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**Quantization** is the process of mapping continuous amplitude (analog) signal into discrete amplitude (digital) signal.

The analog signal is quantized into countable & discrete levels known as **quantization levels**. Each of these levels represents a fixed input amplitude.

During **quantization**, the input amplitude is round off to the nearest quantized level. This rounding off is known as **quantization error**. Quantization error can be reduced by increasing the numbers of quantization levels.

The figure below represents an analog signal. During quantization, the analog signal’s amplitude is sampled and discretized into fixed quantization levels.

In this example, we have used 8 quantization levels. The quantization results in the **loss of information**. The space between two adjacent levels is known as **step size**.

**Step size = V _{ref}/number of levels.**

**V _{ref }**represents the

If the step-size is large then the quantization error will be high. In another word, the loss of information goes higher as the step size gets bigger.

There are two types of quantization.

The type of quantization in which the quantized levels are **uniformly spaced** is known as **uniform quantization**. In uniform quantization, each step size represents a **constant** amount of analog amplitude. it remains constant throughout the signal.

The example of **uniform quantization** is given below,

In this example, the space between any two adjacent step or levels represents 1-volt amplitude.

The type of quantization in which the space between the quantized levels is **non-uniform** & has **logarithmic** relation is called **non-uniform quantization.**

In **non-uniform quantization**, the analog signal is first passed through a **compressor**. The compressor applies a **logarithmic**** function** on the input signal. The input signal has a high difference between its low and high amplitude. In the output signal, the low amplitudes get amplified and the high amplitude levels get attenuated, Thus making a compressed signal.

Suppose the input signal’s amplitude is **m**** & m _{p }**is the peak amplitude of the signal.

As you can see from the graph, that the small input levels **Δm** are mapped onto bigger output levels **Δy**. And the higher input levels are mapped onto smaller output levels.

There are two laws for compression

**μ law** is a compression algorithm used for **non-uniform quantization**. The expression of **μ law** is

**y = (ln(1 + μ(m/m _{p})))/ (ln(1 + μ))**

Where **μ** is the compression parameter and **m** is the input amplitude & **m _{p }**is the peak amplitude of the input signal.

When **μ=0**, then there is no compression and the quantization becomes **uniform**. The characteristic graph for **μ Law** is given below:

This graph shows that if the compression parameter **μ** is higher than the input signal is more compressed.

**A-law** is another algorithm for compression of an analog signal for non-uniform quantization. The expression for **A-law** is:

Where **A** is the compression parameter. When **A=1**, then the quantization is **uniform** because there is no compression. The characteristics graph is given below.

Both laws are applicable with some trade-offs.

**Sampling** is an important step in **analog to digital conversion**. The taking or capturing of samples of input analog amplitude is called **sampling**.

The **sampling**** rate** is the number of **samples** taken in the duration of one second. it is measured in **hertz** or **sample per second**. The continuously varying amplitude of an analog signal is also continuous in time. So it needs to be sampled at a fixed rate. This rate is called **sampling rate** or **sampling frequency**. Example of sampling:

This signal is sampled at a sampling rate of **2 samples per second** or **2 Hz**.

Sampling rate plays important role in the perfect conversion from analog to digital and **reconstruction** of an analog signal from the digital signal.

Sampling rate should not be very low or very high. In both cases, the converted signal is not what we want to achieve. If the sampling rate is low than the original signal is destroyed and if the sampling rate is very high then it’s not economically beneficial.

If the analog signal is **sampled** at a frequency **lower** than the **required rate** then the sampled signal does not appear to be anything like the original signal. And the **reconstruction** of the original signal becomes impossible. Such case is called **aliasing** as shown in the figure below.

In this example, a sinusoidal signal is sampled at a rate of **3/4** of its frequency. which is very lower than its required rate. The reconstructed signal (red signal) is recovered from the sample which does not look anything like the original signal.

The sampling rate or sampling frequency should be greater than twice the input signal’s frequency. **Nyquist theorem** suggests the minimum sampling rate for a signal which can be perfectly reconstructed from its samples.

You may also read:

- Analog To Digital Converter (ADC),Its Block Diagram,Factors & Applications
- The Modulation Concept & Basic Types of Modulation
- Introduction to Signals, Types, Properties, Operation & Application

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The **modulation concept** comes into consideration when the signal needs to be transmitted over a **long distance** through an antenna. Antenna helps transmit the signal over long distance.

The modulation concept makes the communication purely **wireless and mobile**. And because of modulation, we can now roam freely without the fear of getting out of the communication grid.

A signal consisting of significantly lower frequency (up to **10 kHz**) is known as a **baseband signal**. Example of the baseband signal is voice, audio and video signal.

The frequency range of **voice** signal is **300Hz to 3.5 kHz**.

**Audio** signal’s frequency range is** 20 Hz to 20 kHz**.

**Video** signal’s frequency range is **0Hz to 4.5 MHz**

All of these signals contain low frequencies (up to **10 kHz**), which makes them **baseband signals**. The baseband signal cannot be transmitted directly through the antenna. Thus it gives rise to the **concept of modulation**.

If a signal consists of significantly higher frequencies (Higher than **100 kHz**) then it is known as **Passband** or **BandPass** signal. **Bandpass signal** does not contain any frequency lower than **100 kHz**.

**Bandpass** signal can be directly transmitted through the **antenna**.

Using the process of **modulation**, the signal with low frequency, also known as Baseband signal is converted into a signal with high frequency, also known as Bandpass signal.

The signal that is used in modulating the carrier signal during modulation is called the **message signal**.

The message signal is a baseband signal. for example, voice, sound, video, images & data signals are baseband signals.

Suppose a baseband **message signal** **m(t)** is a rectangle signal with **T = 1ms**. To show its frequency spectrum, we need to do its Fourier transform.

We know that the Fourier transform of rectangle function is a sinc function but for the sake of understanding, we will just go with the spectrum given below. The spectrum of **m(t)** signal is given in the figure:

The frequency **f** of **m(t)** ranges from **0 to 1Khz**, which makes it a **baseband signal**.

The sinusoidal signal with a much higher frequency that is used in the modulation is called the **carrier signal**.

Let’s suppose a **carrier signal** **c(t)**, that is a sinusoidal signal with high frequency. And the frequency **f _{c}** of the carrier signal is

As you can see, the spectrum of carrier signal only contains the frequency **300 kHz**. This makes it a **bandpass signal**. It is easily transmitted through the antenna.

We need to transmit the **message signal** **m(t)** with the help of the **carrier signal c(t)**. To make it able to transmit through the antenna, we need to translate the message signal **m(t)** onto the carrier signal **c(t)**.

The resultant signal acquired after modulation of message and carrier signal is called **modulated signal**.

A simple modulated signal is acquired by the **multiplication** of carrier and message signal. The resultant signal is the **modulated signal**.

