Hexadecimal Numbers

In addition to binary, another number base that is commonly used in digital systems is base 16.

This number system is called hexadecimal, and each digit position represents a power of 16.

For any number base greater than ten, a problem occurs because there are more than ten symbols needed to represent the numerals for that number base.

It is customary in these cases to use the ten decimal numerals followed by the letters of the alphabet beginning with A to provide the needed numerals.

Since the hexadecimal system is base 16, there are sixteen numerals required.

The following are the hexadecimal numerals:

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F

The following are some examples of hexadecimal numbers:

10₁₆  47₁₆  3FA₁₆ A03F₁₆

The reason for the common use of hexadecimal numbers is the relationship between the numbers 2 and 16.

Sixteen is a power of 2 (16 = 2⁴).

Because of this relationship, four digits in a binary number can be represented with a single hexadecimal digit.

This makes conversion between binary and hexadecimal numbers very easy, and hexadecimal can be used to write large binary numbers with much fewer digits.

When working with large digital systems, such as computers, it is common to find binary numbers with 8, 16 and even 32 digits. Writing a 16 or 32 bit binary number would be quite tedious and error prone.

By using hexadecimal, the numbers can be written with fewer digits and much less likelihood of error.

To convert a binary number to hexadecimal, divide it into groups of four digits starting with the rightmost digit.

If the number of digits isn’t a multiple of 4, prefix the number with 0’s so that each group contains 4 digits.

For each four digit group, convert the 4 bit binary number into an equivalent hexadecimal digit.

See the Binary, BCD, and Hexadecimal Number Tables at the end of this document for the correspondence between 4 bit binary patterns and hexadecimal digits.

Convert the binary number 10110101 to a hexadecimal number

To convert a hexadecimal number to a binary number, convert each hexadecimal digit into a group of 4 binary digits.

Convert the hex number 374F into binary

There are several ways in common use to specify that a given number is in hexadecimal representation rather than some other radix.

In cases where the context makes it absolutely clear that numbers are represented in hexadecimal, no indicator is used.

Written material where the context doesn’t make it clear what the radix is, the numeric subscript 16 following the hexadecimal number is used.

Programming languages, this method isn’t really feasible, so there are several conventions used depending on the language.

In the C and C++ languages, hexadecimal constants are represented with a ‘0x’ preceding the number, as in: 0x317F, or 0x1234, or 0xAF.

In assembler programming languages that follow the Intel style, a hexadecimal constant begins with a numeric character (so that the assembler can distinguish it from a variable name), a leading ‘0’ being used if necessary.

The letter ‘h’ is then suffixed onto the number to inform the assembler that it is a hexadecimal constant. In Intel style assembler format: 371Fh and 0FABCh are valid hexadecimal constants. Note that: A37h isn’t a valid hexadecimal constant.

It doesn’t begin with a numeric character, and so will be taken by the assembler as a variable name.

In assembler programming languages that follow the Motorola style, hexadecimal constants begin with a ‘$’ character.

So in this case: $371F or $FABC or $01 are valid hexadecimal constants.

Binary Coded Decimal Numbers

Another number system that is encountered occasionally is Binary Coded Decimal.

In this system, numbers are represented in a decimal form, however each decimal digit is encoded using a four bit binary number.

The decimal number 136 would be represented in BCD as follows: 136 = 0001 0011 0110

1     3      6

Conversion of numbers between decimal and BCD is quite simple.

To convert from decimal to BCD, simply write down the four bit binary pattern for each decimal digit.

To convert from BCD to decimal, divide the number into groups of 4 bits and write down the corresponding decimal digit for each 4 bit group.

There are a couple of variations on the BCD representation, namely packed and unpacked.

An unpacked BCD number has only a single decimal digit stored in each data byte.

In this case, the decimal digit will be in the low four bits and the upper 4 bits of the byte will be 0.

In the packed BCD representation, two decimal digits are placed in each byte.

Generally, the high order bits of the data byte contain the more significant decimal digit.

The following is a 16 bit number encoded in packed BCD format:

01010110 10010011

This is converted to a decimal number as follows: 0101 0110 1001 0011

5 6 9 3 The value is 5693 decimal

The same number in unpacked BCD (requires 32 bits)

00000101 00000110 00001001 00000011

5          6            9            3

The use of BCD to represent numbers isn’t as common as binary in most computer systems, as it is not as space efficient.

