**1. COMMUNICATION**

- Communication is a process by which information is exchanged between individuals through a common system of symbols
- It is a technique for expressing ideas effectively
- It is a system of routes for moving troops, supplies, and vehicles
- Communication is the transfer of information from one point in space and time to another point.

**Block diagram of a communication system:**

- Transmitter: couples the message onto the channel using high-frequency signals
- Receiver: restores the signal to its original form
- Channel: the medium used for transmission of signals
- Modulation: the process of shifting the frequency spectrum of a message signal to a frequency range in which more efficient transmission can be achieved
- Demodulation: the process of shifting the frequency spectrum back to the original baseband frequency range and reconstructing the original form, if necessary

**2. Modulation:**

- Modulation may be defined as the process by which some characteristics of a signal called carrier is varied in accordance with the instantaneous value of another signal called modulating the signal.
- The carrier frequency is greater than the modulating frequency. The signal resulting from the process of modulation is called the modulating signal.
**Types of Modulation:**When the carrier wave is continuous in nature, the modulation process is known as Continuous Wave (CW) modulation or analog modulation.- Amplitude Modulation
- Angle Modulation

**Amplitude Modulation:**

- A system of modulation in which the envelope of the transmitted wave contains a component similar to the waveform of the signal to be transmitted.
- The envelope of the modulated carrier has the same shape as the message waveform, achieved by adding the translated message that is appropriately proportional to the unmodulated carrier.
- Amplitude modulation may be defined as a system in which the maximum amplitude of the carrier wave is made proportional to the instantaneous value (amplitude) of the modulating or baseband signal.
- Let c(t) = V
_{c}cos ω_{c}t, and m(t) = V_{m}sin ω_{m}t. Then the amplitude modulated signal is

where µ is known as modulation index.

**Frequency Spectrum of AM:-**

- Significant frequencies from f
_{c}to (f_{c}+ f_{m}) is called an**upper sideband**. - Significant frequencies from (f
_{c}- f_{m}) to f_{c}is called as**lower sideband**.

f_{c} = Carrier frequency f_{m} = Modulating signal frequency

**Modulation Index:**

- In AM system, the modulation index is defined as the measure of the extent of amplitude variation about an unmodulated maximum carrier.

or

- V
_{max}is a Maximum value of amplitude modulated wave, and V_{min}is a Minimum value of amplitude modulated wave. - The baseband or modulating signal will be preserved in the envelope of the AM signal only if we have

- The modulation index is less than or equal to unity.
- If μ > 1or the percentage modulation is greater than 100, the baseband signal is not preserved in the envelope.
- Minimum value of amplitude modulated wave is V
_{min}= (V_{c}- V_{m}) - Maximum value of amplitude modulated wave is V
_{max}= (V_{c}+ V_{m}) - For avoiding phase reversal | μ | < 1

**Power Relation in AM Wave:** The total power P_{AM} of the AM wave is the sum of the carrier power P_{c} and sideband power P_{s}.

P_{AM}=P_{C}+P_{LSB}+P_{USB}

- where, P
_{LSB}= Lower sideband power, P_{USB}= Upper sideband power, and P_{c}= Carrier signal power

- Maximum power dissipated in the AM wave is P
_{AM}= 1.5 P_{c}for μ = 1 and this is maximum power that amplifier can handle without distortion.

**Current Relations in AM Wave:**

- The total power and carrier power can be represented by the following equations:

*I*is the unmodulated carrier current and_{C}*I*is the total, or modulated, the current of an AM transmitter._{T}

- These currents are usually applied or measured at the antenna. Hence,
*R*is the antenna resistance.

**Voltage Relations in AM Wave:**

- The total modulating voltage in AM wave in terms of carrier voltage can be given as

- where, V
_{t}= Total modulating voltage, and V_{c}= Carrier voltage

**Modulated by Several Sine Waves:**

- Let V
_{1}, V_{2}, V_{3}...... etc be the simultaneous modulation voltages. Then the total modulating voltage V_{t}will be

- where μ
_{t}is overall modulation index, μ_{1,}μ_{2}, μ_{3}are respective modulation index for individual waves.

- where P
_{SB}is total sideband power.

