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Angle / Exponential Modulation
Lecture - 1.0 Introduction. 1.1 Instantaneous Frequency. 1.2 Phase Modulation (PM). 1.3 Frequency Modulation (FM). 1.4 Relation between Phase Modulation and Frequency Modulation. 1.5 Single-tone Angle Modulation. 1.5.1 Single-tone Phase Modulation. 1.5.2 Single-tone Frequency Modulation. 1.6 Phase and Frequency deviation. 1.6.1 Units for Phase / Frequency deviation and Modulation indices. 1.6.2 Summary of PM and FM equations. 1.7 Narrowband Frequency Modulation. 1.8 Bandwidth of Single-tone Narrowband Frequency Modulation. 1.9 Phasor diagram for NBFM. 1.10 Spectrum of Narrowband Angle Modulation for Baseband signal 1.11 References
Define and mathematically describe angle modulation Explain the difference between frequency and phase modulation Describe direct and indirect frequency modulation Describe direct and indirect phase modulation Define deviation sensitivity Describe FM and PM waveforms Define phase deviation and modulation index Explain frequency deviation and percent modulation Analyze the frequency content of an angle modulated waveform Describe the Narrowband PM and FM Determine the bandwidth requirement for Narrowband PM and FM
1.0. Introduction: In the previous chapters, we studied the different AM techniques in which the amplitude of some carrier signal is modified according to the message signal. The frequency and phase of the carrier of the carrier signal in all AM modulation techniques were constant. In this chapter, we will study a different method for transmitting information by changing the angle (changing the phase or frequency) of the carrier signal and keeping its amplitude constant usually referred to as Angle Modulation. The phase of carrier is varied in accordance with amplitude of the message signal referred to as phase modulation (PM). In other case the frequency of the carrier is varied in accordance with amplitude of modulating signal is called frequency modulation (FM). The PM and FM are non-linear function of modulating signal which makes them are non-linear modulation process
Frequency modulation: The Frequency of the carrier signal is varied proportional to (in accordance with) the Amplitude of the input modulating signal Explain Frequency modulation with a diagram Refer figure. The input is a single tone sinewave. The carrier and the FM waveform also are shown.
In a more elegant form,
v = A sin [ wct + ( f / fm) sin wmt ]
= A sin [ wct + mf sin wmt ]
A = Amplitude of FM signal. f = Frequency deviation
mf = Modulation Index of FM
mf = f / fm
mf is called the modulation index of frequency modulation.
wm = 2 fm wc = 2 fc
Modulation index of FM is defined as the ratio of the frequency deviation of the carrier to the frequency of the modulating signal
In FM modulation, Deviation ratio is the ratio of the maximum carrier frequency deviation to the highest audio modulating frequency. The deviation ratio of an FM-phone signal having a maximum frequency swing of plus-or- minus 5 kHz when the maximum modulation frequency is 2.5 kHz is 2.0. The deviation ratio of an FM-phone signal having a maximum frequency swing of plus or minus 7.5 kHz when the maximum modulation frequency is 1.5 kHz is 5.0.
The extent of frequency deviation in FM plays an important role in the quality (Signal to ratio) of the base band signal. But more the deviation more the badwidth needed for FM Transmission. Therefore it is important to note that if higher signal to noise ratio (SNR) is needed, the system will require more bandwidth. In Communication systems it is a dilemma always since availability of bandwidth is always limited and yet the signal quality needs to be good. There is always a trade off between SNR and Bandwidth.
As a result the deviation used for FM will be different in for different systems and applications. As seen , in FM Broadcast deviation is typically ±75 kHz. This is known as wideband FM (WBFM). These signals are capable of supporting high quality transmissions, but occupy a large amount of bandwidth. Usually 200 kHz is allowed for each wideband FM transmission.
For radio communications where only speech is involved, lesser bandwidth is used. This is called Narrowband FM. The deviation used in NBFM often between 3 to 5 KHz. The modulation index is typically between ). and 0.5. There will be only one significant side band (as shown in figure for mf = 0.5) and the bandwidth required will be 2 fm which is very less.
