Chapter 4 Amplitude Modulation (Part 2).pptx

Quadrature Amplitude Modulation
2
Prepared By: Mohsin Yousuf, FAST NU, LHR
 DSB signals occupy twice the bandwidth required for the
baseband, i.e., 2B for a signal of bandwidth B Hz.
 This disadvantage can be overcome by transmitting two
DSB signals using carriers of the same frequency but in
phase quadrature.
Phase
Shifters

3
 If the two baseband signals to be transmitted are 𝑚1(𝑡) and
𝑚2(𝑡), the corresponding QAM signal 𝜑𝑄𝐴𝑀(𝑡), the sum of
the two DSB-modulated signals, is
𝜑𝑄𝐴𝑀 𝑡 = 𝑚1 𝑡 cos 𝜔𝑐𝑡 + 𝑚2 𝑡 sin 𝜔𝑐𝑡
 Both modulated signals occupy the same band. Yet two
baseband signals can be separated at the receiver by
synchronous detection using two local carriers in phase
quadrature, as shown in Figure.
 The upper arm of the receiver also known as in-phase (I)
channel can be demultiplexed as;
𝑥1(𝑡) = 2𝜑𝑄𝐴𝑀 𝑡 cos 𝜔𝑐𝑡
= 2[𝑚1 𝑡 cos 𝜔𝑐𝑡 + 𝑚2 𝑡 sin 𝜔𝑐𝑡] cos 𝜔𝑐𝑡
= 𝑚1(𝑡) + 𝑚1(𝑡) cos 2𝜔𝑐𝑡 + 𝑚2(𝑡) sin 2𝜔𝑐𝑡

4
 The lower arm of the receiver is the Quadrature (Q)
channel.
 QAM is somewhat of an exacting scheme. A slight
error in the phase or the frequency of the carrier at the
demodulator in QAM will not only result in loss and
distortion of signals, but will also lead to interference
between the two channels.
 To show this let the carrier at the demodulator be
2 cos(𝜔𝑐𝑡 + 𝜃). In this case,
This is co-channel interference after LPF.

5
Amplitude Modulation:
Single Side-Band (SSB)

6
SSB Coherent Demodulation
SSB signals without any additional carrier, hence,
they are suppressed carrier signals (SSB-SC)

7
Time-Domain Representation of SSB
USB: 𝑀+(𝜔)
LSB: 𝑀−(𝜔)
𝑀+ 𝜔 = 𝑀 𝜔 𝑢(𝜔)
𝑀− 𝜔 = 𝑀 𝜔 𝑢(−𝜔)
Let 𝑚+(𝑡) and 𝑚−(𝑡) be the
inverse Fourier Transforms of
𝑀+(𝜔) and 𝑀−(𝜔).

8
USB: 𝑀+ 𝜔 = 𝑀 𝜔 𝑢(𝜔)
LSB: 𝑀− 𝜔 = 𝑀 𝜔 𝑢(−𝜔)
𝑚+(𝑡) ⇔ 𝑀+(𝜔)
𝑚−(𝑡) ⇔ 𝑀−(𝜔)
Are 𝑀+(𝜔) and 𝑀−(𝜔) even
functions of 𝜔?
NO. 𝑀+(−𝜔) ≠ 𝑀+(𝜔)
• 𝑚+(𝑡) and 𝑚−(𝑡) can not
be real; they are complex.
𝑀+ −𝜔 = 𝑀−(𝜔) are equal
and 𝑀+ 𝜔 = 𝑀−
∗ (𝜔), hence
𝑚+(𝑡) and 𝑚−(𝑡) are
conjugates pairs.

9
𝑚+(𝑡) ⇔ 𝑀+(𝜔)
𝑚−(𝑡) ⇔ 𝑀−(𝜔)
𝑚+(𝑡) and 𝑚−(𝑡) are
complex-conjugates pairs.
𝑚+ 𝑡 + 𝑚− 𝑡 = 𝑚(𝑡)
𝑚ℎ(𝑡) ⇔ 𝑀ℎ(𝜔)

10
𝑚+(𝑡) ⇔ 𝑀+(𝜔)
𝑚−(𝑡) ⇔ 𝑀−(𝜔)
sgn 𝑡 ⇔
2
𝑗𝜔
Symmetry
Property
𝑀ℎ 𝜔 = 𝑀 𝜔 𝐻(𝜔)
𝐻 𝜔 = −𝑗 sgn 𝜔
𝑚ℎ 𝑡 = 𝑚 𝑡 ∗ ℎ(𝑡)
Convolution
Property

11
Hilbert Transformer in SSB
𝑚ℎ 𝑡 = 𝑚 𝑡 ∗ ℎ(𝑡)
𝑚(𝑡) 𝑚ℎ(𝑡)
ℎ 𝑡 =
1
𝜋𝑡
The transfer function, 𝐻 𝜔 of an ideal 𝜋/2 phase shifter

