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L.X.R: miniproject, baseband signal transmission
Master Degree in Electronic Engineering
Analog and Telecommunication Electronic Course
(ATLCE-01NWM)
Prof. Dante Del Corso
Miniproject :
“Baseband signal transmission: technique for modulation
and demodulation”
Name: LI.XINRUI
Student ID: s219989
E-mail:s219989@studenti.polito.it
L.X.R: miniproject, baseband signal transmission
Catalogue
1 --Introduction of technique of baseband signal transmission
1.1 --Typical techniques are applied to transmitted signal.
1.2 --The definition of baseband signal.
1.3 --The role of modulation technology in signal transmission
theory.
2 -- Linear-modulation
2.2 --Linear -modulation -Amplitude Modulation(AM)
2.3 --Linear -modulation –DSB-SC modulation
2.4 --Linear -modulation –SSB-SC modulation
2.5 -- Linear -modulation –VSB-SC modulation
3 --Demodulation
3.1 --AM demodulation
3.2 --DSB-SC demodulation
3.3 --SSB-SC demodulation
3.4 --VSB-SC demodulation
4 --Non-linear modulation
4.1 --Frequency modulation (FM)
5 --The realization of FM circuit
5.1 --Direct FM modulation circuits
5.2 --Indirect FM modulation circuit
6 --Demodulation for FM signals
7 --PM modulation analysis
8 --The applications of modulation techniques
9 -- Advanced technique-Software Defined Radio (SDR)
10 --Reference materials
L.X.R: miniproject, baseband signal transmission
1. Introduction of technique of baseband signal transmission.
Recently, there are dramatically evolution of information techniques,
such as cellphone, computer and network etc, along with the
development of technology. Particularly, in the electronic and
wireless transmission fields, for instance, the speed of network is
much higher than before. Even though, the most popular way to
transmit baseband signal is based on the digital technique, such as,
improving the channel transmission or develop the digital elements,
I would like to study the analog signal transmission in the free space
according to the analog techniques.
What is well known to us is how the audio and the TV and cellphone
works. However, someone is not familiar with the radiation
technique, this thesis is based on the theory analysis and introduction
of how the baseband signal to be transmitted and received without
change or lose the original information.
The following graph illustrates the basic architecture of baseband
transmission between receiver and transmitter.
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A very simple model to demonstrate the transmission principle for
baseband signal. Seeing graph1.1
antenna
antenna
graph1.1
Actually, the graph just gives us a general idea of the structure of
transmission concept. It should contains a lot of elements such as,
filters, amplifiers and so on, which will be shown later.
1.1 Typical techniques are applied to transmitted signal.
Before going to see the contents of modulation and demodulation,
let us have a look at the several techniques for transmitting signals:
Baseband transmission.
Baseband transmission which sends the wanted signal directly
to the destination without the M-DeM techniques is wildly
applied to the computer inner parallel buses, most Local Area
Network (LAN) such as, Ethernet and Token Ring.
transmitter Baseband
signal
receiver Original
signal
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Benefits: convenient for short transmission, low attenuation,
high speed transmission and low error probability.
According to the features of baseband transmission, this technique is
much more popular in digital transmission field and the graph1.2
gives us the basic model.
Graph1.2
Passband transmission.
This technique means the long-distance transmission. Since the
majority of original signals to be transmitted are baseband
signals which have many AC components, hence it is not
suitable for L-D transmission.
Passband transmission technique is related to transmitting
signal directly inner channels and based on the modulation and
demodulation technologies. It is likely to have very high error
probability and low speed but is a good choice for the L-D
transmission.
Enco
der
Scramb
ler
Sou
rce
Mo
du
lator
Deco
der
Descram
bler
sink
Dem
od
ulato
r
channel
noise
L.X.R: miniproject, baseband signal transmission
Broadband transmission
Broadband transmissions are divided into multiple bands or
channels by multiplexers using a multiplexing scheme such as
frequency-division multiplexing (FDM). Each channel has a carrier
frequency that is modulated to carry the signal from a given source.
At the receiving station, multiplexers separate the various signals.
Guard bands are used to prevent interference among channels.
Broadband transmission is typically used for environments in
which video, audio, and data need to be transmitted simultaneously.
Cable television systems are based on broadband transmission
technologies. Other examples of broadband services include
T-carrier services, Asynchronous Transfer Mode (ATM), and
variants of Digital Subscriber Line (DSL). Its bandwidth typical is
higher than 128Kbps.
