# chapter 5 am, fm, and digital modulated systems phase modulation (pm) frequency modulation (fm)

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Chapter 5 AM, FM, and Digital Modulated Systems Phase Modulation (PM) Frequency Modulation (FM) Generation of PM and FM Spectrum of PM and FM Carson’s Rule Narrowband FM. Huseyin Bilgekul Eeng360 Communication Systems I Department of Electrical and Electronic Engineering - PowerPoint PPT PresentationTRANSCRIPT

Chapter 5AM, FM, and Digital Modulated Systems

Phase Modulation (PM)Frequency Modulation (FM)Generation of PM and FMSpectrum of PM and FMCarsons RuleNarrowband FMHuseyin BilgekulEeng360 Communication Systems IDepartment of Electrical and Electronic Engineering Eastern Mediterranean University

AM and FM Modulation (a) Carrier wave. (b) Sinusoidal modulating signal. (c) Amplitude-modulated signal.(d) Frequency modulated signal.

Angle Modulation We have seen that an AM signal can be represented as

Now we will see that information can also be carried in the angle of the signal asNote that in this type of modulation the amplitude of signal carries information.Here the amplitude Ac 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:(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.;

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

Special Case 2:For FM, the phase is proportional to the integral of m(t) so that

where the frequency deviation constant Df 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 (fi) of a signal is defined by

Phase and Frequency ModulationsPhase ModulationFrequency ModulationComparing above two equations , we see that if we have a PM signal modulated by mp(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 mf(t),the corresponding phase modulation on this signal is:

Where f and p denote frequency and phase respectively.

IntegratorPhase Modulator (Carrier Frequency fc)DifferentiatorFrequency 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,Average Power does not change with modulation

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 isSame (t) could also be obtained if FM were usedwhereThe Complex Envelope is:andThe peak frequency deviation would be

Using discrete Fourier series that is valid over all time, g(t) can be written asJn() Bessel function of the first kind of the nth order Taking the fourier transform of the complex envelope g(t), we getSpectrum of PM or FM Signal with Sinusoidal Modulating Signal

Bessel Functions of the First Kind J0()=0 at =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 c nm. 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 indexObservations:Frequency spectrum of FM

Spectra of an FM Signal with Sinusoidal ModulationBTf1.0 The following spectra show the effect of modulation index, , on the bandwidth of an FM signal, and the relative amplitudes of the carrier and sidebands

BTJ0(1.0)J1(1.0)J2(1.0)f1.0Spectra of an FM Signal with Sinusoidal Modulation

BTf1.0Spectra 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.

Based on the Bessel Functions, 98% of the power will be transmitted when the number of sidebands transmitted is 1+ on each side.Carsons rule(1+b)fm

Carsons rule Therefore the Bandwidth required is given by phase modulation index/ frequency modulation indexB bandwidth of the modulating signal Carsons rule : Bandwidth of an FM signal is given by

Narrowband Angle Modulation Narrowband Angle Modulation is a special case of angle modulation where (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 iswherePMFM

Indirect method of generating WBFM

Wideband Frequency modulation

FM Stero System

FM Stero System

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