Angle modulation techniques such as frequency modulation (FM) and phase modulation (PM) were introduced. FM varies the carrier frequency according to the message signal, while PM varies the carrier phase. The chapter covered the concepts of instantaneous frequency, bandwidth of angle modulated signals, generation of FM signals through direct and indirect methods, and demodulation of FM signals using discriminators and phase-locked loops. Key advantages of FM over AM include improved noise immunity and resistance to interference at the cost of increased transmission bandwidth.
Introduction to Angle Modulation, Types of Angle Modulation, Frequency Modulation and Phase Modulation Introduction, Generation of FM, Detection of FM, Frequency stereo Multiplexing, Applications, Difference between FM and PM.
Details: https://electronicsembeddedworld.blogspot.com/2018/06/performance-management-mcq.html
FM demodulation involves changing the frequency variations in a signal into amplitude variations at baseband, e.g. audio. There are several techniques and circuits that can be used each with its own advantages and disadvantages.
In any radio that is designed to receive frequency modulated signals there is some form of FM demodulator or detector. This circuit takes in frequency modulated RF signals and takes the modulation from the signal to output only the modulation that had been applied at the transmitter.
There are several types of FM detector / demodulator that can be used. Some types were more popular in the days when radios were made from discrete devices, but nowadays the PLL based detector and quadrature / coincidence detectors are the most widely used as they lend themselves to being incorporated into integrated circuits very easily...
Introduction to Angle Modulation, Types of Angle Modulation, Frequency Modulation and Phase Modulation Introduction, Generation of FM, Detection of FM, Frequency stereo Multiplexing, Applications, Difference between FM and PM.
Details: https://electronicsembeddedworld.blogspot.com/2018/06/performance-management-mcq.html
FM demodulation involves changing the frequency variations in a signal into amplitude variations at baseband, e.g. audio. There are several techniques and circuits that can be used each with its own advantages and disadvantages.
In any radio that is designed to receive frequency modulated signals there is some form of FM demodulator or detector. This circuit takes in frequency modulated RF signals and takes the modulation from the signal to output only the modulation that had been applied at the transmitter.
There are several types of FM detector / demodulator that can be used. Some types were more popular in the days when radios were made from discrete devices, but nowadays the PLL based detector and quadrature / coincidence detectors are the most widely used as they lend themselves to being incorporated into integrated circuits very easily...
In this video, I will explain what is QAM modulation and what is 16QAM.
QAM Stands for Quadrature Amplitude Modulation. QAM is both an analog and a digital modulation method. But here, we are only talking about QAM as a digital modulation.
Quadrature means that two carrier waves are being used, one sine wave and one cosine wave. These two waves are out of phase with each other by 90°, this is called quadrature.
At the receiving end, the sine and cosine wave can be decoded independently, this means that by using both a sine wave and a cosine wave, the communication channel's capacity is doubled comparing to using only one sine or one cosine wave. That is why quadrature is such a popular technique for digital modulation.
QAM modulation is a combination of Amplitude Shift Keying and Phase Shift Keying, both carrier wave is modulated by changing both its amplitude and phase. As shown in this 8QAM waveform, the top is the sine wave carrier, for bit 000, the sin wave has a phase shift of 0°, and an amplitude of 2. While for bit 110, the phase shift is 180°, and the amplitude now is 1. So both phase and amplitude are changed.
In 16QAM, the input binary data is combined into groups of 4 bits called QUADBITS.
As shown in this picture, the I and I' bits are sent to the sine wave modulation path, and the Q and Q' bits are sent to the cosine wave path. Since the bits are split and sent in parallel, so the symbol rate has been reduced to a quarter of the input binary bit rate. If the input binary data rate is 100 Gbps, then the symbol rate is reduced to only 25 Gbaud/second. This is the reason why 16QAM is under hot research for 100Gbps fiber optic communication.
The I and Q bits control the carrier wave's phase shift, if the bit is 0, then the phase shift is 180°, if the bit is 1, then the phase shift is 0°.
The I' and Q' bits control the carrier wave's amplitude, if bit is 0, then the amplitude is 0.22 volt, if the bit is 1, then the amplitude is 0.821 volt.
So each pair of bits has 4 different outputs. Then they are added up at the linear summer. 4X4 is 16, so there is a total of 16 different combinations at the output, that is why this is called 16QAM.
This illustration shows an example of how the QUADBIT 0000 is modulated onto the carrier waves.
