurity like P, As, Sb, Bi, etc in which negatively charged electrons works as charge carriers, is called n-type semiconductor.

The penta-valent foreign atom becomes effectively positively charged when it donates extra electron.

n-type semiconductor the total number of conduction electrons ne is due to the electrons contributed by donors and those generated intrinsically, while the total number of holes nh is only due to the holes from the intrinsic source. But the rate of recombination of holes would increase due to the increase in the number of electrons. As a result, electrons are the majority carriers and holes the minority carriers.

p-type semiconductor

This is obtained when Si or Ge is doped with a trivalent impurity like Al, B, In, etc. The dopant has one valence electron less than Si or Ge. This atom can form covalent bonds with neighbouring three Si atoms but does not have any electron to offer to the fourth Si atom. So the bond between the fourth neighbour and the trivalent atom has a vacancy or hole.

Since the neighbouring Si atom in the lattice needs an electron in place of a hole, an electron in the outer orbit of an atom in the neighbourhood may jump to fill this vacancy, leaving a vacancy or hole at its own site and the moves increasing the conductivity.

The trivalent foreign atom becomes effectively negatively charged when it shares fourth electron with neighbouring Si atom. Therefore, the dopant atom of p-type material can be treated as core of one negative charge along with its associated hole.

These holes are in addition to the intrinsically generated holes while the source of conduction electrons is only intrinsic generation. Thus, for such a material, the holes are the majority carriers and electrons are minority carriers.

${n}_{h}\gg {n}_{e}$

Conductivity of an extrinsic semiconductor

The crystal as a whole is neutral.

In a doped semiconductor

where ne and nh are the number density of electrons and holes and ni is number density of intrinsic carriers, i.e., electrons or holes.

Electrical conductivity of extrinsic semiconductor is given by

Where ρ is resistivity, μe and μh are mobility of electrons and holes respectively.

p-n junction

An arrangement, consisting of a p-type semiconductor brought into a close contact with n-type semiconductor, is called a p -n junction.

Diffusion of charge and diffusion current

During the formation of p-n junction, and due to the concentration gradient across p-, and n- sides, holes diffuse from p-side to n-side (p→n) and electrons diffuse from n-side to p-side (n→p) and a diffusion current is setup across the junction.

p-n junction formation

Depletion region

Due to diffusion of holes p→n and electrons n→p, a –ve region is created on p-side and a +ve region is created on n-side.

This space-charge region on either side of the junction together is known as depletion region and net charge in this region is 0.

Due to the positive space-charge region on n-side of the junction and negative space charge region on p-side of the junction, an electric field directed from positive charge towards negative charge develops. Due to this field, an electron on p-side of the junction moves to n-side and a hole on n-side of the junction moves to p-side.

Drift of charge carriers and drift current

The motion of charge carriers due to the electric field is called drift and current is called drift current.

Initially, diffusion current is large and drift current is small. As the diffusion process continues, the space-charge regions on either side of the junction extend, thus increasing the electric field strength and hence drift current. This process continues until the diffusion current equals the drift current and p-n junction is formed. In a p-n junction under equilibrium there is no net current.

The loss of electrons from the n-region and the gain of electrons by the p-region; causes a difference of potential across the junction of the two regions. The polarity of this potential is such as to oppose further flow of carriers so that a condition of equilibrium exists.

Potential barrier across a p-n junction

The potential difference across the depletion layer is called potential barrier (Vo).

Semiconductor diode

A semiconductor diode is a p-n junction with metallic contacts provided at the ends for the application of an external voltage. It is a two terminal device.

Forward bias of p-n junction

The p -side is connected to positive terminal and n-side to negative terminal of a battery.

Forward current flows due to majority charge carriers and the width of depletion layer decreases.

The current under forward bias, first increases very slowly till the voltage across the diode crosses a certain value. After this, the diode current increases significantly (exponentially), even for a very small increase in the diode bias voltage. This voltage is called the threshold voltage or cut-in voltage

Reverse bias of a p-n junction

The p-side is connected to negative terminal and n-side to positive terminal of a battery.

Reverse current flows due to minority charge carriers and the width of depletion layer increases.

