Chapter 4 : Frequency Modulation, PPT, Semester, Engineering - Electronics and Communication Engineering (ECE) PDF Download

FREQUENCY MODULATION

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INTRODUCTION

3 properties of an analog signal can be modulated by information signal:
o Amplitude - - -> produce AM
o Frequency - - - > produce FM
o Phase - - - > produce PM

FM & PM are forms of angle modulation and often referred as frequency modulation.

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FM VS AM

FM is considered to be superior to AM.
Transmission efficiency:
AM use linear amplifier to produced the final RF signal.
FM has constant carrier amplitude so it is not necessary to use linear amplifier.
Fidelity (capture effect):
The stronger signal will be capture and eliminate the weaker.
In AM, the weaker signal can be heard in the background.
Noise immunity (noise reduction):
Constant carrier amplitude.
FM receiver have limiter circuit
 

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Disadvantages of FM

Use too much spectrum space.
Requiring a wider bandwidth
Reduce modulation index to minimize BW but in FM although we reduced the modulation index, BW is still larger.
typically used at high frequencies (VHF,UHF & microwave frequencies
More complex circuitry

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ANGLE MODULATION

 Amplitude of the modulated carrier is held constant and either the
phase or the time derivative of the phase of the carrier is varied linearly
with the message signal m(t).
 General angle-modulated signal is given by
 In angle modulation, (t) is prescribed as being a function of the
modulating signal
 If vm(t) is the modulating signal, angle modulation is expressed as

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FM OR PM ?

Both must occur whenever either form of angle modulation is performed.

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MATHEMATICAL ANALYSIS

 Instantaneous frequency deviation
 Instantaneous change in the frequency of the carrier and is defined
as the first time derivative of the instantaneous phase deviation

 Instantaneous frequency
 the precise frequency of the carrier at any given instant of time and is defined as the first time derivative of the instantaneous phase

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 Substituting 2fc for c gives
 Frequency modulation is angle modulation in which the instantaneous frequency deviation, ’(t), is proportional to
the amplitude of the modulating signal, and the instantaneous phase deviation is proportional to the integral of the modulating signal voltage.

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DEVIATION SENSITIVITY

 For modulating signal vm(t), the frequency modulation are frequency modulation = ’(t) = kfvm(t) rad/s
where kf are constant and are the deviation sensitivities of the frequency modulator.
 Deviation sensitivities are the output-versus-input transfer function for the modulators, which gave the relationship
between what output parameter changes in respect to specified changes in the input signal.
 frequency modulator,

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FREQUENCY MODULATION (FM)

 Variation of d/dt produces Frequency Modulation
 Frequency modulation implies that d/dt is proportional to the modulating signal.
 This yields

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Example 4.1

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FM WAVEFORM

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Carrier amplitude remains constant
Carrier frequency is changed by the modulating signal.
amplitude of the information signal varies, the carrier frequency shift proportionately.
modulating signal amplitude increases, the carrier frequency increases.
modulating signal amplitude varies, the carrier frequency varies below and above it normal center or resting, frequency with no modulation.
The amount of the change in carrier frequency produced by the modulating signal known as frequency deviation fd.
Maximum frequency deviation occurs at the maximum amplitude of the modulating signal.
The frequency of the modulating signal determines the frequency deviation rate

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MODULATION INDEX

 Directly proportional to the amplitude of the modulating signal and inversely proportional to the frequency of the modulating
signal
 Ratio of the frequency deviation and the modulating frequency
 FM equation :
  as modulation index :
 Example:
 Determine the modulation index for FM signal with modulating frequency is 10KHz deviated by ±10kHz.
 Answer : (20KHz/10KHz) = 2 .0 (unitless)
 The total frequency change, 10kHz x 2 is called the carrier swing

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Example:

a simple transmitter with an assigned rest frequency of 100MHz deviated by a ±25kHz, the carrier changes frequency with modulation between the limits of 99.975MHz and 100.025MHz
The total frequency change, 25kHz x 2 is called the carrier swing
Table 1 display the transmission band that use FM and the legal frequency deviation limit for each category
Deviation limits are based on the quality of the intended transmissions, wider deviation results in higher fidelity
The frequency deviation is a useful parameter for determining the bandwidth of the FM-signals

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PERCENT MODULATION

 Simply the ratio of the frequency deviation actually produced to the maximum frequency deviation allowed by law stated in percent form
 For example if a given modulating signal produces ±50kHz frequency deviation, and the law stated that maximum frequency deviation allowed is ±75kHz, then

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Example 4.2

A 1 MHz carrier freq with a measured sensitivity of 3 kHz/V is modulated with a 2 V, 4 kHz sinusoid. Determine
1. the max freq deviation of the carrier
2. the modulation index
3. the modulation index if the modulation voltage is doubled
4. the modulation index for vm(t)=2cos[2π(8kHz)t)]V
5. express the FM signal mathematically for a cosine carrier & the cosine-modulating signal of part 4. Carrier amplitude is 10V

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FM RADIO FREQUENCY

Commercial radio FM band, 88MHz – 108MHz
Each station allotted to a frequency deviation of ±75kHz (150 carrier swing) and 25kHz of guard band added above and below the carrier frequency swing
Total bandwidth is 200kHz
Therefore, maximum of 100 stations can be made available

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FREQUENCY ANALYSIS OF FM WAVES

BESSEL TABLE

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The first column gives the modulation , while the first row gives the Bessel function.
The remaining columns indicate the amplitudes of the carrier and the various pairs of sidebands.
Sidebands with relative magnitude of less than 0.001 have been eliminated.
Some of the carrier and sideband amplitudes have negative signs. This means that the signal represented by that amplitude is simply shifted in phase 180 (phase inversion).
The spectrum of a FM signal varies considerably in bandwidth depending upon the value of the modulation index. The higher the modulation index, the wider the bandwidth of the FM signal.
With the increase in the modulation index, the carrier amplitude decreases while the amplitude of the various sidebands increases. With some values of modulation index, the carrier can disappear completely.

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FM BANDWIDTH

The total BW of an FM signal can be determined by knowing the modulation index and Bessel function.
N = number of significant sidebands
fm = modulating signal frequency (Hz)
Another way to determine the BW is use Carson’s rule
This rule recognizes only the power in the most significant sidebands with amplitude greater than 2% of the carrier.

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Example 4.3

Calculate the bandwidth occupied by a FM signal with a modulation index of 2 and a highest modulating frequency of
2.5 kHz. Determine bandwidth with table of Bessel functions. Referring to the table, this produces 4 significant pairs of
sidebands.