Chapter - Angle Modulation – Frequency Modulation PPT, ECE - Computer Science Engineering (CSE) PDF Download

INTRODUCTION

The slides cover the following topics:

1. Frequency Modulation (FM)

2. FM Signal Spectrum

3. Generation of FM Signals

4. V/F Characteristics

5. FM signal waveforms

6. FM spectrum - Bessel Coefficients

7. Significant Sidebands - Spectrum

8. Carsons' Rule for FM bandwidth

9. Narrowband and Wideband FM

10. VHF/FM

11. Power in FM Signals

12. FM Demodulation

13. Phase Locked Loop (PLL)

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Angle Modulation – Frequency Modulation

Consider again the general carrier 

     represents the angle of the carrier.

There are two ways of varying the angle of the carrier.

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Frequency Modulation

In FM, the message signal m(t) controls the frequency fc of the carrier. Consider the carrier

then for FM we may write:

,where the frequency deviation will depend on m(t).

Given that the carrier frequency will change we may write for an instantaneous carrier signal

where φ_i is the instantaneous angle = and θ_i is the instantaneous frequency.

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Frequency Modulation

In FM, the message signal m(t) controls the frequency fc of the carrier. Consider the carrier

then for FM we may write:  ,  where the frequency deviation will depend on m(t).

Given that the carrier frequency will change we may write for an instantaneous carrier signal

where φ_i is the instantaneous angle =   and f_i is the instantaneous frequency.

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Frequency Modulation

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Frequency Modulation

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Frequency Modulation

Note – FM, as implicit in the above equation for vs(t), is a non-linear process – i.e. the principle of superposition does not apply. The FM signal for a message m(t) as a band of signals is very complex. Hence, m(t) is usually considered as a 'single tone modulating signal' of the form

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Frequency Modulation

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Frequency Modulation

The amplitudes drawn are completely arbitrary, since we have not found any value for J_n(β) – this sketch is only to illustrate the spectrum.

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Generation of FM signals – Frequency Modulation

An FM demodulator is:

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V/F Characteristics

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V/F Characteristics

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V/F Characteristics

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Summary of the important points of FM

• The FM signal v_s(t) from which the spectrum may be obtained as

where Jn(β) are Bessel coefficients and Modulation Index,

•  α Hz per Volt is the V/F modulator, gradient or Frequency Conversion Factor, α per Volt

• α is a measure of the change in output frequency for a change in input amplitude.

 

• Peak Deviation (of the carrier frequency from f_c)

 

 

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FM Signal Waveforms

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 FM Signal Waveforms

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 FM Signal Waveforms

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FM Signal Waveforms

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FM Signal Waveforms

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FM Spectrum – Bessel Coefficients

The FM signal spectrum may be determined from

The values for the Bessel coefficients, J_n(β) may be found from graphs or, preferably, tables of ‘Bessel functions of the first kind’.

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FM Spectrum – Bessel Coefficients

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FM Spectrum – Bessel Coefficients

Hence for a given value of modulation index β, the values of J_n(β) may be read off the graph and hence the component amplitudes (V_cJ_n(β)) may be determined.

A further way to interpret these curves is to imagine them in 3 dimensions

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  Examples from the graph

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Significant Sidebands – Spectrum

As may be seen from the table of Bessel functions, for values of n above a certain value, the values of J_n(β) become progressively smaller. In FM the sidebands are considered to be significant if J_n(β) 0.01 (1%).

Although the bandwidth of an FM signal is infinite, components with amplitudes V_cJ_n(β), for which J_n(β) < 0.01 are deemed to be insignificant and may be ignored.

Example: A message signal with a frequency f_m  Hz modulates a carrier f_c to produce FM with a modulation index β = 1. Sketch the spectrum.

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Significant Sidebands – Spectrum

As shown, the bandwidth of the spectrum containing significant components is 6f_m, for β = 1.

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Significant Sidebands – Spectrum

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Significant Sidebands – Spectrum

An approximation for the bandwidth of an FM signal is given by

BW = 2(Maximum frequency deviation + highest modulated frequency)

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Narrowband and Wideband FM

Narrowband FM NBFM

Wideband FM WBFM

For β > 0.3 there are more than 2 significant sidebands. As b increases the number of sidebands increases. This is referred to as wideband FM (WBFM).

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VHF/FM

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Comments FM

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Comments FM

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Power in FM Signals

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Power in FM Signals

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Power in FM Signals

Now consider – if we generate an FM signal, it will contain an infinite number of sidebands. However, if we wish to transfer this signal, e.g. over a radio or cable, this implies that we require an infinite bandwidth channel. Even if there was an infinite channel bandwidth it would not all be allocated to one user. Only a limited bandwidth is available for any particular signal. Thus we have to make the signal spectrum fit into the available channel bandwidth. We can think of the signal spectrum as a ‘train’ and the channel bandwidth as a tunnel – obviously we make the train slightly less wider than the tunnel if we can.

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Power in FM Signals

However, many signals (e.g. FM, square waves, digital signals) contain an infinite number of components. If we transfer such a signal via a limited channel bandwidth, we will lose some of the components and the output signal will be distorted. If we put an infinitely wide train through a tunnel, the train would come out distorted, the question is how much distortion can be tolerated?

Generally speaking, spectral components decrease in amplitude as we move away from the spectrum ‘centre’.

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Power in FM Signals

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Power in FM Signals

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Example

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Example

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FM Demodulation –General Principles

•  An FM demodulator or frequency discriminator is essentially a frequency-to-voltage   converter (F/V). An F/V converter may be realised in several ways, including for   example, tuned circuits and envelope detectors, phase locked loops etc.  Demodulators are also called FM discriminators.

•  Before considering some specific types, the general concepts for FM demodulation will be presented. An F/V converter produces an output voltage, V_OUT  which is proportional to the frequency input, f_IN.

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FM Demodulation –General Principles

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FM Demodulation –General Principles

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FM Demodulation –General Principles

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FM Demodulation –General Principles

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FM Demodulation –General Principles

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Methods

Tuned Circuit – One method (used in the early days of FM) is to use the slope of a tuned circuit in conjunction with an envelope detector.

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Methods

This gives the composite characteristics shown. Diode D₂ effectively inverts the f₂ tuned circuit response. This gives the characteristic ‘S’ type detector.

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Phase Locked Loops PLL

• Note the similarity with a synchronous demodulator. The loop comprises a multiplier, a low pass filter and VCO (V/F converter as used in a frequency modulator).

 

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Phase Locked Loops PLL

 

• The input f_IN is applied to the multiplier and multiplied with the VCO frequency output fO, to produce (f_IN + f_O) and Δ = (f_IN – f_O).

 

• The low pass filter passes only (f_IN – f_O) to give V_OUT which is proportional to (f_IN – f_O).

 

• If f_IN » f_O but not equal, V_OUT = VIN,  af_IN – f_O is a low frequency (beat frequency) signal to the VCO.

• This signal, V_IN, causes the VCO output frequency f_O to vary and move towards f_IN.

 

• When f_IN = f_O, VIN (f_IN – f_O) is approximately constant (DC) and f_O is held constant, i.e locked to f_IN.

 

• As  f_IN  changes, due to deviation in FM, f_O tracks or follows f_IN. V_OUT = V_IN changes to drive f_O to track f_IN.

 

•V_OUT  is therefore proportional to the deviation and contains the message signal m(t).