Consider a closed rectangular path in xy-plane which encloses a current element and the current flows in z-direction.

at center point P is .

By applying Gauss’s law to differential volume element leads to a concept of divergence as similar to that by applying ampere’s law to a current element in a closed path leads to curl.

Consider a conductor of finite length placed along z-axis as shown in the figure

The conductor has a finite length AB , where A and B are located at distances Z_{1} and Z_{2} above the origin with it’s upper and lower ends respectively subtending angles and at P.

P is the point at which is to be determined.

Consider a differential element along the Z-axis at a distance Z from the origin.

where .

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as , and .

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Case 1 :-

when the conductor is semi-finite that is A is located at origin and B at .

i.e, and .

then .

Case 2:-

when conductor is infinite in length A is at and B at implies and .

Consider as infinitely long straight conductor placed along z-axis carrying a current I .

In order to determine at some point P. we allow a closed path which passes through the point P and encloses the current carrying conductor symmetrically such path is known as Amperian path.

To apply Ampere’s law the conditions t be satisfied are

The field is either tangential (or) Normal to the path at each point of the closed path.

The magnitude of must be same at all points of the path where is tangential.

Now, is given by .

The path we are assuming is in the direction of so .

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Ampere’s law is used to find out at P

i.e, from Ampere’s circuit law .

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from Ampere’s law .

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Ampere’s law is applied to find the value of at any point P in it’s field.

Ampere’s Circuit law states that the line integral of the tangential component of around a closed path is the same as the net current (I_{enc}) enclosed by the path.

i.e, .

This is similar to Gauss’s law and can be applied to determine when the current distribution is symmetrical it’s a special case of Biot-savart’s law.

Proof:-

Consider a circular loop which encloses a current element . Let the current be in upward direction then the field is in anti- clock wise .

The current which is enclosed by the circular loop is of infinite length then at any point A is given by

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which is known as the integral form of Ampere’s circuit law.

The function of a receiver in a binary Communication system is to distinguish between two transmitted signals (or) () in the presence of noise.

The performance of Receiver is usually measured in terms of the probability of error P_{e} an the receiver is said to be optimum if it yields the minimum probability of error.

i.e, optimum receiver is the one with minimum probability of error P_{e} .

optimum receiver takes the form of Matched filter when the noise at the receiver input is white noise.

optimum receiver (or) optimum filter:-

The block diagram of optimum receiver is as shown in the figure below

the decision boundary is set to .

Probability of error of optimum filter:-

The probability of error can be obtained as similar to Integrate and dump receiver. Here we will consider noise as Gaussian Noise.

The output of optimum filter is .

The output of sampler is

suppose if Binary ‘1’ is transmitted then the input is , to find the probability of error this transmitted ‘1’ should be received as ‘0’.

this is possible when the condition is true.

1 will be received as 0 .

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similarly a Binary ‘0’ will be received as ‘1’ if and only if

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the conditions are summarized in the table

Noe the Probability Distribution Function of Gaussian noise with zero mean and standard deviation is given by

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Probability of error= probability ‘1’ will be received as ‘0’ =probability ‘0’ will be received as ‘1’.

Signals transmitted over Transmission lines are mostly complex and consists of high frequency components, while passing through the line distortion occurs in the signal , this is commonly known as line distortion.

In ideal Transmission line , it is intended that the waveform at the receiving end of the line must be identical to the wave form at the sending end then the line is said to be distortion less line (or) distortion free line.

It has been seen that distortion in the waveform exists if all frequencies in the complex wave form do not have the same attenuation and same delay during propagation.

when the received signal is not the exact replica of the transmitted signal then the signal is said to be distorted.

causes of distortion in a Transmission Line:-

distortion is caused due to the following three reasons mainly

variation of characteristic impedance with respect to frequency:-The characteristic impedance of the line varies with change in frequency and line should be terminated in an impedance that does not vary with frequency to avoid distortion.

variation of attenuation with respect to frequency:- the attenuation of the line varies with frequency. Hence waves of different frequencies are attenuated by different amounts known as frequency distortion.

variation of phase constant with respect to frequency:- phase distortion due to the variation of phase constant with the frequency which in turn varies the velocity of propagation with frequency . Therefore waves of different frequencies arrive at different times at the end of the line.