In packed BCD, only 10 of the 16 possible bit patterns in each 4 bit unit are used. In unpacked BCD, only 10 of the 256 possible bit patterns in each byte are used.

A 16 bit quantity can represent the range 0-65535 in binary, 0-9999 in packed BCD and only 0-99 in unpacked BCD.

Fixed Precision and Overflow

we haven’t considered the maximum size of the number. We have assumed that as many bits are available as needed to represent the number.

In most computer systems, this isn’t the case. Numbers in computers are typically represented using a fixed number of bits.

These sizes are typically 8 bits, 16 bits, 32 bits, 64 bits and 80 bits.

These sizes are generally a multiple of 8, as most computer memories are organized on an 8 bit byte basis.

Numbers in which a specific number of bits are used to represent the value are called fixed precision numbers.

When a specific number of bits are used to represent a number, that determines the range of possible values that can be represented.

For example, there are 256 possible combinations of 8 bits, therefore an 8 bit number can represent 256 distinct numeric values and the range is typically considered to be 0-255.

Any number larger than 255 can’t be represented using 8 bits. Similarly, 16 bits allows a range of 0-65535.

When fixed precision numbers are used, (as they are in virtually all computer calculations) the concept of overflow must be considered.

An overflow occurs when the result of a calculation can’t be represented with the number of bits available.

For example when adding the two eight bit quantities: 150 + 170, the result is 320.

This is outside the range 0-255, and so the result can’t be represented using 8 bits.

The result has overflowed the available range.

When overflow occurs, the low order bits of the result will remain valid, but the high order bits will be lost.

This results in a value that is significantly smaller than the correct result.

When doing fixed precision arithmetic (which all computer arithmetic involves) it is necessary to be conscious of the possibility of overflow in the calculations.

Signed and Unsigned Numbers

we have only considered positive values for binary numbers.

When a fixed precision binary number is used to hold only positive values, it is said to be unsigned.

In this case, the range of positive values that can be represented is 0 — 2ⁿ-1, where n is the number of bits used.

It is also possible to represent signed (negative as well as positive) numbers in binary.

In this case, part of the total range of values is used to represent positive values, and the rest of the range is used to represent negative values.

There are several ways that signed numbers can be represented in binary, but the most common representation used today is called two’s complement.

The term two’s complement is somewhat ambiguous, in that it is used in two different ways.

First, as a representation, two’s complement is a way of interpreting and assigning meaning to a bit pattern contained in a fixed precision binary quantity.

Second, the term two’s complement is also used to refer to an operation that can be performed on the bits of a binary quantity.

As an operation, the two’s complement of a number is formed by inverting all of the bits and adding 1.

In a binary number being interpreted using the two’s complement representation, the high order bit of the number indicates the sign.

If the sign bit is 0, the number is positive, and if the sign bit is 1, the number is negative.

For positive numbers, the rest of the bits hold the true magnitude of the number.

For negative numbers, the lower order bits hold the complement (or bitwise inverse) of the magnitude of the number.

It is important to note that two’s complement representation can only be applied to fixed precision quantities, that is, quantities where there are a set number of bits.

Two’s complement representation is used because it reduces the complexity of the hardware in the arithmetic-logic unit of a computer’s CPU.

Using a two’s complement representation, all of the arithmetic operations can be performed by the same hardware whether the numbers are considered to be unsigned or signed.

The bit operations performed are identical, the difference comes from the interpretation of the bits.

The interpretation of the value will be different depending on whether the value is considered to be unsigned or signed.

Find the 2’s complement of the following 8 bit number

The 2’s complement of 00101001 is 11010111

Find the 2’s complement of the following 8 bit number 10110101

The 2’s complement of 10110101 is 01001011

The counting sequence for an eight bit binary value using 2’s complement representation appears as follows:

Counting up from 0, when 127 is reached, the next binary pattern in the sequence corresponds to -128.

The values jump from the greatest positive number to the greatest negative number, but that the sequence is as expected after that. (i.e. adding 1 to –128 yields –127, and so on.).

When the count has progressed to 0FFh (or the largest unsigned magnitude possible) the count wraps around to 0. (i.e. adding 1 to –1 yields 0).