Here I and I' is 00, so the output is -0.22 Volt at the 2-to-4-level converter, when timed with the sine wave carrier, we get -0.22sin(2πfct), here fc is the carrier wave's frequency. QQ' is also 00, so the other carrier wave output is -0.22cos(2πfct).
Here is the proof that quadbit 0000 is modulated as a sine wave with an amplitude of 0.311volt and a phase shift of -135°. You can now pause for a moment to study the proof.
This list shows the 16QAM modulation output with different amplitude and phase change for all 16 quadbits. On the right side is the constellation diagram which shows the positions of these quadbits on a I-Q diagram.
You can visit FO4SALE.com f
QAM modulation is a combination of Amplitude Shift Keying and Phase Shift Keying, both carrier wave is modulated by changing both its amplitude and phase...
. Types of Modulation(Analog)
Phase-Frequency Relationships
FM and PM basics
Frequency deviation
MODULATION INDEX
Classification of FM
Narrow Band FM (NBFM)
generating a narrowband FM signal.
Wide Band FM (WBFM).
Carson’s Rule
Generation of WBFM
Average Power
FM BANDWIDTH
Comparing Frequency Modulation to Phase Modulation
In this video, I will explain what is QAM modulation and what is 16QAM.
QAM Stands for Quadrature Amplitude Modulation. QAM is both an analog and a digital modulation method. But here, we are only talking about QAM as a digital modulation.
Quadrature means that two carrier waves are being used, one sine wave and one cosine wave. These two waves are out of phase with each other by 90°, this is called quadrature.
At the receiving end, the sine and cosine wave can be decoded independently, this means that by using both a sine wave and a cosine wave, the communication channel's capacity is doubled comparing to using only one sine or one cosine wave. That is why quadrature is such a popular technique for digital modulation.
QAM modulation is a combination of Amplitude Shift Keying and Phase Shift Keying, both carrier wave is modulated by changing both its amplitude and phase. As shown in this 8QAM waveform, the top is the sine wave carrier, for bit 000, the sin wave has a phase shift of 0°, and an amplitude of 2. While for bit 110, the phase shift is 180°, and the amplitude now is 1. So both phase and amplitude are changed.
In 16QAM, the input binary data is combined into groups of 4 bits called QUADBITS.
As shown in this picture, the I and I' bits are sent to the sine wave modulation path, and the Q and Q' bits are sent to the cosine wave path. Since the bits are split and sent in parallel, so the symbol rate has been reduced to a quarter of the input binary bit rate. If the input binary data rate is 100 Gbps, then the symbol rate is reduced to only 25 Gbaud/second. This is the reason why 16QAM is under hot research for 100Gbps fiber optic communication.
The I and Q bits control the carrier wave's phase shift, if the bit is 0, then the phase shift is 180°, if the bit is 1, then the phase shift is 0°.
The I' and Q' bits control the carrier wave's amplitude, if bit is 0, then the amplitude is 0.22 volt, if the bit is 1, then the amplitude is 0.821 volt.
So each pair of bits has 4 different outputs. Then they are added up at the linear summer. 4X4 is 16, so there is a total of 16 different combinations at the output, that is why this is called 16QAM.
This illustration shows an example of how the QUADBIT 0000 is modulated onto the carrier waves.
Here I and I' is 00, so the output is -0.22 Volt at the 2-to-4-level converter, when timed with the sine wave carrier, we get -0.22sin(2πfct), here fc is the carrier wave's frequency. QQ' is also 00, so the other carrier wave output is -0.22cos(2πfct).
Here is the proof that quadbit 0000 is modulated as a sine wave with an amplitude of 0.311volt and a phase shift of -135°. You can now pause for a moment to study the proof.
This list shows the 16QAM modulation output with different amplitude and phase change for all 16 quadbits. On the right side is the constellation diagram which shows the positions of these quadbits on a I-Q diagram.
You can visit FO4SALE.com f
QAM modulation is a combination of Amplitude Shift Keying and Phase Shift Keying, both carrier wave is modulated by changing both its amplitude and phase...
. Types of Modulation(Analog)
Phase-Frequency Relationships
FM and PM basics
Frequency deviation
MODULATION INDEX
Classification of FM
Narrow Band FM (NBFM)
generating a narrowband FM signal.
Wide Band FM (WBFM).