Suppose the product signal **p(t)** is the modulated signal of **m(t) & c(t)**. It is a sinusoidal signal, where the amplitude of message signal **m(t)** is not **0**. The time domain and frequency domain figures of modulated signals are given below:

The modulated signals **frequency** is shifted by the frequency of the carrier signal **f**** _{c}**. The spectrum shows

The modulated signal’s spectrum consists of **lower** and **higher side**. Lower and higher frequency is determined by **(f _{c}-f)** and

This modulated signal is now a **bandpass signal** and an antenna can easily transmit it.

The process in which one of the characteristic parameter (amplitude, frequency, phase) of the **carrier signal** varies linearly with respect to **message signal**’s **amplitude** is called modulation.

Basic types of Modulation are defined with figures below.

The type of modulation in which the **amplitude** of the carrier signal varies with respect to the amplitude of the message signal is called **Amplitude Modulation**.

The message signal’s information is stored in the **amplitude (envelope)** of the modulated signal.

The modulation which is based on changing the **frequency** or **phase** of the carrier signal with respect to message signal is called **Angle modulation**. Angle modulation comprises of **frequency modulation** & **phase modulation**.

The type of modulation in which the **Frequency** of the carrier signal varies with respect to the amplitude of the message signal is called **Frequency modulation**.

The message signal’s information is stored in the **frequency** of the modulated signal.

The type of modulation in which the phase of the carrier signal varies linearly with respect to the amplitude of message signal or data signal is called **Phase modulation**.

The information of message signal is stored in the phase of the modulated signal.

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In suppressed carrier communication, the demodulation process requires an identical local carrier at the demodulator. This local carrier needs to have same frequency and phase as the transmitted signal. which is acquired using **carrier acquisition.**

The process of acquiring or extracting carrier frequency from the received signal is called

carrier acquisition.

**Amplitude Modulated Suppressed Carrier** signal needs a locally generated signal having the same phase and frequency as the received signal (**carrier signal**).

If the frequency or phase of the signal is different than the received signal, then the demodulated message signal we get will be **distorted** or may be completely **destroyed**. To avoid such problems and get a clear message signal, we need an **identical carrier**.

**Suppose** we receive a **DSB-SC** signal which is **m(t)cos(ω _{c}t + ϴ_{i})** and the carrier generated by demodulator has a frequency

Thus the demodulated signal **e(t)** will be:

**e(t) = m(t) cos(ω _{c}t + ϴ_{i}) 2cos((ω_{c}+Δω)t+ ϴ_{o})**

**e(t) = 2m(t) cos(ω _{c}t + ϴ_{i}) cos((ω_{c}+Δω)t+ ϴ_{o})**

**e(t) = m(t) [cos {(ω _{c}+ω_{c}+Δω) t +ϴ_{i}+ϴ_{o}} + cos(Δωt+ ϴ_{i}-ϴ_{o})]**

**e(t) = m(t) cos {(ω _{c}+ω_{c}+Δω) t +ϴ_{i}+ϴ_{o}} + m(t)cos(Δωt+ ϴ_{i}-ϴ_{o})**

By passing through **Low-pass filter**

**e(t) = m(t)cos(Δωt+ ϴ _{i}-ϴ_{o})**

If the frequency difference **Δω = 0** and phase difference **(ϴ _{i}-ϴ_{o}) = 0**. Then

**e(t) = m(t)**

Which means the message signal is **successfully** received.

However, if the frequency difference **Δω = 0** and phase difference **(ϴ _{i}-ϴ_{o}) ≠0**. Then

**e(t) = m(t)cos(ϴ _{i}-ϴ_{o})**

This means that the message signal is **attenuated** by factor **cos(ϴ _{i}-ϴ_{o})**. if

Another case is if the phase difference **(ϴ _{i}-ϴ_{o}) =0** and frequency difference

**e(t) = m(t)cos(Δωt)**

This equation implies that the same message signal is multiplied with a sinusoid of frequency **Δω**. **Δω** is usually very **small**. which means that the message signal will go from maximum to zero at the rate of two times its frequency. This is called **beating effect**. This beating effect **distorts** the original signal even if the Δω is very small.

There are few different techniques used for carrier acquisition. Some of them are given below.

**Phase locked loop**, commonly known as **PLL** is one of the most widely used circuit for **carrier acquisition**. It tracks the phase and frequency of the incoming/reference signal and generates a stable frequency signal.

A **PLL** is made up of 3 components

- VCO
- Phase detector
- Loop filter

**VCO** stands for the voltage controlled oscillator. It generates frequency signal, which is controlled by an external voltage signal. The frequency signal produced by VCO is

**ω(t) = ω _{c }+ ce_{o}(t)**

**ω _{c }**is

A Multiplier is used as a **phase detector**. It has 2 input signals, a reference signal & the output of VCO.

It generates a signal proportional to the **phase difference **between the two signals.

Suppose the input signal is **Asin(ω _{c}t + ϴ_{i})** & output is

**e(t) = Asin(ω _{c}t + ϴ_{i}) **

**e(t) = AB/2 sin(2ω _{c}t + ϴ_{i }+ ϴ_{o}) + AB/2 sin(ϴ_{i }– ϴ_{o})**

The high-frequency term is filtered the **loop filter** discussed below.

This **loop filter** is actually a **narrow band low pass filter**. It blocks any high-frequency components from its input signal (**output of multiplier**) and generates a **dc voltage**. which is supplied as input to the **VCO.**

The signal after passing through **loop filter** becomes

**e _{o}(t) = AB/2 sin(ϴ_{i }– ϴ_{o})**

If the phase difference **(ϴ _{i }– ϴ_{o})** is not

The process is repeated until the frequency & phase matches the input signal. Such case is called **in phase lock **or **phase coherent **state.

In **DSB-SC** scheme the level carrier can be regenerated using two methods discussed below.

This method is used for carrier acquisition in **DSB-SC** communication.

The block diagram of **signal-squarer** is given below.

The received DSB-SC signal **x(t)** is first passed through a **squarer**, which takes the square of the signal.

The received signal **x(t)** is:

**x(t) = m(t)cos ω _{c}t**

The output **y(t)** of squarer is:

**y(t) = x ^{2}(t)**

**y(t) = (m(t)cos ω _{c}t)^{2}**

**y(t) = m ^{2}(t)cos^{2} ω_{c}t**

**y(t) = ½ m ^{2}(t)(1+cos 2ω_{c}t)**

**y(t) = ½ m ^{2}(t)+ ½ m^{2}(t)cos 2ω_{c}t**

As we can see, **m ^{2}(t)** is a non-negative signal i.e. it is positive for every value of

Let suppose the average value of **m ^{2}(t)/2** is

**½ m ^{2}(t) = k + ϕ(t)**

Now the signal **y(t)** can be expressed as:

**y(t) = ½ m ^{2}(t)+ (k + ϕ(t))cos 2ω_{c}t**

**y(t) = ½ m ^{2}(t)+ k cos 2ω_{c}t + ϕ(t)cos 2ω_{c}t**

After passing through the narrow-band band-pass filter, it will block **m ^{2}(t) **completely because of its

**y _{0}(t) = k cos 2ω_{c}t + ϕ(t)cos 2ω_{c}t**

The next stage is **PLL**. The **PLL** will block any **residual frequencies** & produce a **stable frequency** signal** z(t)**, which is :

**z(t) = k cos 2ω _{c}t**

The last stage of **signal squarer** is the **divider**. The divider divides the frequency of the input signal by two. Thus the output signal becomes a pure sinusoidal wave of frequency **ω _{c}**.