Graph1.3
1.2 The definition of baseband signal.
A signal is baseband if it has a very narrow frequency range, i.e. a
L.X.R: miniproject, baseband signal transmission
spectral magnitude that is nonzero only for frequencies in the
vicinity of the origin (termed f = 0) and negligible elsewhere. It can
be seen from graph 2.1. In telecommunications and signal
processing, baseband signals are transmitted without modulation,
that is, without any shift in the range of frequencies of the signal,
and are low frequency - contained within the band of frequencies
from close to 0 hertz up to a higher cut-off frequency or maximum
bandwidth. Baseband can be synonymous with lowpass or
non-modulated, and is differentiated from passband, bandpass,
carrier-modulated, intermediate frequency, or radio frequency (RF).
Compared with RF signal, the baseband signal has a rather lower
frequency, which can be regard as original signal before transmitted.
Voice, image and audio signals could be stored in the baseband
signal.
Graph 1.4
1.3. The role of modulation technology in signal transmission
theory.
In order to find the influence of modulation, first we need analyze
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the reason why we cannot use the baseband transmission technology
to transmit the baseband signal. To radiate the baseband signal which
has very lower frequency, we need use the radiation system and
electromagnetic theory. Due to the very lower frequency of baseband
signal and the drawback of baseband transmission technique for L-D
transmission, the original signal will be transmitted as the
electromagnetic wave into the space and be recovered by the
demodulation technique.
Now, I give the direct reason why we prefer to use the modulation
technique! According to the antenna theory which is that in order to
radiate the electromagnetic field very far, the length of antenna
should be corresponding with the wavelength. Recalling that
λ = c/f, if f is very low, we get inconvenient to design one antenna
that has a large size. If so, we need shift the spectrum to a radio
frequency (a few MHz-1GHz).
Now let’s give a description of modulation technology.
2. Linear-modulation
The purpose of using the modulation is adding the information
inner baseband signal to the carrier. Carrier is a kind of signal
with higher frequency, which can be derived using frequency
synthesizer. This technique includes the linear modulation and
non-linear modulation.
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Grap
h2.1
dem
onstr
ates
the
gene
ral model of RF circuit
Graph2.1
2.1 Linear -modulation -Amplitude Modulation(AM)-
Amplitude modulation (AM) is a modulation technique in
which the amplitude of a high frequency sine wave (usually at
a radio frequency) is varied in direct proportion to that of a
modulating signal. The modulating signal carries the required
information and often consists of original data, as in the case
of AM radio broadcasts or two-way radio communications.
The high frequency sine wave (the carrier) is modulated by
adding the modulating signal to it in a mixer. A simplified AM
radio transmitter system is shown as graph2.3.
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Graph2.2
The mathematic model is shown as graph2.3
Graph 2.3
Notation: m (t) is called modulation signal, and A0 is the addition
DC component with zero-main which could be random or
determined signal. cos(ωct)=Xc(t) is called carrier and sAM(t) is
modulated signal. The formulas of AM signal in time and frequency
domains are shown as following
Assuming the upper fre-boundary of m(t) is ωH and its band width is
Bm=fH. We therefore can get the waveform and spectrum of AM
signal and the BW of AM signal is twice than modulation signal m(t)
as shown in graph2.4.
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Graph2.4
Totally speaking, from the spectrum graph2.4 (b) we can
conclude that both upper sideband and lower sideband contain the
total origin information. In addition, we can see 2 phases at ω=±ωC
and AM signal is double sideband signal with carrier and its
BW=2Bm=2fH.
The other significant parameters are power of vAM(t),
modulation efficiency ήAM and modulation index m.
power of vAM(t) and modulation efficiency(ME) ήAM
According to the definition of the efficient power with the
AC signal, we have the following formulas:
Recalling that no DC component for m(t),namely
<m(t)>t=0 and <cos2(ωct)>t=<
1
2∗ cos(2ωct) +
1
2 >t=1/2
PAM=A02/2+<m
2(t)>t/2=PC+PS. notation PC= A0
2/2 called
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carrier power and PS=<m2(t)>t/2 called sideband power, so we
get the definition of ή ≜ PS/PAM=<m2(t)>t/(A0
2+<m
2(t)>t) < 1
always!
modulation index m
Modulation index m is defined as the maximum changes of
modulated signal marked as |ΔVAM(t)|max and the magnitude of
carrier. However m can be expressed as (VM-Vm)/(VM+Vm).
m=1 is called full-modulated; m>1 is called over-modulated.
General case is 0<m<1. Now let me give one typical example.
