Environment

1. Introduction
to
Communication Engineering

2. Significance of
Human Communication
 Communication is the process of exchanging information.
 Main barriers are language and distance.
 Contemporary society’s emphasis is now the accumulation, packaging, and
exchange of information.

3. Significance of
Human Communication
Methods of communication:
1. Face to face
2. Signals
3. Written word (letters)
4. Electrical innovations:
Telegraph
Telephone
Radio
Television
Internet (computer)

4. Communication Systems
 Basic components:
 Data Source (where the data originates)
 Transmitter (device used to transmit data)
 Transmission Medium (cables or non cable)
 Receiver (device used to receive data)
 Destination (where the data will be placed)
 Noise degrades or interferes with transmitted
information.

5. Communication Systems
A general model of all communication systems.

6. Examples of Communication

7. Communication Systems
Transmitter
 The transmitter is a collection of electronic components and circuits that converts the
electrical signal into a signal suitable for transmission over a given medium.
 Transmitters are made up of oscillators, amplifiers, tuned circuits and filters,
modulators, frequency mixers, frequency synthesizers, and other circuits.

8. Communication Systems
Communication Channel
 The communication channel is the medium by which the electronic signal is sent from
one place to another.
 Types of media include
 Electrical conductors
 Optical media
 Free space
 System-specific media (e.g., water is the medium for sonar).

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Transmission Media Speed
• Bandwidth: The amount of data which can be transmitted
on a medium over a fixed amount of time (second). It is
measured on Bits per Second or Baud
• Bits per Second (bps): A measure of transmission
speed. The number of bits (0 0r 1) which can be
transmitted in a second
• Baud Rate: Is a measure of how fast a change of state
occurs (i.e. a change from 0 to 1)

10. Communication Systems
Receivers
 A receiver is a collection of electronic components and circuits that accepts the
transmitted message from the channel and converts it back into a form understandable
by humans.
 Receivers contain amplifiers, oscillators, mixers, tuned circuits and filters, and a
demodulator or detector that recovers the original intelligence signal from the
modulated carrier.

11. Communication Systems
Transceivers
 A transceiver is an electronic unit that incorporates circuits that both send and
receive signals.
 Examples are:
• Telephones
• Fax machines
• Handheld CB radios
• Cell phones
• Computer modems

12. Communication Systems
Attenuation
 Signal attenuation, or degradation, exists in all media of wireless transmission. It is
proportional to the square of the distance between the transmitter and receiver.

13. Communication Systems
Noise
 Noise is random, undesirable electronic energy that enters the communication system
via the communicating medium and interferes with the transmitted message.

14. Types of Electronic Communication
 Electronic communications are classified according to whether they are
1. One-way (simplex)
2. two-way (full duplex or half duplex) transmissions
3. Analog or digital signals.

15. Types of Electronic Communication
Simplex
 The simplest method of electronic communication is referred to as simplex.
 This type of communication is one-way. Examples are:
 Radio
 TV broadcasting
 Beeper (personal receiver)

16. Types of Electronic Communication
Full Duplex
 Most electronic communication is two-way and is referred to as duplex.
 When people can talk and listen simultaneously, it is called full duplex. The telephone is
an example of this type of communication.

17. Types of Electronic Communication
Half Duplex
 The form of two-way communication in which only one party transmits at a time is
known as half duplex. Examples are:
 Police, military, etc. radio transmissions
 Citizen band (CB)
 Family radio
 Amateur radio

18. Types of Electronic Communication
Analog Signals
 An analog signal is a smoothly and continuously varying voltage or current. Examples
are:
 Sine wave
 Voice
 Video (TV)

19. Types of Electronic Communication
Analog signals (a) Sine wave “tone.” (b) Voice. (c) Video (TV) signal.

20. Types of Electronic Communication
Digital Signals
 Digital signals change in steps or in discrete increments.
 Most digital signals use binary or two-state codes. Examples are:
 Telegraph (Morse code)
 Continuous wave (CW) code
 Serial binary code (used in computers)

21. Types of Electronic Communication
Digital signals (a) Telegraph (Morse code). (b) Continuous-wave (CW) code. (c)
Serial binary code.

22. Types of Electronic Communication
Digital Signals
 Many transmissions are of signals that originate in digital form but must be converted
to analog form to match the transmission medium.
 Digital data over the telephone network.
 Analog signals.
They are first digitized with an analog-to-digital
(A/D) converter.
The data can then be transmitted and processed by
computers and other digital circuits.