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BINARY NUMBER SYSTEM

The number system that you are familiar with, that you use every day, is the decimal number system, also commonly referred to as the base-10 system.

When you perform computations such as 3 + 2 = 5, or 21 – 7 = 14, you are using the decimal number system.

This system, which you likely learned in first or second grade, is ingrained into your subconscious; it’s the natural way that you think about numbers.

Evidence exists that Egyptians were using a decimal number system five thousand years ago.

The Roman numeral system, predominant for hundreds of years, was also a decimal number system (though organized differently from the Arabic base-10 number system that we are most familiar with).

Indeed, base-10 systems, in one form or another, have been the most widely used number systems ever since civilization started counting.

In dealing with the inner workings of a computer, though, you are going to have to learn to think in a different number system, the binary number system, also referred to as the base-2 system.

Consider a child counting a pile of pennies. He would begin: “One, two, three, …, eight, nine.”

Upon reaching nine, the next penny counted makes the total one single group of ten pennies.

He then keeps counting: “One group of ten pennies two groups of ten pennies three groups of ten pennies eight groups of ten pennies nine groups of ten pennies”.

Upon reaching nine groups of ten pennies plus nine additional pennies, the next penny counted makes the total thus far: one single group of one hundred pennies.

Upon completing the task, the child might find that he has three groups of one hundred pennies, five groups of ten pennies, and two pennies left over: 352 pennies.

More formally, the base-10 system is a positional system, where the rightmost digit is the ones position (the number of ones), the next digit to the left is the tens position (the number of groups of 10), the next digit to the left is the hundreds position (the number of groups of 100), and so forth.

The base-10 number system has 10 distinct symbols, or digits (0, 1, 2, 3,…8, 9).

In decimal notation, we write a number as a string of symbols, where each symbol is one of these ten digits, and to interpret a decimal number, we multiply each digit by the power of 10 associated with that digit’s position.

For example, consider the decimal number: 6349. This number is:

Consider: Computers are built from transistors, and an individual transistor can only be ON or OFF (two options).

Similarly, data storage devices can be optical or magnetic.

Optical storage devices store data in a specific location by controlling whether light is reflected off that location or is not reflected off that location (two options).

Likewise, magnetic storage devices store data in a specific location by magnetizing the particles in that location with a specific orientation.

We can have the north magnetic pole pointing in one direction, or the opposite direction (two options).

Computers can most readily use two symbols, and therefore a base-2 system, or binary number system, is most appropriate.

The base-10 number system has 10 distinct symbols: 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9.

The base-2 system has exactly two symbols: 0 and 1. The base-10 symbols are termed digits.

The base-2 symbols are termed binary digits, or bits for short. All base-10 numbers are built as strings of digits (such as 6349).

All binary numbers are built as strings of bits (such as 1101).

Just as we would say that the decimal number 12890 has five digits, we would say that the binary number 11001 is a five-bit number.

The Binary Number System

Consider again the example of a child counting a pile of pennies, but this time in binary.

He would begin with the first penny: “1.”

The next penny counted makes the total one single group of two pennies. What number is this?

When the base-10 child reached nine (the highest symbol in his scheme), the next penny gave him “one group of ten”, denoted as 10, where the “1” indicated one collection of ten.

Similarly, when the base-2 child reaches one (the highest symbol in his scheme), the next penny gives him “one group of two”, denoted as 10, where the “1” indicates one collection of two.

 Back to the base-2 child: The next penny makes one group of two pennies and one additional penny: “11.”

The next penny added makes two groups of two, which is one group of 4: “100.”

The “1” here indicates a collection of two groups of two, just as the “1” in the base-10 number 100 indicates ten groups of ten.

Upon completing the counting task, base -2 child might find that he has one group of four pennies, no groups of two pennies, and one penny left over: 101 pennies.

The child counting the same pile of pennies in base-10 would conclude that there were 5 pennies.

So, 5 in base-10 is equivalent to101 in base-2.

To avoid confusion when the base in use if not clear from the context, or when using multiple bases in a single expression, We append a subscript to the number to indicate the base, and write:

5₁₀ =101₂

Just as with decimal notation, we write a binary number as a string of symbols, but now each symbol is a 0 or a 1.