Voice signal modulation:
A simple form of amplitude modulation was originally used to
modulate audio voice signals onto a low-voltage direct current (dc)
carrier on a telephone circuit. A microphone in the telephone handset
acts as a transducer, and uses the sound waves produced by the
human voice to vary the current passing through the circuit. At the
other end of the telephone line, a second transducer (in the form of a
small loudspeaker mounted in the remote handset) uses the varying
voltage to produce sound waves that are close enough to the original
speech patterns to be recognizable as the voice of the caller.
Although the human voice is composed of frequencies ranging from
300 to approximately 20,000 hertz, the public switched telephone
system limits the frequencies used to between 300 and 3,400 hertz,
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giving a total bandwidth of 3,100 hertz. This bandwidth is perfectly
adequate for purely voice transmission, since the higher frequencies
in the human voice (i.e. those above 3,100 hertz) are not really
needed for recognizable speech reproduction. The use of a limited
bandwidth also makes the telephone system much simpler from an
engineering perspective.
Whereas telephone signals can be transmitted at audio
frequencies, the same is not really a practical proposition for radio
transmissions. The main reason for this is that the optimum length of
a radio antenna is a half or a quarter of a wavelength. Since a typical
audio frequency of 3,000 hertz has a wavelength of approximately
100 kilometers, the antenna would need to have a length of 25
kilometers to be effective - not a realistic proposition. By
comparison, a radio frequency of 100 megahertz would have a
wavelength of approximately 3 meters, and could use an antenna 80
centimeters long. It becomes necessary, therefore, to use a radio
frequency carrier signal in order to transmit audio signals, which are
used to modulate the carrier waveform.
L.X.R: miniproject, baseband signal transmission
Graph2.5
2.2 Linear -modulation –DSB-SC modulation
Introduction: DSB-SC is also one technique for amplitude
modulation. Since from the expression of ME (modulation
efficiency ), only PS is related to the information or we can say
baseband signal or modulating signal and the denominator of ME is
the sum of PS and PC, while PC is only related to the additional
component A0,therefore we can see the ME is not high for
modulating signal. What’s more, We can conclude that only the
sideband signal has much significant for transmitting information or
massage. In order to economize the resources of channel, we prefer
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to take measures to avoid the carrier component to be sent to the
space, and then we derive the definition of DSB-SC, which can
compensate this drawback.
Definition: Double-sideband suppressed-carrier transmission
(DSB-SC) is transmission in which frequencies produced by
amplitude modulation (AM) are symmetrically spaced above and
below the carrier frequency and the carrier level is reduced to the
lowest practical level, ideally being completely suppressed.
In the DSB-SC modulation, unlike in AM, the wave carrier is not
transmitted; thus, much of the power is distributed between the
sideband, which implies an increase of the cover in DSB-SC,
compared to AM, for the same power used. Above all, DSB-SC
transmission is a special case of double-sideband reduced carrier
transmission. It is used for radio data systems.
The basic mathematics model is shown as figure2.6
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Graph2.6
The basic real circuit is shown as following circuit
The expression can be described as following one:
Notation: m(t)=Vmcos(ωmt) is called modulating signal and
Vccos(ωct)=xc(t) is called carrier.
Spectrum analysis of DSB-SC
DSB-SC is basically an amplitude modulation wave without the
carrier, therefore reducing power waste, giving it 100% efficiency.
This is an increase compared to normal AM transmission (DSB),
which has a maximum efficiency of 33.333%, since 2/3 of the power
is in the carrier which carries no intelligence, and each sideband
carries has same information. The spectrum can be seen from
graph2.7
L.X.R: miniproject, baseband signal transmission
Graph2.7
From the above figure, we can summary that the DSB-SC signal
suppresses the carrier component, and the modulation efficiency
(ME)=100%. The graph2.8 shows us very important information that
when m(t)=0, the SDSB(t) has a phase shift 180o, which is the big
difference from general AM signal.
graph2.8
Numerical analysis of the DSB-SC ME and power:
PDSB=<m2(t)>t/2 is the same as PAM, however its ME ήDSB=2*ήAM
means it improve the ME.
Since from figure 2.7, we can also find the disadvantage that is
wasting the channel capacity to transmit information by DSB-SC.
Actually, we can use some method to get the single upper or lower
sideband instead of DSB to avoid sending the information repeatedly
Phase shift 180o
L.X.R: miniproject, baseband signal transmission
with 2 sideband signals, thus, we can economize half resources
compared to DSB-SC.
2.3 Linear -modulation –SSB-SC modulation
Single-Side Band Suppressed-Carrier (SSB-SC) is a refinement of
amplitude modulation which uses transmitter power and bandwidth
more efficiently. Amplitude modulation produces an output signal
that has twice the bandwidth of the original baseband signal.