**Transmission Efficiency:**

- In AM wave, transmission efficiency may be defined as the percentage of total power contributed by the sidebands.
- Transmission efficiency,

- The maximum transmission efficiency of the AM is only 33.33%. This implies that only one-third of the total power is carried by the sidebands and the rest two-thirds is wasted.
- In AM, it is generally more convenient to measure the AM transmitter current than the power.
- The modulation index may be calculated from the values of unmodulated and modulated currents in the AM transmitter.

**Types of AM:**

**1. DOUBLE-SIDEBAND SUPPRESSED-CARRIER MODULATION**

In the standard form of amplitude modulation, the carrier wave c(t) is completely independent of the message signal m(t), which means that the transmission of the carrier wave represents a waste of power. This is a disadvantage of amplitude modulation; namely that only a fraction of the total transmitted power is affected by m(t). To overcome this , we may suppress the carrier component from the modulated wave, resulting in double-sideband suppressed carrier modulation.

**(i) Time-Domain Description**

To describe a double-sideband suppressed-carrier (DSBSC) modulated wave as a function of time, we write

s(t) = c(t)m(t) = A_{c} cos(2πf_{c}t) m(t)

**(ii) Frequency-Domain Description**

The suppression of the carrier from the modulated wave is well-appreciated by examining its spectrum. Specifically, by taking the Fourier transform whereas before, S(f) is the Fourier transform of the modulated wave s(t) and M(f) is the Fourier transform of the message signal m(t). When the message signal m(t) is limited to the interval –W ≤ f ≤ W, except for a change in scale factor, the modulation process simply translates the spectrum of the baseband signal ±f_{c}. Of course, the transmission bandwidth required by DSBSC modulation is the same.

**2. Single Sideband Technique:**

Assume the above spectrum an SSB signal in which lower side band is removed.

Let m(t) have a Fourier transform M(f), thus to eliminate the LSB we write the equation as

**Angle modulation and demodulation**

**Angle Modulation:**

- Angle modulation may be defined as the process in which the total phase angle of a carrier wave is varied in accordance with the instantaneous value of the modulating or message signal while keeping the amplitude of the carrier constant.
- There are two types of angle modulation schemes as under
- Phase Modulation (PM)
- Frequency Modulation (FM)

- These modulation schemes are also called as non-linear modulation schemes.

**(i) Phase Modulation (PM):**

- PM is that type of angle modulation in which the phase angle φ is varied linearly with a baseband or modulating signal x(t) about an unmodulated phase angle:

_{p}= Phase sensitivity of the modulator

**(ii) Frequency Modulation (FM):**FM is that type of angle modulation in which the instantaneous frequency ω

_{i}is varied linearly with a message or baseband signal x(t) about an unmodulated frequency ω

_{c}.

_{f}= Frequency sensitivity of the modulator

**(iii) Representation of FM and PM Signals:**

_{c }cos [θ(t)]

_{p}and k

_{f}are phase and frequency deviation constants respectively.

**Key Points**

- By passing message through a differentiator, then through a FM modulator we get PM modulated signal.
- By passing message through a integrator and then PM modulator we get FM modulated signal.

**(iv) PM and FM Modulated Signals for Sinusoidal Message Signal:**

_{c}is called

**frequency deviation**which depends upon the magnitude and sign of k

_{f }m(t). Frequency deviation:

**Carrier Swing:**The total variation in frequency from the lowest to the highest point is called carrier swing.

**Key Points**

- The amount of frequency deviation or variation depends upon the amplitude (loudness) of the modulating (audio) signal. This means that louder the sound, greater the frequency deviation and vice-versa.
- The frequency deviation is useful in determining the FM signal bandwidth.
- In FM broadcast, the highest audio frequency transmitted is 15 kHz.

**Modulation Index:**For FM, the modulation index is defined as the ratio of frequency deviation to the modulating frequency.

_{f}= frequency deviation / modulating frequency

**Note:**The m

_{f}may be greater than unity.

**Per cent Modulation:**The term 'per cent modulation as it is used in reference to FM' refers to the ratio of actual frequency deviation to the maximum allowable frequency deviation.

**Another Representation of PM and FM Signals for Sinusoidal Message:**

**Bandwidth of the Angle Modulated Signal:**In general, the effective bandwidth of an angle modulated signal, which contains at least 98% of the signal power is given by.

_{c}= 2 (β + 1) f

_{m}is also known as Carson's formula

- By seeing the graph of angle modulation signal we can't tell whether it is PM or FM.
- FM receiver may be fitted with amplitude limiters to remove the amplitude variations caused by noise.

**Relation between PM and FM:**

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