For low modulation indices, fm is much larger than f , then
B.W WBFM = 2 fm Hz
For large modulation indices, f is much larger than fm , then
B.W WBFM = 2 f Hz
One of the most important difference between Angle Modulation and Amplitude Modulation is the
distribution of power in the modulated wave. Unlike AM, the total power in an angle modulated wave is
equal to the power of un-modulated carrier. Therefore with angle modulation, the power that was originally
in the un-modulated carrier is redistributed among the carrier and its sidebands. The average power of an
angle modulated wave is independent of the modulating signal, the modulation index and the frequency
deviation. It is equal to the average power of the un-modulated carrier, regardless of the depth of
modulation.
Mathematically, the average power in the un-modulated carrier is
The carrier phase deviation will be more if the input signal amplitude increases and vice versa.
Figure shows phase modulation. In this example, When the input amplitude increases (+ve slope) the carrier undergoes phase lead. When the input amplitude decreases (-ve slope) the carrier undergoes phase lag. Therefore as the input amplitude increases, the magnitude of the phase lead also goes on increasing from instant to instant. For example if the phase lead was 30 degrees at t =1 sec, the phase lead increases to 35 degrees at t = 1.1 sec and so on. Similarly, as the input amplitude decreases, the magnitude of the phase lag also goes on increasing from instant to instant. For example if the phase lag was 30 degrees at t =1 sec, the phase lag increases to 35 degrees at t = 1.1 sec and so on Therefore PM waveform will be similar to FM waveform in all aspects.
Since m(t) switches from +1 to -1 and vice versa, the FM wave Frequency switches between 99.9 MHz and 100.1 MHz. This is called and is a digital format.
In FM transmission very often speech is an input (modulating) signal.
Speech spectrum is shown below. It can be seen that human speech has higher energy levels in the low
frequency band upto 1 kHz and falls off rapidly at higher frequencies. Above 1 kHz, the falloff is approximately 6
dB per octave.
But the noise spectrum in the channel is flat. Noise has the same energy levels irrespective of frequency.
Therefore if we modulate speech without any preprocessing, the signal to noise ratio at higher frequencies will be
significantly lower than SNR at lower frequencies. Quality will be seriously eroded at upper frequencies. To
overcome this situation most of the FM circuits use techniques known as Pre-emphasis at the transmitter and
De-emphasis at the receiver. Preemphasis artificially boosts (amplifies) the speech signal at higher frequencies.
thro RC circuits before modulation. At the receiver a deemphasis RC circuit restores the high frequencies back to
their original values.
The boosts high frequency signal components such that they will have higher magnitude to
combat noise components. This results in improved SNR at high frequency region of input speech signals.
Fig. Pre-emphasis
Preemphasis circuit consists of R and C components. The design is such that t = R1*C where in t should be
about 75 μs. This circuit will have lower frequency cutoff at 2123 Hz ( ). As seen in the curve, all the
frequencies higher than 2123 is amplified at the rate of 6dB/octave.
Pre-emphasis circuit also has upper cutoff frequency beyond which no further boosting of signal happens.This
Upper cutoff frequency,
Preemphasis in general is a High Pass Filter.
The performs exactly the reverse of the Pre-emphasis. It is used at the receiver. It restores the
pre-emphasized signal back to the normal amplitude level. It is a simple Low Pass Filter with time constant of
about 75 μs.
Fig. De-emphasis
De-emphasis circuit will have cutoff frequency of about 2123 Hz. To bring the signal back to normal level, all the
frequency components above 2123 Hz is attenuated at 6dB/octave.
2.1 Introduction.
2.2 Wide Band FM.
2.3 Spectrum of WBFM.
2.4 Observations.
2.5 Bandwidth of FM.
3.0 Introduction.
3.1 Indirect FM Generation.
3.2 Direct FM Generation / Parameter Variation Methods.
3.2.1 Reactance Modulator
3.2.2 Varactor Diode Modulator
3.2.3 Limitations of direct methods of FM generation
3.3 FM Demodulators:
Direct type FM detector:
3.3.1 Single ended slope detector
3.3.2 Balanced slope detector
3.3.3 Foster-Seeley / Phase discriminator
3.3.4 Ratio detector
3.3.5 Zero crossing detector
Indirect type FM detector:
3.3.6 PLL based FM detector
3.4 Performance Comparison of FM Demodulators.
3.5 FM versus PM
3.6 Angle Modulation versus Amplitude Modulation.
3.6.1: Advantages of Angle Modulation
3.6.2: Disadvantages of Angle Modulation
3.7 References.