The current under reverse bias voltage is independent up to a critical reverse bias voltage, known as breakdown voltage (Vbr). When V = Vbr, the diode reverse current increases sharply. Even a slight increase in the bias voltage causes large change in the current. If the reverse current is not limited by an external circuit, the p-n junction will get destroyed.

V-I characteristics of a diode

A graph between V and I is plotted as shown in the figure. In forward bias measurement, a milliammeter is used, since the expected current is large (as explained in the earlier section) while a micrometer is used in reverse bias to measure the current.

In forward bias, the current first increases negligibly, till the voltage across the diode crosses a certain value. After the characteristic voltage, the diode current increases exponentially, even for a very small increase in the diode bias voltage. This voltage is called the threshold voltage or cut-in voltage (~0.2V for germanium diode and ~0.7 V for silicon diode).

For the diode in reverse bias, the current is very small (~μA) and almost remains constant with change in bias. It is called reverse saturation current. However, for special cases, at very high reverse bias (break down voltage), the current suddenly increases.

The p-n junction diode primarily allows the flow of current only in one direction (forward bias). The forward bias resistance is low as compared to the reverse bias resistance. This property is used for rectification of ac voltage.

Dynamic resistance

The ratio of small change in voltage ΔV to a small change in current ΔI:

Application of junction diode as a rectifier

The device which restricts the current (or voltage) to only one direction is called rectifier.

A p-n junction diode can be utilized as a rectifier.

If an alternating voltage is applied across a diode the current flows only in that part of the cycle when the diode is forward biased.

The rectifier circuit, which rectifies only the half-wave, is called a half-wave rectifier.

The secondary of a transformer supplies the desired ac voltage across terminals A and B. When the voltage at A is positive, the diode is forward biased and it conducts. When A is negative, the diode is reverse-biased and it does not conduct. The reverse saturation current of a diode is negligible and can be considered equal to zero for practical purposes.

The reverse breakdown voltage of the diode must be sufficiently higher than the peak ac voltage at the secondary of the transformer to protect the diode from reverse breakdown.

Full-wave rectifier

The circuit using two diodes as in the figure gives output rectified voltage for both the positive as well as negative half of the ac cycle. Hence, it is known as full-wave rectifier. The secondary of the transformer is provided with a centre tapping and so it is called centre-tap transformer.

Here the p-side of the two diodes is connected to the ends of the secondary of the transformer. The n-sides of the diodes are connected together and the output is taken between this common point of diodes and the midpoint of the secondary of the transformer.

Each diode rectifies only for half the cycle, but the two do so for alternate cycles. Thus, the output between their common terminals and the centre tap of the transformer becomes a full-wave rectifier output.

Electric filter

The rectified voltage is in the form of pulses of the shape of half sinusoids and does not have a steady value. To get steady dc output a capacitor is connected across the output terminals (parallel to the load RL) or an inductor in series with RL. This arrangement is called filter.

Role of capacitor in the filter

• When the voltage across the capacitor is rising, it gets charged. If there is no external load, it remains charged to the peak voltage of the rectified output.

• When there is a load, it gets discharged through the load and the voltage across it begins to fall. In the next half-cycle of rectified output it again gets charged to the peak value.

• The rate of fall of the voltage across the capacitor depends upon the inverse product of capacitor C and the effective resistance RL used in the circuit and is called the time constant.

Some special types of diodes

Zener diode is designed to operate under reverse bias in the breakdown region and used as a voltage regulator.

Zener diode as voltage regulator

The unregulated dc voltage (filtered output of a rectifier) is connected to the Zener diode through a series resistance Rs such that the Zener diode is reverse biased.

If the input voltage increases, the current through Rs and Zener diode also increases. This increases the voltage drop across Rs without any change in the voltage across the Zener diode. This is because in the breakdown region, Zener voltage remains constant even though the current through the Zener diode changes.

Similarly, if the input voltage decreases, the current through Rs and Zener diode also decreases. The voltage drop across Rs decreases without any change in the voltage across the Zener diode. Thus any increase/decrease in the input voltage results in, increase/decrease of the voltage drop across Rs without any change in voltage across the Zener diode.

Thus the Zener diode acts as a voltage regulator.

• We have to select the Zener diode according to the required output voltage and accordingly the series resistance Rs.

