2. 2
Outlines
• Introduction
• Base-band and Carrier Communication
• Amplitude Modulation (AM):DSB-Large Carrier
• Amplitude Modulation: Double sideband- Suppressed
Carrier (DSBSC)
• Quadrature amplitude Modulation (QAM)
• Single Sideband Modulation (SSB)
• Vestigial Sideband (VSB)
• Frequency mixing
• Superhetrodyne AM radio.
• Frequency division multilplexing (FDM).
3. 3
Introduction
• Modulation is a process that causes a shift in
the range of frequencies of a message signal.
• A communication that does not use modulation
is called baseband communication
• A communication that uses modulation is
called Carrier communication
6. 6
Baseband and Carrier
Communication
• Baseband signal: is message signal
(information bearing signal) delivered by the
information source or the input transducer .it is
usually low frequency signal.
• Communication that uses modulation to shift
the frequency spectrum of message signal is
known as carrier communication.
–Amplitude modulation (AM),
–Frequency modulation (FM)
–Phase modulation (PM)
9. 9
Another example of AM Waveform
( ) sin 2
( ) sin 2
c
m
c t Ec f t
m t Em f t
π
π
=
=
( ) ( ( ))sin 2 cS t Ec m t f tπ= +
( ) sin 2
( ) sin 2
c
m
c t Ec f t
m t Em f t
π
π
=
=
( ) ( ( ))sin 2 cs t Ec m t f tπ= +
10. 10
Modulation Index
• The amount of modulation in AM signal is given by
its modulation index:
max min
max min
, min ( )
p
p
m E E
or m m t
A E E
µ
−
= =
+
When mp = A , µ =1 or 100% modulation.
Over-modulation, i.e. mOver-modulation, i.e. mpp >A>A , should be avoided, should be avoided
because it will create distortions.because it will create distortions.
max min,p pE A m E A m= + = −
14. 14
Sideband and Carrier Power
• Carrier Power
• Sideband Power
• Total power
• Power efficiency
• For single tone modulation
2
2
c
A
P =
sc
s
PP
P
+
=η
2
2
22
100%, [1 ]
2
tot cP P µµ
η
µ
= = +
+
2
m
s
P
P =
tot c sp P P= +
16. 16
Example
• Conventional AM signal with a sinusoidal
message has the following parameters:
A=10, µ=0.5, fc= 1MHz, and fm= 1kHz
1. Find time-domain expression
2. Find its Fourier transform
3. Sketch its spectrum
4. Find the signal power, carrier power and the
power efficiency
5. Find the AM signal bandwidth
( )Ams t
17. 17
Example
• A given AM (DSB-LC) broadcast station
transmits an average carrier power output
of 40kW and uses a modulation index of
0.707 for sine-wave modulation. Calculate
a) the total output power
b) the power efficiency
c) the peak amplitude of the output if the
antenna is represented by a 50-Ω
resistance load.
19. Square-law modulator
2
( ) ( ) ( )o i iv t av t bv t= +
'
( ) [ 2 ( )]cos2o cv t aA Abm t f tπ= +
3cf B≥ To avoid overlap the spectrum of
2
( ) and ( )cm t M f f−
20. Switching modulator
• Assume
1
1
'
( ) ( ) ( ),
1 2 ( 1)
( ) cos2 (2 1)
2 2 1
2
( ) [ ( )]cos2
2
o i
n
c
n
o c
v t v t w t where
w t f n t
n
A
v t m t f t
π
π
π
π
−∞
=
=
−
= + −
−
⇒ = +
∑
( ) ,and diode an ideal switchm t A=
21. 21
Demodulation of AM signals
• AM signals can be demodulated by
–Envelope detector
–Rectifier detector
–Coherent (synchronous) detector.
34. 34
DSBSC Modulators
• DSBSC signal can be generated using
several types of modulators:
–Multiplier Modulators
–Nonlinear Modulators
–Switching Modulators
51. SSB time representation
ˆ( ) ( )cos2 ( )sin 2 ,
:
:
1
ˆ ( ) ( ) Hilpert transform of ( )
SSB c cS t m t f t m t f t
USB
LSB
m t m t m t
t
π π
π
=
−
+
= ∗
m
@
57. 57
Phase–Shift Method (Cont.)
