Multiplexing
Multiplexing is the process of allowing two or more signals to share the same medium or
channel. A multiplexer converts the individual baseband signals to a composite signal that is
used to modulate a carrier in the transmitter.
Multiplexing at the transmitter
De-multiplexing at the receiver
At the receiver, the composite signal is recovered at the demodulator, then sent to a demultiplexer where the individual baseband signals are regenerated
Mixing is the process of combining 2 or more
signals which is very essential in communication.
2 types
1. Linear summing or mixing
2. Non-linear summing or mixing
Linear summing occurs when 2 or more signals
combine in a linear device like passive network or
small signal amplifier
•Linear mixer:
The linear
mixer is a summing amplifier
which is used widely in audio
and other applications to sum
signals. Audio mixers used in
studios and many other
areas use this technology. It
is this type of mixer that is
uses a summing amplifier,
i.e. each signal is summed in
a totally linear fashion.
Single input frequency
Multiple-input frequencies
Single input frequency
Non-linear mixing occurs when two
or more signals are combined in a
non-linear device like diodes and
power amplifiers
Multiplying or non-linear mixer.
This type of mixer is used in RF
applications. It uses the non-linear
characteristics of a circuit to multiply two
signals together and in this way generate
further frequencies. This type of mixer is
used for applications including frequency
changing.
Multiple-input frequencies
Cross product frequencies
These are the frequencies produced from the sum and difference of the fundamental frequencies
and its harmonics
cross products = m fa ± n fb
±
ELECTRICAL NOISE
Noise is an unwanted signal which interferes with the original message signal and corrupts the
parameters of the message signal.
Noise is the undesirable electrical signal which interferes with, or distorts the desired signal which is
most likely to be entered at the channel or the receiver.
Noise refers to variations in voltage or current that are often random, usually of relatively low
amplitude, and always undesirable.
Effects of noise in electrical systems
•Computer malfunctions such as shutdowns, computer locks, download gaps, network
problems, data drops, internet errors
•Power quality issues such as equipment failure, resets, voltage drops
•Inaccurate readings in measuring instruments
•Video quality issues such as display bars and stripes, distorted pictures
•Audio: sound with hamming and buzzing noises
•AC drive burnouts and errors
•Errors in precision instruments
Types of noise according to source
1. External Noise
2. Internal Noise
External Noise. This noise is produced by the external sources which may occur in the medium
or channel of communication, usually. This noise cannot be completely eliminated. The effects of
external noise are minimized by shielding or changing the location of the equipment affected by
the noise.
• Man made noise. It is noise attributed to man. The sources include spark-producing mechanisms or
devices which produce quick changes (spikes, arc discharges) in voltage or current. Example of industrial
noise are welding equipment, switch gear, electrical motors, aircraft and automotive ignition, fluorescent
lights, leakage from high voltage lines .
• Atmospheric noise: this is random and comes from lightning discharges and other naturally occurring
electrical disturbances. The atmospheric noise spreads over a wide frequency range and affects the
communication equipment most.
• Extraterrestrial noise. It is a noise that originates outside the earth’s atmosphere and sometimes called
deep-space noise. Extraterrestrial noise is significant for frequencies from approximately 8MHz to 1.5GHz
2 Sources of ET NOISE
Solar Noise – noise that is generated from the sun’s heat. It therefore radiates over a very broad frequency spectrum whjch includes the
frequencies we use for communication.
Cosmic Noise - distant stars are also suns and have high temperatures, they radiate RF noise in the same manner as our sun, and what
they lack in nearness they nearly make up in numbers which in combination can become significant. The noise received is called blackbody noise and is distributed fairly uniformly over the entire sky. We also receive noise from the center of our own galaxy (the Milky Way),
from other galaxies, and from other virtual point sources such as "quasars" and "pulsars." This galactic noise is very intense, but it comes
Internal noise
It is a noise created by any of the active or passive devices found in receivers. Such noise is generally
random, impossible to treat on an individual voltage basis i.e., instantaneous value basis, but easy to
observe and describe statistically. Random noise power is proportional to the bandwidth over which it is
measured
Thermal Noise. Most internal noise is caused by a phenomenon known as thermal agitation, the random
motion of free electrons in a conductor caused by heat. Increasing the temperature causes this atomic
motion to increase
Thermal agitation is often referred to as Brownian noise,white noise or Johnson noise, after J. B. Johnson, who
discovered it in 1928.
The noise generated in a resistance or the resistive component is random and therefore it is also referred to
as thermal agitation noise.
The noise power generated by a resistor is proportional to its absolute temperature, in addition to being
proportional to the bandwidth over which the noise is to be measured.
What is the open-circuit noise voltage across a 100-kΩ resistor over the frequency range of
direct current to 20 kHz at room temperature (25°C)?
The bandwidth of a receiver with a 75-Ω input resistance is 6 MHz. The temperature is
29°C. What is the input thermal noise voltage?
An amplifier operating over the frequency range from 18 to 25 MHz has a
10-kilohm input resistor. What is the rms noise voltage at the input to
this amplifier if the ambient temperature is 27°C?