23. Modulation and Multiplexing
Modulation and multiplexing are electronic techniques
for transmitting information efficiently from one place to
another.
Modulation makes the information signal more compatible
with the medium.
Multiplexing allows more than one signal to be
transmitted concurrently over a single medium.

24. Modulation and
Multiplexing
Multiplexing at the transmitter.

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Signal
 A signal is a pattern of variation that carry information.
 Signals are represented mathematically as a function of one or more independent variable
Signal can be:-
Electrical signals like voltages, current and EM field in circuit
Acoustic signals like audio or speech signals (analog or digital)
Video signals like intensity variation in an image
Biological signal like sequence of bases in gene
Noise which will be treated as unwanted signal

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Signal classification
Continuous-time and Discrete-time (Analog/Digital)
Energy and Power
Real and Complex
Periodic and Non-periodic
Analog and Digital
Even and Odd
Deterministic and Random

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Analog and Digital Signals
Analog Signals
 Continuous
 Infinite range of values
 More exact values, but more difficult to work
with
Digital Signals
 Discrete
 Finite range of values (2)
 Not as exact as analog, but easier to work with
Example:
A digital thermostat in a room displays a temperature of 72. An
analog thermometer measures the room temperature at 72.482. The
analog value is continuous and more accurate, but the digital value is
more than adequate for the application and significantly easier to
process electronically.

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Example of Analog Signals
 An analog signal can be any time-varying signal.
 Minimum and maximum values can be either positive or negative.
 They can be periodic (repeating) or non-periodic.
 Sine waves and square waves are two common analog signals.
 Note that this square wave is not a digital signal because its minimum value is negative.
0 volts
Sine Wave Square Wave
(not digital)
Random-Periodic

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Parts of an Analog Signal
Amplitude
(peak-to-peak)
Amplitude
(peak)
Period
(T)
Hz
T
1
F 
Frequency:

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Logic Levels
Before examining digital signals, we must define logic levels. A logic level is a voltage
level that represents a defined digital state.
Logic HIGH: The higher of two voltages, typically 5 volts
Logic LOW: The lower of two voltages, typically 0 volts
5.0 v
2.0 v
0.8 v
0.0 v Logic Low
Logic High
Invalid
Logic
Level
Logic Level Voltage True/False On/Off 0/1
HIGH 5 volts True On 1
LOW 0 volts False Off 0

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Example of Digital Signals
 Digital signal are commonly referred to as square waves or clock signals.
 Their minimum value must be 0 volts, and their maximum value must be 5 volts.
 They can be periodic (repeating) or non-periodic.
 The time the signal is high (tH) can vary anywhere from 1% of the period to 99%
of the period.
0 volts
5 volts

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Parts of a Digital Signal
Amplitude
Time
High
(tH)
Time
Low
(tL)
Period (T)
Rising Edge
Falling Edge
Amplitude:
For digital signals, this will ALWAYS be
5 volts.
Period:
The time it takes for a periodic signal to
repeat. (seconds)
Frequency:
A measure of the number of
occurrences of the signal per second.
(Hertz, Hz)
Time High (tH):
The time the signal is at 5 v.
Time Low (tL):
The time the signal is at 0 v.
Duty Cycle:
The ratio of tH to the total period (T).
Rising Edge:
A 0-to-1 transition of the signal.
Falling Edge:
A 1-to-0 transition of the signal.
Hz
T
1
F 
Frequency:
%
100


T
t
DutyCycle H

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Deterministic and Random signal
A signal is random whose future values can NOT be predicted with
 complete accuracy
Behavior of these signals is random i.e. not predictable w.r.t time.
There is an uncertainty with respect to its value at any time.
These signals can’t be expressed mathematically.
 For example (Thermal) Noise generated is non deterministic signal.

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Deterministic and Random signal
Random signals whose future values can be statistically determined
based on the past values are correlated signals.
Random signals whose future values can NOT be statistically
determined from past values are uncorrelated signals and are
more random than correlated signals.