Optoelectronic devices

Semiconductor diodes in which carriers are generated by photons (photo-excitation are called optoelectronic devices.

1. Photodiode is used for detecting optical signal (photo-detectors). It works under reverse bias.

1. Light emitting diode (LED) converts electrical energy into light and emits light.

LEDs have the following advantages over conventional incandescent low power lamps:

1. Low operational voltage and less power.

2. Fast action and no warm-up time required.

3. The bandwidth of emitted light is 100 Å to 500 Å or in other words it is nearly (but not exactly) monochromatic.

4. Long life and ruggedness.

5. Fast on-off switching capability.
1. Photovoltaic devices (solar cells) convert optical radiation into electricity.

A solar cell is basically a p-n junction which generates emf when solar radiation falls on the p-n junction. It works on the same principle as the photodiode, except that no external bias is applied and the junction area is kept much larger for solar radiation to get more power.

The generation of emf by a solar cell, when light falls on, is due to three basic processes: generation, separation and collection:

1. Generation of e-h pairs due to light (with hν > Eg ) close to the junction;

2. Separation of electrons and holes due to electric field of the depletion region. Electrons are swept to n-side and holes to p-side;

3. The electrons reaching the n-side are collected by the front contact and holes reaching p-side are collected by the back contact. Thus p-side becomes positive and n-side becomes negative giving rise to photo-voltage.
• The important criteria for the selection of a material for solar cell fabrication are
1. band gap (~1.0 to 1.8 eV),

2. high optical absorption (~104 cm–1),

3. electrical conductivity,

4. availability of the raw material, and

5. cost

• Solar cells are used to power electronic devices in satellites and space vehicles and also as power supply to some calculators.

JUNCTION TRANSISTOR

Transistor is an n-p-n or p-n-p junction device. The central thin and lightly doped block is called ‘Base’ while the other electrodes are ‘Emitter’ and ‘Collectors’. The emitter-base junction is forward biased while collector-base junction is reverse biased. Since other types of transistors are also known, the junction transistor is called the Bipolar Junction Transistor (BJT).

Types of transistors

1. n-p-n transistor

The two segments of n-type semiconductor (emitter and collector) are separated by a segment of p-type semiconductor (base).

 The schematic representations of n-p-n transistor The symbolic representations of n-p-n transistor
1. p-n-p transistor

The two segments of p-type semiconductor (emitter and collector) are separated by a segment of n-type semiconductor (base).

 The schematic representations of p-n-p transistor The symbolic representations of p-n-p transistor
• All the three segments of a transistor have different thickness and doping levels.

• In the symbols used for representing p-n-p and n-p-n transistors the arrowhead shows the direction of conventional current in the transistor.

• In a p-n-p transistor the current enters from emitter into base whereas in a n-p-n transistor it enters from the base into the emitter.

• Emitter is the segment on one side of the transistor. It is of moderate size and heavily doped. It supplies a large number of majority carriers for the current flow through the transistor.

• Base is the central segment in the transitor. It is very thin and lightly doped.

• Collector is the segment on other side of the transistor. It collects a major portion of the majority carriers supplied by the emitter. The collector side is moderately doped and larger in size as compared to the emitter.

• Two depletion regions are formed at the emitter-base junction and the base-collector junction.

• The charge carriers move across different regions of the transistor when proper voltages are applied across its terminals.

• The biasing of the transistor is done differently for different uses.

Saturated, active and cutoff states of transistor

• The transistor can be used in two ways, as an amplifier and as a switch. When the transistor is used in the cutoff or saturation state it acts as a switch. On the other hand for using the transistor as an amplifier, it has to operate in the active region.

• Transistor in saturation region: The transistor acts like a short circuit. Current freely flows from collector to emitter.

VC < VB and VE < VB for n-p-n

• Transistor in cut-off region: The transistor acts like an open circuit. No current flows from collector to emitter.

VC > VB and VE > VB for n-p-n

• Transistor in active region: The current from collector to emitter is proportional to the current flowing into the base.

VC > VB > VE for n-p-n

Basic transistor circuit configurations and transistor characteristics

The transistor can be connected in one of the following three configurations:

• Common Emitter (CE),

• Common Base (CB),

• Common Collector (CC)

The CE configuration of n-p-n Si transistors is the most common configuration.

