## What is a Resistor

A Resistor is a passive electronic component having two terminals, that limits the flow of electrons through a circuit. Passive components are the components that can only consume power (they cannot generate power).

## Uses of Resistors

The main use of resistors is to reduce the flow of current in a circuit, but it is not limited to this only. Resistors find applications in various fields like-
*Resistors can be used to divide voltages (as voltage divider)
*Terminating transmission lines
*To bias active elements
*Timing and frequency applications
*In heating applications etc.

Resistors can broadly be categorized into two types-
*Fixed Resistors
*Variable Resistors

#### Fixed resistors

As clear by its name, fixed resistors cannot change it's value.
The fixed resistors can again be classified into following three types-
*Carbon composition resistors
*Metalized resistors
*Wire wound resistors

#### Variable resistors

The resistance of variable resistors can be changed continually or can be set to a certain value as per the requirement.
On the basis of this the variable resistors can again be of two types-
*The variable resistors that can change its value continually like that used in volume control applications and
*The variable resistors that can be set to a fixed value as desired like in case of potentiometers (adjustable resistor).

## Working Principle of resistor

#### Ohm's Law

For an ideal resistor the Ohm's law is given as -
According to Ohm's law the voltage (V) across a resistor is directly proportional to the current (I) flowing through it. Here the constant of proportionality is the resistance (R).
This relationship between voltage and current is given as-
V=IR

## Unit of Resistance (R) and Conductance (G)

Unit of electrical resistance is Ohm (Ω) . Ohm is the SI unit of resistance. Other unit of resistance can be obtained from the Ohm's law.
By Ohm's law-
R=V/I
Therefore the unit of resistance is- Volt per Ampere or V/A.
Conductance (G) is opposite to the resistance. Conductance can be defined as the ease with which the current flows through a substance. Formerly the unit of conductance was mho (℧)(opposite of Ohm, the unit of resistance). The standard unit of conductance is siemens (S).

FREQUENCY SPECTRUM OF AMPLITUDE MODULATION (WAVEFORMS AND EQUATIONS DERIVATION)

AMPLITUDE MODULATION (TIME DOMAIN EQUATIONS AND WAVEFORMS)

STEP INDEX OPTICAL FIBER (MULTIMODE AND SINGLE MODE STEP INDEX FIBERS)

PULSE MODULATION TECHNIQUES (PAM, PWM, PPM, PCM)

OPTICAL FIBER: STRUCTURE AND WORKING PRINCIPLE

PULSE AMPLITUDE MODULATION (PAM)

COMPARISON OF PAM, PWM, PPM MODULATION TECHNIQUES

PULSE WIDTH MODULATION (PWM)

CONTINUOUS TIME AND DISCRETE TIME SIGNALS (C.T. AND D.T. SIGNALS)

NEED AND BENEFITS OF MODULATION

PULSE POSITION MODULATION (PPM)

OPTICAL FIBERS IN COMMUNICATION: COVERS ALL IMPORTANT POINTS

OPTICAL FIBER SOURCES (DESIRABLE PROPERTIES)

SAMPLING THEOREM AND RECONSTRUCTION (SAMPLING AND QUANTIZATION)

SUPERPOSITION THEOREM (BASICS, SOLVED PROBLEMS, APPLICATIONS AND LIMITATIONS)

Digital Modulation Techniques (ASK, FSK, PSK, BPSK)/ Amplitude, Frequency and Phase Shift Keying

Conventional AM Vs DSB-SC Vs SSB-SC Vs VSB (Comparison of AM Systems)

What are Microwaves and their Applications (Uses) in various fields

Basic Structure of Bipolar Junction Transistor (BJT) - BJT Transistor - Working and Properties

Polar Plots of Transfer Functions in Control Systems (How to Draw Nyquist Plot Examples)

Generation of Binary Phase Shift Keying (BPSK Generation) - Block Diagram of Binary Phase Shift Keying (BPSK)