• Advantages:
–Does not deploy bandpass filter.
–Suitable for message signals with
frequency content down to dc.
• Disadvantage:
–Practical realization of a wideband 90o
phase shift circuit is difficult.
58. 58
Demodulation of SSB Signals
• Demodulation of SSB signals can be
accomplished by using a synchronous detector
as used in the demodulation of normal AM and
DSBSC signals.
• If we want to use an envelope detector, it can
be shown that we must insert a pilot carrier
signal Acos(2 πfct) to the SSB signal,
where A >> m(t) and A >> m^(t).
• The pilot signal carries most of the transmission
power which becomes inefficient.
59. 59
Example
• A DSB-LC signal is generated using a 1-kHz
carrier and the input is m(t)= cos(200πt). The
modulation index is 80%. The lower sideband
is attenuated (assume ideal filter). Find an
expression for the resulting SSB-LC signal if it
develops 0.58 W across a one-Ohm resistive
load.
69. 69
VSB+C
• VSB modulated signals can also be
detected by an envelope detector.
• As in the demodulation of a SSB signal,
we need to send a pilot carrier signal,
resulting an inefficient use of available
transmitted power.
70. 70
Comparison of conventional AM,
DSB-SC, SSB and VSB.
• Conventional AM: simple to modulate and to
demodulate, but low power efficiency (50%
max) and double the bandwidth
• DSB-SC: high power efficiency, more complex
to modulate & demodulate, double the
bandwidth
• SSB: high power efficiency, the same
(message) bandwidth, more difficult to
modulate & demodulate.
• VSB: lower power efficiency & larger bandwidth
but easier to implement.
71. 71
Multiplexing
• Multiplexing: combining a number of message
signals into a composite signal to transmit them
simultaneously over a wideband channel.
• Two commonly-used types: time-division
multiplexing (TDM) and frequency division
multiplexing (FDM).
• TDM: transmit different message signals in
different time slots (mostly digital).
• FDM: transmit different message signals in
different frequency slots (bands) using different
carrier frequencies.
78. Frequency mixing
• It is desired in communication system to translate
the spectrum of the modulated signal up word or
down word in frequency to be centered around
desired frequency
0
0
: up conversio
:down conversio
l c
l c
c l
f f f
f f n
f
f f n
= −
−
⇒ =
−
85. 85
Introduction to Carrier Acquisition
• Consider a DSB-SC demodulator where a
received signal is m(t) cos(ωct) and the
local carrier is 2 cos[(ωc+∆ω) t+δ ] . Find
the LPF output if
a) ∆ω=0, and
b) δ=0
86. 86
Carrier Acquisition
• To ensure identical carrier frequencies at the
transmitter and the receiver, we can use quartz
crystal oscillators, which are generally very
stable.
• At very high carrier frequencies, the quartz-
crystal performance may not be adequate, we
can use the phased-locked loop (PLL)
87. 87
Phased-Locked Loop (PLL)
• Phase-locked loop is one of the most
commonly used circuit in both
telecommunication and measurement
engineering.
• PLL can be used to track the phase and the
frequency of the carrier component of an
incoming signal.
88. 88
• A PLL has three basic components:
1. A voltage controlled oscillator
2. A multiplier
3. A loop filter H(s)
recovered carrier signal
vout(t)
vin(t) e0(t)x(t) Loop Filter
H(s)
Voltage-Controlled
Oscillator (VCO)
89. 89
• In every application, the PLL tracks the
frequency and the phase of the input signal.
However, before a PLL can track, it must first
reach the phase-locked condition.
• In general, the VCO center frequency differs
from the frequency of the input signal.
• First the VCO frequency has to be tuned to the
input frequency by the loop. This process is
called frequency pull-in.
• Then the VCO phase has to be adjusted
according to the input phase. This process is
known as phase lock-in.
90. 90
How the PLL works?