Transistor in common base configuration

When the base is the common terminal for the two power supplies whose other terminals are connected to emitter and collector, it is called common base configuration. The power supplies are named as follows.

VCC - power supply between base and collector

VEE – power supply between emitter and base

 p-n-p transistor: common base - emitter base forward bias n-p-n transistor: common base - emitter base forward bias

The voltage between emitter and base is represented as VEB and that between the collector and the base as VCB.

Transistor in common emitter configuration

When the emitter is the common terminal for the two power supplies whose other terminals are connected to base and collector, it is called common emitter configuration. The power supplies are named as follows.

VBB - power supply between base and emitter

VCC – power supply between collector and emitter

Transistor as an amplifier

The transistor works as an amplifier, when its emitter-base junction is forward biased and the base-collector junction is reverse biased. This state of transistor is called active state.

Explanation (emitter-base junction forward biased and base-collector junction reverse biased)

The heavily doped emitter has a high concentration of majority carriers, which will be holes in a p-n-p transistor and electrons in an n-p-n transistor.

These majority carriers enter the base region in large numbers. The base is thin and lightly doped, hence has very few majority carriers. Since base in a p-n-p is n-type, the majority carriers in the base are electrons. The large number of holes entering the base from the emitter, outnumber the small number of electrons there. The base collector-junction is reverse biased, hence the holes which are the minority carriers at the junction, easily cross the junction and enter the collector. The holes in the base could move either towards the base terminal to combine with the electrons entering from outside or cross the junction to enter into the collector and reach the collector terminal. The base is made thin so that most of the holes cross the junction instead of moving to the base terminal.

Now since emitter-base is forward biased, a large current enters the emitter-base junction, but most of it is diverted to adjacent reverse-biased base-collector junction and the current coming out of the base becomes a very small fraction of the current that entered the junction.

Let us assume that the current entering into the emitter from outside is equal to the emitter current IE, the current emerging from the base terminal is IB and that from collector terminal is IC.

If we represent the hole current and the electron current crossing the forward biased junction by Ih and Ie respectively then the total current in a forward biased diode is the sum IE = Ih + Ie.

The base current IB << IE, because most of IE goes to the collector instead of coming out of the base terminal.

Applying Kirchhoff’s law, we can see,

IE = IC + IB and also IC ≈ IE

We can describe the paths followed by the majority and minority carriers in a n-p-n is exactly the same as that for the p-n-p transistor. In this case the electrons are the majority carriers supplied by the n-type emitter region. They cross the thin p-base region and are able to reach the collector to give the collector current, IC .

• Hence in the active state of the transistor the emitter-base junction acts as a low resistance while the base collector acts as a high resistance.

Common emitter transistor characteristics

When a transistor is used in CE configuration, the input is between the base and the emitter and the output is between the collector and the emitter. The variation of the base current IB with the base-emitter voltage VBE is called the input characteristic.

The variation of the collector current IC with the collector-emitter voltage VCE is called the output characteristic.

The output characteristics are controlled by the input characteristics, i.e., the collector current changes with the base current.

To study the input characteristics of the transistor in CE configuration, a curve is plotted between the base current IB against the base-emitter voltage VBE. The collector-emitter voltage VCE is kept fixed while studying the dependence of IB on VBE.

The collector-emitter voltage VCE is kept large enough to make the base collector junction reverse biased.

We can see that, VCE = VCB + VBE

For Si transistor VBE is 0.6 to 0.7 V, VCE must be sufficiently larger than 0.7 V. Since the transistor is operated as an amplifier over large range of VCE, the reverse bias across the base-collector junction is high most of the time.

The input characteristics may be obtained for VCE somewhere in the range of 3 V to 20 V. Since the increase in VCE appears as increase in VCB, its effect on IB is negligible. As a consequence, input characteristics for various values of VCE will give almost identical curves.

Hence, it is enough to determine only one input characteristics.

The output characteristic is obtained by observing the variation of IC as VCE is varied keeping IB constant.