Low Level and High Level Modulation Block Diagram (AM Transmitter Block Diagram)

Block Diagram of CRO (Cathode Ray Oscilloscope), Components of CRO and CRT with Structure and Working

Slope Overload Distortion and Granular (Idle Noise), Quantization Noise in Delta Modulation

Frequency Translation/Frequency Mixing/Frequency Conversion/Heterodyning (Basic Concepts and Need)

Quadrature Phase Shift Keying Modulation (QPSK) Basics, Waveform and Benefits

Pulse Code Modulation (PCM) Vs Differential Pulse Code Modulation (DPCM)

## Definition of Electronics

Electronics is a science that deals with electrical devices and circuits, that operate by controlling the flow of electrons or other electrically charged particles. This branch of science deals with how electrons behave in gases, vacuum or semiconductors.
Following are the different branches of Electronics with some details about each branch -

## Branches of Electronics

### 1.Analog electronics

Analogue electronics deals with analogue signals. Analogue signals are continuously variable signals. This is in contrast to the digital signals that generally take only two levels.

### 2.Digital electronics

The digital electronics deals with digital signals. Digital Signals are the signals that take usually 2 levels.

### 3.Power electronics

Power Electronics acts as an interface between the electrical source and electrical load. It is the application of solid state electronics to the control and conversion of electric power.

### 4.Microelectronics

As clear by the name itself, microelectronics is the branch of Electronics that is related to the electronic designs at very small level.

The circuit design includes, designing basic electronic components to complex electronic systems.

### 6.Integrated circuits

Integrated circuits are commonly known as IC in short. An integrated circuit is a small chip that may contain millions of electronic components like resistors, capacitors or transistors.

### 7.Optoelectronics

As the name suggests, the optoelectronics is the branch of Electronics that combines optics (light) with electronics. It includes the use of light sources, light detectors and mechanism to carry and control light.

### 8.Embedded systems

Embedded systems are the systems that are designed to perform a fixed function with no or minimum human interference. Embedded systems are controlled by a real time operating system and are the combination of computer hardware and software.

### 9.Semiconductor devices

Semiconductor devices make use of semiconductor materials like silicon, Germanium, gallium arsenide. The conductivity of semiconductors lie between that of conductors and insulators.

FREQUENCY SPECTRUM OF AMPLITUDE MODULATION (WAVEFORMS AND EQUATIONS DERIVATION)

AMPLITUDE MODULATION (TIME DOMAIN EQUATIONS AND WAVEFORMS)

STEP INDEX OPTICAL FIBER (MULTIMODE AND SINGLE MODE STEP INDEX FIBERS)

PULSE MODULATION TECHNIQUES (PAM, PWM, PPM, PCM)

OPTICAL FIBER: STRUCTURE AND WORKING PRINCIPLE

PULSE AMPLITUDE MODULATION (PAM)

COMPARISON OF PAM, PWM, PPM MODULATION TECHNIQUES

PULSE WIDTH MODULATION (PWM)

CONTINUOUS TIME AND DISCRETE TIME SIGNALS (C.T. AND D.T. SIGNALS)

NEED AND BENEFITS OF MODULATION

PULSE POSITION MODULATION (PPM)

OPTICAL FIBERS IN COMMUNICATION: COVERS ALL IMPORTANT POINTS

OPTICAL FIBER SOURCES (DESIRABLE PROPERTIES)

SAMPLING THEOREM AND RECONSTRUCTION (SAMPLING AND QUANTIZATION)

SUPERPOSITION THEOREM (BASICS, SOLVED PROBLEMS, APPLICATIONS AND LIMITATIONS)

Digital Modulation Techniques (ASK, FSK, PSK, BPSK)/ Amplitude, Frequency and Phase Shift Keying

Conventional AM Vs DSB-SC Vs SSB-SC Vs VSB (Comparison of AM Systems)

What are Microwaves and their Applications (Uses) in various fields

Basic Structure of Bipolar Junction Transistor (BJT) - BJT Transistor - Working and Properties