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Periodic and Non-periodic Signals
A signal is said to be periodic if it repeats after a fixed time period.
Given x(t) is a continuous-time signal
 x (t) is periodic if x(t) = x(t+Tₒ) for any T and any
integer n
 Example
 x(t) = A cos(wt)
x(t+Tₒ) = A cos[w(t+Tₒ)]
= A cos(wt+wTₒ)
= A cos(wt+2p)
= A cos(wt)
Note: Tₒ =1/fₒ ; w2pfₒ

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Periodic and Non-periodic Signals Contd.
 A signal is said to be non periodic if it does not repeat.
 For non-periodic signals
x(t) ≠ x(t+Tₒ)
 A non-periodic signal is assumed to have a period T = ∞
 Example of non periodic signal is an exponential signal

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Periodic and Non-periodic Signals Contd.

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Scaling of signal

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Scaling of signal

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43. The Electromagnetic Spectrum
 EM wave is a signal made of oscillating electric and magnetic fields.
 The range of electromagnetic signals encompassing all frequencies is referred to
as the electromagnetic spectrum.

44. The Electromagnetic Spectrum
The electromagnetic spectrum.

45. The Electromagnetic Spectrum
Frequency and Wavelength:
Frequency
A signal is located on the frequency spectrum according
to its frequency and wavelength.
Frequency is the number of cycles of a repetitive wave
that occur in a given period of time.
A cycle consists of two voltage polarity reversals,
current reversals, or electromagnetic field oscillations.
Frequency is measured in cycles per second (cps).
The unit of frequency is the hertz (Hz).

46. The Electromagnetic Spectrum
Frequency and Wavelength:
Wavelength
Wavelength is the distance occupied by one cycle of a
wave and is usually expressed in meters.
Wavelength is also the distance traveled by an
electromagnetic wave during the time of one cycle.
The wavelength of a signal is represented by the Greek
letter lambda (λ).

47. The Electromagnetic Spectrum
Frequency and wavelength. (a) One cycle. (b) One wavelength.

48. The Electromagnetic Spectrum
Example:
What is the wavelength if the frequency is 4MHz?
Frequency and Wavelength: Wavelength
Wavelength (λ) = speed of light ÷ frequency
Speed of light = 3 × 108 meters/second
Therefore:
λ = 3 × 108 / f
λ = 3 × 108 / 4 MHz
= 75 meters (m)

49. The Electromagnetic Spectrum
Frequency Ranges from 30 Hz to 300 GHz
 The electromagnetic spectrum is divided into segments:
Extremely Low Frequencies (ELF) 30–300 Hz.
Voice Frequencies (VF) 300–3000 Hz.
Very Low Frequencies (VLF) include the higher end of the human hearing
range up to about 20 kHz.
Low Frequencies (LF) 30–300 kHz.
Medium Frequencies (MF) 300–3000 kHz
AM radio 535–1650 kHz.

50. The Electromagnetic Spectrum
Frequency Ranges from 30 Hz to 300 GHz
High Frequencies (HF)
(short waves; VOA, BBC broadcasts; government and
military two-way communication; amateur radio, CB.
3–30 MHz
Very High Frequencies (VHF)
FM radio broadcasting (88–108 MHz), television
channels 2–13.
30–300 MHz
Ultra High Frequencies (UHF)
TV channels 14–67, cellular phones, military
communication.
300–3000 MHz

51. The Electromagnetic Spectrum
Frequency Ranges from 30 Hz to 300 GHz
Microwaves and Super High Frequencies (SHF)
Satellite communication, radar, wireless LANs,
microwave ovens
1–30 GHz
Extremely High Frequencies (EHF)
Satellite communication, computer data, radar
30–300 GHz

52. The Electromagnetic Spectrum
Optical Spectrum
The optical spectrum exists directly
above the millimeter wave region.
Three types of light waves are:
Infrared
Visible spectrum
Ultraviolet

53. The Electromagnetic Spectrum
Optical Spectrum: Infrared
Infrared radiation is produced by any physical equipment that generates
heat, including our bodies.
Infrared is used:
In astronomy, to detect stars and other physical bodies in the
universe,
For guidance in weapons systems, where the heat radiated from
airplanes or missiles can be detected and used to guide missiles to
targets.
In most new TV remote-control units, where special coded signals are
transmitted by an infrared LED to the TV receiver to change channels,
set the volume, and perform other functions.
In some of the newer wireless LANs and all fiber-optic communication.

