Principles of Communication system

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Module-2

Mrs. Bhavya S and Dr Rashmi Samanth

Senior Assistant Professor, ECE,

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Principles of Communication system

• ANGLE MODULATION: Basic definitions, Frequency Modulation: Narrow Band FM, Wide Band FM, Transmission bandwidth of FM Signals, Generation of FM Signals, Demodulation of FM Signals, FM Stereo Multiplexing, Phase–Locked Loop: Nonlinear model of PLL, Linear model of PLL, Nonlinear Effects in FM Systems. The Superheterodyne Receiver

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Outline

Module-2

Angle Modulation

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Let carrier signal is represented as

s (t) = Ac cos ϴ(t)

Here phase angle is varied by the message signal m(t).

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Angle Modulation

• We have seen that an AM signal can be represented as

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• Now we will see that information can also be carried in the angle of the signal as

Note that in this type of modulation the amplitude of signal carries information.

Here the amplitude A_c remains constant and the angle is modulated.

This Modulation Technique is called the Angle Modulation

Angle modulation: Vary either the Phase or the Frequency of the carrier signal

• Phase Modulation and Frequency Modulation are special cases of Angle Modulation

Angle Modulation

Representation of PM and FM signals:

θ(t) - linear function of the modulating signal m(t)

g(t) - Nonlinear function of the modulation.

Special Case 1:

For PM the phase is directly proportional to the modulating signal. i.e.;

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Where D_p is the Phase sensitivity of the phase modulator, having units of radians/volt.

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Special Case 2:

For FM, the phase is proportional to the integral of m(t) so that

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where the frequency deviation constant D_f has units of radians/volt-sec.

Angle Modulation

• Phase Modulation occurs when the instantaneous phase varied in proportion to that of the message signal.

Dp is the phase sensitivity of the modulator

• Instantaneous Frequency (f_i) of a signal is defined by

Phase and Frequency Modulations

• Phase Modulation

• Frequency Modulation

Comparing above two equations , we see that if we have a PM signal modulated by m_p(t), there is also FM on the signal, corresponding to a different modulation wave shape that is given by:

Similarly if we have a FM signal modulated by m_f(t),the corresponding phase modulation on this signal is:

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Where f and p denote frequency and phase respectively.

Integrator

Phase Modulator (Carrier Frequency fc)

Differentiator

Frequency Modulator (Carrier Frequency fc)

Generation of FM from PM and vice versa

FM Signal

PM signal

Generation of FM using a Phase Modulator:

Generation of PM using a Frequency Modulator:

FM with sinusoidal modulating signal

• The Instantaneous Frequency of the FM signal is given by:

• The Peak Frequency Deviation is given by:

• The Frequency Deviation from the carrier frequency:

FM with sinusoidal modulating signal

But,

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Average Power does not change with modulation

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Angle Modulation

Advantages:

• Constant amplitude means Efficient Non-linear Power Amplifiers can be used.
• Superior signal-to-noise ratio can be achieved (compared to AM) if bandwidth is sufficiently high.

Disadvantages:

• Usually require more bandwidth than AM
• More complicated hardware

Modulation Index

• The Peak Phase Deviation is given by:

Spectra of Angle modulated signals

• Spectra for AM, DSB-SC, and SSB can be obtained with simple formulas relating S(f) to M(f).
• But for angle modulation signaling, because g(t) is a nonlinear function of m(t). Thus, a general formula relating G(f) to M(f) cannot be obtained.
• To evaluate the spectrum for angle-modulated signal, G(f) must be evaluated on a case-by-case basis for particular modulating waveshape of interest.

Spectrum of PM or FM Signal with Sinusoidal Modulating Signal

• Assume that the modulation on the PM signal is

Same θ(t) could also be obtained if FM were used

where

The Complex Envelope is:

and

The peak frequency deviation would be

Using discrete Fourier series that is valid over all time, g(t) can be written as

J_n(β) – Bessel function of the first kind of the nth order

Taking the fourier transform of the complex envelope g(t), we get

Spectrum of PM or FM Signal with Sinusoidal Modulating Signal

Bessel Functions of the First Kind

J₀(β)=0 at β=2.4, 5.52 & so on

Bessel Functions of the First Kind

• The FM modulated signal in time domain

• From this equation it can be seen that the frequency spectrum of an FM waveform with a sinusoidal modulating signal is a discrete frequency spectrum made up of components spaced at frequencies of ω_c± nω_m.
• By analogy with AM modulation, these frequency components are called sidebands.
• We can see that the expression for s(t) is an infinite series. Therefore the frequency spectrum of an FM signal has an infinite number of sidebands.
• The amplitudes of the carrier and sidebands of an FM signal are given by the corresponding Bessel functions, which are themselves functions of the modulation index

Observations:

Frequency spectrum of FM

Spectra of an FM Signal with Sinusoidal Modulation

B_T

f

1.0

• The following spectra show the effect of modulation index, β, on the bandwidth of an FM signal, and the relative amplitudes of the carrier and sidebands

B_T

J₀(1.0)

J₁(1.0)

J₂(1.0)

f

1.0

Spectra of an FM Signal with Sinusoidal Modulation

B_T

f

1.0

Spectra of an FM Signal with Sinusoidal Modulation

• Although the sidebands of an FM signal extend to infinity, it has been found experimentally that signal distortion is negligible for a bandlimited FM signal if 98% of the signal power is transmitted.

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• Based on the Bessel Functions, 98% of the power will be transmitted when the number of sidebands transmitted is 1+β on each side.

Carson’s rule

(1+β)f_m

Carson’s rule

• Therefore the Bandwidth required is given by

β – phase modulation index/ frequency modulation index

B – bandwidth of the modulating signal

• Carson’s rule : Bandwidth of an FM signal is given by

Narrowband Angle Modulation

• Narrowband Angle Modulation is a special case of angle modulation where θ(t) is restricted to a small value.

• The complex envelope can be approximated by a Taylor's series in which only first two terms are used.

becomes

• The Narrowband Angle Modulated Signal is

• The Spectrum of Narrowband Angle Modulated Signal is

where

PM

FM

Indirect method of generating WBFM

Wideband Frequency modulation

FM Stero System

FM Stero System

Phase–Locked Loop

Phase–Locked Loop

Phase–Locked Loop

Phase–Locked Loop

Phase–Locked Loop- Linear model

Phase–Locked Loop- Linear model

Phase–Locked Loop- Linear model

Phase–Locked Loop- Linear model

The Superheterodyne Receiver �

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