Carson’s Rule
Generation of WBFM
Average Power
FM BANDWIDTH
Comparing Frequency Modulation to Phase Modulation
Power point presentation of Amplitude modulation from DSBSC.pptxvairaprakash3
The equation of AM wave in simple form is given by,
eAM(t) = Ec sin 2πfct+(mE_c)/2 cos2π(fc + fm)t - (mE_c)/2 cos2π(fc - fm)t
Here, power of the carrier does not convey any information. Most of the power is transmitted in the carrier is not used for carrying information. Hence the carrier is suppressed and only sidebands are transmitted.Therefore, if the carrier is suppressed, only sidebands remain in the spectrum requiring less power.
DSB-SC Contains two side bands i.e USB & LSB
Power efficiency is 100%
% Power saving in DSB-SC w.r.t AM is 66.67%.
Frequency modulation is the encoding of information in a carrier wave by varying the instantaneous frequency of the wave. The technology is used in telecommunications, radio broadcasting, signal processing, and computing.
The presentation is made by me. I am a student of EEE, RUET.
Model Attribute Check Company Auto PropertyCeline George
In Odoo, the multi-company feature allows you to manage multiple companies within a single Odoo database instance. Each company can have its own configurations while still sharing common resources such as products, customers, and suppliers.
The French Revolution, which began in 1789, was a period of radical social and political upheaval in France. It marked the decline of absolute monarchies, the rise of secular and democratic republics, and the eventual rise of Napoleon Bonaparte. This revolutionary period is crucial in understanding the transition from feudalism to modernity in Europe.
For more information, visit-www.vavaclasses.com
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An EFL lesson about the current events in Palestine. It is intended to be for intermediate students who wish to increase their listening skills through a short lesson in power point.
Operation “Blue Star” is the only event in the history of Independent India where the state went into war with its own people. Even after about 40 years it is not clear if it was culmination of states anger over people of the region, a political game of power or start of dictatorial chapter in the democratic setup.
The people of Punjab felt alienated from main stream due to denial of their just demands during a long democratic struggle since independence. As it happen all over the word, it led to militant struggle with great loss of lives of military, police and civilian personnel. Killing of Indira Gandhi and massacre of innocent Sikhs in Delhi and other India cities was also associated with this movement.
Read| The latest issue of The Challenger is here! We are thrilled to announce that our school paper has qualified for the NATIONAL SCHOOLS PRESS CONFERENCE (NSPC) 2024. Thank you for your unwavering support and trust. Dive into the stories that made us stand out!
The Roman Empire A Historical Colossus.pdfkaushalkr1407
The Roman Empire, a vast and enduring power, stands as one of history's most remarkable civilizations, leaving an indelible imprint on the world. It emerged from the Roman Republic, transitioning into an imperial powerhouse under the leadership of Augustus Caesar in 27 BCE. This transformation marked the beginning of an era defined by unprecedented territorial expansion, architectural marvels, and profound cultural influence.
The empire's roots lie in the city of Rome, founded, according to legend, by Romulus in 753 BCE. Over centuries, Rome evolved from a small settlement to a formidable republic, characterized by a complex political system with elected officials and checks on power. However, internal strife, class conflicts, and military ambitions paved the way for the end of the Republic. Julius Caesar’s dictatorship and subsequent assassination in 44 BCE created a power vacuum, leading to a civil war. Octavian, later Augustus, emerged victorious, heralding the Roman Empire’s birth.
Under Augustus, the empire experienced the Pax Romana, a 200-year period of relative peace and stability. Augustus reformed the military, established efficient administrative systems, and initiated grand construction projects. The empire's borders expanded, encompassing territories from Britain to Egypt and from Spain to the Euphrates. Roman legions, renowned for their discipline and engineering prowess, secured and maintained these vast territories, building roads, fortifications, and cities that facilitated control and integration.
The Roman Empire’s society was hierarchical, with a rigid class system. At the top were the patricians, wealthy elites who held significant political power. Below them were the plebeians, free citizens with limited political influence, and the vast numbers of slaves who formed the backbone of the economy. The family unit was central, governed by the paterfamilias, the male head who held absolute authority.
Culturally, the Romans were eclectic, absorbing and adapting elements from the civilizations they encountered, particularly the Greeks. Roman art, literature, and philosophy reflected this synthesis, creating a rich cultural tapestry. Latin, the Roman language, became the lingua franca of the Western world, influencing numerous modern languages.