54. The Electromagnetic
Spectrum
Optical Spectrum: The Visible Spectrum
 Just above the infrared region is the visible spectrum we
refer to as light.
 Red is low-frequency or long-wavelength light
 Violet is high-frequency or short-wavelength light.
 Light waves’ very high frequency enables them to
handle a tremendous amount of information (the
bandwidth of the baseband signals can be very wide).

55. The Electromagnetic Spectrum
Optical Spectrum: Ultraviolet
Ultraviolet is not used for communication
Its primary use is medical.

56. Gain, Attenuation,
and Decibels
 Most circuits in electronic communication are used to manipulate signals to
produce a desired result.
 All signal processing circuits involve:
Gain
Attenuation

57. Gain, Attenuation,
and Decibels
Gain
Gain means amplification. It is the ratio of a circuit’s
output to its input.
An amplifier has gain.
AV = =
output
input
Vout
Vin

58. Gain, Attenuation,
and Decibels
 Most amplifiers are also power amplifiers, so the
same procedure can be used to calculate power
gain AP where Pin is the power input and Pout is the
power output.
Power gain (Ap) = Pout / Pin
 Example:
The power output of an amplifier is 6 watts (W). The
power gain is 80. What is the input power?
Ap = Pout / Pin therefore Pin = Pout / Ap
Pin = 6 / 80 = 0.075 W = 75 mW

59. Gain, Attenuation,
and Decibels
 An amplifier is cascaded when two or more stages are
connected together.
 The overall gain is the product of the individual circuit
gains.
 Example:
Three cascaded amplifiers have power gains
of 5, 2, and 17. The input power is 40 mW.
What is the output power?
Ap = A1 × A2 × A3 = 5 × 2 × 17 = 170
Ap = Pout / Pin therefore Pout = ApPin
Pout = 170 (40 × 10-3) = 6.8W

60. Gain, Attenuation,
and Decibels
Attenuation
Attenuation refers to a loss introduced by a circuit or
component. If the output signal is lower in amplitude
than the input, the circuit has loss or attenuation.
The letter A is used to represent attenuation
Attenuation A = output/input = Vout/Vin
Circuits that introduce attenuation have a gain that is
less than 1.
With cascaded circuits, the total attenuation is the
product of the individual attenuations.

61. Gain, Attenuation,
and Decibels
Total attenuation is the product of individual attenuations of each cascaded
circuit.

62. Gain, Attenuation,
and Decibels
Decibels
 The decibel (dB) is a unit of measure used to express the gain or loss of a circuit.
The decibel was originally created to express hearing
response.
A decibel is one-tenth of a bel.
 When gain and attenuation are both converted into decibels, the overall gain or attenuation of a circuit can be
computed by adding individual gains or attenuations, expressed in decibels.

63. Gain, Attenuation,
and Decibels
Decibels: Decibel Calculations
 Voltage Gain or Attenuation
dB = 20 log Vout/ Vin
 Current Gain or Attenuation
dB = 20 log Iout/ Iin
 Power Gain or Attenuation
dB = 10 log Pout/ Pin

64. Gain, Attenuation,
and Decibels
Decibels: Decibel Calculations
 Example:
An amplifier has an input of 3 mV and an output of 5 V.
What is the gain in decibels?
dB = 20 log 5/0.003
= 20 log 1666.67
= 20 (3.22)
= 64.4

65. Gain, Attenuation,
and Decibels
Decibels: Decibel Calculations
 Example:
A filter has a power input of 50 mW and an output of 2 mW.
What is the gain or attenuation?
dB = 10 log (2/50)
= 10 log (0.04)
= 10 (−1.398)
= −13.98
 If the decibel figure is positive, that denotes a gain.

66. Bandwidth
 Bandwidth (BW) is that portion of the electromagnetic spectrum occupied by a
signal.
 It is the difference between the upper and lower frequency limits of the signal.
 Channel bandwidth refers to the range of frequencies required to transmit the
desired information.

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Bandwidth requirements for various signals
Telegraph Signals:-
 Telegraph speed is often expressed in terms of the reciprocal of the duration in the seconds, of the
shorted signaling element termed as band.
 The shortest time element is of 20 milliseconds.
 Therefore the Bandwidth required is,
BW = 1/20X10^-3
= 50Hz

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Voice/Speech signal:-
 Voice signal ranges from 300Hz to 3000Hz so the Bandwidth required is 2700 Hz.
Music Signal:-
 Musical Instruments produce harmonics whose orders and amplitude decides the quality of musical output.
 For this purpose a frequency range of 30Hz to 15 KHz is needed for high quality music transmission.
 Therefore for music transmission bandwidth required is,
14.970 KHz (15000-30)

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Television Signals:-
 For television signals bandwidth required is 6 MHz
For digital data transmission:-
 Many digital data transmission utilize telephone channels, the bandwidth of the telephone is an appropriate
consideration.
 The faster the rate of data transmission, the greater the bandwidth required.
 The telephone channel occupies the frequency range of
300 Hz to 3400 Hz.