Thus for a line to be distortion less the characteristic impedance , attenuation and phase constant should be independent of frequency.

An Optical fiber transmission link comprises the elements shown in the given figure.

The key sections are

A transmitter consisting of a light source and its associated drive circuitry.

A cable offering mechanical and environmental protection to the optical fibers contained inside it.

A receiver consisting of a Photo detector plus amplification and signal restoring circuitry.

Additional components include optical connectors, splicers, couplers (or) beam splitters and repeaters.

Cable:-

optical fiber is one of the most important elements in an optical fiber link. The cable may contain copper wires for powering repeaters which are needed for periodically amplifying and reshaping the signal in long distance communication.

The cable generally contains several cylindrical hair-thin glass fibers, each of which is an independent communication channel.

Similar to copper cables, the installation of optical fiber cables can be either aerial, in ducts, under sea (or) buried directly in the ground.

As a result of installation and (or) manufacturing limitations, individual cable lengths will range from several hundred meters to several kilo meters for long distance applications.

The real size and cable weight determines the actual length of a single cable section.

Cable in ducts—- shorter length

Aerial/ buried applications—– longer lengths.

The complete long-distance transmission line is formed by splicing (or) connecting together these cable sections.

In optical fibers attenuation is a function of wave length .

In early stages of technology, optical fibers were used in

First window: (800nm-900nm) wave length.

Later on optical fibers are used in the long-wave length region.

Long-wave length region (1100-1600) nm

Second window-centered around 1300nm.

Third window- centered around 1550nm.

Transmitter:-

Once the fiber cable is installed a light source (which is dynamically compatible with the fiber cores) is used to launch power into the fiber.

The electric i/p signal is either analog (or) digital form the Transmitter circuit converts this electric signal to an optical signal.

Optical source is a square-law device. In (800-900) nm region the light source is made up of

Ga Al As and in long distance region (1100nm-1600nm) In Ga AsP is the alloy used.

after an optical signal (light) has been launched into the fiber, it will be attenuated and distorted with increasing distance because of scattering, absorption and dispersion mechanisms in the wave guide.

Receiver:-

The attenuated and distorted , modulated optical power emerging from the fiber end will be detected by photo diode (or) photo detector.

Photo detector converts optical power into electrical signal (it also uses a square-law).

photo detectors are PIN diodes, Avalanche photo diodes and the type of material it is made up of is In Ga As.

further the electrical signal will be amplified and restored.

therefore the design of the receiver is more complex than that of transmitter.

The meaning of QPSK is that the carrier signal takes on different phases Π/4, 3Π/4, 5Π/4 and 7Π/4 based on incoming di-bit combination or symbol.

= 0, elsewhere, where i = 1,2,3,4.

E_{b} and T_{b} are the bit energy and bit-interval , E_{s} and T_{s} are the energy per symbol and symbol duration. T_{s }= 2 T_{b} .

The carrier frequency f_{c} = n_{c} /T_{s}. where n_{c} is a fixed integer.

each possible value of phase corresponds to a unique di-bit. then the foregoing phase values to represent the gray encoded set of di-bits 11,01,10 and 00, where only a single bit is changed from one di-bit to the next.

QPSK equation can be represented in another format as follows

= 0, elsewhere ,where i=0,1,2,3.

The above two equations are same, there is a change in i values. alternately the equation can be represented as follows.

, where i= 1,2,3,4.

The above equation can be expanded cos(A+B). There are two orthogonal functions Φ_{1}(t) and Φ_{2}(t) where

Draw the h-parameter equivalent model of transistor in CE configuration and define the four h- parameters.

Explain the construction of JFET (either n-channel or p-channel).

Explain the current components of a BJT in detail with a neat sketch.

Short Answer Questions:

Write the differences between JFET and BJT.

What are three possible configurations of BJT?

Define α, β and γ of a BJT write the relationship between them.

What are three possible regions of a transistor (write about cut-off, active and saturation regions).

What is base width modulation?

Define four h-parameters of transistor. And draw general h-parameter model of a BJT.

Define the following

Bandwidth of an amplifier.

Gain or amplification factor.

