Slides By: Dr. N. Ioannides (Feb. 2010)CT1037NI - L.02 - Analogue Signal Characteristics - pp 1/43...

Slides By: Dr. N. Ioannides (Feb. 2010)

CT1037NI - L.02 - Analogue Signal Characteristics - pp 1/43

CT1037NICT1037NIIntroduction to CommunicationsIntroduction to Communications

Analogue Signal CharacteristicsEr. Saroj Sharan Regmi

Lecture 02



• Introduction to the Module: CT1037NI.• Introduction to Telecommunications.• Telecommunications have made great progress over the past

150 years.• There are a number of organizations responsible for

standards.• Discussed Social Implications from Telecommunications.

Last Lecture: 01Last Lecture: 01Introduction to TelecommunicationsIntroduction to Telecommunications



• Signal Overview and Definitions.• Voltage, Resistance, Current & Power.• Characteristics of Sinusoidal Waveforms.• Electro-Magnetic Spectrum.• International System (SI) of Units.• Scientific Notation and Decimal Prefixes in Engineering.• Logarithms and Decibel.• Signal Attenuation.• Power Budget.• Noise in Analogue Signals and Types of Noise.• Periodic Waveforms.• Bandwidth.

Today’s Lecture: 02Today’s Lecture: 02Analogue Signal CharacteristicsAnalogue Signal Characteristics



SignalsSignals• Signal: An electrical voltage or current which varies with time

and is used to carry messages or information from one point to another.

Analogue signals vary continuously with time:

Digital signals vary abruptly and change between distinct voltage or current levels.



• Voltage ( V ): an electrical force, or pressure, that occurs when electrons and protons are separated.

The unit of voltage measurement is the Volt (V).• Resistance ( R ): the opposition to the movement of

electrons through materials. The unit of resistance measurement is the Ohm (Ω).

• Current ( I ): Caused by the flow of free electrons in a circuit. The unit of current measurement is the Ampere (A). The Ampere is defined as the number of charges per

second that pass by a point along a path.• Electrons ONLY flow in CLOSED circuits, or COMPLETE loops.

Voltage, Resistance & CurrentVoltage, Resistance & Current



Open vs Closed CircuitsOpen vs Closed Circuits• Electrons ONLY flow in CLOSED circuits, or COMPLETE loops.• Example: The Torchlight.

Open Switch / Open CircuitCurrent does NOT flow !

Closed Switch / Closed CircuitCurrent DOES flow !



Current FlowCurrent Flow• Current can flow in one of two

ways: Direct Current (DC):

DC always flows in the same direction, and DC voltages always have the same polarity.

Alternating Current (AC): AC varies over time by changing its polarity, or direction.

• Note: For AC and DC electrical systems, the flow of electrons is always from a negatively charged source to a positively charged source.



Current vs Electron FlowCurrent vs Electron Flow• For AC and DC electrical systems:

Current Flow: always from a positive terminal to a negative terminal.

Electron Flow: always from a negatively charged source to a positively charged source.

Current flow

Electron flow



Alternating vs Direct CurrentAlternating vs Direct Current• The work done by the AC and DC currents is NOT equivalent:

DC performs constant work due to the constant nature of the flow of current.

AC performs variable work due to the alternating / varying nature of the flow of current.

• Root Mean Square (RMS) Value: the effective value of a varying voltage or current.

RMS is the equivalent DC value which gives the same work.

The following equations hold for sinusoidal waveform signals:V rms =

V peak

√2…(V )

I peak = √2×I rms …( A)I rms =I peak

√2…( A)

V peak = √ 2×V rms …(V )



Ohm’s LawOhm’s Law• Identifies the relationship among Voltage, Resistance and

Current: DC Systems:

V = I×R …(V )

I =VR

…( A)

R =VI

…(Ω)

• Note: Ohm’s Law considers the flow of current in the conventional way which sees the current flowing from the positive towards the negative.

AC Systems:V rm s = I rm s× R …(V )

I rms =V rms

R…(A)

R =V rms

I rms…(Ω)



PowerPower• Power ( P ): The work performed by an electrical current.

The unit of power measurement is the Watt (W). DC Circuits:

P = V 2

R…(W )

P = V×I …(W )

P = I 2× R …(W )

AC Systems:

P =V

rms2

R…(W )

P = V rms× I rm s … (W )

P = Irms2×R …(W )



International System (SI) of UnitsInternational System (SI) of Units• The SI is the modern metric system of measurement.• A unit is a particular physical quantity, defined and adopted

by convention, with which other particular quantities of the same kind are compared to express their value.

• A physical quantity is a quantity that can be used in the mathematical equations of science and technology.

• The value of a physical quantity is the quantitative expression of a particular physical quantity as the product of a number and a unit, the number being its numerical value.