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When data is sent over telephone channel, the speed
must be limited to ensure that the bandwidth required
by the data transmission will not exceed the telephone
channel bandwidth.
The data rates of common systems are limited to a
maximum rate of about 10,800 bits per second (bps)
for a telephone channel.

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Noise
What is Noise?
 With reference to an electrical system, noise may be defined as any unwanted form of energy which tends to
interfere with proper reception and reproduction of wanted signal.
OR
 Noise is random, undesirable electrical energy that enters the communications system via the communicating
medium and interferes with the transmitted message. However, some noise is also produced in the receiver.

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Classification of Noise
Noise may be put into following two categories.
 External noises, i.e. noise whose sources are external.
 External noise may be classified into the following three types:
–Atmospheric noises
–Extraterrestrial noises
–Man-made noises or industrial noises.

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Internal noise in communication:-
 Noises which get, generated within the receiver or communication system.
 Internal noise may be put into the following four categories.
–Thermal noise or white noise or Johnson noise
–Shot noise.
–Transit time noise
–Miscellaneous internal noise.

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 External noise cannot be reduced except by changing the location of the receiver or the entire system.
 Internal noise on the other hand can be easily evaluated Mathematically and can be reduced to a great
extent by proper design.
 As already said, because of the fact that internal noise can be reduced to a great extent, study of noise
characteristics is a very important part of the communication engineering.

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Atmospheric Noise
 Atmospheric noise or static is caused by lighting discharges in thunderstorms and other natural electrical
disturbances occurring in the atmosphere.
 These electrical impulses are random in nature. Hence the energy is spread over the complete frequency
spectrum used for radio communication.
 Atmospheric noise accordingly consists of spurious radio signals with components spread over a wide frequency
range.

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 These spurious radio waves constituting the noise get propagated over the earth in the same fashion as the
desired radio waves of the same frequency.
 Accordingly at a given receiving point, the receiving antenna picks up not only the signal but also the static from
all the thunderstorms, local or remote.
 The field strength of atmospheric noise varies approximately inversely with the frequency

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 Thus large atmospheric noise is generated in low and medium frequency (broadcast) bands while very little
noise is generated in the VHF and UHF bands.
 Further VHF and UHF components of noise are limited to the line-of-sight (less than about 80 Km) propagation.
 For these two-reasons, the atmospheric noise becomes less severe at Frequencies exceeding about 30 MHz

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Extraterrestrial Noise
There are numerous types of extraterrestrial noise
or space noises depending on their sources.
However, these may be put into following two
subgroups.
Solar noise
Cosmic noise

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Solar Noise
 This is the electrical noise emanating from the sun.
 Under quite conditions, there is a steady radiation of noise from the sun.
 This results because sun is a large body at a very high temperature and radiates electrical energy in the form
of noise over a very (exceeding 6000°C on the surface), wide frequency spectrum including the spectrum used
for radio communication.

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 The intensity produced by the sun varies with time. In fact, the sun has a repeating 11-Year noise cycle.
 During the peak of the cycle, the sun produces some amount of noise that causes tremendous radio signal
interference, making many frequencies unusable for communications.
 During other years the noise is at a minimum level.

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Cosmic noise
 Distant stars are also suns and have high temperatures. These stars, therefore, radiate noise in the same way
as our sun.
 The noise received from these distant stars is thermal noise (or black body noise) and is distributing almost
uniformly over the entire sky.
 We also receive noise from the center of our own galaxy (The Milky Way) from other distant galaxies and from
other virtual point sources such as quasars and pulsars.