Roman architecture and engineering achievements were monumental. They perfected the arch, vault, and dome, constructing enduring structures like the Colosseum, Pantheon, and aqueducts. These engineering marvels not only showcased Roman ingenuity but also served practical purposes, from public entertainment to water supply.
Embracing GenAI - A Strategic ImperativePeter Windle
Artificial Intelligence (AI) technologies such as Generative AI, Image Generators and Large Language Models have had a dramatic impact on teaching, learning and assessment over the past 18 months. The most immediate threat AI posed was to Academic Integrity with Higher Education Institutes (HEIs) focusing their efforts on combating the use of GenAI in assessment. Guidelines were developed for staff and students, policies put in place too. Innovative educators have forged paths in the use of Generative AI for teaching, learning and assessments leading to pockets of transformation springing up across HEIs, often with little or no top-down guidance, support or direction.
This Gasta posits a strategic approach to integrating AI into HEIs to prepare staff, students and the curriculum for an evolving world and workplace. We will highlight the advantages of working with these technologies beyond the realm of teaching, learning and assessment by considering prompt engineering skills, industry impact, curriculum changes, and the need for staff upskilling. In contrast, not engaging strategically with Generative AI poses risks, including falling behind peers, missed opportunities and failing to ensure our graduates remain employable. The rapid evolution of AI technologies necessitates a proactive and strategic approach if we are to remain relevant.
2024.06.01 Introducing a competency framework for languag learning materials ...Sandy Millin
http://sandymillin.wordpress.com/iateflwebinar2024
Published classroom materials form the basis of syllabuses, drive teacher professional development, and have a potentially huge influence on learners, teachers and education systems. All teachers also create their own materials, whether a few sentences on a blackboard, a highly-structured fully-realised online course, or anything in between. Despite this, the knowledge and skills needed to create effective language learning materials are rarely part of teacher training, and are mostly learnt by trial and error.
Knowledge and skills frameworks, generally called competency frameworks, for ELT teachers, trainers and managers have existed for a few years now. However, until I created one for my MA dissertation, there wasn’t one drawing together what we need to know and do to be able to effectively produce language learning materials.
This webinar will introduce you to my framework, highlighting the key competencies I identified from my research. It will also show how anybody involved in language teaching (any language, not just English!), teacher training, managing schools or developing language learning materials can benefit from using the framework.
Unit 8 - Information and Communication Technology (Paper I).pdfThiyagu K
This slides describes the basic concepts of ICT, basics of Email, Emerging Technology and Digital Initiatives in Education. This presentations aligns with the UGC Paper I syllabus.
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Francesca Gottschalk from the OECD’s Centre for Educational Research and Innovation presents at the Ask an Expert Webinar: How can education support child empowerment?
2. Outlines
• Introduction
• Concepts of instantaneous frequency
• Bandwidth of angle modulated signals
• Narrow-band and wide-band frequency
modulations
• Generation of FM signals
• Demodulation of FM signals
• superhetrodyne FM radio
3. Introduction
• Angle modulation: either frequency modulation
(FM) or phase modulation (PM).
• Basic idea: vary the carrier frequency (FM) or
phase (PM) according to the message signal.
4.
5.
6. • While AM is linear process, FM and PM are
highly nonlinear.
• FM/PM provide many advantages (main –
noise immunity, interference, exchange of
power with bandwidth ) over AM, at a cost of
larger transmission bandwidth.
• Demodulation may be complex, but modern
ICs allow cost-effective implementation.
Example: FM radio (high quality, not
expensive receivers).
7. Concepts of Instantaneous
Frequency
• A general form of an angle modulated signal is
given by
is the instantaneous angle
is the instantaneous phase deviation.
• The instantaneous angular frequency of
( ) cos ( ) cos(2 ( ))EM i c iS t A t A f t tθ π φ= = +
( ) ( )
( ) i i
i c
d t d t
t
dt dt
θ φ
ω ω= = +
( )i tθ
( )i tφ
( )EMS t
8. • The instantaneous frequency of
• The instantaneous frequency deviation
( ) ( )1 1
( )
2 2
i i
i c
d t d t
f t f
dt dt
θ φ
π π
= = +
( )1
( )
2
i
i
d t
f t
dt
φ
π
∆ =
( )EMS t
9. Example
• for the signal below find the
instantaneous frequency and maximum
frequency deviation.