Thus, the numerical value of a particular physical quantity depends on the unit in which it is expressed.



Scientific NotationScientific Notation• Commonly used in Physics, Chemistry and Engineering.• A way of separating the range of expressible numbers from

their precision:

Examples: 3.14 = 0.314 × 101 = 3.14 × 100

0.000001 = 0.1 × 10-5 = 1.0 × 10-6

1941 = 0.1941 × 104 = 1.941 × 103

n = f ×ref: fraction or mantissa,r: radix or base number,e: +ve or -ve integer called the

exponent.

• The range is determined by the number of digits in the exponent.

• The precision is determined by the number of digits in the fraction.



Decimal Prefixes of Units in EngineeringDecimal Prefixes of Units in EngineeringMultiplication FactorMultiplication Factor PrefixPrefix SymbolSymbol

1 000 000 000 000 000 000 1018 exa E

1 000 000 000 000 000 1015 peta P

1 000 000 000 000 1012 tera T

1 000 000 000 109 giga G

1 000 000 106 mega M

1 000 103 kilo k

1 100 - -

0.001 10-3 milli m

0.000 001 10-6 micro μ

0.000 000 001 10-9 nano n

0.000 000 000 001 10-12 pico p

0.000 000 000 000 001 10-15 femto f

0.000 000 000 000 000 001 10-18 atto a



• Logarithm is the power to which a number (base) must be raised to equal a given number.

LogarithmsLogarithms

• By transforming very small or very large numbers into logarithms it makes them easy to work with.

Logarithms are referenced to the base of the number system being used (base 10 logarithms are often abbreviated as log).

Used commonly in calculating decibels (dB): a way of measuring signals on copper, optical, and wireless media.

x = logb n b: the base,n: the given

number.bx = n



Examples on LogarithmsExamples on Logarithms• Logarithm is the power to which a number (base) must be

raised to equal a given number:

10 = 1011 = 100

100 = 102

1000 = 103

11000

= 10−3 = 0 .003

Log10 (101 ) = 1

Log 10 ( 100 ) = 2

Log10 (103 ) = 3

Log10 (10−3 ) = −3

Log10 (100 ) = 0



Revision on LogarithmsRevision on Logarithms

Log 10 ( x× y ) = Log 10 x + Log 10 y

Log10 (xy) = Log10 x − Log 10 y

Log10 ( xy ) = y × Log 10 x

• Important logarithms:.

Log10 (12) =−0 . 3Log 10 ( 2 ) = +0 . 3



Decibels (dB)Decibels (dB)• The most frequently used unit in Telecommunications.• Defined as:

• The decibel is a means of logarithmically expressing the ratio between two signal levels (eg: output vs input, or output vs noise).

The result is based on the ratio of a final value (signal strength) to another reference value (input signal or noise value).

• The decibel is a RELATIVE measure, ie one quantity with respect to another quantity.

dB ≡ 10×log (P out

P in) …( dB)



Decibels (dB) (…2)Decibels (dB) (…2)

? dB = 20×log (V out

V in) …(dB )

Vout = Signal amplitude at output in Volts

Vin = Signal amplitude at input in Volts

? dB = 10×log (P out

P in) …(dB )

Pout = Signal amplitude at output in Watts

Pin = Signal amplitude at input in Watts

• Decibels state the amount of gain or loss of power, voltage or current that occurs in a circuit or system.

• Decibels are expressed as: Amplification: Gain or + (only one is used, never

both). Weakening: Loss or – (only one is used, never both).



Power vs Voltage Decibel (dB) ValuesPower vs Voltage Decibel (dB) ValuesdB Gain/LossdB Gain/Loss Gain Power RatioGain Power Ratio Loss Power RatioLoss Power Ratio Voltage GainVoltage Gain Voltage LossVoltage Loss

0 1.00 1.00 1.00 1.00

1 1.26 0.79 1.12 0.89

2 1.58 0.63 1.26 0.79

3 2.00 0.50 1.41 0.71

4 2.51 0.40 1.58 0.63

5 3.16 0.32 1.78 0.56

6 3.98 0.25 2.00 0.50

7 5.01 0.20 2.24 0.45

8 6.31 0.16 2.51 0.40

9 7.94 0.13 2.82 0.35

10 10.00 0.10 3.16 0.32

20 100.00 0.01 10.00 0.10

30 1000.00 0.001 31.62 0.03

40 10000.00 0.0001 100.00 0.01

50 100000.00 0.00001 316.23 0.003

60 1000000.00 0.000001 1000.00 0.001



• Special dB-based scales define a certain reference signal level as 0 dB (gain of 1) and compare all other signal levels to that defined point.

• If 0 dB is defined as a particular signal level, then one of the special scales can be defined.