Single-sideband modulation avoids this bandwidth doubling, and the
power wasted on a carrier, at the cost of increased device complexity
and more difficult tuning at the receiver.
The general ideas to create the SSB signal is based on two
techniques, namely filtering method and phase shift by 90o, which
will be introduced later.
HPF or LPF filtering to create SSB
One method of producing an SSB signal is to remove one of the
sidebands via filtering, leaving only either the upper sideband
(USB), the sideband with the higher frequency, or less
commonly the lower sideband (LSB), and the sideband with the
lower frequency. Most often, the carrier is reduced or removed
entirely (suppressed), being referred to in full as single sideband
suppressed carrier (SSBSC). Assuming both sidebands are
symmetric, which is the case for a normal AM signal, no
L.X.R: miniproject, baseband signal transmission
information is lost in the process. Since the final RF
amplification is now concentrated in a single sideband, the
effective power output is greater than in normal AM (the carrier
and redundant sideband account for well over half of the power
output of an AM transmitter).
The mathematics model is shown as graph2.9
Graph2.9
Where HSSB(ω) is the transfer function of sideband filter, whose
function is transferring the DSB-SC signal to SSB-SC signal
without change the shape which corresponding the wanted
information.
Corresponding to get the upper or lower sideband signal, there
are two kinds of filters, namely HPF and LPF, which can be
seen from graph2.10.
Lower sideband
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Graph2.10
Phase-shift method for SSB-SC
Using filtering method to create the SSB-SC is a kind rather
easy way to create SSB in theory, however the single-side band
filter is very difficult to realize. The mean reason why we
cannot is that ideal such kind of filters is not feasible. The true
filter usually has a transition band from pass band to stop band,
however, a majority of modulating signals have many low
frequency components, which made the modulated DSB signal
has very narrow band between upper and lower sidebands,
hence we need a dramatic cut-off characteristic at fcut-off. Such
kinds of filters are rather difficult to make, which tends us to
drive another way to realize SSB-SC signals.
In time domain, the SSB-SC signal can be expressed as:
Notation: m (t) is modulating signal, m(t)-hat is the Hilbert
upper sideband
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transform of m(t), ωc is carrier frequency,”-” represents lower
sideband signal vs “+” represents upper sideband signal.
The model for creating SSB-SC is shown as graph 2.11
Graph2.11
Notation: Hh(ω) is the transfer function of Hilbert transform
filter, which translate all the components coming from m(t) with
phase shift -90o. It is also the big problem for obtaining such
kinds filters with accuracy -90o phase shift.
Parameter analysis
Bandwidth: the BW is half of DSB signal and similar
with that of modulating signal
BWSSB=1
2BWDSB=Bm=fH , where fH is the highest
frequency component of m(t)
Power
ME(modulation efficiency) ήSSB
L.X.R: miniproject, baseband signal transmission
Since its spectrum has no carrier frequency component,
ME is 100%, namely ήSSB=100%.
2.4 Linear -modulation –VSB-SC modulation
VSB-SC is called Vestigial Sideband suppression carrier. The idea is
design a kind of filter called VSB filter to filter one kind sideband
and keeps a little part of the other one. The model is shown as graph
2.12
Graph2.12
Notation that in order to demodulate the baseband signal from sVSB(t),
the condition is HVSB(ω+ωC)+HVSB(ω-ωC)=constant for |ω|<=ωH.
In other word, the transfer function HVSB(ω) is reciprocal around
carrier frequency ωc, which can be seen clearly from graph 2.13
Graph2.13
According to the theory, we can drive its spectrum SVSB(ω)
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The whole principle for VSB technique can be seen from graph 2.14
(a)
(b)
Graph2.13
3. Demodulation
Demodulation is the inverse processor corresponding to
modulation techniques, which is translated modulated signal,
such as SAM(t), SDSB(t), SSSB(t) and SVSB(t) to modulating signal
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m(t). there are devise demodulation methods for different kinds of
modulation signals, which are displayed as following cases.
3.1 AM demodulation
Two techniques will be introduced for AM signal
demodulation, namely envelope detection and coherent
demodulation process.
envelope detection
From grap2.4 (a), we can conclude that the envelope of
sAM(t) is corresponding to the shape of m(t). We therefore
can use detector to detect the envelope of sAM(t). The
detector can be built by half-wave rectifier or full-wave
rectifier and a LPF.