12
USB/LSB spectrum of SSB

Prepared By: Mohsin Yousuf, FAST NU, LHR 13
Example 4.7

Generation of SSB Signals
 Selective-Filtering Method

Generation of SSB Signals
 Phase-Shift Method

Envelope Detection of SSB Signals
with a Carrier (SSB+C)

17
AM: Vestigial Sideband (VSB)
A gradual
cut-off of
one
sideband

18
VSB Modulator and Demodulator
What type of detector is in the Rx?
A synchronous detector
Can we recover it using Envelope
Detector?
Yes, if a large carrier is transmitted
with the VSB signal
• 𝑯𝒊(𝝎) is VSB Shaping Filter
• VSB Signal Spectrum is
• The bandwidth of VSB signal
is typically 25 to 33 % higher
than that of the SSB signals.

19
Synchronous Demodulation of VSB
𝑯𝒐(𝝎) is a low-pass equalizer fiter

Example 4.8

Use of VSB in Broadcast TV

Carrier Acquisition
 In the suppressed-carrier amplitude-modulated system
(DSB-SC, SSB-SC, and VSB-SC), one must generate a local
carrier at the receiver for the purpose of synchronous
demodulation.
 Ideally, the local carrier must be in frequency and phase
synchronism with the incoming carrier. Any discrepancy in
the frequency or phase of the local carrier gives rise to
distortion in the detector output.
 Consider a DSB-SC case where a received signal is
𝑚 𝑡 cos 𝜔𝑐𝑡 and the local carrier is 2 cos[ 𝜔𝑐 + ∆𝜔 𝑡 + 𝛿].
 The local-carrier frequency and phase errors in this case are
∆𝜔 and 𝛿, respectively.

Carrier Acquisition
The product of the received signal and the local carrier is 𝑒(𝑡), given by
Case-I: ∆𝜔 = 0
Case-II: 𝛿 = 0
Attenuation
Attenuation + Distortion at
beat frequency ∆𝜔
Distortion if 𝛿 = 𝑓(𝑡)

Carrier Acquisition
 To ensure identical carrier frequencies at the transmitter and the
receiver, we can use quartz crystal oscillators, which generally are
very stable. Identical crystals are cut to yield the same frequency
at the transmitter and the receiver.
 At very high carrier frequencies, where the crystal dimensions
become too small to match exactly, quartz-crystal performance
may not be adequate.
 In such a case, a carrier, or pilot, is transmitted at a reduced level
(usually about -20 dB) along with the sidebands. The pilot is
separated at the receiver by a very narrow-band filter tuned to
the pilot frequency. It is amplified and used to synchronize the
local oscillator.
 The phase-locked loop (PLL), which plays an important role in
carrier acquisition, will now be discussed.

Phase-Locked Loop (PLL)
 The phase-locked loop (PLL) can be used to track the phase and
the frequency of the carrier component of an incoming signal. It
is, therefore, a useful device for synchronous demodulation of AM
signals with suppressed carrier or with a little carrier (the pilot).
 It can also be used for the demodulation of angle-modulated
signals, especially under low SNR conditions.
 For this reason, the PLL is used in such applications as space-
vehicle-to-earth data links, where there is a premium on
transmitter weight, or where the loss along the transmission path
is very large; and, more recently, in commercial FM receivers.
 A PLL has three basic components:
1. A voltage-controlled oscillator (VCO)
2. A multiplier, serving as a phase detector (PD) or a phase comparator
3. A loop filter H(s)

Phase-Locked Loop (PLL)
The operation of the PLL is similar to that of a feedback system shown above. In a typical
feedback system, the signal fed back tends to follow the input signal. If the signal fed back
is not equal to the input signal, the difference (known as the error) will change the signal
fed back until it is close to the input signal.
A PLL operates on a similar principle, except that the quantity fed back and compared is
not the amplitude, but the phase. The VCO adjusts its own frequency until it is equal to
that of the input sinusoid. At this point, the frequency and phase of the two signals are in
synchronism (except for a possible difference of a constant phase).

Voltage Controlled Oscillator (VCO)
An oscillator whose frequency can be controlled by an external voltage is a voltage-
controlled oscillator (VCO). In a VCO, the oscillation frequency varies linearly with the
input voltage. If a VCO input voltage is 𝑒𝑜(𝑡), its output is a sinusoid of frequency 𝜔 given
by;
𝜔 𝑡 = 𝜔𝑐 + 𝑐𝑒𝑜(𝑡)
where 𝑐 is a constant of the VCO and 𝜔𝑐 is the free-running frequency of the VCO [the
VCO frequency when 𝑒𝑜(𝑡) = 0]. The multiplier output is further low-pass-filtered by the
loop filter and then applied to the input of the VCO. This voltage changes the frequency of
the oscillator and keeps the loop locked.