If VBE is increased by a small amount, both hole current from the emitter region and the electron current from the base region will increase. As a consequence both IB and IC will increase proportionately. This shows that when IB increases IC also increases. The plot of IC versus VCE for different fixed values of IB gives one output characteristic. So there will be different output characteristics corresponding to different values of IB.

The linear segments of both the input and output characteristics can be used to calculate some important ac parameters of transistors.

1. Input resistance of transistor (ri): This is defined as the ratio of change in base-emitter voltage (ΔVBE) to the resulting change in base current (ΔIB) at constant collector-emitter voltage (VCE). This is dynamic (ac resistance) and its value varies with the operating current in the transistor:

2. Output resistance of transistor (ro): This is defined as the ratio of change in collector-emitter voltage (ΔVCE) to the change in collector current (ΔIC) at a constant base current IB.

The output characteristics show that initially for very small values of VCE, IC increases almost linearly. This happens because the base-collector junction is not reverse biased and the transistor is not in active state. In fact, the transistor is in the saturation state and the current is controlled by the supply voltage VCC (=VCE) in this part of the characteristic. When VCE is more than that required to reverse bias the base-collector junction, IC increases very little with VCE. The reciprocal of the slope of the linear part of the output characteristic gives the values of ro.

The output resistance of the transistor is mainly controlled by the bias of the base-collector junction. The high magnitude of the output resistance (of the order of 100 kΩ) is due to the reverse-biased state of this diode. This is also the reason why the resistance at the initial part of the characteristic, when the transistor is in saturation state, is very low.

1. Current amplification factor (β): This is defined as the ratio of the change in collector current to the change in base current at a constant collector-emitter voltage (VCE) when the transistor is in active state.

This is also known as small signal current gain and its value is very large.

The ratio of IC and IB is called βdc of the transistor.

• Since IC increases with IB almost linearly and IC = 0 when IB = 0, the values of both βdc and βac are nearly equal. So, for most calculations βdc can be used. Both βac and βdc vary with VCE and IB (or IC) slightly.

Transistor as a device

The transistor can be used as a device application depending on the configuration used (namely CB, CC and CE), the biasing of the E-B and B-C junction and the operation region namely cutoff, active region and saturation.

1. Transistor as a switch - base-biased CE configuration

Applying Kirchhoff’s voltage rule to the input and output sides of this circuit, we get,

VBB = IBRB + VBE and VCE = VCC – ICRC.

Let us assume VBB is a dc input voltage Vi, then VCE will also be a dc output voltage VO. Hence,

Vi = IBRB + VBE

and Vo = VCC – ICRC.

For an Si transistor,

• As long as input Vi is less than 0.6 V, the transistor will be in cut off state and current IC will be zero. Hence Vo = VCC

• When Vi becomes greater than 0.6 V the transistor is in active state with some current IC in the output path. The output voltage Vo decreases as the term ICRC increases. Since, IC increases almost linearly as Vi increases, Vo decreases linearly till its value becomes less than about 1.0 V.

• Beyond this, the change becomes non linear and transistor goes into saturation state. With further increase in Vi the output voltage is found to decrease further towards zero though it may never become zero. If we plot the Vo vs Vi curve, [also called the transfer characteristics of the base-biased transistor], we see that there are regions non-linearity between cut off state and active state and also between active state and saturation state. This shows that the transitions from cutoff state to active state and from active state to saturation state are not sharply defined.

• As long as Vi is low and unable to forward-bias the transistor, Vo is high (at VCC). If Vi is high enough to drive the transistor into saturation, then Vo is low, very near to zero. When the transistor is not conducting it is said to be switched off and when it is driven into saturation it is said to be switched on.

• We can define low and high states as below and above certain voltage levels corresponding to cutoff and saturation of the transistor. We see that a low input switches the transistor off and a high input switches it on. Alternatively, we can say that a low input to the transistor gives a high output and a high input gives a low output. The switching circuits are designed in such a way that the transistor does not remain in active state.