Compare CE, CB and CC transistors.( in terms of input resistance, o/p resistance, current gain, voltage gain, phase shift and applications).

What are the advantages of FET over BJT?

Why FET is more preferable than BJT?

How FET is known as uni polar device ? how do you compare FET with BJT?

Why FET is called as voltage controlled device?

What are the parameters of FET?

What are the three possible configurations of FET?

Give the relationship between g_{m} , r_{d} and µ.

Draw the equivalent circuit diagram of FET in CS configuration.

Why BJT is called as Current controlled device.

Draw transfer and output characteristics of FET.

Draw the symbols of NPN transistor,n channel FET and SCR.

If the emitter of a transistor is open will there be any collector current.

Long Answer Questions:

What is CB configuration? Draw the input and output characteristics of CB transistor. Explain in detail.

Define α and β of a transistor and derive the relationship between them.

Explain the current components of BJT in detail.

Explain how transistor is working as an amplifier?

Explain the working of CE amplifier with a neat circuit diagram. Derive expression for input resistance, and current gain using h parameter equivalent circuit.

Draw the hybrid equivalent circuit of an NPN BJT in CE configuration. Derive expressions for Av, Ai, Ri,

Calculate the values of Ic and Ib, for a transistor with α=.99,Ico=5µA,Ib=20µA.

Draw a simple inverter circuit and explain its operation.

Draw the h-parameter model of CE transistor and explain how h-parameters are calculated from CE characteristics.

Explain the construction and working of FET (either n-channel or p-channel).

Draw output and transfer characteristics of FET explain the working of /FET through them.

Derive the relationship between g_{m}, r_{d} and µ.

Write the comparisons between FET and BJT.

How FET is working as an amplifier?

Explain the working operation of NPN and PNP transistors.

Explain various operation regions of a transistor in detail.

What is CE configuration? Draw the input and output characteristics of CB transistor. Explain in detail.

What is CC configuration? Draw the input and output characteristics of CB transistor. Explain in detail.

What are the disadvantages of BJT? Why FET is preferred over BJT? Give the applications of FET.

Explain the working of JFET And explain the parameters of JFET.

Note: Read the questions in the following order i. Assignment questions ii. Class test iii. Expected questions iv. Tutorials For every unit.

Unit1:

ASSIGNMENT- UNIT 1

Explain the working of Bridge rectifier in detail with a neat circuit diagram and derive the expression for ripple factor and efficiency. 10M.

Explain the working of PN-junction diode in detail in forward and reverse bias conditions. 10M.

A 230v, 60 Hz voltage is applied to the primary of a step down center tapped transformer of a FWR with turns ratio 5:1 is connected to a load resistance of 1 KΩ i. i. Determine voltage across the load. ii. DC current through the load. If there is a resistance of 100Ω for the transformer secondary and diode forward Resistance is given as 10Ω.

Short Answer Questions:

Write the expression of diode current equation and explain each term in detail.

Define cut in or threshold voltage of a diode. Give the values of Vof Si and Ge diode.

Write the differences between Extrinsic and Intrinsic semiconductors.

What are P-type and N-type semiconductors?

Write in detail about Drift and Diffusion currents.

Draw the Energy Band Diagrams of an insulator, semiconductor, Conductor.

Write the differences between insulators, conductors and semi conductors.

Define the following a. Mobility b. Conductivity c. Mass Action law. d.Fermi level in semi conductors.

Draw the diagrams for Fermi-level in Intrinsic, N-type and P-type semi conductors and write the formula for E_{F} in the above two cases.

Define Hall Effect and write the uses or applications of Hall Effect.

What properties of semi conductor are defined from Hall Effect?

What is a diode and write the applications of Diode.

Draw the VI-Characteristics of a diode. And calculate Static and Dynamic resistances from the characteristics.

Write about diffusion and Transition capacitances of a diode.

Define avalanche breakdown and zener breakdown.

What is avalanche effect and zener effect?

What is a rectifier? Differentiate between Half Wave Rectifier and Full Wave Rectifier.

Draw the equivalent circuit of practical Diode under forward bias and Reverse Bias.

Draw the equivalent circuit of ideal Diode under forward bias and Reverse Bias.

Define Peak Inverse Voltage (PIV) of a diode in a rectifier circuit. Write the PIV values in HWR, FWR and Bridge Rectifier.