Polar Plots of Transfer Functions in Control Systems (How to Draw Nyquist Plot Examples)

Generation of Binary Phase Shift Keying (BPSK Generation) - Block Diagram of Binary Phase Shift Keying (BPSK)

Low Level and High Level Modulation Block Diagram (AM Transmitter Block Diagram)

Block Diagram of CRO (Cathode Ray Oscilloscope), Components of CRO and CRT with Structure and Working

Slope Overload Distortion and Granular (Idle Noise), Quantization Noise in Delta Modulation

Frequency Translation/Frequency Mixing/Frequency Conversion/Heterodyning (Basic Concepts and Need)

Quadrature Phase Shift Keying Modulation (QPSK) Basics, Waveform and Benefits

Pulse Code Modulation (PCM) Vs Differential Pulse Code Modulation (DPCM)

### What is Electronics - Definition of Electronics

Let's understand what is electronics and the definition of electronics -

## Definition of Electronics

Electronics is a science that deals with electrical devices and circuits, that operate by controlling the flow of electrons or other electrically charged particles. This branch of science deals with how electrons behave in gases, vacuum or semiconductors.

## Active and Passive Components

Different types of passive electrical components and active electrical components are used in electronics.
A passive component is a component that does not produce any energy but consumes energy or is not capable of power gain. Most commonly used passive components in electronics are resistors, capacitors and inductors. If an electronic circuit is completely made up of passive electrical components then it is known as a passive circuit.
While active electrical components are the components that are not passive. Common examples of active electrical components are diodes, transistors, silicon controlled rectifiers (SCR) etc.

FREQUENCY SPECTRUM OF AMPLITUDE MODULATION (WAVEFORMS AND EQUATIONS DERIVATION)

AMPLITUDE MODULATION (TIME DOMAIN EQUATIONS AND WAVEFORMS)

STEP INDEX OPTICAL FIBER (MULTIMODE AND SINGLE MODE STEP INDEX FIBERS)

PULSE MODULATION TECHNIQUES (PAM, PWM, PPM, PCM)

OPTICAL FIBER: STRUCTURE AND WORKING PRINCIPLE

PULSE AMPLITUDE MODULATION (PAM)

COMPARISON OF PAM, PWM, PPM MODULATION TECHNIQUES

PULSE WIDTH MODULATION (PWM)

CONTINUOUS TIME AND DISCRETE TIME SIGNALS (C.T. AND D.T. SIGNALS)

NEED AND BENEFITS OF MODULATION

PULSE POSITION MODULATION (PPM)

OPTICAL FIBERS IN COMMUNICATION: COVERS ALL IMPORTANT POINTS

OPTICAL FIBER SOURCES (DESIRABLE PROPERTIES)

SAMPLING THEOREM AND RECONSTRUCTION (SAMPLING AND QUANTIZATION)

SUPERPOSITION THEOREM (BASICS, SOLVED PROBLEMS, APPLICATIONS AND LIMITATIONS)

Digital Modulation Techniques (ASK, FSK, PSK, BPSK)/ Amplitude, Frequency and Phase Shift Keying

Conventional AM Vs DSB-SC Vs SSB-SC Vs VSB (Comparison of AM Systems)

What are Microwaves and their Applications (Uses) in various fields

Basic Structure of Bipolar Junction Transistor (BJT) - BJT Transistor - Working and Properties

Polar Plots of Transfer Functions in Control Systems (How to Draw Nyquist Plot Examples)

Generation of Binary Phase Shift Keying (BPSK Generation) - Block Diagram of Binary Phase Shift Keying (BPSK)

Low Level and High Level Modulation Block Diagram (AM Transmitter Block Diagram)

Block Diagram of CRO (Cathode Ray Oscilloscope), Components of CRO and CRT with Structure and Working

Slope Overload Distortion and Granular (Idle Noise), Quantization Noise in Delta Modulation

Frequency Translation/Frequency Mixing/Frequency Conversion/Heterodyning (Basic Concepts and Need)

Quadrature Phase Shift Keying Modulation (QPSK) Basics, Waveform and Benefits

Pulse Code Modulation (PCM) Vs Differential Pulse Code Modulation (DPCM)

## What is Hilbert Transform?

If x(t) is a signal and we represent its hilbert transform by xh(t), then xh(t) is obtained by providing '/2' phase shift to every frequency component present in x(t).