To interpret a binary number, we multiply each digit by the power of 2 associated with that digit’s position.

For example, consider the binary number 1101. This number is:

Since binary numbers can only contain the two symbols 0 and 1, numbers such as 25 and 1114000 cannot be binary numbers.

We say that all data in a computer is stored in binary—that is, as 1’s and 0’s.

It is important to keep in mind that values of 0 and 1 are logical values, not the values of a physical quantity, such as a voltage.

The actual physical binary values used to store data internally within a computer might be, for instance, 5 volts and 0 volts, or perhaps 3.3 volts and 0.3 volts or perhaps reflection and no reflection.

The two values that are used to physically store data can differ within different portions of the same computer.

All that really matters is that there are two different symbols, so we will always refer to them as 0 and 1.

A string of eight bits (such as 11000110) is termed a byte.

A collection of four bits (such as 1011) is smaller than a byte, and is hence termed a nibble.

This is the sort of nerd-humor for which engineers are famous.

The idea of describing numbers using a positional system, as we have illustrated for base-10 and base-2, can be extended to any base. For example, the base-4 number 231 is:

Converting Between Binary Numbers and Decimal Numbers

We humans about numbers using the decimal number system, whereas computers use the binary number system.

We need to be able to readily shift between the binary and decimal number representations.

Converting a Binary Number to a Decimal Number

To convert a binary number to a decimal number, we simply write the binary number as a sum of powers of 2.

For example, to convert the binary number 1011 to a decimal number, we note that the rightmost position is the ones position and the bit value in this position is a 1.

So, this rightmost bit has the decimal value of 1⋅2⁰.

The next position to the left is the twos position, and the bit value in this position is also a 1.

So, this next bit has the decimal value of 1⋅ 2¹.

The next position to the left is the fours position, and the bit value in this position is a 0.

The leftmost position is the eights position, and the bit value in this position is a 1.

So, this leftmost bit has the decimal value of 1⋅2³.

Thus:

The binary number 110110 as a decimal number. Solution:

For example, to convert the binary number 10101 to decimal, we annotate the position values below the bit values:

Then we add the position values for those positions that have a bit value of 1: 16 + 4 + 1 = 21.

Thus 10101₂ = 21₁₀

You should “memorize” the binary representations of the decimal digits 0 through 15 shown below.

You may be wondering about the leading zeros in the table above.

For example, the decimal number 5 is represented in the table as the binary number 0101.

We could have represented the binary equivalent of 5 as 101, 00101, 0000000101, or with any other number of leading zeros.

All answers are correct.

Sometimes, though, you will be given the size of a storage location.

When you are given the size of the storage location, include the leading zeros to show all bits in the storage location.

For example, if told to represent decimal 5 as an 8-bit binary number, your answer should be 00000101.

Converting a Decimal Number to a Binary Number:

Method 2

The second method of converting a decimal number to a binary number entails repeatedly dividing the decimal number by 2, keeping track of the remainder at each step. To convert the decimal number x to binary:

Step 1. Divide x by 2 to obtain a quotient and remainder. The remainder will be 0 or 1.

Step 2. If the quotient is zero, you are finished: Proceed to Step 3. Otherwise, go back to Step 1, assigning x to be the value of the most-recent quotient from Step 1.

Step 3. The sequence of remainders forms the binary representation of the number.

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BIPOLAR JUNCTION TRANSISTOR

A bipolar junction transistor is a three terminal semiconductor device in which the operation depends on the interaction of majority and minority carriers.

Transistor refers to Transfer Resistor

i.e., signals are transferred from low resistance circuit into high resistance circuit.

BJT BIPOLAR JUNCTION TRANSISTOR consists of silicon crystal in which a layer of ‘N’ type silicon is sandwiched between two layers of ‘P’ type silicon.

The semiconductor sandwiched is extremely smaller in size.

In other words, it consists of two back to back PN junction joined together to form single piece of semiconductor crystal.

These two junctions gives three region called Emitter, Base and Collector.

There are two types of transistors such as PNP and NPN.

The arrow on the emitter specifies whether the transistor is PNP or NPN type and also determines the direction of flow of current, when the emitter base junction is forward biased.

Emitter: 

It is more heavily doped than any of the other region because its main function is to supply majority charge carriers to the base.