The basic structure of detector is shown as graph3.1.
sAM(t) m(t)
graph3.1
Rectifier can be realized by simple structure consisting of only diode,
R and C. When 1/ωc <<RC<<1/ωH is satisfied, the output envelop
from detector is quite similar with that of m(t),, which is roughly
expressed by mo(t)=A0+m(t), in case of distortion of demodulated
signal, A0>=|m(t)max|.
Using LPF is to filter the wave fluctuation coming from carrier; the
Rectifier LPF
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whole structure can be seen from following circuit.
The equivelent detector circuit is shown as below picture
The physical meaning of detection process is that LPF consists of
resistor and capacitor and the recharge time-constant is based on
RDC (RD is the conductance of diode VD), which is very small and
the discharge time-constant is based on RC which is very large. The
envelope therefore can be kept finally, moreover DC components
can be filtered by the capacitor C. the output is just the envelope of
modulating signal.
High demodulation efficiency and feasibility are the significant
features for detector. Compared with coherent method, there is no
need of same carrier signal in the receiver.
Graph3.2 shows us the general process of envelop detection
Low-frequenc
y amplifier
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Graph3.2
The bridge built with diodes also can be applied to detect envelope.
The structure is using four diodes in each branch instead of single
diode without any changes of resistor and capacitor.
Bridge-detector component
coherent demodulation
From mathematics analysis, we can conclude that applying
the mixer with inputs sAM(t) and xc(t) can recover the
modulating signal m(t).
Only one LPF is needed to separate the modulating signal,
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which can be written as mo(t) = 1/2[Ao+m(t)].
Graph 3.3 and graph3.4 give us the basic idea realization for
coherent demodulation process
Graph3.3
Graph3.4
The reference signal xc(t) can be generated by PLL
technique.
Phase-lock loop (PLL) with one input of original carrier
and output signal from PLL, this technique shown as
graph3.5 is good for creating stable local frequency
component ωc. this method corresponds to graph3.5
Graph3.5 Graph3.6
Graph3.6 illustrates the whole circuit for coherent demodulation.
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3.2 DSB-SC demodulation
As what we can see from graph2.8, the waveform is not
corresponding to the envelope of modulating signal m(t). We
therefore need use the coherent demodulation process to
recover m(t), which is quite similar with AM coherent
demodulation. According to the graph3.3, the output from the
mixer for DSB demodulation is following expression.
From the LPF, we can get mo(t)=1
2𝑚(𝑡) and the process can
be seen as graph3.7
Graph3.7
Here, the reference signal xω(t) can be create in another way.
When using DSB modulation, we let the demodulated signal
contain a part carrier component, which can be used to recover
the carrier (reference signal) at the receiver point.
3.3 SSB-SC demodulation
With the same factor as DSB-SC, the coherent demodulation is
also applied for SSB-SC demodulation process with the same
principle circuit as graph3.3.
The mathematics expressions are displayed as following
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The output from multiplier is
Via PLF, we get mo(t) = 1
4𝑚(𝑡), finally we get the modulating
signal without any distortion. The whole process is shown as
graph3.8
Graph3.8
3.4 VSB-SC demodulation
Coherent technique is also applied to VSB demodulation
shown as graph3.9
Graph 3.9
Output from the multiplier is in time
domain.
In frequency domain, we have
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After the LPF, we obtain that
From above equation, we can conclude that in order to get the
modulating signal m (t) without distortion from VSB-SC
signal, we have HVSB(ω+ωC)+HVSB(ω-ωC)=constant for |ω|<=ω
H
The whole process is seen as following picture.
Up to now, we have analyzed some kinds of the linear
modulation and demodulation techniques. Now the following
table1 provides us comparison among them.
Modulation type Demodulation
methods
benefits drawbacks
AM Envelope detector
and coherent
demodulation
Simple structure
for demodulation
process; envelope
detection can be
applied;
Low modulation
efficiency;
Large band is
occupied
DSB-SC Coherent
demodulation
No carrier power;
High modulation
Large band is
occupied
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efficiency
SSB-SC Coherent
demodulation
No carrier power;
High modulation
efficiency;
Few band
occupied;
Difficult to
realize steep
sideband filter;
VSB-SC Coherent
demodulation
No carrier power;
High modulation
efficiency;
Few band
occupied;
Strict condition
limited
Table1
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4. Non-linear modulation
Apart from modulating the amplitude of carrier, we can also
modulate the frequency or phase in carrier with m(t). The frequency
or phase vary along with the variations of m(t). According to this
purpose, we have FM and PM two different techniques.
In communication system, if we use baseband signal to
modulate the angle or phase for carrier or we do the reverse
procedure, we have to apply the non-linear spectrum transformation.