• Such scales commonly used in electronics / networking are: dBm: Power ratio related to 1 mW dBW: Power ratio related to 1 W

Special dB-based ScalesSpecial dB-based Scales



Defining the dBm & dBWDefining the dBm & dBW• When we define an output power with respect to 1mW (1 x

10-3) we produce the dBm:

dBm = 10×log (P

1 mW) …( dBm )

dBW = 10×log (P

1 W) …( dBW )

P = 1 mW × 10 dBm /10 . . .(mW )

P = 1 W × 10dBW /10 . . .(W )

• When we define an output power with respect to 1W we produce the dBW:

• Both the dBm and the dBW are ABSOLUTE measures of power.

0 dBm = 1 mW 0 dBW = 1 W-3 dBm = 0.5 mW -3 dBW = 0.5 W+3 dBm = 2 mW +3 dBW = 2W



Adding the dB with dBm & dB with dBWAdding the dB with dBm & dB with dBW• Very importantly, we can add these logarithmic quantities

and work out an output power ‘absolutely’.• Example:

0.5 W x 2 W = 1 Wlogarithmically:

-3 dBW + 3 dBW = 0 dBW• Another Example:

Input Amplifier Attenuator Amplifier Output

+5 dB -9 dB x dB1mW(0dBm) 6 dBm

0 dBm + 5 dB – 9 dB + x dB = 6 dBm x = +10dB



Taking AntilogsTaking Antilogs

5 dBW = 10×log (Pout

1 W)+5dBW

• Example:

P out = 1 W × 105 /10 = 3. 16 W

−3 dBm = 10× log (Pout

1 mW)-3dBm

P out = 1 mW × 10−0 . 3 = 0 . 5 mW10−3/10=Pout

1 mW

• Another Example:

105/10=P out

1 W



• The fundamental building block of all communications systems is the sinusoidal waveform.

Sinusoidal WaveformsSinusoidal Waveforms



D: distancet: time

ν =Dt

…(m/ s )

f =1T

…(Hz )

ν =λT

…(m / s )

T =1f

…( s)

λ =νf

…(m)

f =νλ

…(Hz )

ν = λ× f …(m / s )

λ

• Periodic Time (T)

• Frequency (f)

• Velocity (v)

• Wavelength ( )

Characteristics of Sinusoidal WaveformsCharacteristics of Sinusoidal Waveforms• Displacement (d)• Amplitude Peak (Ap)• Amplitude Peak-to-Peak (Ap-p)



The Electromagnetic (EM) SpectrumThe Electromagnetic (EM) Spectrum• Electromagnetic Energy: The energy produced when an

electric charge vibrates.• Electromagnetic Spectrum: Wavelength continuum.• Velocity of EM Wave

in free space:3 x 108 m/s =300,000 km/s =186,283 miles/s



Signal VelocitySignal Velocity

ν coax =c

√ε r…(m /s )

c = speed of light = 3 x 108 m/s

• The velocity of a signal depends on the communications medium:

• Examples: Air: = 1 vair = 3 x 108 m/s

ν fibre =cn

…(m / s )

ε r

ε r

ε r

For a coaxial cable, on the dielectric constant ( ) of the insulator:

For an optical fibre, on the refractive index (n) of the glass core:

Fibre: n = 1.46 (glass) vfibre = 2.055 x 108 m/s

Coaxial Cable: = 2.25 (polythene)vcoax = 2 x 108 m/s



• Signals attenuate (weaken) as they travel away from the source.

• They arrive with less strength than when they started.• All transmission media weaken, or attenuate, the strength of

the signal.

Signal AttenuationSignal Attenuation

λ λ λ



• Attenuation is a measure of how much loss a signal experiences when it travels down a communications medium. All transmission media weaken, or attenuate, the

strength of the signal. As the signal travels down the medium part of the signal

is dispersed as heat or absorbed by the transmission medium.

The longer the distance that the signal travels, the greater will be the attenuation that the signal suffers.

If the medium is too long, no signal will arrive at the end, or the signal will be so small that cannot be used (buried in noise).

Signal Attenuation (…2)Signal Attenuation (…2)



α = 20×log (V out

V in) …(dB )

α = 20×log (I outI in

) …(dB )

Vout = Signal amplitude at output

in Volts (Voltage)Vin = Signal amplitude at input

in Volts (Voltage)Iout = Signal amplitude at output

in Amperes (Current)Iin = Signal amplitude at input

in Amperes (Current)

• Attenuation is measured in decibels (dB).


If half the signal voltage or current is lost by the time it reaches the destination then it has suffered a 6 dB loss.