)sin()( icin tAtv θω +=
)cos()( ocout tBtv θω +=
vout(t)
vin(t) e0(t)x(t) Loop Filter
H(s)
Voltage-Controlled
Oscillator (VCO)
In telephony, the baseband is the audio band(0-3.5 kHz). In television, the baseband is the video band (0-4.3 MHz) For digital data or PCM using bipolar signaling at a rate of R b pulses per sec, the baseband is 0 to R b Hz. Consider a sinusoidal signal x(t)= A cos(2 f t+ ) A change in A is AM A change in f is FM A change in is PM
Consider the information signal m(t) shown above. Here, we have two cases depending on A Case1: A+m(t) > 0 for all t Case2: A+m(t) not positive for all t Observe both cases and tell me your remarks? In case 1, the envelope has the same shape as m(t) In case 2, the envelope is not the shape of m(t) How can we benefit from these observation? In the 1 st case, we can detect m(t) by detecting the envelope. So demodulation is obtained by envelope detection. Envelope detection is not suitable for case 2.
for modulation index>1 distortion of the envelope is observed..
Note that as , . Since is between 0 and 1 max =33% , for =1 Note that most of the power is wasted and not used
The bandpass filter tuned to f c suppresses all the other term
Coherent or synchronous demodulation method is more expensive and will defeat the very purpose of AM, so it is seldom used in practice. We will focus on the envelope and rectifier detector
The figure shows the simplest form of an envelope detector consisting of a diode and a resistor capacitor combination During the positive cycle of the input signal, the diode conducts and the capacitor charges up to the peak voltage of the input signal. RsC<1/fc. As the input voltage fall below the maximum, the diode turns off. The capacitor now gets slowly discharged through the resistor R. The process of charging and discharging alternate with each cycle. Thus the output voltage y(t) closely follows the envelope of the input
Notice in the Figure how the output voltage y(t) closely follows the envelope of the input. The ripple can be reduced by increasing the time constant RC so that the capacitor discharges very little between positive peaks. RC >1/f c and RC < 1/B Where B is the highest frequency in m(t). The ripple may be reduced further by another low pass (RC) filter.
The negative part of the AM wave will be suppressed. The output across the resistor is a half-wave rectified version of the AM signal. Diode function as ideal switch. The output of the LPF of bandwidth B is [ A+ m(t)]/ The dc term (A/ ) is blocked by the capacitor
Modulation can also be achieved by using nonlinear devices such as semiconductor diodes or transistors The Figure shows one possible scheme which uses 2 identical nonlinear elements.
Let w(t) be a periodic signal with fundamental radian frequency c . w(t) can be expressed by trigonometric Fourier series The switch (a-b) is controlled by w(t), and the output will be Output = m(t) w(t)
In Figure, w(t) is a square pulse train. It can control the switch (a-b) on and off. Thus it involves switching the signal m(t) on and off periodically. The output is the product m(t) w(t) In chapter 2, it was shown that The signal m(t) w(t) is given by
Therefore the spectrum of m(t) w(t) consists of the spectrum of M( ) and M( ) shifted to c , 3 c, 5 c ,… The modulated component m(t) cos( c t) can be obtained by using a bandpass filter of bandwidth 2B Hz, centered at the frequency c .
This Figure shows an example of an electronic switch for the diode bridge modulator driven by the signal v cd = A cos ( c t) When v cd >0, all diodes conducts and a-b is shorted, that is switch is on When v cd <0, all diodes opens and a-b is open circuit, that is switch is off. Thus the diode bridge serves as a desired electronic switch, where the terminals a and b are open and close periodically with the carrier frequency f c .
Another switching modulator is the ring modulator. When the carrier signal is >0, D 1 and D 3 conducts, D 2 and D 4 are open. Thus terminals a is connected to c and b is connected to d. Output is proportional to m(t). When the carrier signal is <0, D 2 and D 4 conducts, D 1 and D 3 are open. Thus terminals a is connected to d and b is connected to c. Output is proportional to [-m(t)]. The voltage v i (t)=m(t) w 0 (t) where w 0 (t) is a square pulse train.
The voltage v i (t)=m(t) w 0 (t) where w 0 (t) is a square pulse train. The modulated component m(t) cos( c t) can be obtained by using a bandpass filter of bandwidth 2B Hz, centered at the frequency c .
We have seen that DSB signals require a transmission bandwidth (2B) equal to twice the bandwidth of the message signal m ( t ). To increase the transmission bandwidth efficiency, it is possible to send two DSB signals using carriers of the same frequency but in phase quadrature. Both modulated signals occupy the same frequency band. Yet they can be separated at the receiver by synchronous detection using two local carriers in phase quadrature. The technique is known as Quadrature Amplitude Modulation (QAM ) or quadrature multiplexing and the arrangement is shown in Figure.
