Communication system eecb353 chapter 3 part i angle modulation
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COMMUNICATION SYSTEM EECB353 Chapter 3 Part I ANGLE MODULATION. Dept of Electrical Engineering Universiti Tenaga Nasional. Introduction. Amplitude Modulation (AM) – Amplitude of the carrier varies accordingly to the message signal.

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COMMUNICATION SYSTEM EECB353 Chapter 3 Part I ANGLE MODULATION

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Communication system eecb353 chapter 3 part i angle modulation

COMMUNICATION SYSTEM EECB353Chapter 3 Part IANGLE MODULATION

Dept of Electrical Engineering

Universiti Tenaga Nasional


Introduction

Introduction

  • Amplitude Modulation (AM) – Amplitude of the carrier varies accordingly to the message signal.

  • Angle Modulation (FM and PM) – Angle of the carrier varies accordingly to the message signal while amplitude of the carrier is constant.

    where m(t) = angle modulated waveform

    Vc = peak carrier amplitude

    c = carrier radian frequency (=2fc)

    (t) = instantaneous phase deviation (radians)

(1)


Introduction1

Introduction

  • Angle modulation as a function of modulating signal can be expressed mathematically as

    (t) = F [vm(t)](2)

    where vm(t) = Vmsin(mt)

    Vm = peak modulating signal amplitude

    m = modulating signal radian frequency (=2fm)

Figure: Angle modulation vs amplitude modulation


Introduction2

Introduction

  • Whenever the frequency of a carrier varied, the phase is also varied and vice versa.

  • Thus, FM and PM must both occur whenever either form of angle modulation is performed.

  • If the freq of the carrier is varied directly in accordance with the modulating signal, FM results.

  • If the phase of the carrier is varied directly in accordance with the modulating signal, PM results.

  • Therefore, direct FM is indirect PM and direct PM is indirect FM.

  • DirectFM/PM – frequency/phaseof the constant amplitude carrier is varied proportionally to the amplitude of the modulating signal at a rate equal to the frequency of the modulating signal.


Introduction3

Introduction

  • How carrier freq, fc change in accordance to modulating signal vm(t)?

  • +ve increase in modulating signal amplitude causes increase in carrier freq.

  • Deacrease (or –ve increase) in modulating signal amplitude causes decrease in carrier freq.

Figure: Angle modulated wave in frequency domain


Mathematical analysis

Mathematical Analysis

Instantaneous phase deviation = = (3)

Instantaneous frequency deviation = = (4)

where Kpand Kf are constant (deviation sensitivity of phase and freq)

  • For a modulating signal,

    • Phase modulation,

      (5)

    • Frequency modulation,

      (6)


Communication system eecb353 chapter 3 part i angle modulation

Carrier

Modulating signal

FM

PM

Figure : Phase and Frequency Modulation of sinusoidal carrier by a single-freq modulatingsignal.


Communication system eecb353 chapter 3 part i angle modulation

PM

The phase deviation of modulator o/p is prop. to m(t). The freq deviation is prop. to the derivative of the phase deviation, thus the i is max when the slope of m(t) is max and min when the slope of m(t) is min

FM

Freq. deviation is prop. to m(t), thus the i is max when the m(t) is max and min when m(t) is min

Note that m(t) is not shown along with the modulator o/p. It would not be possible to distinguish the PM and FM o/p

Accos 2fct

PM

FM

Output of PM and FM modulators for a sinusoidal, Accos 2fct


Communication system eecb353 chapter 3 part i angle modulation

Comparison of PM and FM modulator outputs for a unit-step input.

(a) Message signal. (b) Unmodulated carrier. (c) Phase modulator output (kp = ½). (d) Frequency modulator output.

PM

i =fc for t<t0 and t>t0

The phase of unmodulated carrier is advanced by kp=/2 rads for t>t0 giving rise to a signal that is discontinues at t=t0

FM

i =fc for t<t0 and,

= fc+ fdfor t>t0

The modulator o/p phase is, however, continues at t=t0


Mathematical analysis1

Mathematical Analysis

  • For FM – maximum freq deviation (change in the carrier freq) occurs during the maximum +ve and –ve peaks of the modulating signal i.e freq deviation  to the amplitude of the modulating signal.

  • For PM – maximum freq deviation occurs during zero crossings of the modulating signal i.e freq deviation  to the slope or first derivative of modulating signal.

  • For FM and PM – rate of freq change is equal to the modulating signal freq.

  • Example : A transmitter operates on a frequency of 915 MHz. The maximum FM deviation is +/- 12.5 kHz. What are the maximum and minimum frequencies that occur during modulation?

  • Example : A phase modulator has Kp= 2 rad/V. What voltage of sinewave would cause a peak phase deviation of 60 degrees ?


Phase deviation and modulation index m

Phase Deviation and Modulation Index, m

Kf = deviation sensitivity for frequency

Kp = deviation sensitivity for phase

m = modulation index and peak phase deviation, ∆Ѳ rad


Frequency deviation and percent modulation

Frequency Deviation and Percent Modulation

  • Frequency Deviation – the change in frequency that occurs in the carrier when it is acted on by a modulating-signal frequency.

  • Typically given as a peak frequency shift in hertz (f).

  • The peak-to-peak freq deviation (2f) is called carrier swing.

  • For FM, the deviation sensitivity, Kf is often given in hertz/volt. Thus, the peak freq deviation can be expressed mathematically as:


Frequency deviation and percent modulation1

Frequency Deviation and Percent Modulation

  • With PM, modulation index and peak phase deviation are directly proportional to the amplitude of the modulating signal and unaffected by its frequency.

  • With FM, both modulation index and freq deviation are directly proportional to the amplitude of the modulating signal, and modulation index is inversely proportional to its freq.

  • Percent Modulation – the ratio of actual freq deviation to the maximum freq deviation allowed in percentage form.

    % modulation = (27)


Angle modulation summary

Angle Modulation Summary


Examples

Examples

  • Determine the peak frequency deviation (f) and modulation index (m) for an FM modulator with a deviation sensitivity, Kf = 5kHz/V and a modulating signal vm(t) = 2 cos(22000t).

  • Determine the peak phase deviation (m) for a PM modulator with a deviation sensitivity Kp = 2.5rad/V and a modulating signal vm(t) = 2 cos(22000t).

  • Below is the angle modulated signal produced after FM modulator;

    Determine:

    • Modulation index

    • Peak frequency deviation


Examples1

Examples

4. For a direct FM modulation, an information signal, is used to modulate a carrier, . For a deviation sensitivity of 2.5rad/s/V, calculate

  • The peak frequency deviation in Hz

  • The modulation index

  • The percent modulation for maximum frequency deviation of 75kHz

  • Using part (b), the deviation sensitivity for the indirect PM

  • The carrier swing

  • Write out the mathematical expression of the FM wave


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