Base:

It forms the middle section of the transistor.

It is very thin as compared to either the emitter or collector and is very lightly doped.

Collector: 

Its main function is to collect the majority charge carriers coming from the emitter and passing through the base.

In most transistors, collector region is made physically larger than the emitter because it has to dissipate much greater power.

Operation of Transistor

The basic operation will be described using the pnp transistor.

The operation of the pnp transistor is exactly the same if the roles played by the electron and hole are interchanged.

One p-n junction of a transistor is reverse-biased, whereas the other is forward-biased.

Both biasing potentials have been applied to a pnp transistor and resulting majority and minority carrier flows indicated.

Majority carriers (+) will diffuse across the forward-biased p-n junction into the n-type material.

A very small number of carriers (+) will through n-type material to the base terminal. Resulting IB is typically in order of microamperes.

The large number of majority carriers will diffuse across the reverse-biased junction into the p-type material connected to the collector terminal.

Majority carriers can cross the reverse-biased junction because the injected majority carriers will appear as minority carriers in the n-type material.

Applying KCL to the transistor :

I_E = I_C + I_B

The comprises of two components – the majority and minority carriers

IC = ICmajority + ICOminority

I_CO – I_C current with emitter terminal open and is called leakage current.

Common Base configuration

Common-base terminology is derived from the fact that the :

base is common to both input and output of the configuration.

base is usually the terminal closest to or at ground potential.

All current directions will refer to conventional (hole) flow and the arrows in all electronic symbols have a direction defined by this convention.

Note that the applied biasing (voltage sources) are such as to establish current in the direction indicated for each branch.

To describe the behavior of common-base amplifiers requires two set of characteristics: o Input or driving point characteristics.

Output or collector characteristics

The output characteristics has 3 basic regions:

Active region –defined by the biasing arrangements

Cutoff region – region where the collector current is 0A

Saturation region- region of the characteristics to the left of

V_CB = 0V

The curves (output characteristics) clearly indicate that a first approximation to the relationship between IE and IC in the active region is given by

I_C ≈IE

Once a transistor is in the ‘on’ state, the base-emitter voltage will be assumed to be

V_BE = 0.7V

In the dc mode the level of I_C and I_E due to the majority carriers are related by a quantity called alpha

 α = I_C / I_E

I_C = α I_E + I_CBO

It can then be summarize to IC = αI_E (ignore I_CBO due to small value)

For ac situations where the point of operation moves on the characteristics curve, an ac alpha defined by

Alpha a common base current gain factor that shows the efficiency by calculating the current percent from current flow from emitter to collector. The value of  is typical from 0.9 ~ 0.998.

Common Emitter configuration

It is called common-emitter configuration since :

emitter is common or reference to both input and output terminals.

emitter is usually the terminal closest to or at ground potential.

Almost amplifier design is using connection of CE due to the high gain for current and voltage.

Two set of characteristics are necessary to describe the behavior for CE; input (base terminal) and output (collector terminal) parameters.

Input characteristics for CE configuration

I_B in microamperes compared to milliamperes of I_C.

 I_B will flow when V_BE > 0.7V for silicon and 0.3V for germanium

Before this value I_B is very small and no I_B.

Base-emitter junction is forward bias

Increasing V_CE will reduce I_B for different values.

Output characteristics for CE configuration

For small V_CE (V_CE < V_CESAT, I_C increase linearly with increasing of V_CE

V_CE > V_CESAT I_C not totally depends on V_CE   — > constant I_C

I_B(uA) is very small compare to I_C (mA). Small increase in I_B cause big increase in I_C

I_B=0 A  — >  I_CEO occur.

Noticing the value when I_C=0A. There is still some value of current flows.

Common Collector configuration

• Also called emitter-follower (EF).
• It is called common-emitter configuration since both the
• Signal source and the load share the collector terminal as a common connection point.
• The output voltage is obtained at emitter terminal.
• The input characteristic of common-collector configuration is similar with common-emitter. configuration.
• Common-collector circuit configuration is provided with the load resistor connected from emitter to ground.
• It is used primarily for impedance-matching purpose since it has high input impedance and low output impedance.
• For the common-collector configuration, the output characteristics are a plot of I_E vs V_CEfor a range of values of I_B.