α = 10×log (Pout

P in) …( dB ) Pout = Signal amplitude at output

in Watts (Power)Pin = Signal amplitude at input

in Watts (Power) If half the signal power is lost by the time it reaches the

destination then it has suffered a 3 dB loss.



Power BudgetPower Budget• The summation of all gains and losses within a system to

determine the overall system output power.• Consider the following communications link:

Cables(attenuate)

InitialPower

Amplifier

Source

Receiver

Amplifier

Final Power(Amplification)



Power Budget ExamplePower Budget Example

Amplifier20 dB

ReceiverAmplifier

30 dB

Cablel2 = 30 kmCable

l1 = 45 km Cablel3 = 35 km

InitialPower

Pin = 15 dBmSource

ReceiverAmplificationPout = 75 dB

• To find the power budget for the system above simply add the gains and subtract the losses:

System Power Output =+ 15 dBm – 22.5 dB + 20 dB – 15 dB + 30 dB – 17.5 dB + 75

dB == 85 dB

Cable Attenuationα = 0.5 dB/km



Noise in Analogue SignalsNoise in Analogue Signals• Noise: A usually interferential random frequency current or

voltage signal extending over a considerable frequency spectrum and having no useful purpose.

• Noise Level: The amplitude of ambient electrical noise generated inside or outside an electronic circuit.

• Signal to Noise Ratio: The ratio of signal amplitude to noise amplitude.

Measured in decibels (dB).



• If the transmitting electronics are not properly shielded then signals of other frequency could be superimposed on the signal of interest. This will also be a form of noise.

• Noise added to the analogue signal can greatly affect the accuracy of the information.

• Noise is always unwanted and efforts are always taken to minimise its effect but limiting the level of noise is not an easy or inexpensive process.

Noise in Analogue Signals (…2)Noise in Analogue Signals (…2)



Types of NoiseTypes of Noise• White Noise: Random noise (acoustic or electric) distributed

equally over a given frequency band. Example: the noise resulting from the random motion of

free electrons in conductors and semiconductors.• Pink Noise: Electrical noise whose amplitude is inversely

proportional to frequency in a limited frequency spectrum.• Shot Noise: Caused by random fluctuations in the motion of

charge carriers in a conductor.• Thermal (Johnson) Noise: Any form of noise generated within

a circuit and depends on temperature. Electrical noise caused by the agitation of electrons in a

material due to heat. Frequency independent.



Signal to Noise Ratio (SNR)Signal to Noise Ratio (SNR)• Signal to Noise Ratio: The ratio of signal amplitude to noise

amplitude.

SN

= 20×log (V S

V N) …(dB )

SN

= 10×log (P S

P N) …( dB )

VS = Signal amplitude in Volts (Voltage)

VN = Noise amplitude in Volts (Voltage)

PS = Signal amplitude in Watts (Power)

PN = Noise amplitude in Watts (Power)

SN

= 20×log (I SI N

) …(dB )IS = Signal amplitude in Amperes

(Current)IN = Noise amplitude in Amperes

(Current)



• A collection of sinusoidal waveforms can compose any practical signal no matter how complex it may be.

• All periodic waveforms can be built up from a series of pure sinusoidal waveforms of distinct but related frequencies.

• These related frequencies are: Fundamental frequency (the frequency of interest). Harmonics (integer multiples of the fundamental

frequency).• The production of such complex periodic waveforms requires

electronic circuitry whose bandwidth (BW) is large enough to accommodate the range covering all frequencies involved, i.e. from the lowest to the highest.

Periodic WaveformsPeriodic Waveforms



Example of a Complex Periodic WaveformExample of a Complex Periodic Waveform



Bandwidth (BW)Bandwidth (BW)• The range of frequencies that …:

… can be carried across a given transmission medium. … a telecommunications system is able to support.

• Examples of Bandwidth: Telephone Voice Channel: BW = 3 kHz, Hi-Fi Music: BW = 15 kHz, CD Stereo Player: BW = 22 kHz, AM Radio Station: BW = 10 kHz FM Radio Station: BW = 200 kHz, TV Channel on CATV: BW = 6 MHz.



SummarySummary• Overviewed and Defined Signals.• The fundamental building block of all communications

systems is the sinusoidal waveform.• Sinusoidal Waveform Characteristics: Amplitude,

Frequency, Period, Wavelength, Velocity.• Periodic Waveforms: A collection of sinusoidal waveforms

can compose any practical signal no matter how complex it may be.

• Bandwidth: the range of frequencies of a system.• Electro-Magnetic Spectrum.• Signal Attenuation: the weakening of signals.• Noise in Analogue Signals and Types of Noise. Noise is

always unwanted and efforts are always taken to minimise its effect.

Slides By: Dr. N. Ioannides (Feb. 2010)CT1037NI - L.02 - Analogue Signal Characteristics - pp 1/43...

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