Therefore, we call such kinds of techniques are non-linear
modulations.
Frequency Modulation (FM) : frequency variation of carrier Δωc
is proportional to modulating signal m(t).
Phase Modulation (PM): phase variation of carrier ΔΦ is
proportional to modulating signal m(t).
4.1. Frequency modulation (FM)
In telecommunications and signal processing, frequency
modulation (FM) is the encoding of information in a carrier
wave by varying the instantaneous frequency of the wave.
Compare with amplitude modulation, in which the
instantaneous frequency of the carrier wave varies, while the
amplitude remains constant.
In analog signal applications, the difference between the
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instantaneous and the base frequency of the carrier is directly
proportional to the instantaneous value of the input-signal
amplitude.
Frequency modulation is used in radio, telemetry, radar,
especially for broadcasting music and speech, two-way radio
systems, magnetic tape-recording systems and some
video-transmission systems. In radio systems, frequency
modulation with sufficient bandwidth provides an advantage in
cancelling naturally-occurring noise.
Concept for instantaneous phase and frequency
For an oscillator, the local output signal
(t)Aa(t) m cos with Am is the amplitude; (t) is the
total phase
According to the relationship between phase and frequency,
we have
dt
(t)dt ω
tdtωtt
00
)(t called instantaneous radius and 0 called initial phase.
If )(t is related to the time variation, instantaneous phase
can be written as 00
tdtωtt
and the general form is
00
cos tdtωAtat
m .
Basic analysis of FM
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If the information to be transmitted (i.e. the baseband signal)
is xm(t) and the sinusoidal carrier is xc(t) = Accos (2πfct),
where fc is the carrier's base frequency, and Ac is the carrier's
amplitude, the modulator combines the carrier with the
baseband data signal to get the transmitted signal:
Notation: f(τ) is the instantaneous frequency of local os-
cillator and fΔ is the frequency deviation, which represents
the maximum shift away from fc in one direction, assuming
xm(t) is limited to the range ±1 namely, xm(t)=sin(2πfmt).
Generally speaking, a baseband modulated signal may be
approximated by a sinusoidal continuous wave signal with a
frequency fm. the integral of such a kind signal is
In this case the, the expression for y(t) simplifies to:
where the amplitude Am of the modulating sinusoid is
represented by the peak deviation fΔ.
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Modulation index
As in other modulation systems, the value of the modulation
index indicates by how much the modulated variable varies
around its unmodulated level. It relates to variations in the
carrier frequency:
Where fm is the highest frequency component present in
modulating signal xm(t), Δf is the maximum deviation of the
instantaneous frequency from the carrier frequency, general
when h<<1, the modulation is called narrowband FM
otherwise wideband FM.
According to the signal theory, since we use the sinusoidal
signal which has harmonics components. We have to
consider and analyze them but are not shown here.
Graph 4.1 gives us the general concept of FM technique.
Graph4.1
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We can see from the blue carve that the frequency of FM signal is
related to the amplitude variation of m(t).
5. The realization of FM circuit
There are two different ways to realize FM circuit, namely direct
and indirect FM modulation circuits according to different fields.
5.1. Direct FM modulation circuit
According to the expression and definition of FM, the general
idea for building FM circuit is trying to control the output
frequency for resonance circuit with modulating signal m
(t).This technique is called direct FM modulation. Its junction
capacitance varies with the inverse voltage. The basic
characteristic of resonance circuit is shown as graph5.1
Graph5.1
fr=1
2π√𝐿𝐶
FM circuit with var-diode
The var-diode can be inserted in LC resonance circuit.
Moreover, m(t) controls its capacitance directly and also
)1(
0
D
jj
Vu
CC
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it controls resonance frequency ωr or fr indirectly.
Barrier capacitance
After adding bias and modulating voltage, the total
voltage
Finally we can get
Therefore, we replace the capacitor C with Cj showing as
graph5.2
graph5.2
According to the resonance circuit theory, the
instantaneous frequency is
Crystal oscillator FM circuit
Due to have the high stability at center frequency, we
prefer to choose crystal oscillator circuit. Using the
series structure of Cj and crystal oscillator, which is
Ω tUV(T)UVu Ω mQΩQ cos
Ω t)m(
Cjo
)VV
Ω tU()
V
V(
C
)V
Ω tUV(
C
Vu(
CC
c
γ
QD
Ω mγ
D
Q
j
γ
D
Ω mQ
j
D
jj
cos1
cos11
cos1
)1
0
00
22 )1())(
1(1)(
xVV
tuLCx c
QD
cj
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shown as graph5.3
Graph5.3
The principle for this structure is quite similar with the
above one. Using m(t) controls resonance frequency.