2
( ) cos(10 )x t A t tπ π= +
10. • For phase modulation (PM), the instantaneous
phase deviation is
•
kp is the phase sensitivity of the PM modulator
expressed in (rad/ V) if m(t) is in Volts
• The instantaneous frequency of
( )
( )i c p
dm t
f t f k
dt
= +
Phase modulation (PM)
( ) ( )i t kp m tφ =
( ) cos [2 ( )]PM c pS t A f t k m tπ= +
( )PMS t
11. • For Frequency Modulation (FM), the
instantaneous phase deviation is
• kf is the frequency sensitivity of the FM
modulator expressed in rad/ V s if m(t) in Volts.
• The instantaneous frequency of
( ) cos 2 ( )
t
FM c fS t A f t k m dπ α α
−∞
= +
∫
Frequency Modulation (FM)
( ) ( )
t
i ft k m dφ α α
−∞
= ∫
( )FMS t
( ) ( )
2
f
i c
k
f t f m t
π
= +
14. • A PM/FM modulator may be used to
generate an FM/PM waveform
• FM is much more frequently used than PM
• All the properties of a PM signal may be
deduced from that of an FM signal
• In the remaining part of the chapter we
deal mainly with FM signals.
15. Example 5.1
• Sketch FM and PM waves for the modulating
signal m(t) shown in Fig. 5.4a. The constants kf
and kp are 2πx105
and 10π, respectively, and the
carrier frequency fc is 100 MHz..
18. Bandwidth of Angle Modulated
Signals
1) FM signals
[ ]
2 3
2 3
( ) cos(2 ) ( )sin(2 )
( )cos(2 ) ( )sin(2 ) ...
2! 3!
FM c f c
f f
c c
S t A f t k a t f t
k k
A a t f t a t f t
π π
π π
= −
+ − + +
where ( ) ( )
t
a t m dα α
−∞
= ∫
19. • Narrow-Band Frequency Modulation
(NBFM):
• Narrow-Band Phase Modulation (NBPM):
[ ]( ) cos(2 ) ( )sin(2 )NBFM c f cS t A f t k a t f tπ π≈ −
( ) cos(2 ) ( )sin(2 )NBPM c p cS t A f t k m t f tπ π ≈ −
BBNBFM 2=
| ( ) | 1fk a t <<
2NBPMB B=
| ( ) | 1Pk m t <<
22. • If
∆f: maximum carrier frequency deviation
β: deviation ratio or modulation index
• Wide- Band Frequency Modulation (WBFM)
|kf a(t)|>>1 or β>100 fBWBFM ∆= 2
π2
pf mk
f =∆
)1(2)(2 +=+∆= βBBfBFM
B
f∆
=β
| ( ) | 1fk a t ?
max ( )Pm m t=
23. • For phase modulation: if
π2
'
ppmk
f =∆
| ( ) | 1Pk m t ?
2( ) 2 ( 1)PMB f B B β= ∆ + = +
' '
max ( )Pm m t=
2WBPMB f= ∆
24. Single tone modulation
• Let
[ ])2sin(2cos)( tftfAtx mcFM πβπ +=
[ ]∑
∞
−∞=
+=
n
mcnFM tfnfJAtx )(2cos)()( πβ
( ) cos2 mm t f tα π=
25.
26.
27.
28.
29.
30.
31.
32.
33. • The results is valid only for sinusoidal signal
• The single tone method can be used for
finding the spectrum of an FM wave when
m(t) is any periodic signal.
2 ( 1)
2
FM m
f
m
B f
k
f
f
f
β
α
π
β
= +
∆ =
∆
=
34. Example 1
• A single tone FM signal is
Determine
a) the carrier frequency fc
b) the modulation index β
c) the peak frequency deviation
d) the bandwidth of xFM(t)
6 3
FMx (t)=10 cos[ 2 (10 )t+ 8 sin(2 (10 )t)]π π
35. Example 2
• A 10 MHz carrier is frequency modulated by
a sinusoidal signal such that the peak
frequency deviation is ∆f=50 KHz. Determine
the approximate bandwidth of the FM signal if
the frequency of the modulating sinusoid fm is
a) 500 kHz, b) 500 Hz, c) 10 kHz.
36. Example 3
• An angle modulated signal with carrier
frequency 100kHz is
Find
a) the power of xFM(t)
b) the frequency deviation ∆f
c) The deviation ratio β
d) the phase deviation ∆φ
e) the bandwidth of xFM(t).