The output **r(t)** of signal squarer is:

**r(t) = k cos ω _{c}t**

**John P.Costas** was an Electrical engineer. In 1950, he invented the method to use a **modified PLL** to regenerate the carrier signal in suppressed carrier communication. This circuit is known as **Costas loop**.

Costas loop is used to acquire the carrier signal in DSB-SC communication.

The **block diagram** of Costas loop is given below:

This diagram shows the received signal DSB-SC signal **m(t)cos(ω _{c}t+ϴ_{i})** is multiplied with local carriers

The VCO generates the local carrier **cos(ω _{c}t+ϴ_{o})**, which is phase shifted by

The signal **x _{1}(t)** and

**x _{1}(t) = m(t)cos(ω_{c}t+ϴ_{i}) cos(ω_{c}t+ϴ_{o})**

**x _{1}(t) = ½ m(t){cos(ϴ_{i}– ϴ_{o}) +cos(2ω_{c}t+ ϴ_{i} +ϴ_{o})}**

**x _{1}(t) = ½ m(t)cos(ϴ_{i}– ϴ_{o}) +½ m(t)cos(2ω_{c}t+ ϴ_{i} +ϴ_{o})**

**x _{2}(t) = m(t)cos(ω_{c}t+ϴ_{i}) sin(ω_{c}t+ϴ_{o})**

**x _{2}(t) = ½ m(t){sin(ϴ_{i}– ϴ_{o}) +sin(2ω_{c}t+ ϴ_{i} +ϴ_{o})}**

**x _{2}(t) = ½ m(t)sin(ϴ_{i}– ϴ_{o}) +½ m(t)sin(2ω_{c}t+ ϴ_{i} +ϴ_{o})**

The signal **x _{1}(t)** &

**y _{1}(t) = ½ m(t)cos(ϴ_{i}– ϴ_{o})**

**y _{2}(t) = ½ m(t)sin(ϴ_{i}– ϴ_{o})**

These two signals **y _{1}(t) **&

**z(t) = ½ m(t)cos(ϴ _{i}– ϴ_{o}) ½ m(t)sin(ϴ_{i}– ϴ_{o})**

**z(t) = ⅛ m ^{2}(t){sin(0) + sin2(ϴ_{i}– ϴ_{o})}**

**z(t) = ⅛ m ^{2}(t) sin2(ϴ_{i}– ϴ_{o})**

Thus the signal **z(t)** will produce a DC voltage depending on the phase difference **(ϴ _{i}– ϴ_{o})**.

If there is any phase difference then this signal will produce DC voltage.

The **narrowband**** low-pass filter** will suppress any frequency components and produce a **pure DC signal**. This DC signal will either increase or decrease the frequency of the VCO.

When the frequency and phase of the input signal and matches the VCO output, then the phase difference **(ϴ _{i}– ϴ_{o}) = 0** and the

The output of the **VCO** is the acquired carrier we need & the signal **y _{1}(t)** is the demodulated message signal.

**y _{1}(t) = ½ m(t)cos(ϴ_{i}– ϴ_{o})**

**y _{1}(t) = ½ m(t)cos(0)**

**y _{1}(t) = ½ m(t)**

In **single sideband** (**SSB) communication**, the methods of **carrier acquisition** do not work as it did in the DSB-SC. The **signal-squaring** method & **Costas loop** does not work. The reason is that after **squaring** SSB signal, the product terms does not contain a pure sinusoid of the carrier frequency as in **DSB-SC**. So extracting the carrier through such method does not work.

However, if we transmit a carrier signal of low power with **SSB signal**, it can be extracted using a **narrowband band-pass filter**. The said signal is then amplified, in such way the demodulator will know the **frequency **&** phase** of the carrier signal.

**Vestigial Sideband (VSB)** has the same situation as **SSB** and it also needs a separate carrier with the transmitted signal.

you may also read:

- Phase Locked Loop, its Operation, Characteristics & Application
- Introduction to Signals, Types, Properties, Operation & Application
- Amplitude modulation and its types

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The

phase locked looporPLLis an electronic circuit with avoltage controlled oscillator, whose output frequency is continuously adjusted according to the input signal’s frequency.

A **Phase locked loop** is used for tracking **phase** and **frequency** of the input signal. It is a very useful device for synchronous communication. **PLL** acquires the carrier frequency in suppressed carrier mode of communication and produces a coherent carrier signal inside the receiver for demodulation.

A PLL operates like a typical **feedback system**. It updates the output frequency of **VCO** until it matches the frequency of the input signal i.e. **in sync** with the input signal.

The operation of **Phase locked loop** is based on the **phase difference **between the input and output signals. The phase difference between of two signals can be understood by the figures given below.

The figure above shows two sinusoidal signals having a **constant phase difference**. When two signals have** constant phase difference** then they are said to have the **same frequency**. They only have shifted phase. Thus it shows that the two signals are at the **same frequency**.

However, this figure shows two signals having a **var****ying** phase difference. This changing difference shows that the two signals are **non-coherent**. It means that the two signals are totally different signals with different frequencies.

It is clear from the discussion above that the phase difference is related to the frequency of the signal. The **Phase locked loop** makes the phase difference constant between its input & output signal. And produce a stable frequency signal same as the input signal.

This key concept is put to use in PLL device.

There are 3 components of PLL and the **operation** of each component is given below.

The **Voltage Controlled Oscillator** often known as **VCO** is a type of oscillator that produces a sinusoidal signal whose frequency can be controlled by an external voltage. The frequency produced by **VCO** is varied linearly with respect to the input voltage. The sinusoidal output of the** VCO** is

**ω(t) = ω _{c} + c e_{o}(t)**

Where **c** is the constant of **VCO** & **e _{o}(t)** is the voltage proportional to the phase difference between the input signal’s frequency and

The output of **VCO** is **ω _{c}** if

The **phase detector** is an electronic circuit that compares two signals and generates a voltage signal which is proportional to the **phase difference** between the two signals.

Basically, a phase detector is a **multiplier**. It multiplies the two sinusoidal signals i.e. the input/reference signal & the output of **VCO**.

Suppose the input signal is **A sin(ω _{c}t+ϴ_{i})** & the output signal of

Then the output of phase detector **x(t) **is**:**

**x(t) = A sin(ω _{c}t+ϴ_{i}) B cos(ω_{c}t+ϴ_{o})**

**x(t) = AB sin(ω _{c}t+ϴ_{i}) cos(ω_{c}t+ϴ_{o})**

**x(t) = AB/2 {sin(ω _{c}t+ϴ_{i}+ ω_{c}t+ϴ_{o})+ sin(ω_{c}t+ϴ_{i}– ω_{c}t-ϴ_{o})}**

**x(t) = AB/2 {sin(2ω _{c}t+ϴ_{i}+ϴ_{o})+ sin(ϴ_{i}-ϴ_{o})}**

**x(t) = AB/2 sin(2ω _{c}t+ϴ_{i}+ϴ_{o})+ AB/2 sin(ϴ_{i}-ϴ_{o})**

The **high frequency** component is then removed by using the loop filter discussed below.