How the PLL Works:
Input 1: 𝐴 sin(𝜔𝑐𝑡 + 𝜃𝑖) and
Input 2: 𝐵 cos 𝜔𝑐𝑡 + 𝜃𝑜 which is an output of VCO
The multiplier output: 𝑥 𝑡 = 𝐴𝐵 sin(𝜔𝑐𝑡 + 𝜃𝑖) cos 𝜔𝑐𝑡 + 𝜃𝑜
=
𝐴𝐵
2
[sin 𝜃𝑖 − 𝜃𝑜 + sin 2𝜔𝑐𝑡 + 𝜃𝑖 + 𝜃𝑜 ]
𝑒𝑜 𝑡 =
𝐴𝐵
2
sin 𝜃𝑒 , 𝜃𝑒 = 𝜃𝑖 − 𝜃𝑜

How the PLL Works:
𝑒𝑜 𝑡 =
𝐴𝐵
2
sin 𝜃𝑒 ,
𝑃𝑎𝑠𝑒 𝐸𝑟𝑟𝑜𝑟; 𝜃𝑒 = 𝜃𝑖 − 𝜃𝑜

Some Definitions:
Hold-in / Lock Range:
Thus, the PLL tracks the input sinusoid. The two signals are said to
be mutually phase coherent or in phase lock. The VCO thus tracks
the frequency and the phase of the incoming signal. A PLL can track
the incoming frequency only over a finite range of frequency shift.
This range is called the hold-in or lock range.
Pull-in / Capture Range:
Moreover, if initially the input and output frequencies are
not close enough, the loop may not acquire lock. The frequency
range over which the input will cause the loop to lock is called the
pull-in or capture range. Also if the input frequency changes too
rapidly, the loop may not lock.

Carrier Acquisition in DSB-SC
Signal-Squaring Method:
Works for Analog Signals
because of the sign
ambiguity in the carrier
generated.

Carrier Acquisition in DSB-SC
Costas Loop:

Carrier Acquisition in SSB-SC
Similar argument can be
given for VSB-SC

SUPERHETERODYNE AM RECEIVER
The RF section is basically a tunable
filter and an amplifier that picks up
the desired station by tuning the filter
to the right frequency band.

Frequency mixer (converter), translates the carrier
from 𝜔𝑐 to a fixed IF frequency of 455 kHz. For this
purpose, it uses a local oscillator whose frequency 𝑓𝐿𝑂
is exactly 455 kHz above the incoming carrier
frequency 𝑓𝐶; i.e.,
𝑓𝐿𝑂 = 𝑓𝐶 + 𝑓𝐼𝐹 𝑤ℎ𝑒𝑟𝑒, 𝑓𝐼𝐹 = 455 𝑘𝐻𝑧
Note that this is up-conversion.

• The tuning of the local oscillator and the
RF tunable filter is done by one knob.
Tuning capacitors in both circuits are
ganged together and are designed so that
the tuning frequency of the local
oscillator is always 455 kHz above the
tuning frequency of the RF filter.
• This means every station that is tuned in
is translated to a fixed carrier frequency
of 455 kHz by the frequency converter.
The reason for translating all stations to a
fixed carrier frequency of 455 kHz is to
obtain adequate selectivity.

• IF amplifier is a three-stage amplifier,
which does have good selectivity. This is
because the IF frequency is reasonably
low, and, second, its center frequency is
fixed and factory-tuned.
• The IF section can effectively suppress
adjacent-channel interference because of
its high selectivity. It also amplifies the
signal for envelope detection.

• The main function of the RF section is
image frequency suppression.
• Mixer, or converter output is;
𝑓𝐼𝐹 = 𝑓𝐿𝑂 − 𝑓𝐶
• Example:
𝑓𝐶 = 1000 𝑘𝐻𝑧
𝑓𝐿𝑂 = 𝑓𝐶 + 𝑓𝑅𝐹 = 1000 + 455 = 1455 𝑘𝐻𝑧
• But another carrier, 𝑓𝐶
′
= 1455 + 455 =
1910 𝑘𝐻𝑧, will also be picked up because
the difference, 𝑓𝐶
′
− 𝑓𝐿𝑂 is also 455 𝑘𝐻𝑧.

• The station at 1910 𝑘𝐻𝑧 is said to be the
image of the station of 1000 𝑘𝐻𝑧.
• Station that are 2 𝑓𝐼𝐹 = 910 𝑘𝐻𝑧 apart are
called image stations and would both
appear simultaneously at the IF output if
it were not for the RF filter at receiver
input.
The RF filter may provide poor selectivity
against adjacent stations separated by
10 𝑘𝐻𝑧, but it can provide reasonable
selectivity against a station separated by
910 𝑘𝐻𝑧. Thus, when we wish to tune in a
station at 1000 𝑘𝐻𝑧, the RF filter, tuned to
1000 𝑘𝐻𝑧, provides adequate suppression of
the image station at 1910 𝑘𝐻𝑧.

Chapter 4 Amplitude Modulation (Part 2).pptx

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