EM cx (t)=10 cos[ 2 f t+ 5 sin(3000 t)+10 sin(2000 t) ]π π π
37. Example 5.3 (Txt book)
a) Estimate BFM and BPM for m(t) when
kf= 2πx105
rad/sV and kp= 5πrad/V
b) Repeat the problem if the amplitude of m(t)
is doubled.
38. Features of Angle Modulation
• Channel bandwidth may be exchanged for
improved noise performance. Such trade-off
is not possible with AM
• Angle modulation is less vulnerable than AM
to small signal interference from adjacent
channels and more resistant to noise.
• Immunity of angle modulation to
nonlinearities thus used for high power
systems as microwave radio.
39. • FM is used for: radio broadcasting, sound
signal in TV, two-way fixed and mobile
radio systems, cellular telephone systems,
and satellite communications.
• PM is used extensively in data
communications and for indirect FM.
• WBFM is used widely in space and
satellite communication systems.
• WBFM is also used for high fidelity radio
transmission over rather limited areas.
40. Generation of FM Signals
• There are two ways of generating FM
waves:
–Indirect generation
–Direct generation
42. Indirect Generation of
Wideband FM
• In this method, a narrowband frequency-
modulated signal is first generated and then a
frequency multiplier is used to increase the
modulation index.
m(t)
NBFM
xFM(t)
Frequency
Multiplier
45. Direct Generation
• The modulating signal m(t) directly controls
the carrier frequency. [ ]
• A common method is to vary the inductance
or capacitance of a voltage controlled
oscillator.
( ) ( )i c ff t f k m t= +
46.
47. • In Hartley or Colpitt oscillator , the frequency is
given by
• We can show that for k m(t) << C0
LC
1
=ω
+=
02
)(
1
C
tmk
cωω
0
1
LC
c =ω
49. • Advantage - Large frequency deviations are
possible and thus less frequency multiplication
is needed.
• Disadvantage - The carrier frequency tends to
drift and additional circuitry is required for
frequency stabilization.
To stabilize the carrier frequency, a phase-
locked loop can be used.
50. Example 5.6
• Discuss the nature of distortion inherent in the
Armstrong FM generator
–Amplitude distortion
–Frequency distortion
51. Example
• A given angle modulated signal has a peak
frequency deviation of 20 Hz for an input
sinusoid of unit amplitude and a frequency of
50 Hz. Determine the required frequency
multiplication factor, N, to produce a peak
frequency deviation of 20 kHz when the input
sinusoid has unit amplitude and a frequency
of 100Hz, and the angle-modulation used is
(a) FM; (b) PM
52. Demodulation of FM Signals
• Demodulation of an FM signal requires a
system that produces an output proportional to
the instantaneous frequency deviation of the
input signal.
• Such system is called a frequency
discriminator.
FM
Demodulator
[ ])(cos)( ttAtx c φω +=
dt
td
kty
)(
)(
φ
=
53.
54. • A frequency-selective network with a transfer
function of the form |H(ω)|= a ω+b over the
FM band would yield an output proportional
to the instantaneous frequency.
• There are several possible examples for
frequency discriminator, the simplest is the
FM demodulator by direct differentiation
55. FM demodulator by direct differentiation
• The basic idea is to convert FM into AM
and then use AM demodulator.
[ ]'
( ) 2 ( ) sin 2 ( )
t
c c f c fs t A f k m t f t k m dπ π α α
−∞
= − + +
∫
57. • Any signal which exceeds the preset limits are
simply chopped off
58. Practical Frequency Demodulators
• There are several possible networks for
frequency discriminator
–FM slope detector
–Balanced discriminator
– Quadrature Demodulator
• Another superior technique for the
demodulation of the FM signal is to use the
Phased locked loop (PLL)
70. Zero-Crossing Detectors
• Zero-Crossing Detectors are also used
because of advances in digital integrated
circuits.
• These are the frequency counters designed to
measure the instantaneous frequency by the
number of zero crossings.
• The rate of zero crossings is equal to the
instantaneous frequency of the input signal
71. Summary
• Concepts of instantaneous frequency
• FM and PM signals
• Bandwidth of angle modulated signals
NBFM and WBFM
• Generation of FM signals
– Direct and indirect generation
• Demodulation of FM signals
– frequency discriminator
– PLL
Angle modulation encompasses phase modulation (PM) and frequency modulation (FM). The phase angle of a sinusoidal carrier signal is varied according to the modulating signal.