The filter used in the loop of **PLL** is a **narrow band low pass filter**. It filters any high-frequency components from the output signal of the phase detector and provides a fixed voltage signal to **VCO**.

After passing the signal **x(t)** through loop filter it blocks the term of high frequency.

**x(t) = AB/2 sin(2ω _{c}t+ϴ_{i}+ϴ_{o})+ AB/2 sin(ϴ_{i}-ϴ_{o})**

The output signal **e _{o}(t)** of

**e _{o}(t) = AB/2 sin(ϴ_{i}-ϴ_{o})**

Where **AB=2 **&** (ϴ _{i}-ϴ_{o})** is the

As long as there is a phase difference it will keep maintaining its frequency until it is **locked**. In such condition, both signals have same frequency & constant phase. These both signals are said to be **phase coherent** or **in phase lock.**

Suppose the **PLL** is locked & the **VCO **is generating a stable frequency. Suddenly the input signal’s frequency **increases** i.e. **ω _{c}+k**

**A sin((ω _{c }+k)t+ϴ_{i}) = A sin(ω_{c}t+kt+ϴ_{i})**

Then the output of **loop filter** will be

**e _{o}(t) = AB/2 sin(kt+ϴ_{i}-ϴ_{o})**

This, in turn, increases the difference and the voltage output of loop filter increases. Due to which the frequency of the **VCO** output signal increase.

**Phase-locked loop**s are designed for a Specific**range**of frequencies. This range of frequency is called**Capture Range**of**PLL**. A**PLL**can lock onto a signal if its frequency lies in its Capture Range.- When the
**PLL**is locked onto an input signal, the input signal can be changed. Suddenly, the input signal changes then the**PLL**will start tracking its phase and frequency in a fixed range. This tracking range is called**Lock Range**. - The most important feature of
**PLL**is the**noise filtering**. It completely blocks any unwanted low power frequencies from the input signal and provides a**pure and stable**sinusoidal wave.

It is the most widely used circuit in modern communication.

- It is used in
**demodulation**of Amplitude Modulated**suppressed carrier**signal. - It is also used for demodulation of
**Frequency**Modulated & Phase Modulated signals. - It can also be used in
**clock recovery**from a signal. - Because of its stable nature, it is used as
**frequency synthesizer**in almost every digital device. - A crystal oscillator can generate stable frequency up to 300Mhz. while PLL can generate signals of a high & stable frequency
**greater than 300 Mhz**. - It is used in different devices such as a
**signal analyzer**,**signal generator**, radar, cell phones & radio etc.

you may also read:

- Amplitude modulation and its types
- Modulation – Types and Classification of Analog Modulation
- Introduction to Signals, Types, Properties, Operation & Application

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A

signalis defined as anyphysicalorvirtual quantitythat varies withtimeorspaceor any other independent variable or variables.

Graphically, the **independent variable** is represented by **horizontal axis** or x-axis. And the **dependent variable** is represented by **vertical axis** or y-axis.

Mathematically, a signal is a function of one or more than one independent variables.

It depends on a single independent variable. It either varies linearly or non-linearly depending on the expression of the signal. Examples of single variable signal are:

**S(x) = x+5**

**S(x) = x ^{2}+5** Where

**S(t) = cos(wt+ϴ)** Where **t** is the variable

A **two variable signal** varies with the change in the two independent variables. Example of a two variable signal is

**S(x,y) = 2x+ 5y**

A signal is defined by its characteristics. It shows the nature of the signal. These characteristic are given below:

Amplitude is the **strength **or** height** of the signal waveform. Visually, it is the height of the waveform from its center line or x-axis. The y-axis of a signal’s waveform shows the amplitude of a signal. The amplitude of a signal varies with time.

For example, the amplitude of a sine wave is the maximum height of the waveform on Y-axis.

The signal’s strength is usually measured in **decibels db**.

Frequency is the rate of repetitions of a signal’s waveform in a second.

Periodic signals repeat its cycle after some time. The number of cycles in a second is known as **Frequency**. The unit of Frequency is **hertz (Hz)** and **one hertz** is equal to **one cycle** per second. It is measured along the x-axis of the waveform.

For example, a sine wave of **5 hertz** will complete its **5 cycles** in a **one second**.

The time period of a signal is the time in which it completes its one full cycle. The unit of the time period is **Second**. The time period is denoted by **‘T’** and it is the **inverse** of **frequency**. I.e.

**T=1/F**

For example, a sine wave of time period **10 sec** will complete its **one full cycle** in **10 seconds**.

The phase of a sinusoidal signal is the **shift** or **offset** in its origin or starting point. The phase shift can be **lagging** or **leading**. Usually, the **original** sinusoidal signals have **0°** degree phase and start at 0 amplitude but an offset in phase will shift its starting amplitude to other than 0.

An example of **45°** phase shift is given below. The signal remains same but its origin is shifted to **45°**.

The phase shift can be from **0° to 360°** in **degrees** or **0 to 2π** in **radians**. 360° degree or 2π radians is one complete period.

The size of a signal is a number that shows the **strength** or largeness of that signal. As we know, a signal’s amplitude varies with respect to time. Because of this variation, we cannot say that its amplitude can be its size. To measure the signal size, we have to take into account the **area covered** by the amplitude of the signal within the time duration.

According to the size of the signal, there are two parameters.

The energy of the signal is the area of the signal under its curve. But the signal can be in both positive and negative region. Due to which, it will cancel each other’s effect resulting in a smaller signal. To eradicate this problem, we take the **square of the signal’s amplitude** which is always positive.

For a signal g(t), the area under the **g ^{2}(t)** is known as the

This energy is not taken as in its conventional sense, but it shows the signal size. Therefore, its unit is not joule. The unit of energy **depends on the signal**. If it is a **voltage signal** then its unit will be **volts ^{2}/second**.

The energy of a signal can be measured only if the **signal** is **finite.** The **infinite signal** will have **infinite energy**, which is absurd. A **finite signal’s** amplitude **goes to 0** as the time (t) approaches to **infinity** (∞).

So it is **necessary** that the signal is a **finite** **signal** if you want to measure its energy.

If the signal is an **infinite signal** i.e. its **amplitude** does not go to **0** as time t approaches to **∞**, we cannot measure its energy. In such case, we take the time average (**Time period**) of the energy of the signal as the power of the signal.

Similar to Energy of the signal, this power is also not taken in the conventional sense. It will also **depend** on the **signal to be measured**. If the signal is **voltage signal**, then the power will be in **volts ^{2}**.

Just like the energy of signal, the measurement of the power of a signal also has some limitation that the signal **must** be of a **periodic nature**. An **infinite** and **non-periodic** signal neither have **energy nor power**.