Transistor as a device

1. Transistor as an amplifier

Amplification of dc voltage: In the active region transistor behaves like an amplifier. For Vo versus Vi curve, the slope of the linear part of the curve represents the rate of change of the output with the input. It is negative because the output is VCC – ICRC and not ICRC. Hence, the output voltage of the CE amplifier decreases as input voltage increases. In this case the output is said to be out of phase with the input. If we consider ΔVo and ΔVi as small changes in the output and input voltages then $\frac{\mathrm{\Delta }{\mathrm{V}}_{\mathrm{o}}}{\mathrm{\Delta }{\mathrm{V}}_{\mathrm{i}}}$ is called the small signal voltage gain AV of the amplifier.

If the VBB voltage has a fixed value corresponding to the midpoint of the active region, the circuit will behave as a CE amplifier. The dc base current IB would be constant and corresponding collector current IC will also be constant.

The voltage gain AV can be expressed in terms of the resistors in the circuit and the current gain of the transistor as follows.

We have, Vo = VCC – ICRC

Therefore, ΔVo = 0 – RC Δ IC

Similarly, from Vi = IBRB + VBE

ΔVi = RB ΔIB + ΔVBE

But ΔVBE is negligibly small in comparison to ΔIBRB in this circuit.

Also, the dc voltage VCE = VCC - ICRC would remain constant. The operating values of VCE and IB determine the operating point, of the amplifier.

Amplification of ac signal

If a small sinusoidal voltage with amplitude vs is superposed on the dc base bias by connecting the source of that signal in series with the VBB supply, then the base current will have sinusoidal variations superimposed on the value of IB. As a consequence the collector current also will have sinusoidal variations superimposed on the value of IC, producing in turn corresponding change in the value of VO. We can measure the ac variations across the input and output terminals by blocking the dc voltages by large capacitors.

Let us superimpose an ac input signal vi, to be amplified, on the bias VBB (dc). The output is taken between the collector and the ground.

To start with let us assume that vi = 0. Then applying Kirchhoff’s law to the output loop, we get,

Vcc = VCE + ICRC

And from the input loop, we get,

VBB = VBE + IB RB

When vi is not zero, we get,

VBE + vi = VBE + IB RB + ΔIB (RB + ri)

Or vi = ΔIB (RB + ri) = r ΔIB

The power gain Ap can be expressed as the product of the current gain and voltage gain. Mathematically

Ap = βac × AV

• The transistor is not a power generating device. The energy for the higher ac power at the output is supplied by the battery.

Feedback amplifier and transistor oscillator

In an oscillator, we get ac output without any external input signal. To attain this, a portion of theoutput power is returned back (feedback) to the input in phase with the starting power. This process is termed positive feedback

The feedback can be achieved by inductive coupling (through mutual inductance) or LC or RC networks. Different types of oscillators essentially use different methods of coupling the output to the input (feedback network), apart from the resonant circuit for obtaining oscillation at a particular frequency.

Working of feedback amplifier

Consider the circuit as shown in which the feedback is accomplished by inductive coupling from one coil winding (T1) to another coil winding (T2). The coils T2 and T1 are wound on the same core and hence are inductively coupled through their mutual inductance.

When switch S1 is put on to apply proper bias for the first time, a surge of collector current flows in the transistor. This current flows through the coil T2. This current increases from X to Y, as shown in the graph.

The inductive coupling between coil T2 and coil T1 causes a current to flow in the emitter circuit, the ‘feedback’ from input to output. As a result of this positive feedback, The current in T1 (emitter current) increases from X´ to Y´.

The current in T2 (collector current) connected in the collector circuit acquires the value Y when the transistor becomes saturated. The collector current can increase no further. Since there is no further change in collector current, the magnetic field around T2 stops to grow and there will be no further feedback from T2 to T1. Without continued feedback, the emitter current begins to fall. Consequently, collector current decreases from Y towards Z. However, a decrease of collector current causes the magnetic field to decay around the coil T2. Thus, T1 is now seeing a decaying field in T2. This causes a further decrease in the emitter current till it reaches Z′ when the transistor is cut-off. Both IE and IC are zero. Therefore, the transistor has reverted back to its original state (when the power was first switched on).

• The whole process now repeats itself. That is, the transistor is driven to saturation, then to cut-off, and then back to saturation. The time for change from saturation to cut-off and back is determined by the constants of the tank circuit or tuned circuit (inductance L of coil T2 and C connected in parallel to it).