Watch the Complete Video Here

Now let's see formula to calculate hilbert transform and inverse hilbert transform.

## Hilbert Transform Formula

With the help of following formula we can easily calculate the hilbert transform

## Inverse Hilbert Transform Formula

The formula provided here can be used to find the inverse hilbert transform

Now let's discuss properties of hilbert transform

## Properties of Hilbert Transform

1. A signal x(t) and its hilbert transform xh(t) have the same energy density spectrum.

2. A signal x(t) and it's a hilbert transform xh(t) have the same autocorrelation function

3. A signal x(t) and its hilbert transform xh(t) are mutually orthogonal. We can write it mathematically as-

4. If xh(t) is a hilbert transform of x(t) then the hilbert transform of xh(t) is -x(t).

It means -

if H[x(t)] = xh(t)

then H[xh(t)] = -x(t)

Here 'H' denotes the Hilbert transform.

FREQUENCY SPECTRUM OF AMPLITUDE MODULATION (WAVEFORMS AND EQUATIONS DERIVATION)

AMPLITUDE MODULATION (TIME DOMAIN EQUATIONS AND WAVEFORMS)

STEP INDEX OPTICAL FIBER (MULTIMODE AND SINGLE MODE STEP INDEX FIBERS)

PULSE MODULATION TECHNIQUES (PAM, PWM, PPM, PCM)

OPTICAL FIBER: STRUCTURE AND WORKING PRINCIPLE

PULSE AMPLITUDE MODULATION (PAM)

COMPARISON OF PAM, PWM, PPM MODULATION TECHNIQUES

PULSE WIDTH MODULATION (PWM)

CONTINUOUS TIME AND DISCRETE TIME SIGNALS (C.T. AND D.T. SIGNALS)

NEED AND BENEFITS OF MODULATION

PULSE POSITION MODULATION (PPM)

OPTICAL FIBERS IN COMMUNICATION: COVERS ALL IMPORTANT POINTS

OPTICAL FIBER SOURCES (DESIRABLE PROPERTIES)

SAMPLING THEOREM AND RECONSTRUCTION (SAMPLING AND QUANTIZATION)

SUPERPOSITION THEOREM (BASICS, SOLVED PROBLEMS, APPLICATIONS AND LIMITATIONS)

Digital Modulation Techniques (ASK, FSK, PSK, BPSK)/ Amplitude, Frequency and Phase Shift Keying

Conventional AM Vs DSB-SC Vs SSB-SC Vs VSB (Comparison of AM Systems)

What are Microwaves and their Applications (Uses) in various fields

Basic Structure of Bipolar Junction Transistor (BJT) - BJT Transistor - Working and Properties

Polar Plots of Transfer Functions in Control Systems (How to Draw Nyquist Plot Examples)

Generation of Binary Phase Shift Keying (BPSK Generation) - Block Diagram of Binary Phase Shift Keying (BPSK)

Low Level and High Level Modulation Block Diagram (AM Transmitter Block Diagram)

Block Diagram of CRO (Cathode Ray Oscilloscope), Components of CRO and CRT with Structure and Working

Slope Overload Distortion and Granular (Idle Noise), Quantization Noise in Delta Modulation

Frequency Translation/Frequency Mixing/Frequency Conversion/Heterodyning (Basic Concepts and Need)

Quadrature Phase Shift Keying Modulation (QPSK) Basics, Waveform and Benefits

Pulse Code Modulation (PCM) Vs Differential Pulse Code Modulation (DPCM)

## What is Carson's Rule?

Carson's formula is used to calculate the bandwidth (BW) of a single tone wideband FM.
According to carson's rule, the FM bandwidth is given as, twice the sum of frequency deviation and the highest modulating frequency.
But it should be noted here that this rule is just an approximation.