Signals are classified into different categories based on their characteristics. Some of these categories are given below.

The signal can be classified into analog or digital category base on their **amplitude**. This classification is based on only **vertical-axis** (amplitude) of the signal. And it does not have any relation with horizontal-axis (time axis).

The amplitude of an **analog signal** can have **any value** (including fractions) at any point in time. That means analog signal have **infinite values**.

However, the **digital signal’s** amplitude can only have **finite** and **discrete** values.

The **special case** of Digital signal having **two discrete** values is known as **Binary signal**. However, the number of values for amplitude in a digital signal is **not limited** to **only two**.

Analog signal is converted into Digital signal using **A to D converter (ADC)**.

This classification is based on the **horizontal axis** (time axis) of the signal.

Continuous and discrete time signals should not be confused with analog and digital signal respectively.

A **continuous time** signal is a signal whose value (amplitude) exists for **every fraction** of **time** t.

A **discrete time** signal exists only for a **discrete value** of **time t**.

**Remember**, there is **no limitation** on the **amplitude** of the signal. That is why it should not be confused with the analog or digital signal.

A signal is **Energy signal** if its **amplitude** goes to **0** as **time** approaches **∞**. Energy signals have finite energy.

Similarly, a signal with finite power is known as Power signal. A **power signal** is a **periodic signal** i.e. it has a time period.

An **Energy signal** has **finite Energy** but **zero power**. And a **Power signal** has **finite Power** but **infinite Energy**. So a signal can be **either energy signal** or **power signal** but it **cannot** be **both**.

An **infinite signal** that has **no periodic nature** is neither **Energy nor Power signal**.

A **periodic signal** is a signal which keeps **repeating** its pattern after a **minimum fixed time**. That time is known as **Time period ‘T’** of that signal. Periodic signal does not change if it is time-shifted by any multiple of Time period “T”.

The mathematical expression for periodic signal **g(t)** is:

**T _{0 }**is the Time period of signal

**Periodic signal** starts from **t=-∞** and continues to **t=+∞**. A signal which starts at **t=0** will not be the same signal if it is time-shifted by +T because it did not exist for negative **t.**

The **aperiodic** or **non-periodic** signal is a signal which does **not repeat** itself after a specific time. These signals have **no repetitions** of any pattern.

A signal which can be represented in **mathematical** or **graphical form** is called **deterministic signal**. Deterministic signals have **specified amplitude, frequency** etc. They are easy to process as they are defined over a long period of time and we can **Evaluate** its **outcome** if they are applied to a specific system based on its expression.

The **random** or **non-deterministic** signal is a signal which can only be represented in **probabilistic expression** rather than its full mathematical expression. Every signal that has some kind of **uncertainty** is a **random signal**. **Noise signal** is the best example of random signal.

Generally, every message signal is a random signal because we are uncertain of the information to be conveyed to the other side.

Some basic operation of signals are given below

**Time-shifting** means **movement** of the signal across the **time axis** (**horizontal axis**). A time shift in a signal does not change the signal itself but only shifts the origin of the signal from its original point along time-axis.

Basically, **addition in time** is time shifting. To time-shift a signal **g(t)**, **t** should be replaced with **(t-T)**, where **T** is the seconds of **time-shift**. Therefore, **g(t-T)** is the time-shifted signal by **T** seconds.

Time shift can be **right-shift** (delay) or **left-shift** (advance).

If the time-shift **T** is **positive** than the signal will shift to the **right** (delay). For example, the signal **g(t-4)** is the shifted version of **g(t)** with **4** seconds **delay**.

If the time-shift **T** is **negative** than the signal will shift to the **left** (advance). The signal **g(t+4)** is the shifted version of **g(t)** with **4** seconds to the **left**.

**Time scaling** of a signal means to **compress** or **expand** the signal. It is achieved by **multiplying** the **time variable** of the signal by a **factor**. The signal expands or compresses depending on the factor.

Suppose a signal **g(t)** than its scaled version is **g(at)**.

If the factor **a>1** then the signal will **compress**. And the operation is called **signal compression**. Compressing a signal will make the signal **fast** as it becomes smaller and its time duration become less.

If **a<1** then the signal will **expand**. And the operation is called **signal dilation**.

After scaling, the **origin** of the signal remains unchanged. Expanding the signal will make the signal **slow** as it becomes wider and covers more time duration.

In **time inversion**, the signal is **flipped** about the **y-axis** (vertical axis). The resultant signal is the **mirror image** of the original signal.

Time inversion is a special case of **time-scaling** in which the **factor a=-1**. Therefore to invert a * signal*, we replace it’s

Mathematically, the time-invert of signal g(t) is g(-t).

You may also read:

- Different Types of Modulation Techniques
- Boolean Logic And Basic Logic Gates
- Communication systems and its types

The post Introduction to Signals, Types, Properties, Operation & Application appeared first on Electronics Engineering.

]]>The post Amplitude modulation and its types appeared first on Electronics Engineering.

]]>The type of modulation in which the

amplitudeof the carrier signalvaries linearlywith respect to theinstantaneous amplitudeof the message signal is called.Amplitude modulation

There are several types of Amplitude modulations.

**Double sideband** is a type of Amplitude modulation in which the frequency spectrum of the message signal is symmetrically situated above & below the carrier signal’s frequency.

The upper & lower frequencies are known as **sidebands** of the modulated signal. **Upper ****sideband** **(USB)** has frequency components higher than the carrier frequency and the **lower ****sideband (LSB)** has lower frequency components than the carrier frequency.

Suppose the message signal is sinusoidal signal.

**m(t) = A _{m}cos ω_{m}t**

The carrier signal is a high frequency sinusoidal signal.

**c(t) = A _{c }cos ω_{c}t**

The Amplitude modulated **DSB SC** signal will be

**ϕ _{DSB-SC}(t) = A_{DSB} cos ω_{c}t**

**A _{DSB } = A_{c} + m(t)**

Substituting **A _{DSB }**

**ϕ _{DSB-SC}(t) = (A_{c} + m(t)) cos ω_{c}t ……….eq(1)**

**ϕ _{DSB-SC}(t) = A_{c }cos ω_{c}t + m(t) cos ω_{c}t**

Substituting **m(t)**

**ϕ _{DSB-SC}(t) = A_{c }cos ω_{c}t + A_{m}cos ω_{m}t cos ω_{c}t**

**ϕ _{DSB-SC}(t) = A_{c }cos ω_{c}t + A_{m}/2 cos (ω_{m }+ ω_{c}) t + A_{m}/2 cos (ω_{m }– ω_{c}) t**

The modulated signal has three terms.

The first term represents the **carrier signal**. The second term represents the **message signal’s frequency shifted** to the left by **ω _{c}**. The third term represents the

Suppose the message signal’s spectrum is

The spectrum of carrier signal is

The **DSB SC** modulated signal’s spectrum is

The message spectrum is centered at **ω _{c }**having two halves. The upper half

In Amplitude modulation, it describes the level of carrier signal amplitude over the level of the message signal.