The QAM signal is
If we suppress the high-frequency components by LPF, y 1 (t)= m 1 (t) and y 2 (t)= m 2 (t) Upper channel in-phase channel and lower channel is quadrature channel Any phase error produces loss, distortion and interference.
Suppose that the local carrier signal is cos (2 f c t + 0 ), then the multiplier output in the upper portion of the circuit becomes If we suppress the second and the last terms by a LPF The desired signal m 1 ( t ) and the unwanted signal m 2 ( t ) appear in the upper portion of the circuit. Also, it can be shown that y 2 ( t ) contains the desired signal m 2 ( t ) and the unwanted signal m 1 ( t ). Modulated signals having the same carrier frequency now interfere with each other. This is called co-channel interference and must be avoided. Worse problems arise when the local carrier frequency is in error. Therefore, the local carrier must not only be of the same frequency but must be synchronized in phase with the carrier signal.
Ordinary AM and DSB signals require a transmission bandwidth equal to twice the bandwidth of the message signal m ( t ) and waste more power. The upper sideband (USB) or the lower sideband (LSB) contains the complete information of the message signal. We can conserve bandwidth and save power by transmitting only one sideband. The modulation is called single-sideband (SSB) modulation . It is widely used by the military and by radio amateurs in high-frequency (HF) communication systems. There are two common methods to generate a single-sideband signal: Selective filtering method (also called frequency discrimination method) and Phase–shift method .
In the filter method, a balanced modulator is used to generate a DSB-SC signal, and the desired sideband signal is then selected by a bandpass filter for transmission. Figures here and next slide show the generation of a SSB signal using the filter method, and the spectra associated with it.
The technique is suitable for message signals with very little frequency content down to dc and hence does not require sharp filter cut-off characteristics. Demodulation of SSB signals can be accomplished by using a synchronous detector as used in the demodulation of normal AM and DSB signals.
M + ( ): the upper sideband of M( ) M + ( ) = ½ M( ) u( )=1/2 M( ) [1+sgn( )] = ½ M( )+1/2 M( ) sgn( )
Generating SSB signal using phasing method. A single-sideband signal is given by where the (-) sign is associated with the USB and the (+) sign is associated with the LSB. m ^ ( t ) is obtained by shifting the phase of all frequency components of m ( t ) by -90 o . m ^ ( t ) is called the Hilbert transform of m ( t ) and is defined as
Block diagram of a 90 o phase-shift network can be obtained using Hilbert transform. m ^ ( t ) is called the Hilbert transform of m ( t ) and is defined as The inverse Hilbert transform of m ^ ( t ) is
Application for SSB communications: Telephone Channel Multiplexing voice channel 4 kHz Envelope detection of SSB signals with a carrier (SSB+C)
Drill Problem 5.4.1 (Stremler, 2 nd Ed., pp. 244)
Vestigial sideband modulation is a compromise between DSB and SSB modulations. It relaxes the sharp cutoff requirement of a SSB signal by retaining a trace of the other sideband in the transmitted signal. Typically, the bandwidth of a VSB modulated signal is about 1.25 times that of the corresponding SSB modulated signal. It is commonly used for transmission of video signals in commercial television broadcasting. This slide and next slide show the generation of a VSB signal, and the spectra associated with it. By inspection of spectrum , the Fourier transform of a VSB modulated signal S c (f)=[ M(f-f c )+ M(f+f c )] H(f)/2 where H ( f ) is the transfer function of the bandpass filter.
Vestigial sideband modulation is a compromise between DSB and SSB modulations. It relaxes the sharp cutoff requirement of a SSB signal by retaining a trace of the other sideband in the transmitted signal. Typically, the bandwidth of a VSB modulated signal is about 1.25 times that of the corresponding SSB modulated signal. It is commonly used for transmission of video signals in commercial television broadcasting. This slide and next slide show the generation of a VSB signal, and the spectra associated with it. By inspection of spectrum , the Fourier transform of a VSB modulated signal S c (f)=[ M(f-f c )+ M(f+f c )] H(f)/2 Or S c ( )=0.5 [ M( + c )+ M( - c )] * H( ) where H ( f ) is the transfer function of the bandpass filter.