Vn = 4 ∗ 1.38𝑥10−23 ∗ 27 + 273 ∗ 25 − 18 𝑥106 ∗ 10000
Vn = 34.047 uV
SHOT NOISE
Shot noise is by the random movement of electrons or holes across a PN junction. Current flow
in any device is not direct and linear. The current carriers, electrons or holes, sometimes take
random paths from source to destination, whether the destination is an output element, tube
plate, or collector or drain in a transistor. It is this random movement that produces the shot
effect.
The amount of shot noise is directly proportional to the amount of dc bias flowing in a device.
The bandwidth of the device or circuit is also important.
The rms noise current in a device is calculated with the formula
A system is operating at a bandwidth of 12.5Khz . If the dc bias
current passing thru the diode is 0.1 mA, determine the noise
current of the system
Addition of Noise due to Several Sources
To calculate the noise voltage due to several resistors in series or parallel; find the total
resistance by standard methods, and then substitute this resistance into the equation
Addition of Noise due to Several Amplifiers in Cascade
To find the equivalent input noise voltage it is even better to go one step further and find an equivalent
resistance for such an input voltage, i.e., the equivalent-noise resistance for the whole receiver. This is the
resistance that will produce the same random noise at the output of the receiver, replacing an actual
receiver amplifier by an ideal noiseless one with an equivalent noise resistance Req located across its input.
Consider a two-stage amplifier. The gain of the first stage is A1 and that of the second is A2.The first stage has
a total input-noise resistance R1, the second amplifier R2 and the output resistance is R3.
The rms noise voltage at the output due to R3 is
R’2
R’3
Three (3) cascaded amplifiers has the characteristics shown in the
Table below. Determine the equivalent input noise resistance and
noise voltage of the system if the system is an FM broadcast and
temp is 27 degrees centigrade
Amplifier 1 Amplifier 2 Amplifier 3
gain
25
10
25
input resistor
500
220k
470k
equivalent noise
resistance
1500
4.7k
5.6k
output resistance
180K
330k
1M
R1
R2
R3
R4
= 500 +1500 = 2K
= (180K//220K) +4.7K = 103.7K
=( 330K//470K) + 5.6K = 199475 ohms
=1M
Req = 2k +103.7K/25^2 + 199475/(25^2*10^2) + 1M/(25^2*10^2*25*2)
Req = 2169.14 ohms
Vn = 4 ∗ 1,38x10^-23
Vn = 2.68uV
Signal-to-Noise Ratio
When equivalent noise resistance is difficult to obtain, the signal-to-noise ratio (S/N) is very
often used to evaluate the performance of a communication system/equipment. The signal-tonoise (S/N) ratio, also designated SNR, indicates the relative strengths of the signal and the
noise in a communication system. It is defined as the ratio of signal power to noise power at the
same point.
Noise Factor and Noise Figure. The noise factor is the ratio of the S/N power at the input to
the S/N power at the output. The device under consideration can be the entire receiver or a single
amplifier stage. The noise factor or noise ratio (NR) is computed with the expression
Amplifiers and receivers always have more noise at the output than at the input because of the
internal noise, which is added to the signal.
When the noise factor is expressed in decibels, it is called the noise figure
When a device has multiple stages, each stage contributes noise, but the first stage is the most
important because noise inserted there is amplified by all other stages. Friis equation for overall
noise figure becomes
power gain
Noise Temperature. Most of the noise produced in a device is thermal noise, which
is directly proportional to temperature. Therefore, another way to express the noise
in an amplifier or receiver is in terms of noise temperature.
Teq = 290(F − 1)
Where
Teq = equivalent noise temperature in kelvins
F = noise factor
The noise temperature due to the equipment must be added to the noise temperature contributed by the
antenna and its transmission line to find the total system noise temperature. In terms of the antenna
resistance
F = 1 + ( Req’/Ra)
Where Req’ - equivalent input noise resistance of the system – input resistance
Ra - antenna resistance
An RF amplifier has an S/N ratio of 8 at the input and an S/N ratio of 6 at the output.
What are the noise factor and noise figure?
Noiseless amplifier
typical amplifier
For the amplifier shown above determine the following:
A receiver connected to an antenna whose resistance is 50 ohms has an
equivalent noise resistance of 30 ohms . Calculate the receiver's noise figure in
decibels and its equivalent noise temperature.