According to the eq(1)

**ϕ _{DSB-SC}(t) = (A_{c} + m(t)) cos ω_{c}t **

Substituting **m(t)**

**ϕ _{DSB-SC}(t) = (A_{c} + A_{m}cos ω_{m}t) cos ω_{c}t**

**ϕ _{DSB-SC}(t) = A_{c} (1 + A_{m}/A_{c }cos ω_{m}t) cos ω_{c}t**

**ϕ _{DSB-SC}(t) = A_{c} (1 + μ cos ω_{m}t) cos ω_{c}t**

where **μ= A _{m}/A_{c }**is the modulation index.

Modulation index plays important role in **traditional AM** discussed in this article below.

The bandwidth **B.W** of **DSB-SC** is the **difference** between the **maximum and minimum** frequency of the modulated signal.

**B.W = (f _{c}+ f_{m}) – (f_{c}– f_{m} )**

**B.W = f _{c}+ f_{m} – f_{c}+ f_{m}**

**B.W = 2 f _{m}**

The **bandwidth** of the **DSB-SC** modulated signal is **twice **the** bandwidth** of the **message signal**.

Demodulationis the process ofacquiringtheoriginal signal(message signal) from themodulated signal(received signal).

To demodulate a **DSB-SC** signal, it is multiplied with the carrier signal (coherent frequency).

Assume the modulated signal is

**ϕ(t) = m(t) cos ω _{c}t**

Then the modulated signal will be

**e(t) = m(t) cos ω _{c}t cos ω_{c}t**

** e(t) = ½ m(t) (1 + cos 2ω _{c}t)**

**e(t) = ½ m(t) +½ m(t) cos 2ω _{c}t**

The demodulated signal contains two terms, a **message signal** and a **high frequency** term. The high frequency term is **filtered out** by passing through **Low Pass Filter**.

- The modulation process is very simple
- No need for filtering during modulation for sidebands.

- Demodulation need coherent carrier source.
- It carrier less information about the carrier.
- Carrier power is wasted
- Envelop detection is not possible.
- High bandwidth compares to SSB, VSB.

In **DSB-FC**, the carrier signal is utilized during demodulation. The message signal is stored in the **envelope** of the modulated signal. In order to acquire this envelope, the amplitude of message signal in the modulated signal should not go **below Zero**. i.e.

**A _{c }+ m(t) ≥ 0**

carrier amplitude **A _{c}** should be adjusted to satisfy the equation.

**A _{c }– A_{m} ≥ 0**

**A _{m }**= lowest peak amplitude of message signal.

**A _{c } ≥ A_{m}**

**1 ≥ A _{m}/ A_{c}**

**1 ≥ μ**

where **μ = A _{m}/ A_{c}**

**0 ≥ μ ≥ 1**

Thus the **modulation** index **μ** should be between **0 & 1** for **envelope detection** at receiver.

**DSB-FC** or **traditional AM** can be demodulated by using coherent source or envelope detector. Envelop detector is very simple and inexpensive process.

An **envelope detector** is a simple diode, capacitor and resistor circuit. It does not need any coherent source or any low pass filter.

The message signal is rectified out using this envelope detector.

- The receiver is very simple and low cost.
- Broadcasting is very efficient.

- Waste too much power.
- Overall low efficiency (about 33%).
- AM is affected by noise.

**Quadrature Amplitude Modulation** is the type of Amplitude modulation in which **two** different **message signals** are transmitted on **same frequency carrier** with **different phase shift**.

The DSB modulated signal has double bandwidth of the modulating signal. To overcome excessive bandwidth, QAM is applied by sending two message signals on the same frequency carrier signal with **90° phase difference**.

The block diagram of **QAM** is given below:

This block diagram shows modulation of two message signals. The carrier source produces carrier signal. The carrier signal with **0° phase shift** is used with **first message signal m _{1}(t)** and the carrier signal with

Suppose two message signals are **m _{1}(t)**,

The carrier signal is

**c(t)= cos ω _{c}t.**

So the **90°** degree phase shifted signal of **c(t)** will be

**c(t)= cos (ω _{c}+90°)t = sin ω_{c}t.**

So the modulated single will be

**Φ _{QAM}(t) = m_{1}(t) cos ω_{c}t + m_{2}(t) sin ω_{c}t**

**QAM** modulated signal cannot be demodulated using **envelope detection** technique because it contains two message signals. The messages signals are demodulated by **multiplying** the QAM signal with its **coherent carrier** signal as follows.

To get **m _{1}(t)**, the received signal is multiplied with

**e(t)= (m _{1}(t) cos ω_{c}t + m_{2}(t) sin ω_{c}t) cos ω_{c}t**

**e(t)= m _{1}(t) cos^{2} ω_{c}t + m_{2}(t) sin ω_{c}t cos ω_{c}t**

**e(t)= ½ m _{1}(t) (1+cos 2ω_{c}t) + ½ m_{2}(t) sin 2ω_{c}t**

**e(t)= ½ m _{1}(t) +½ m_{1}(t) cos 2ω_{c}t) + ½ m_{2}(t) sin 2ω_{c}t**

By passing through **Low Pass Filter**

**e(t)= ½ m _{1}(t)**

To get **m _{2}(t)**, the received signal is multiplied with

**e(t)= (m _{1}(t) cos ω_{c}t + m_{2}(t) sin ω_{c}t) sin ω_{c}t**

**e(t)= m _{1}(t) cos ω_{c}t sin ω_{c}t + m_{2}(t) sin^{2} ω_{c}t**

**e(t)= ½ m _{1}(t) sin 2ω_{c}t + ½ m_{2}(t) (1-cos 2ω_{c}t)**

**e(t)= ½ m _{1}(t) sin 2ω_{c}t + ½ m_{2}(t) – ½ m_{2}(t) cos 2ω_{c}t)**

By passing through **Low Pass Filter**

**e(t)= ½ m _{2}(t)**

- Can carry more than one message signal.
- Utilize low bandwidth as compared to the information transmitted.

- It has complex design of transmitter and receiver.
- Envelope detection technique does not work.

The type of **Amplitude modulation**, in which only single side band is transmitted thorough antenna is called single **sideband communication**.

Unlike **DSB**, the **SSB** modulated signal has only single side-band either upper side-band (usually) or lower side-band.

The **SSB modulated signal** is made from **DSB signal** by passing it through a **bandpass filter**. The bandpass filter cutoff the DSB modulated signal at ω_{c }and filter out either **upper sideband** or **lower sideband** as shown in fig below.

The bandwidth of the **SSB signal** is **equal** to the bandwidth of the **message signal**.

If the received signal is **SSB suppressed carrier** signal then the demodulator needs a **coherent source**. which generates the same frequency carrier as the received signal. After demodulation, the signal is passed through **low pass filter** to filter out **high-frequency** components.

If the received signal is **SSB full carrier** signal then it is best to use an **Envelope detector or Rectifier**. The **SSB full carrier** transmission is a type of SSB transmission in which the **carrier amplitude** is very large compared to message signal amplitude.