S c ( )=0.5 [ M( + c )+ M( - c )] * H( ) Demodulation of VSB signals can be accomplished by using a synchronous detector.
Let s c ( t ) be the input signal to the synchronous detector. At the receiving end, the bandpass signal is multiplied by a locally generated carrier signal cos(2 f c t) , which is in synchronism with the transmitted carrier signal. The output of the multiplier is x(t)= s c (t) cos( c t) X( )= 0.5 [ S c ( + c )+ S c ( - c )] = 0.25*[ M( ) H( - c )+ M( - 2 c ) H( - c )] + 0.25*[ M( ) H( + c )+ M( +2 c ) H( + c )] X( )= 0.25*M( ) [H( - c )+ H( + c )] +0.25*[M( - 2 c ) H( - c )+ M( +2 c ) H( + c )] To be able to recover m(t) by a LPF, we need H( - c )+ H( + c )= const, for | |< 2 B
Envelope detection of VSB signals with a large carrier (VSB+C) x VSB+C (t)= x VSB (t)+ A cos( c t), where A is larger than AM case and smaller than the SSB+C
One of the basic problems in communication engineering is the design of a system which allows many individual signals from users to be transmitted simultaneously over a single communication channel.
Suppose that we have several different signals of the same bandwidth. If we translate each one of the signals to a different frequency region such that the translated signal spectra do not overlap each other, then all these signals can now be transmitted along a single communication channel. At the receiving end, the signals can be separated and recovered. We now have a frequency multiplexed system. Such a multiplexing technique is called frequency division multiplexing (FDM) .
Frequency translation can be accomplished by multiplying a low frequency modulating signal with a high-frequency sinusoidal carrier signal. This slide and next ones, shows the transmitter, the receiver, and the spectrum of a 5-user FDM system with carrier frequencies f c 1 < f c 2 < ... < f c 5 .
Similar to FDM, the signals are separated in time (instead of frequency)
Suppose we would like to receive 100 stations. If we use the set-up above, we will need to build 100 bandpass filters and 100 demodulator which is not practical. To use one demodulator and few filters, we can utilize the Superheterodyne AM Receiver
Most popular type of a radio receiver so far. It is used for AM/FM & TV broadcasting, cellular & satellite systems, radars, GPS etc. Main idea: downconvert RF signal to some fixed lower (intermediate) frequency, then amplify it and detect. RF amplifier: amplifies a weak RF signal coming out of the antenna. Rejects the unwanted one. Bandwidth: much wider than the signal bandwidth. • Mixer: together with the local oscillator downconverts the RF signal to the IF frequency band. • IF amplifier: amplifies the IF signal significantly (up to 10 6 ) and rejects adjacent channel signals and interference. Its bandwidth is the same as the signal bandwidth. • Detector (demodulator): demodulates (recovers) the message signal. Local oscillator: allows tuning the receiver to a desired channel (frequency). AGC limits the amplification to prevent overload and distortion.
The antenna not only provides very low amplitude input signals but it picks up all available transmissions at the same time + the added noise. The RF amplifier amplifies the incoming signal above the level of the internally generated noise and also start the process of selecting the wanted station and rejecting the unwanted ones. The overall effect of the selectivity is that whereas the incoming signals each have the same amplitude, the outputs vary between 1mV and 50 mV so we can select, or 'tune', the amplifier to pick out the desired station.
The mixer in the receiver combines the signal from the RF amplifier and the frequency input from the local oscillator to produce three frequencies: f lo -f c , f lo +f c , and f c The same tuning control is used to adjust the frequency of both the local oscillator and the center frequency of the RF amplifier so that f IF =f lo -f c =455 kHz E.g. If the radio transmits at 800 kHz, f c = 800 kHz, f Lo = f IF +f c =455+800=1255kHz If f c = 700 kHz, f Lo = f IF +f c =1155kHz If for another station f c =1.61 MHz, f LO =f c -f IF =1155 MHz? So I am receiving two stations at the same time? It is called image frequency . Note f img = f c +2f IF Image stations can be removed by the RF amplifier.
f c =850 kHz, f LO =f c1 +f IF =1.305 MHz f img =f c +2f IF =1.760 MHz Note the RF amplifier will select only the desired station.