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Man-Made Noise (Industrial Noise)
 It is the electrical noise produced by such sources as automobiles and aircraft ignition, electrical motors and
switch gears, leakage from high voltage lines, fluorescent lights, and numerous other heavy electrical machines.
 Such noises are produced by the arc discharge taking place during operation of these machines. Such man-made
noise is most intensive in industrial and densely populated areas.
 Man-made noise in such areas far exceeds all other sources of noise in the frequency range extending from
about 1 MHz to 600 MHz

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Internal Noise
Thermal Noise
 Conductors contain a large number of 'free" electrons and "ions" strongly bound by molecular forces. The ions
vibrate randomly about their normal (average) positions, however, this vibration being a function of the
temperature.
 Continuous collisions between the electrons and the vibrating ions take place. Thus there is a continuous
transfer of energy between the ions and electrons.

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 The movement of free electrons constitutes a current which is purely random in nature and over a long time
averages zero. There is a random motion of the electrons which give rise to noise voltage called thermal or
thermal agitation or Johnson noise.
“Thus noise generated in any resistance due to random motion of electrons is called thermal noise or white or
Johnson noise.”
 The analysis of thermal noise is based on the Kinetic theory.

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• At -273°C (or zero degree Kelvin) the kinetic energy of the particles of a body becomes zero .Thus we can relate
the noise power generated by a resistor to be proportional to its absolute temperature and the bandwidth over
which it is measured. From the above discussion we can write down.
Pn ∝ TB
Pn = KTB ------ (1)
Where
Pn = Maximum noise power output of a resistor.
K = Boltzmann’s constant = 1.38 x10-23 joules I Kelvin.
T = Absolute temperature.
B = Bandwidth over which noise is measured.

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 From equation (1), an equivalent circuit can be drawn as shown in below figure

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 From equation (2), we see that the square of the rms noise voltage is proportional to the absolute
temperature, the value of the resistor, and the bandwidth over which it is measured. En is quite independent
of the Frequency.
Example
 R.F. amplifier is saving an input resistor of 8Kohm and works in the frequency range of 12 to 15.5 MHz
Calculate the rms noise voltage at the input to this amplifier at an ambient temperature of 17oC?
• Solution:

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Shot Noise
 It produces by the random arrival of electrons or holes at the output element, at the plate in a tube, or at
the collector or drain in a transistor.
 Shot noise is also produced by the random movement of electrons or holes across a PN junction.

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 Even through current flow is established by external bias voltages, there will still be some random movement of
electrons or holes due to discontinuities in the device.
 An example of such a discontinuity is the contact between the copper lead and the semiconductor materials.
The interface between the two creates a discontinuity that causes random movement of the current carriers.

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Transit Time Noise
 Another kind of noise that occurs in transistors is called transit time noise.
 Transit time is the duration of time that it takes for a current carrier such as a hole or current to move
from the input to the output.
 The devices themselves are very tiny, so the distances involved are minimal. Yet the time it takes for the
current carriers to move even a short distance is finite.

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 At some frequencies this time is negligible. But when the frequency of operation is high and the signal
being processed is the magnitude as the transit time, then problem can occur.
 The transit time shows up as a kind of random noise within the device, and this is directly proportional to
the frequency of operation.
 It is also called as high frequency noise.

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MISCELLANEOUS INTERNAL NOISES
Flicker Noise (Low frequency Noise)
 Flicker noise or modulation noise is the one appearing in transistors operating at low audio frequencies(below
few KHz).
 Flicker noise is proportional to the emitter current and junction temperature.
 However, this noise is inversely proportional to the frequency hence it is sometime referred as 1/f noise. Hence it
may be neglected at frequencies above about 500 Hz and it, Therefore, possess no serious problem.

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Transistor Thermal Noise
 Within the transistor, thermal noise is caused by the emitter, base and collector internal resistances. Out of
these three regions, the base region contributes maximum thermal noise.
Partition Noise
 Partition noise occurs whenever current has to divide between two or more paths, and results from the random
fluctuations in the division. It would be expected, therefore, that a diode would be less noisy than a transistor (all
other factors being equal) If the third electrode draws current (i.e.., the base current). It is for this reason that
the inputs of microwave receivers are often taken directly to diode mixers.

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Correlated Noise
Inter-modulation distortion
• When two or more signals are amplified in non-linear device, such as large signal amplifiers some unwanted sum
and difference frequencies are generated
• The distortion due to unwanted frequencies are called inter-modulation distortion
• The sum and difference frequencies are called cross products.
Cross product = mf1 ± mf2
where
f1,f2= fundamental frequencies
m and n = positive integer between one and infinity