Define the following i. Ripple factor ii. Regulation or Percentage of Regulation. iii. From factor and peak factor. iv. Efficiency of a rectifier v. RMS value and average value of voltage or current wave in half wave rectifier.

Write the applications of Zener Diode.

Explain how Zener diode works as a regulator.

What is the concentration of holes in Si crystals having donor concentration of 1.4 x 10^{24}/m^{3} when the intrinsic carrier concentration is 1.4 x 10^{18}/m^{3} ? Find the ratio of electron to hole concentration.

Problems on motilities of n-type and p-type semiconductors.

An n-type Ge crystal has a current density of 100A/m^{2}. The crystal has a resistivity of 0.5 Ω-m and electron mobility of 0.4 m^{2}/V-s. Calculate the drift velocity and the time taken by the electron to travel 10 micrometer in the crystal. Assume q= 1.6 x 10^{-19}

Problems on Fermi levels.

Problems on diode current equation in forward bias and reverse bias.

Write the advantages of full wave and bridge rectifiers over half wave rectifier.

Long Answer Questions:

Define Hall Effect. Derive the expression for Hall voltage and hall coefficient and explain the uses of Hall Effect.

Derive the expression for transition and diffusion capacitances of a diode.

Explain the working of Zener Diode as a regulator.

Derive the expression for ripple factor and efficiency of a Half Wave rectifier and full wave rectifier.

Derive the expression for ripple factor and efficiency of a bridge rectifier.

Compare half wave rectifier, FWR and Bridge rectifier in terms of (ripple factor, percentage of regulation, efficiency, PIV, from factor and peak factor etc…… read the comparison table in text book).

How will you find the dynamic and static resistance of the diode using a graph?

What is an ideal diode? How can it be represented as a switch? Draw the equivalent circuit and its characteristics.

Draw the VI-Characteristics of a PN junction diode in forward and reverse biased conditions. Define forward resistance and reverse resistances and explain how they can be obtained from the characteristics.

Draw the circuit diagram of a half wave rectifier and explain its operation with wave forms.

Draw the circuit diagram of bridge rectifier and explain its operation with wave forms.

Draw the circuit diagram of a full wave rectifier and explain its operation with wave forms. What is its advantage over half wave rectifier?

What is static resistance of the diode? How will you find the dynamic resistance?

Explain the zener and avalanche thermal breakdown mechanisms. What will be their thermal coefficients?

How is a PN junction formed? Draw the circuit diagram of PN-Junction diode in forward bias and reverse bias. Explain its operation and give VI-characteristics.

What is a rectifier? Draw the circuit diagram for bridge rectifier with LC-filter and explain its operation.

Explain bridge wave rectifier with circuit diagram and output wave forms. Find i. RMS value of current. ii. Ripple factor. iii. TUF iv. Efficiency v. Peak factor.

Explain avalanche breakdown and zener breakdown in PN diode.

Derive the expression for ripple factor of a FWR (or HWR/ Bridge) with shunt capacitance filter.

Derive the expression for ripple factor of a FWR (or HWR/ Bridge) with series inductance filter.

Derive the expression for ripple factor of a FWR (or HWR/ bridge) with LC π section filter.

Derive an expression for current in a diode.

Compare drift and diffusion currents.

Tutorial -1 Questions

A Full Wave Rectifier has a Secondary Voltage of 230V from one-end of the transformer to ground. then calculate i. DC load Current. ii. RMS value of output current. If diode has a resistance of 10Ω and the resistance of secondary winding is negligible. Given R_{L}=5KΩ.

Find the conductivity of P-type semi conductor, if the concentration of holes is 4.2X10^{22}atoms/m^{3} and mobility of holes is 1800 Cm^{2}/V.

Write the expression for Hall voltage and find Hall voltage if the Magnetic field strength of 1000 Wb/m^{2} where the current flowing through the semi conducting material is 9A. Width of semi conducting material is 2m with resistivity of 100 Mhos-m. Also find the Hall coefficient?

Write a short note on P-type and N-type semi conductors.

The following Attachment Consists of Experiments in both Analog Communication & Digital Communication using Communication kits and the same experiments were generated using Matlab Programming.