It can provide a better discrimination (robustness) against noise and interference than AM This improvement is achieved at the expense of increased transmission bandwidth In case of angle modulation, channel bandwidth may be exchanged for improved noise performance Such trade-off is not possible with AM
(t)=10 t+ t 2 f i =d (t)/dt x (1/2 )= 5+ t (Hz)
For phase modulation (PM), the instantaneous phase deviation ( t ) is proportional to the modulating signal m ( t ). Thus ( t ) = k p m ( t )+ 0 where k p is a constant Let 0 =0, ( t ) = k p m ( t ) So a PM signal is represented by x PM ( t ) = A cos [ c t + k p m ( t )]
For FM, the instantaneous frequency deviation is proportional to the modulating signal m(t) The instantaneous angular frequency is i (t) So an FM signal is represented by x FM (t)
Because frequency and phase modulation are closely related, any variation in phase will necessarily result in a variation in frequency and vice versa. By looking at an-angle modulated carrier is generally impossible to tell whether it is FM or PM.
Phase and frequency modulation are inseparable x PM ( t ) = A cos [ c t + k p m ( t )] If we integrate the modulating signal m(t ) and phase-modulate using the integrated signal, we get a FM signal. On the other hand, If we differentiate the modulating signal m ( t ) and frequency-modulate using the differentiated signal, we get a PM signal. Therefore, we can generate a PM signal using a frequency modulator or we can generate an FM signal using a PM modulator.
Frequency modulation: (a) Modulating signal,
(b) instantaneous frequency, and (c) FM signal.
Bandwidth of Angle Modulated Signals
m p = max |m(t)|
m p ’ = max |m’(t)|
The last significant spectral component is for n= +1
J n ( ) gets smaller as n decreases and decreases.
WBFM is used widely in space and satellite communication systems. The large bandwidth expansion reduces the required SNR and thus reduces the transmitter power requirement. WBFM is also used for high fidelity radio transmission over rather limited areas.
The modulation index is small ( < 0.2)
When the modulation index is not small, a narrowband frequency-modulated signal is first generated using an integrator and a phase modulator as shown earlier. A frequency multiplier is then used to increase the modulation index from to N (that is increase the peak frequency deviation from f to N f ) . A frequency multiplier is a nonlinear device. Example the square law device: e 0 (t)= a e i 2 (t) If N=12 We can use 12 th order nonlinear device or two 2 nd order and one 3 rd order devices. Use of frequency multiplication normally increases the carrier frequency from f c to n f c . What if the desired carrier frequency is not multiple of f c ?
What if the desired carrier frequency is not multiple of f c ? A mixer or double-sideband modulator is required to shift the spectrum down to the desired range for further frequency multiplication or transmission as shown.
Example: Armstrong Indirect FM Transmitter (Fig. 5.10) The final output is required to have 91.2 MHz and f=75kHz. Note total multiplication=64x48=3072, if no frequency conversion is used, we get f=76.8kHz but f c = 614.4 MHz
In the direct method of generating an FM signal, the modulating signal m(t) directly controls the carrier frequency. A common method is to vary L or C of a tuned electric oscillator. Any oscillator whose frequency is controlled by the modulating signal is called a voltage controlled oscillator (VCO). We can use varactor diode whose capacitance varies with the bias voltage. Assuming that the capacitance of the tuned circuit varies linearly with the modulating signal m ( t ), we have C = C 0 - k m ( t ) L can be varied by a current in a second coil of a core reactance..
C = C 0 - k m ( t ) We can show that for [k m(t)] << C 0 ,
The varactor diode is a semiconductor diode that is designed to behave as a voltage controlled capacitor. When a semiconductor diode is reverse biased no current flows and it consists of two conducting regions separated by a non-conducting region. This is very similar to the construction of a capacitor. By increasing the reverse biased voltage, the width of the insulating region can be increased and hence the capacitance value decreased. If the information signal is applied to the varactor diode, the capacitance will therefore be increased and decreased in sympathy with the incoming signal.