Reactance tube FM circuit
Reactance tube which is the same as var-diode is also
voltage control device. Controlled source can be electron
tube, transistor and FET. The circuit is graph5.4
Graph5.4
5.2. Indirect FM modulation circuit
Do the integration for modulating signal m(t) and after that do
the phase modulation. As for m(t), the process is frequency
M(t)
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modulation. Therefore, the key point for this technique is
phase modulation circuit. At this point, we can also use
var-diode inserted in oscillator circuit for high frequency
amplifier. Due to the effect of var-diode, the resonance
frequency will change. Finally, the carrier will has phase shift
when coming to this resonance circuit. Graph 5.5 is single
stage PM circuit.
Graph5.5
Var-diode Cj and inductor L create a resonance circuit as the
phase shift network. R1,R2 and R3 are called isolation resistors.
Three capacitors whose values are 0.001uF are short circuit for
high frequency and open circuit for modulating signal m(t).
6. Demodulation for FM signals
FM and PM demodulation processes are called frequency
output M(t)
Carrier in
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detector and phase detector respectively. However, they have
some differences.
First, we have to change FM signal into AM signal or pulses
with different duty circle, then use AM demodulation techniques
or rectifier for pulse to demodulate m(t) from FM signal. This
process is shown as graph5.6
Graph5.6
The relationship between output voltage uΩ(t) and input FM
instantaneous frequency offset Δf is called discriminator curve,
which is shown as graph5.7
Graph5.7
From the above curve we can obtain two important parameters for
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FM demodulation process, namely discriminator transconductance
gd and bandwidth B
and B=2Δf in general
Several different circuits for FM demodulation process:
Slope discriminator
Slope discriminator depends on LC parallel resonance
circuit to change FM to AM and uses the
amplitude-frequency curve of resonance circuit. Most
popular circuit is double loop detuning frequency
discriminator which is graph 5.8
graph5.8(a) circuit graph5.8(b) discriminator curve
For this circuit, resonance frequency f1is lower than center
frequency fc in the first loop and resonance frequency f2 is
larger than fc. when fc-f1=f2-fc, we can get the
discriminator curve graph5.8(b).
Phase discriminator
Phase discriminator is based on the phase-frequency
cff
ddf
dug
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curve for resonance circuit to change the FM signal to
AM signal.
The principle is shown as graph5.9(a) and the equivalent
circuit is graph 5.9(b)
Graph5.9 (a)
Graph5.9 (b)
We can see from graph5.9(a), there is a inductor coupler
(transformer). Two branches with resistor R and
capacitor C3 and C4 are symmetric.
Ratio discriminator
Ratio discriminator has both discrimination function and
clipping function, which is shown as graph5.10
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Graph5.10
PLL-discriminator
A short description of PLL. PLL consists of phase
detector, loop filter, voltage control oscillator
components.
Graph5.11 provides us the basic structure of it.
Graph5.11
Notation: VI is called input signal, VO is called output
signal from VCO, VD is called error voltage from PD,
VC is control voltage for VCO.
From its characteristic curve, we can conclude it works
as a bandpass filter, whose equivalent bandwidth is
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The characteristics can be seen from graph5.12
Graph5.12
More details of PLL can be seen from the
material ”learning notes for pll from analog and
telecommunication electronic in polito”. The link is
http://areeweb.polito.it/didattica/corsiddc/01NVD/
which is authored by prof. Dante Del Corso.
FM PLL demodulation is based on the PLL feature. We
can write Fp=Fpo+KM(t).From graph5.12, we can see that
there is full Fp spectrum in the lock range marked by L
and VC(t) is proportional to M(t). Due to the idea, we
can use this structure by letting PLL working at this
state to demodulate FM.
7. PM modulation analysis
As we all know, the phase Φ is the integration of angle frequency
ω therefore, the PM modulation technique is quite similar with FM
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modulation to some degree. We give the definition as following.
PM process is that using modulating signal m(t) control the phase of
carrier, thus the carrier phase variation ΔΦ is proportional to m(t).
According to the definition, PM expression is shown as
and instantaneous phase can be
with kp called proportion coefficient, (t)Δ p called instantaneous
phase shift.