The AGC is used to prevent overload and distortion
very high carrier frequencies: (>1GHz). See next article NEL Frequency Controls Introduces Ultra High Frequency Crystal Oscillator New Oscillator Provides Frequencies up to 2.0 GHz in a 9 x 14 mm package Burlington, WI (March 9, 2005) NEL Frequency Controls, Inc. announces the release of its new patent pending Ultra High Frequency Crystal Oscillator available at frequencies up to 2 GHz with either Differential Sine or PECL outputs. This frequency control solution is ideal for high speed digital designs where signal integrity is critical. The surface mount package measures 9x14mm. “Now design engineers have a better solution available in obtaining a high frequency clock reference,” notes Chuck Ulland, Vice President of Sales and Marketing at NEL Frequency Controls. “Typical approaches of attaining higher frequencies are either using a lower frequency clock with a PLL frequency multiplier or using a SAW oscillator. Both of these approaches have problems: PLL’s introduce added jitter, while SAW’s have poor stability over temperature performance. NEL’s solution offers extremely low jitter and outstanding stability over temperature characteristics.” RMS Random jitter performance is less than 1 psec, from 12 KHz to 10 MHz. Stabilities are from +/-20ppm over a temperature range of 0 to 70 C. The Ultra High Frequency Crystal Oscillator undergoes the rigors of NEL’s HALT/ HASS reliability program. NEL Frequency Controls is a U.S. based manufacturer of crystal oscillators, located in Burlington, WI. The company is recognized worldwide for its leading edge frequency control solutions and supports mission critical applications through its HALT/HASS reliability program that ensures oscillator robustness and start-up reliability. NEL Frequency Controls is ISO 9001-2000 certified. For more information about NEL, call the company at 262-763-3591 or visit their Web site at www.nelfc.com. Company Information: NEL Frequency Controls, Inc. 357 Beloit St., Burlington, WI 53105-0457,USA Phone: 262-763-3591, FAX: 262-763-2881 http:// www.nelfc.com / Contact Information: A ndrea Weitzenfeld
PLL is a useful device for synchronous demodulation of AM signals with suppressed carrier or with little carrier (the pilot). It can also be used for the demodulation of angle modulated signals.
Voltage-controlled oscillator ( VCO ): VCO generates a sinusoidal signal The instantaneous VCO frequency is controlled linearly by its input voltage. Eg. (t)= c + c e 0 (t) where c is constant. Multiplier: A multiplier serves as a phased detector (PD) or phase comparator It produces an error signal that is proportional to the phase error , i.e., to the difference between the phases of input and output signals of the phase-locked loop Loop filter: It is a Low-pass filter characterized by its transfer function H ( s ) LPF suppresses the noise and unwanted PD outputs. It determines the dynamics of phase-locked loop
This slide is about Carrier acquisition using PLL Both the frequency pull-in and phase lock-in processes are parts of acquisition which is a highly nonlinear process and is very hard to analyze After acquisition the PLL achieves the phase-locked condition , where the PLL tracks the input phase. Under this phase-locked condition , the VCO frequency is equal to the input frequency
x(t)=AB/2 [sin( i - o )+sin(2 c t+ i + o )] The output of the LPF is e 0 (t)=0.5 AB sin( i - o )= 0.5 AB sin( e ) where e = i - o Phase detector (PD) compares the phase of the input signal v in (t) against the phase of the VCO output v 0 (t) and produces an error signal x ( t ) This error signal is then filtered, in order to remove noise and other unwanted components of the input spectrum. The filter output e 0 ( t ) controls the instantaneous VCO frequency: (t)= c + c e 0 (t)
One method for carrier regeneration at the receiver in DSB-SC. The incoming signal is squared and then passed through a narrow bandpass filter tuned to c . The output of the filter is the sinusoid k cos(2 c t) with some residual unwanted signal. This signal is applied to a PLL to obtain a cleaner sinusoid of twice the carrier frequency, which passed through a 2:1 frequency divider to obtain a local carrier in phase and frequency synchronism with the incoming carrier. Other methods Costas loop (see textbook for details)