Solution: f 2 =20kHz; f 1 =20Hz, N= f 2 / f 1 = 1000 f 2 =20kHz; f 1 =(100/50) 20=40 Hz, N= f 2 / f 1 = 500
The information in an FM signal resides in the instantaneous frequency. i = d (t)/dt= c + d (t)/dt = c + k f m(t) Demodulation of an FM signal requires a system that produces an output proportional d (t)/dt. Such system is called a frequency discriminator. For FM signal, y(t)=k d (t)/dt= k k f m(t)
The characteristics of an ideal frequency discriminator can be better described by a linear voltage/frequency characteristic as shown in Figure. i (t)= c + k f m(t) The instantaneous frequency i (t) changes linearly with m(t) The basic requirement of any FM demodulator is therefore to convert frequency changes into changes in output voltage, with the minimum amount of distortion.
There are several possible networks with such characteristics the simplest is the ideal differentiator
Since c + k f m(t)>0 for all t, m(t) can be obtained by envelope detection as in AM demodulation. Note that for a differentiator, H( )= j The basic idea is to convert FM into AM and then use AM demodulator. In practice, channel noise and other factors may cause A to vary. If A varies, y ( t ) will vary with A . Hence, it is essential to maintain the amplitude of the input signal to the frequency discriminator using a bandpass limiter (amplitude limiter). For demodulation of PM signals, we simply integrate the output of a frequency discriminator. This yields a signal which is proportional to m ( t ).
A bandpass limiter consists of hard limiter and BPF. It is usually used to eliminate any amplitude variations. A hard limiter is a device which limits the output signal to (say) +1 or -1 volt. Figure shows the input-output characteristic of a hard limiter. If the input is x(t)=A(t) cos (t) = A(t) cos[ c t+ (t)] The output of the low pass filter is (4/ ) cos[ c t+ (t)] For proof see textbook page 234-235.
An amplitude limiter circuit is able to place an upper and lower limit on the size of a signal. In Figure, the preset limits are shown by dotted lines. Any signal which exceeds these levels are simply chopped off. This makes it very easy to remove any unwanted amplitude modulation due to noise or interference.
The FM slope detector is composed of two parts: Frequency to amplitude converter (Tuned circuit) Envelope detector The magnitude frequency response |H(f)| of the frequency to amplitude converter is shown in next slide
The magnitude frequency response |H(f)| of the frequency to amplitude converter is shown. Note the frequency band for linear FM/AM conversion. Note that we can use the linear part in the left of f 0 or its right. The frequency f c must be in the centre of the linear part. However, the slope detection suffers from the fact that the slope of |H(f)| is linear over only a small band and, hence, causes considerable distortion in the output.
The slope detection suffers from the fact that the slope of |H(f)| is linear over only a small band and, hence, causes considerable distortion in the output. This fault can partially be corrected by a balanced discriminator. The balanced discriminator is composed of two slope detectors, one tuned f c1 and the other f c2 such that the desired carrier frequency f c falls in between Frequency response of the tuned circuit#1 and #2 and their overall response is shown.
Frequency response of the tuned circuit#1 and #2 and their overall response.
In this case, FM is converted into PM then PM detector is used to recover message signal The block diagram for a quadrature demodulator is shown. It contains a phase shifter, a phase comparator and a LPF. In modern systems if a noncoherent FM discriminator is required then the quadrature demodulator is used: Low- and medium-quality FM receivers Audio FM discriminator of TV sets TRF6900A SoC RF transceiver
Simplified circuit diagram of a quadrature Demodulator. Principle of operation 1. Phase shifter converts FM modulation into PM but preserves the FM 2. Analog multiplier serves as a phase detector (PD) and produces an output being linearly proportional to PM. PD is not sensitive to FM 3. Low-pass filter suppresses sum-frequency output
1. The phase shift is linearly proportional to the instantaneous frequency deviation about the carrier frequency fc = 10 : 7 MHz 2. FM modulation is converted into PM (FM is preserved) 3. Phase shift at carrier frequency is equal to -90 o
Quadrature demodulator: Almost exclusively used circuit configuration to implement a modern frequency discriminator
x(t)=AB/2 [sin( i - o )+sin(2 c t+ i + o )] The higher component is suppressed by the loop filter The output of the Loop filter is e 0 (t)=h(t)*0.5 AB sin( i - o )= h(t)*0.5 AB sin( e ) where e = i - o . The PLL will keep i (t) o (t), VCO (t)= c + c e 0 (t) The instantaneous frequency of the VCO output is VCO (t)= c + d o /dt Thus d o /dt= c e 0 (t) During phase-locked i (t) o (t), and Thus e 0 (t) c -1 d i /dt= (k f /c) m(t)