Small Signal Amplifier

When the input signal is so weak as to produce small fluctuations in the collector current compared to its quiescent value, the amplifier is known as Small Signal Amplifier.

In other words, as the name indicates, the input applied to the circuit is V_in << V_th. It has only one amplifying device.

Α = I_C / I_E

I_C = α  I_E + I_CBO

Voltage and current equation for hybrid parameters:

V₁ = h₁₁i₁ + h₁₂V₂

I₂ = h₂₁i₁ + h₂₂V₂

The values of h-parameters:

h₁₁ = V₁/ i₁

h₁₂ = V₁ / V₂

h₂₁ = i₂ / i₁

h₂₂ = i₂ / V₂

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RECTIFIERS

The rectifiers is a circuit that converts AC voltages and currents into pulsating DC voltages and currents.

It consists of DC components and the unwanted ac ripple or harmonic components which can be removed by using filter circuit.

Thus the output obtained will be steady DC voltage and magnitude of DC voltage can be varied by varying the magnitude of AC voltage.

Filters: A circuit that removes ripples (unwanted ac components) present in the pulsating dc voltage.

Regulator: A circuit that maintains the terminal voltage as constant even if the input voltage or load current varying.

Types of rectifiers:

Rectifiers are grouped into two categories depending on the period of conduction.

(a)Half wave rectifier

(b) Full wave rectifier

Half wave Rectifier:

Principle

It is a circuit that converts alternating voltage or current into pulsating voltage or current for half the period of input cycle hence it is named as “half wave rectifier”.

Construction

• It consists of step-down transformer, semiconductor diode and the load resistance.
•  The step-down transformer – reduce the available ac voltage into required level of smaller ac voltage.
•  The diode can be used to convert the ac into pulsating dc.

Operation

• During the positive half cycle of input, the diode D is forward biased, it offers very small resistance and it acts as closed switch and hence conducts the current through the load resistor.
• During the negative half cycle of the input diode D is heavily reverse biased, it offers very high resistance and it acts as open switch hence it does not conduct any current.
• The rectified output voltage will be in phase with AC input voltage for completely resistive load.

Full wave Rectifier:

Principle

A circuit that converts the ac voltage or current into pulsating voltage or current during both half cycle of input is known as “full wave rectifier”.

Operation

• During positive half cycle of ac input, diode D₁ becomes forward biased, provides very small resistance and acts as closed switch, resulting in the flow of current.
• During negative half cycle, diode D₁ reverse biased, offers high resistance and it acts as open circuit.

 Voltage Regulation:

Ratio of Difference of secondary voltage to Primary voltage to secondary voltage.

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ZENER EFFECT

ZENER EFFECT: In a general purpose PN diode the doping is light; as a result of this the breakdown voltage is high.

If a P and N region are heavily doped then the breakdown voltage can be reduced.

 When the doping is heavy, even the reverse voltage is low, the electric field at barrier will be so strong thus the electrons in the covalent bonds can break away from the bonds.

This effect is known as Zener effect.

 ZENER DIODE

A diode which exhibits the zener effect is called a Zener Diode. Hence it is defined as a reverse biased heavily doped PN junction diode which operates in breakdown region.

The zener diodes have been designed to operate at voltages ranging from a few volts to several hundred volts.

 Zener Breakdown occurs in junctions which is heavily doped and have narrow depletion layers.

The breakdown voltage sets up a very strong electric field.

This field is so strong enough to break or rupture the covalent bonds thereby generating electron hole pairs.

Even a small reverse voltage is capable of producing large number of current carrier.

When a zener diode is operated in the breakdown region care must be taken to see that the power dissipation across the junction is within the power rating of the diode otherwise heavy current flowing through the diode may destroy it.

V-I characteristics of Zener diode

The illustration above shows this phenomenon in a current vs voltage graph with a zener diode connected in the forward direction.

It behaves exactly as a standard diode.

 In  the  reverse  direction  however  there  is  a  very  small  leakage  current  between  0v and the zener voltage

i.e. just a tiny amount of current is able to flow.

Then, when the voltage reaches the breakdown voltage (vz),suddenly current can flow freely through it.

 Application of Zener diode

• As voltage regulator
• As peak clippers
• For reshaping waveforms

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PN JUNCTION DIODE

PN JUNCTION DIODE:

A p–n junction is formed by joining P-type and N-type semiconductors together in very close contact.