- Bandwidth is equal to message signal.
- Save half power by transmitting one sideband.

- Filtering one sideband is very difficult and add complexity to the transmitter circuit
- It needs a bandpass filter with very sharp cutoff. An ideal filter.

As we know that a real **bandpass filte**r does not have a **sharp cutoff** and it does not filter all the frequencies outside of cutoff region. A real filter allows some frequency content outside of the cutoff region. Because of this problem vestigial sideband is implemented.

In VSB, one sideband and a **little portion (25%)** of the second sideband is transmitted as shown in the figure below.

The bandwidth of **VSB** modulated signal is **greater** than **SSB** but it is **lower** than **DSB** modulated signal. The bandwidth of **VSB** modulated signal is **25% greater** than the bandwidth of the message signal.

**B.W = f _{m} + 25% f_{m}**

If the received signal is **VSB** suppressed carrier signal, then the demodulation only needs coherent carrier source. The rest of the demodulation process is same as **SSB** and **DSB** suppressed carrier demodulation.

If the received signal is **VSB** with the carrier, then an **envelope detector** can also demodulate the signal. The **VSB full carrier** needs very **large carrier amplitude** as compared to message signal’s amplitude.

You may also read:

- Modulation – Types and Classification of Analog Modulation
- Types of Communication Systems and its Components
- Boolean Logic And Basic Logic Gates

The post Amplitude modulation and its types appeared first on Electronics Engineering.

]]>The post Modulation – Types and Classification of Analog Modulation appeared first on Electronics Engineering.

]]>

The process of varying any of the three characteristics as the Amplitude, Frequency or the Phase of a carrier signal is called asmodulation

We know that the information signal to be transmitted can be of any form such as data, music, video etc. But before transmission, it is converted into its equivalent electrical form. The electrical equivalent form of the original signal is called **baseband signal**.

Every electrical signal possesses basic characteristics such as **Amplitude**, **Frequency**, and **Phase.** We need to change the characteristics of the signal to make it more appropriate for the transmission.

.

We need modulation because of the following reasons:

- It reduces the height of the antenna used for the transmission.
- It increases the range of the communication.
- Using Modulation avoids the mixing of the signal.
- Modulation makes multiplexing of the signal possible.

This block diagram shows a modulator with two inputs i.e. modulating signal and carrier signal. And at the output, we get the modulated signal.

The modulating signal is nothing but the information signal. This modulating signal is primarily of two forms such as analog signal and digital signal.

The carrier signal is the signal upon which the modulating signal is modulated. The modulated signal is the resultant output signal of the modulator.

Modulation is divided into two types;

- Analog Modulation
- Digital modulation

Analog modulation is further divided into three types;

- Amplitude modulation
- Frequency modulation
- Phase modulation

Whereas, Digital modulation is further divided into three types;

- Pulse Amplitude modulation (PAM)
- Pulse width modulation (PWM)
- Pulse code modulation (PCM)

In this article, we will cover Analog modulation and its types.

Analog modulation deals with an analog signal. The types of analog modulation are briefly discussed below.

**Amplitude modulation** is a type of **analog modulation** in which the amplitude of the high-frequency carrier signal is changing with respect to the instantaneous amplitude of the modulating signal.

In amplitude modulation, the amplitude of the carrier signal changes. However, the frequency and the phase of the carrier signal remains constant. Thus the information is contained in the amplitude of the carrier signal.

Suppose the modulating signal is a sinusoidal signal, it can be represented as:

**m(t) = A _{m} cos ω_{m}t**

where:

**m(t)** = instantaneous amplitude of the modulating signal

**A _{m}** = Peak amplitude of the modulating signal

**ω _{m}** = 2πf

**f _{m}** = Frequency of modulating signal

Similarly, the carrier signal is represented as;

**c(t) = A _{c} cos ω_{c} t**

Where:

** A _{c}** = Peak amplitude of the carrier signal

**ω _{c}** = 2πf

**f _{c}** = Frequency of carrier signal

The Amplitude modulated wave is represented as:

**m _{am}(t) = A_{am} cos ω_{c} t**

Where;

**A _{am}** is the instantaneous amplitude of the envelope of the modulated signal. So it is represented as

**A _{am} = A_{c} + m(t)**

**A _{am} = A_{c} + A_{m} cos ω_{m}t**

Substituting **A _{am}** into

**m _{am}(t) = (A_{c} + A_{m} cos ω_{m}t) cos ω_{c} t**

**m _{am}(t) = Ac (1 + (A_{m}/A_{c}) cos ω_{m}t) cos ω_{c} t**

Where modulation index is;

**μ = A _{m}/A_{c}**

Thus

**m _{am}(t) = A_{c} (1 + μ cos ω_{m}t) cos ω_{c} t**

**Modulation index μ** should be between **0 to 1** for envelope detection during **demodulation**.

The representation of frequency content of a signal using a graph is called spectrum.

The mathematical equation of **AM modulated wave**;

**m _{am}(t) = (A_{c} + A_{m} cos ω_{m}t) cos ω_{c} t**

**m _{am}(t) = A_{c} cos ω_{c} t + A_{m} cos ω_{m}t cos ω_{c} t**

Using trigonometric identity **2 cos A cos B = cos (A+B) + cos (A-B)**

**m _{am}(t) = A_{c} cos ω_{c} t + (A_{m}/2) cos (ω_{m} + ω_{c} )t + (A_{m}/2) cos (ω_{m} – ω_{c} )t**

Where:

** A _{c} cos ω_{c} t** = Carrier signal

(**A _{m}/2) cos (ω_{m} + ω_{c} )t** = Message spectrum shifted ω

**(A _{m}/2) cos (ω_{m} – ω_{c} )t** = Message spectrum shifted ω

Thus we get the spectrum of **AM** as follows;

Where the bandwidth of the signal is the difference between **F _{LSB}** and

Bandwidth = **F _{LSB} – F_{USB}**

Bandwidth = **(f _{c} – f_{m}) – (f_{c} + f_{m})**

Bandwidth = **2f _{m}**

The basic components of **AM transmitters** are **oscillator** and **power amplifier**.

The **oscillator** is a circuit which generates **sinusoidal waveforms of different frequencies**. The crystal oscillator is generally used in AM transmitter for generating a carrier signal of high frequency.

Power amplifiers are used for the amplification of the modulated signal before feeding it to the antenna for transmission. The modulated signal has low power and it cannot be transmitted without amplification.

Bipolar junction transistors are used as Power amplifiers in AM transmitter.

**There are 3 classes of Power Amplifiers.**

The class A amplifier operates for the whole cycles of the signal.These amplifiers amplify the whole signal thus wasting too much power. Class A amplifier has low efficiency.

Class B amplifiers operate only for half of the input signal thus the efficiency of the Class B amplifiers ranges up to 80%.

While Class C amplifiers only operate for only 25% (positive high portion) of the signal. Thus the efficiency of class C amplifiers is 90%.

There are 2 types of AM transmitters

In the low-level transmitter, a crystal oscillator is used for generating the carrier signal. The carrier and modulating signal is amplified using class A amplifier before modulation. After modulation, the modulated signal is amplified again before transmission.