Then, we can drive instantaneous frequency
from above equation,
we can immediately get
like AM and FM, it also has modulation index called mp which is
defined as maximum phase shift ,namely m =
The waveform is show as graph5.13
graph5.13
(t)uktωUu ΩpccmPM cos
(t)Δtω(t)uktω(t) pcΩpc
)()()(
)( tdt
tduk
dt
tdt pcpc
dt
tdukt pp
)()(
maxtΔ p maxtΔ p
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Fortunately, we can use FM modulation to realize PM signal, which
means when we do the FM modulation meanwhile we also have
modulated carrier phase. Therefore, we also have some kinds of
circuits to do PM modulation. seeing FM modulation circuit part to
get more details.
In particular for a single large sinusoidal signal, PM is similar to FM,
and its bandwidth is approximately 2(mp + 1)fM, where fM =ωm/2π
and mp is modulation index.
8. The applications of modulation techniques
AM, FM and PM are widely used for radio and radar fields, even
if they are almost replaced by digital field. They are also still
necessary for some certain fields.
Graph 8.1 is the basic structure of BeiDou Navigation
Satellite System,BDS ,designed by China. We can see there
are AM modulation and I-Q demodulation processes in the
transmitter and receiver respectively.
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Graph8.1
For considering AM decoder, we can analysis NE567 IC,
whose internal circuit is shown as graph8.2.
Graph8.2
Actually, for this chip, we can use it in the lab, but just get the
amplitude of input signal demodulated at the output. The part of
its datasheet can be seen as following figure
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Figure1
The typical characteristics are shown as following serial figures.
stereo FM transmitter
Graph8.3 is a small stereo FM transmitter. Output can be tuned
from 88to 108Mhz and the transmitter can be battery powered.
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Graph8.3
This circuit is based on the Rohm BA1404 datasheet. The
maximum voltage should not exceed 3V. The IC can be driven
from a 7805 Regulator with a couple of 1N4001 diodes to reduce
the supply voltage to about 2.8 Volts. The IC can dissipate
500mW (this is not RF power output but power dissipated by the
IC). RF output power is typically 500mW but range depends
upon antenna coupling and efficiency, environment and size of
antenna. A small telescopic whip has an expected range of at
least 100 meters or more.
LM1596/LM1496 Balanced Modulator-Demodulator
The LM1596/LM1496 are doubled balanced
modulator-demodulators, which produce an output voltage
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proportional to the product of an input (signal) voltage and a
switching (carrier) signal. Typical applications include
suppressed carrier modulation, amplitude modulation,
synchronous detection, FM or PM detection, broadband
frequency doubling and chopping.
The basic connection can be seen from graph8.4
The typical characteristics are the followings
9. Advanced technique-Software Defined Radio (SDR).
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Introduction: Software-defined radio (SDR) is a radio
communication system where components that have been typically
implemented in hardware (e.g. mixers, filters, amplifiers,
modulators/demodulators, detectors, etc.) are instead implemented
by means of software on a personal computer or embedded system.
The basic structure can be seen from graph9.1
Graph9.1
One of a basic component is called software defined antennas,
which adaptively "lock onto" a directional signal, so that receivers
can better reject interference from other directions, allowing it to
detect fainter transmissions. Wireless mesh network where every
added radio increases total capacity and reduces the power required
at any one node. Each node only transmits loudly enough for the
message to hop to the nearest node in that direction, reducing
near-far problem and reducing interference to others.
Since SDR is the advanced knowledge, here there is not enough
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descriptions and more details and applications can be seen in the
future.
Nowadays, digital transmission is much more popular than analog
transmission due to the good properties for digital signal, such as
high transmission speed, low error probability, etc. Digital devices
translate and reassemble data and in the process are more prone to
loss of quality as compared to analog devices. Computer
advancement has enabled use of error detection and error correction
techniques to remove disturbances artificially from digital signals
and improve quality. Recalling that cellphones in 40 years ago are
based on analog signal transmission with a lot of noises. That’s the
reason why it is replaced with 2nd generation technique (GSM),
which is based on modulation and demodulation technologies. After
that there exits 3rd generation (3G), which improves the speed of
information transmission dramatically.
10. Reference materials
1. <<Fundamentals of Telecommunications>>, published by
John Wiley & Sons.1999 ISBNs: 0-471-29699-6 (Hardback);
0-471-22416-2 (Electronic).
2. <<High frequency electrons>> published by Chen He,
version-2004.
3. Datasheet of LM1596/LM1496 Balanced
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Modulator-Demodulator.
4. Datasheet of IC SI4730 based on broadcast AM/FM/SW/LW
radio receiver.
5. http://www.allaboutcircuits.com/vol_3/chpt_9/6.html
6. http://www.radio-electronics.com/info/rf-technology-design/a
m-amplitude-modulation/what-is-am-tutorial.php
http://en.wikipedia.org/wiki/Frequency_modulation
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