Watch the Complete Video Here

So Carson's rule can be written mathematically as-

BW = 2(∆w + wm)

But mf = ∆w/wm

Therefore

BW = 2(mfwmwm)

= 2wm (mf + 1)

Now we have two special cases for the carson's rule -

1 - If ∆w << wm and

2- ∆w >> wm

Case 1- If ∆w << wm

Since mf = ∆w/wm

If ∆w << wm

=> mf << 1

=> It is the case for narrowband FM

Since the bandwidth by the carson's rule is given
as-

BW = 2(∆w + wm)

BW = 2(mfwmwm)

= 2wm (mf + 1)

Therefore for m<< 1

BW = 2wm

Note here that this is equivalent to Amplitude Modulation (AM)

Case 2- ∆w >> wm

Since mf = ∆w/wm

Therefore if ∆w >> wm

=> m>> 1   as is the case for wideband FM
Then, since by Carson's rule

BW = 2wm (mf + 1)

Therefore for mf  >> 1

BW = 2wmmf

But wmmf = ∆w

Therefore

BW = 2∆w

Note- For large values of m this BW relationship can be considered accurate for all practical purposes.

FREQUENCY SPECTRUM OF AMPLITUDE MODULATION (WAVEFORMS AND EQUATIONS DERIVATION)

AMPLITUDE MODULATION (TIME DOMAIN EQUATIONS AND WAVEFORMS)

STEP INDEX OPTICAL FIBER (MULTIMODE AND SINGLE MODE STEP INDEX FIBERS)

PULSE MODULATION TECHNIQUES (PAM, PWM, PPM, PCM)

OPTICAL FIBER: STRUCTURE AND WORKING PRINCIPLE

PULSE AMPLITUDE MODULATION (PAM)

COMPARISON OF PAM, PWM, PPM MODULATION TECHNIQUES

PULSE WIDTH MODULATION (PWM)

CONTINUOUS TIME AND DISCRETE TIME SIGNALS (C.T. AND D.T. SIGNALS)

NEED AND BENEFITS OF MODULATION

PULSE POSITION MODULATION (PPM)

OPTICAL FIBERS IN COMMUNICATION: COVERS ALL IMPORTANT POINTS

OPTICAL FIBER SOURCES (DESIRABLE PROPERTIES)

SAMPLING THEOREM AND RECONSTRUCTION (SAMPLING AND QUANTIZATION)

SUPERPOSITION THEOREM (BASICS, SOLVED PROBLEMS, APPLICATIONS AND LIMITATIONS)

Digital Modulation Techniques (ASK, FSK, PSK, BPSK)/ Amplitude, Frequency and Phase Shift Keying

Conventional AM Vs DSB-SC Vs SSB-SC Vs VSB (Comparison of AM Systems)

What are Microwaves and their Applications (Uses) in various fields

Basic Structure of Bipolar Junction Transistor (BJT) - BJT Transistor - Working and Properties

Polar Plots of Transfer Functions in Control Systems (How to Draw Nyquist Plot Examples)

Generation of Binary Phase Shift Keying (BPSK Generation) - Block Diagram of Binary Phase Shift Keying (BPSK)

Low Level and High Level Modulation Block Diagram (AM Transmitter Block Diagram)

Block Diagram of CRO (Cathode Ray Oscilloscope), Components of CRO and CRT with Structure and Working

Slope Overload Distortion and Granular (Idle Noise), Quantization Noise in Delta Modulation

Frequency Translation/Frequency Mixing/Frequency Conversion/Heterodyning (Basic Concepts and Need)

Quadrature Phase Shift Keying Modulation (QPSK) Basics, Waveform and Benefits

Pulse Code Modulation (PCM) Vs Differential Pulse Code Modulation (DPCM)