F = 1 + ( Req’/Ra) = 1+ (30/50) = 1.6
NF(db) = 10 log 1.6 = 2.04 dB
Teq = 290 (1.6-1) = 174 kelvins
The first stage of a two-stage amplifier has a voltage gain of 10, a 600-Ω input resistor, a
1600-Ω equivalent noise resistance and a 27-kΩ output resistor. For the second stage, these
values are 25, 81 kΩ, 10 kΩ and 1 megaohm , respectively. If this two-stage amplifier is driven
by a generator whose output impedance is 50Ω, calculate the noise figure
1 + (1918/50) = 39.4
NF = 10 log 39.4 = 15.95 dB
STAGE
POWER
GAIN
NOISE
FACTOR
1
10
2
2
25
4
3
30
5
Ap total = 10*25*30 = 7500
Aptotal (dB) = 10 log of 7500 = 38.75 dB
Ft = 2 + (4-1)/10 + (5-1)/(10*25) = 2.32
NFt(db) = 10 log 2.32 = 3.65 dB
Teq = 290 (2.32-1) = 382.8 kelvins
A receiver with a 75-Ω input resistance operates at a temperature of 31°C. The received signal is
has a bandwidth of 6 MHz. The received signal voltage of 8.3 μV is applied to an amplifier with a
noise figure of 2.8 dB. Find (a) the input noise power, (b) the input signal power, (c) S/N, in
decibels, (d) the noise factor and S/N of the amplifier, and (e) the noise temperature of the
amplifier
Vn= 2.75 uV
Pn =( 2.75 uV)^2/75 = 0.1pW
A receiver with a 75-Ω input resistance operates at a temperature of 31°C. The received signal is has a
bandwidth of 6 MHz. The received signal voltage of 8.3 μV is applied to an amplifier with a noise
figure of 2.8 dB. Find (a) the input noise power, (b) the input signal power, (c) S/N, in decibels, (d) the
noise factor and S/N of the amplifier, and (e) the noise temperature of the amplifier
Harmonic Distortion. All undesired harmonics are considered harmonic distortion. Harmonic distortion is
produced when a single frequency signal passes through a non-linear device .
From the figure above, determine the second order, third order
and total harmonic distortion
Intermodulation Distortion
These are unwanted cross product frequencies produced when 2 or more input signal passes thru a non-linear device.
2nd order cross product frequencies: (2A-B)
fa1 +fa2 – fb1
fa1+fa2 – fb2
2fa1 – fb1
2fa1 – fb2
2fa2 – fb1
2fa2 – fb2
Determine the 2nd order cross product frequencies if
A-Band : 1374 KHz and 1385 KHz
B-Band : 856 KHz and 863KHz
Arrange it from highest to lowest
= 35.35%
A receiver for satellite transmissions at 4 GHz consists of an antenna preamplifier with a noise
temperature of 127 K and a gain of 20 dB. This is followed by an amplifier with a noise figure of 12
dB and a gain of 40 dB. Compute the overall noise figure and equivalent noise temperature of the
receiver. What would be the value of the noise figure if the order of the amplifier and preamplifier
would be exchanged? Assume that the amplifiers are at a physical temperature of 290 K.
G1 = 20 dB
Teq1=172 K
NF2 = 12 dB
G2 = 40 dB
G1dB = 10 log G1 ; 20dB = 10 log G1 ; G1 = antilog (20/10) = 100
NF2dB = 10 log F2 ; 12dB = 10 log F2; F2 = antilog (12/10) = 15.85
G2dB = 10 log G2 ; 40dB = 10 log G2 – G2 = antilog (40/10) = 10000
Teq = 290 (F-1)
172K = 290K (F-1)
F1 = (172/290) +1 = 1.593
Ft = 1.593+ [(15.85-1)/100] = 1.7415
NFt = 10 log Ft = 10 log 1.7415 = 2.41 dB
Teqt = 290 (Ft – 1) = 290(1.7415-1) = 215.035 K
G1dB = 10 log G1 ; 20dB = 10 log G1 ; G1 = antilog (20/10) = 100
NF2dB = 10 log F2 ; 12dB = 10 log F2; F2 = antilog (12/10) = 15.85
G2dB = 10 log G2 ; 40dB = 10 log G2 – G2 = antilog (40/10) = 10000
Teq = 290 (F-1)
172K = 290K (F-1)
F1 = (172/290) +1 = 1.593
Ft = F2 = (f1-1)/G2 = 15.85 + [(1.593-1)/10000] = 15.85
NFt = 10 log 15.85 = 12 dB
Teqt = 290(15.85-1) = 4306.5K
OSCILLATOR
An oscillator is a circuit that produces a periodic waveform on its output with only the dc supply voltage as an input.
Two major classifications for oscillators are feedback oscillators and relaxation oscillators.
Feedback Oscillators. One type of oscillator is the feedback oscillator, which returns a fraction of the output signal to the
input with no net phase shift, resulting in a reinforcement of the output signal. After oscillations are started, the loop gain
is maintained at 1 to maintain oscillations. A feedback oscillator consists of an amplifier for gain (either a discrete transistor
or an op-amp) and a positive feedback circuit that produces phase shift and provides attenuation.
Positive feedback is characterized by the condition wherein a portion of the output voltage of an
amplifier is fed back to the input with no net phase shift, resulting in a reinforcement of the output
signal.
Relaxation Oscillators A second type of oscillator is the relaxation oscillator. Instead of feedback, a relaxation
oscillator uses an RC timing circuit to generate a waveform that is generally a square wave or other
nonsinusoidal waveform.
Conditions for Oscillation BARKHAUSEN CRITERIA TO SUSTAIN OSCILLATION)
1. The phase shift around the feedback loop must be effectively equal to zero
degrees or 360 degrees
2. The voltage gain, around the closed feedback loop (loop gain) must equal 1
(unity).