The low-level transmitter does not need high-efficiency Amplifiers thus its design is much simpler.

The high-level transmitter has the same design as low-level transmitter except it uses Class C amplifier at modulation stage. Because of class C amplifier, this transmitter has high efficiency and complex design.

In the High-level transmitter, the carrier signal and modulating signal is amplified using linear amplifiers. At the modulation block, both signals are amplified with modulation and then fed to the antenna for transmission. Block diagram of the High-level transmitter is as follows.

- AM transmitters have a simple design.
- AM receivers are also simple. Envelope detectors are the simplest receivers.
- Due to high power, AM signals have a long range of transmission.
- The AM signal has low Bandwidth.

- Because the information is stored in the amplitude of the modulated signal, which is affected by the noise in the medium.
- AM need high power for its transmission.

- Because of its long range, it can be used for Radio broadcasting.
- It can be used for Television broadcasting.

In** frequency modulation**, the frequency of the carrier signal varies with respect to the instantaneous amplitude of the modulating (message) signal.

The amplitude and phase of the carrier signal remain unchanged. Only frequency of the carrier signal changes. Thus the information is stored in the frequency of the FM modulated signal.

The frequency of the carrier signal increases with increase in the amplitude of the modulating signal and it decreases with the decrease in the amplitude of the modulating signal.

The difference between the original frequency of the carrier signal and modulated frequency is called frequency deviation.

It is directly proportional to the amplitude of the modulating signal.

Consider the FM modulating signal to be a sinusoidal signal.

**m(t) = A _{m} cos(2πf_{m}t)**

The carrier signal is represented as:

**c(t) = A _{c} cos (2πf_{c}t)**

the instantaneous frequency of the modulated signal is:

**f _{i}(t) = f_{c} + K_{f} m(t) K_{f} = constant**

**f _{i}(t) = f_{c} + K_{f} A_{m} cos(2πf_{m}t)**

**f _{i}(t) = f_{c} + δ_{f} cos(2πf_{m}t)**

Where:

** δ _{f} = K_{f} A_{m}** = maximum frequency deviation

The minimum and maximum frequency of the FM modulated signal is:

**F _{min} = f_{c} – δ_{f}**

**F _{max} = f_{c} + δ_{f}**

And the bandwidth of the FM modulated signal is:

**B.W = 2 f _{c} x number of side-bands**

**B.W = 2 (f _{c} + δ) Carson’s Rule**

In FM transmitter the modulating signal is mixed directly with the high frequency carrier signal.

A general block diagram of FM transmitter is given below:

- FM modulated signal is immune to noise as noise only affects the amplitude of the signal. And the information is stored in the frequency of the signal.
- FM signal consumes less power as compared to AM signal.
- The transmitted power remains constant as the amplitude of the signal remains constant.
- Due to high frequency, the antenna of FM receiver is very small.

- FM signal covers large bandwidth as compared to AM signal.
- The design of FM transmitters and receivers are very complex.

Applications: - FM can be used for radio broadcasting.

The process in which the phase of the carrier signal varies with the instantaneous amplitude of the modulating (message) signal is called phase modulation.

Consider the message signal is a sinusoidal signal.

**m(t) = A _{m} cos(ω_{m}t)**

The carrier signal is a high-frequency sinusoidal signal.

**c(t) = A _{c} cos(ω_{c}t + ϴ)**

**ϴ** is the phase of the signal and normally it is zero.

The Phase modulated signal is given below:

**ϕ _{pm}(t) = A_{c} cos(ω_{c}t + ϴ + K_{p }m(t))**

**ϕ _{pm}(t) = A_{c} cos(ω_{c}t + ϴ + K_{p} A_{m} cos(ω_{m}t))**

**K _{p} **= constant of proportionality for phase modulation.

The instantaneous frequency of PM signal is;

**ω _{i} = d/dt (ω_{c}t + ϴ + K_{p}m(t))**

**ω _{i} = {ω_{c}+ K_{p} d/dt(m(t)}**

The equation of the instantaneous frequency shows that in PM the derivative of modulating signal is added with the frequency of the carrier signal.

Thus it proves that if we take the derivative of the modulating signal before feeding it to Frequency modulator we get Phase modulation.

Phase deviation is the maximum difference between the original phase of the carrier signal and the modulated signal. The equation of phase modulated signal is;

**ϕ _{pm}(t) = A_{c} cos(ω_{c}t + ϴ + K_{p}m(t))**

Substituting **m(t)**

**ϕ _{pm}(t) = A_{c} cos(ω_{c}t + ϴ + K_{p} A_{m} cos(ω_{m}t))**

**ϕ _{pm}(t) = A_{c} cos(ω_{c}t + ϴ + δ_{p} cos(ω_{m}t))**

Where **δ _{p} = K_{p}A_{m}** = maximum phase deviation

**Phase modulation** has same properties as **Frequency modulation**, that is why they have same advantages and disadvantages.

You may also read:

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]]>

The

transferofinformationfrom one place to another place using some sort ofmediumis called. The information could be in sound or visual or any other form.Communication

There are two main types :

The type of communication that doesn’t need the **modulation** for the transmission of the signal is termed as **baseband communication**. The signal that is transmitted is said to be **baseband signal** or message signal. Baseband signals have sizable power. So it has to be transmitted through a **wire, coaxial cables or fiber**.

The type of communication which requires the **modulation** of the signal for its transmission is called **carrier communication**. In modulation, the original signal is superimposed on a **carrier signal** with a higher frequency range. Which can be easily transmitted using an **antenna**.

A typical communication system comprises of following components.

1) Source

2) Input Transducer

3) Transmitter

4) Channel

5) Receiver

6) Output transducer

7) Destination

The **source** is something which originates the message. It can be human’s voice, camera’s video, a typed message or data.

A **transducer** is a **sensor** which **converts** any other form (pressure, light) of a signal into **electrical signal**. **Input transducer** converts any other form of energy into **electrical signals**. This electrical signal is information which needs to be transmitted.

The **transmitter** is a circuit which modifies the input electrical signal into a suitable form and transmits it through an antenna.

The **transmitter** contains a modulator. In baseband communication, the modulator is not necessary.

The modulator superimposes the baseband signal onto a carrier signal with high frequency. Due to modulation, the signal’s frequency range shifts into higher frequency range. This modulated signal is ready for efficient transmission through the specified medium.

Channel is the medium by which the modulated signal is transmitted to the receiver. Wire, coaxial cable, radio link, an optical fiber and a waveguide are the examples of a channel.

Unfortunately, there are noises in the channel. which also adds up and modifies the transmitted signal.

The receiver receives the transmitted signal. The receiver consists of a demodulator.

The demodulator demodulates the received signal (modulated signal) using demodulation technique and recovers the baseband signal (original signal).

The output transducer converts the electrical signal into its original form. Because we need the original message that the source originated. It converts it into a form which can be understood by the destination unit.

The destination is the unit to which the message is communicated.

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