[A tank circuit or tuned circuit is a parallel combination of a capacitor and inductor]

• The resonance frequency (ν) of this tuned circuit determines the frequency at which the oscillator will oscillate.

If the tank or tuned circuit is connected in the collector side, it is known as tuned collector oscillator. If the tuned circuit is on the base side, it will be known as tuned base oscillator.

Digital electronics and logic gates

Analog signal

The signal (current or voltage) in the form of continuous, time-varying voltage or current is called analog signal.

Digital signal

A signal with discrete values of voltages or current is called digital signal.

If there are only two discrete values possible, we use binary numbers to represent such signals. A binary number has only two digits ‘0’ (say, 0V, for low) and ‘1’ (say, 5V, for high).

Logic gates

A logic gate is a digital circuit that follows curtain logical relationship between the input and output voltages. They control the flow of information. The five common logic gates used are NOT, AND, OR, NAND, NOR. The logic gates can be realised using semiconductor devices.

A logic gate is an elementary building block of a digital circuit. Most logic gates have two inputs and one output. At any given moment, every terminal is in one of the two binary conditions low (0) or high (1), represented by different voltage levels.

Logic gates are used in calculators, digital watches, computers, robots, industrial control systems, and in telecommunications.

Each logic gate is indicated by a symbol and its function is defined by a truth table that shows all the possible input logic level combinations with their respective output logic levels.

1. NOT gate: The output of this gate is the negative or inverse of the input, i.e., it produces a ‘1’ output if the input is ‘0’ and vice-versa. It is also known as an inverter.
 Symbol Truth Table NOT gate Input Output A Y 0 1 1 0
1. OR gate: An OR gate has two or more inputs with one output. The output Y is 1 when either input A or input B or both are 1s, that is, if any of the input is high, the output is high.
 Symbol Truth Table OR gate Input Output A B Y 0 0 0 0 1 1 1 0 1 1 1 1
1. AND gate: An AND gate has two or more inputs and one output. The output Y of AND gate is 1 only when input A and input B are both 1.
 Symbol Truth Table AND gate Input Output A B Y 0 0 0 0 1 0 1 0 0 1 1 1
1. NAND gate: This is an AND gate followed by a NOT gate. If inputs A and B are both ‘1’, the output Y is not ‘1’. The gate gets its name from this NOT AND behaviour. NAND gates are also called Universal Gates since by using these gates you can realise other basic gates like OR, AND and NOT.
 Symbol Truth Table NAND gate Input Output A B Y 0 0 1 0 1 1 1 0 1 1 1 0
1. NOR gate: It has two or more inputs and one output. A NOT- operation applied after OR gate gives a NOT-OR gate (or simply NOR gate). Its output Y is ‘1’ only when both inputs A and B are ‘0’, i.e., neither of the inputs is ‘1’. NOR gates are considered as universal gates because we can obtain all the gates like AND, OR, NOT by using only NOR gates
 Symbol Truth Table NOR gate Input Output A B Y 0 0 1 0 1 0 1 0 0 1 1 0

Integrated circuits

The conventional method of making circuits is to choose components like diodes, transistor, R, L, C etc., and connect them by soldering wires in the desired manner. Despite the miniaturisation introduced by the discovery of transistors, such circuits were still bulky. Apart from this, such circuits were less reliable and less shock proof.

An entire circuit; consisting of many passive components like R and C and active devices like diode and transistor; on a small single block (or chip) of a semiconductor is known as Integrated Circuit (IC). The chip dimensions are very small, as small as 1nm × 1nm.

Depending on nature of input signals, IC’s can be grouped in two categories:

1. Linear or analogue IC’s: The linear IC’s process analogue signals which change smoothly and continuously over a range of values between a maximum and a minimum. The output is more or less directly proportional to the input, i.e., it varies linearly with the input. One of the most useful linear IC’s is the operational amplifier.

2. Digital IC’s: The digital IC’s process signals that have only two values. They contain logic gates. Depending upon the level of integration (i.e., the number of circuit components or logic gates), the ICs are termed as Small Scale Integration, SSI (logic gates < 10); Medium Scale Integration, MSI (logic gates < 100); Large Scale Integration, LSI (logic gates < 1000); and Very Large Scale Integration, VLSI (logic gates > 1000).