The term junction refers to the boundary interface where the two regions of the semiconductor meet.

Diode is a two-terminal electronic component that conducts electric current in only one direction.

The crystal conducts conventional current in a direction from the p-type side (called the anode) to the n-type side (called the cathode), but not in the opposite direction.

Symbol of PN junction diode

Biasing

“Biasing” is providing minimum external voltage and current to activate the device to study its characteristics.

There are two operating regions and two “biasing” conditions for the standard Junction Diode and they are

Zero Bias:

 When a diode is Zero Biased no external energy source is applied and a natural Potential Barrier is developed across a depletion layer.

(i) Forward Bias:

When the positive terminal of a battery is connected to P-type semiconductor and negative terminal to N-type is known as forward bias of PN junction.

The applied forward potential establishes an electric field opposite to the potential barrier.

Therefore the potential barrier is reduced at the junction. As the potential barrier is very small (0.3V for Ge and 0.7V for Si),a small forward voltage is sufficient to completely eliminate the barrier potential, thus the junction resistance becomes zero.

In otherwords, the applied positive potential repels the holes in the ‘P’ region so that the holes moves towards the junction and applied negative potential repels the electrons in the ‘N’ region towards the junction results in depletion region starts decreasing.

When the applied potential is more than the internal barrier potential then the depletion region completely disappear, thus the junction resistance becomes zero.

Once the potential barrier is eliminated by a forward voltage, j unction establishes the low resistance path for the entire circuit, thus a current flows in the circuit, it is called as forwardcurrent.

(ii)Reverse Bias:

For reverse bias, the negative terminal is connected to P-type semiconductor and positive terminal to N type semiconductor.

When reverse bias voltage is applied to the junction, all the majority carriers of ‘P’ region are attracted towards the negative terminal of the battery and the majority carriers of the N region attracted towards the positive terminal of the battery, hence the depletion region increases.

The applied reverse voltage establishes an electric field which acts in the same direction of the potential barrier.

Therefore, the resultant field at the junction is strengthened and the barrier width is increased.

This increased potential barrier prevents the flow of charge carriers across the junction, results in a high resistance path.

This process cannot continue indefinitely because after certain extent the junction break down occurs.

As a result a small amount of current flows through it due to minority carriers. This current is known as “reverse saturation current”.

 V I characteristics of PN junction diode

Forward Bias:

The application of a forward biasing voltage on the junction diode results in the depletion layer becoming very thin and narrow which represents a low impedance path through the junction thereby allowing high currents to flow.

The point at which this sudden increase in current takes place is represented on the static I-V characteristics curve above as the “knee” point.

Reverse Bias:

In Reverse biasing voltage a high resistance value to the PN junction and practically zero current flows through the junction diode with an increase in bias voltage.

However, a very small leakage current does flow through the junction which can be measured in microamperes, (μA).

One final point, if the reverse bias voltage Vr applied to the diode is increased to a sufficiently  high enough value, it will cause the PN junction to overheat and fail due to the avalanche effect around the junction.

This may cause the diode to become shorted and will result in the flow of maximum circuit current, and this shown as a step downward slope in the reverse static characteristics curve below.

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Bipolar Junction Transistor(BJT)

Classification of Semiconductor

Classification of Semiconductor

• Intrinsic Semiconductor
• Extrinsic Semiconductor

Intrinsic Semiconductor

 An intrinsic semiconductor also called an undoped semiconductor or i- type semiconductor.

It is a pure semiconductor without any significant dopant species present.

The number of charge carriers determined by the properties of the m aterial itself instead of the amount of impurities.

In intrinsic semiconductors the number of excited electrons and the number of holes are equal: n = p.

Conductivity of Intrinsic semiconductor

• The electrical conductivity of intrinsic semiconductors can be due to crystal defects or to thermal excitation.
• Both electrons and holes contribute to current flow in an intrinsic semiconductor.
• The current which will flow in an intrinsic semiconductor consists of both electron and hole current.
• That is, the electrons which have been freed from their lattice positions into the conduction band can move through the material.
• In addition, other electrons can hop between lattice positions to fill the vacancies left by the freed electrons.
• This additional mechanism is called hole conduction because it is as if the  holes  are migrating across the material in the direction opposite to the free electron movement.
• The current flow in an intrinsic semiconductor is influenced by the density of energy states which in turn influences the electron density in the conduction band.
• This current is highly temperature dependent.

Thermal excitation:

In an intrinsic semiconductor like silicon at temperatures above absolute zero, there will be some electrons which are excited across the band gap into the conduction band and which can produce current.

When the electron in pure silicon crosses the gap, it leaves behind an electron vacancy or “hole” in the regular silicon lattice.

Under the influence of an external voltage, both the electron and the hole can move across the material.

In n-type semiconductor:

The dopant contributes extra electrons, dramatically increasing the conductivity

In p-type semiconductor:

The dopant produces extra vacancies or holes, which likewise increase the conductivity.

Extrinsic Semiconductor

• The electrical conductivity of a pure semiconductor is very small.
• To increase the conductivity, impurities are added.
• The impurity added semiconductor is called extrinsic semiconductor.
• The process of adding impurity is called doping.
• The added impurity is called dopant.
• Usually one or two atoms of impurity is added per 106 atoms of a semiconductor.
• There are two types (i) p-type and (ii) n-type semiconductors.
• When an impurity, from V group elements like arsenic (As), antimony having 5 valence electrons is added to Ge (or Si), the impurity atom donates one electron to Ge (or Si).
• The 4 electrons of the impurity atom is engaged in covalent bonding with Si atom.
  • The fifth electron is free. This increases the conductivity.
  • The impurities are called donors.
  • The impurity added semiconductor is called n-type semiconductor, because their increased conductivity is due to the presence of the negatively charged electrons, which are called the majority carriers.
• The energy band of the electrons donated by the impurity atoms is just below the conduction band.
• The electrons absorb thermal energy and occupy the conduction band.
• Due to the breaking of covalent bond, there will be a few holes in the valence band at this temperature.
• These holes in n-type are called minority carriers.

• If a III group element, like indium (In), boron (B), aluminium (AI) etc., having three valence electrons, is added to a semiconductor say Si, the three electrons form covalent bond.
• There is a deficiency of one electron to complete the 4th covalent bond and is called a hole.The presence of the hole increases the conductivity because these holes move to the nearby atom, at the same time the electrons move in the opposite direction.
• The impurities added semiconductor is called p-type semiconductor.
• The impurities are called acceptors as they accept electrons from the semiconductor
• Holes are the majority carriers and the electrons produced by the breaking of bonds are the minority carriers.

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Semiconductor Devices And Applications

Classification of Materials

PN Junction Diode

Zener Effects

Rectifiers and Types of rectifiers

Bipolar Junction Transistor(BJT)

Classification of Materials

CLASSIFICATION OF MATERIALS

The materials are classified based on their conducting property.

Energy band theory can be used to explain the classification of materials.

Conductors

Conductor is materials that easily conducts or pass the current.

There are plenty of free electrons available for electric conduction.

In terms of energy band theory, the conductors have overlapping of valence band and conductive band.

Example: 

Copper, Aluminum, iron, etc

Properties:

1. It is rigid, non directional and crystalline in nature.
2. Conductivity is good.
3. Low melting and boiling temperatures.

Semiconductors

Semiconductor is a material with partially filled conduction band and valence band.

The current in the semiconductor is due to the movement of electrons and holes.

As the temperature increases the conduction increases.

Example: Silicon, Germanium, etc.

Properties: 

1. It is rigid, directional and crystalline in nature.
2. Conductivity can be increased if proper doping material is added.
3. Low melting and boiling temperatures.

Insulators

In the case of insulators, the valence electrons are very tightly bound to their parent atom.

The valence band and conduction band are separated by a large forbidden energy gap.

The insulators have full valence band and an empty conduction band.

Example: Paper, Mica. Sodium chloride, etc.

Properties: 

1. It is rigid, Unidirectional and crystalline in nature.
2. Conductivity is poor in the solid form.
3. High melting and boiling temperatures.

Comparison of Conductors,Semiconductors and Insulators

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Semiconductor Devices And Applications

Classification of Semiconductor

PN Junction Diode

Zener Effects

Rectifiers and Types of rectifiers

Bipolar Junction Transistor(BJT)