Noise basics and its modelling

03/05/2023 IEC 503 ANALOG COMMUNICATION SYSTEM BY DR N R KIDWAI, INTEGRAL UNIVERSITY 1

Noise


What is noise? In electrical terms, it is an unwanted signal, which interfere with the desired signal.

Example: In radio receiver: ‘Hiss’ sound from speakerIn TV: ‘Snow’ or ‘confetti’(colored snow) display on the picture.

Drawback of Noiseo For a given transmitted power ,it limit the range of systems

o It affects the Sensitivity of receivers

o Sometimes Force reduction in bandwidth of the system


Sources of NoiseExternal Noise : Noise created outside the receiver Internal Noise : Noise created inside the receiver

Source of External Noise: • Atmospheric Noise• Extraterrestrial Noise

• Solar Noise• Cosmic Noise

• Industrial Noise

Source of Internal Noise: • Thermal Agitation Noise or Johnson Noise• Shot Noise• Transit Time Noise


. Atmospheric Noise or Static noise

caused by lighting discharges in thunderstorms,

the electrical impulses are random in nature and spread over most of the RF spectrum used in broadcasting.

Atmospheric Noise consists of false radio signals and distributed over wide range of frequencies.

It is propagated over the earth and at any point on the ground atmospheric noise will be received from the thunderstorms.

Since Field strength is inversely proportional to frequency , so this Noise will interfere more with radio receiver then the television.

Atmospheric noise is less severe above about 30 MHz.


Extraterrestrial Noise or Space Noise caused by radiation of RF noise by sun and distant stars.

Sun is a large body at a very high temperature over 6000 0C on the surface) and Radiates over a very broad frequency spectrum which includes the frequencies we Use for communication.

Distant stars are also suns and have high temperatures, they radiate RF noise in the same manner as our sun .

The noise received is called thermal (or black-body ) noise and is distributed uniformly over the entire sky.

This noise is observable at frequencies in the range from about 8 MHz to 1.43 GHz


Industrial NoiseThis noise is effective in industrial and densely populated area

Source of industrial noise are

1.Automobile and aircraft ignition

2.Leakage from high voltage lines

3.Heavy electric machines

4.Fluorescent light ,etc

This noise is observable at frequencies in the range from 1MHz to 600 MHz


Internal Noise Created by the active or passive devices present in the receiver Distributed randomly over the entire radio spectrum Impossible to treat instantaneous voltage basis ,in place of that it is easily describe statistically.

Source of Internal Noise

1.Thermal,agitation,white or Johnson noise

2. Shot Noise

3.Transit-Time Noise


Thermal agitation or white or Johnson noise

• Randomly distributed over the bandwidth• Generated in resistance or the resistive component• Generated due to the random motion of atoms and electrons inside the components• Noise generated by the resistor is proportional to its absolute temperature and bandwidth • Noise power output from a resistor,

Pn = KTf Here K = Boltzmann constant = 1.38X10-23J/k, T= 0A,

B=bandwidth of interestQuestion: If the resistor is operating at 27oc and the bandwidth of interest is 2 MHz, then what is the maximum noise power output of a resistor ? Ans 0.0828X10-12 Watts


Noise Voltage across resistor R Maximum power transfer will happen when R= Ri

Then noise power at the input of next stage is i.e equivalent rms noise voltage, Similarily, equivalent rms noise voltage, where conductance

RRnoiseless

Vn

R(noiseless)

Vn

RiVn/2 R Rnoiseless

In

R(noiseless)

Vn

RiVn/2 R Rnoiseless

In


Noise Voltage across resistor R Question : An amplifier operating over the frequency range from 18 to 20 MHz has a 10-Kiloohm input resistor. What is the rms noise voltage at the input to this amplifier if the ambient temperature is 27oC? Ans K= 1.38 x 10-23J/0K, T= 27oC = 300oK, B= (20-18) MHz = 2 x 106Hz, R= 10x 103Vn = (4KTf R)

= (4 x 1.38 x 10-23 x 300 x 2 x 106x 10x103 ) = (331.2x10-12)

= 18.2x10-6 V =18.2 V

IEC 503 ANALOG COMMUNICATION SYSTEM BY DR N R KIDWAI, INTEGRAL UNIVERSITY 11

Noise rms Voltage: resistance in series/ parallel

03/05/2023


Reactance and Equivalent noise bandwidthInductance and capacitance do not generate noise

Let us assume that capacitance C1 generate noise power P1 while capacitance C2 generate noise power P2

then according to thermal equilibrium, power generated must be equal to power consumed.

As reactance do not consume power, so

P1 = P2 =0 i.e reactance do not generate noise, instead it limits the noise power.

C1 C2P2P1


Reactance and Equivalent noise bandwidth

Frequency response Output noise spectral density As =KT

Considering only positive frequencies, noise power at the output

Effective bandwidthNoise voltage


Reactance and Equivalent noise bandwidth: Tuned circuit

Resonant frequency Quality factor = Where dynamic resistance =

Noise power at the output

Thus effective bandwidth 3 dB bandwidth


Example

Ex. A 100 K resistance is connected in parallel with 1 pf capacitor at room temperature (27 0C). Calculate effective bandwidth and equivalent noise voltage at the output. Sol:Effective bandwidthNoise voltage


Example

Ex. A 10 K resistance is connected in RLC circuit of pass band 10 KHz, tuned at 1 MHz frequency. Calculate the dynamic resistance of the circuit, equivalent noise voltage at the output across the capacitor. Also calculate effective bandwidth at room temperature (27 0C). Capacitance used is 10 pf. Sol:Quality factor dynamic resistance =Noise voltage Thus effective bandwidth 3 dB bandwidth


Addition of noise due to amplifier in cascade

The output resistance is R3, the noise voltage The noise voltage at the output will be same if R3 is assumed to be noiseless and a equivalent noisy resistance is placed at the input of second stage, such that i.e Now total noise voltage at the input of second amplifier will be generated by equivalent resistance such that Similarly equivalent noise voltage at the output of first amplifier can be replaced by a noise voltage generated at the input of first amplifier such that The total noise voltage at the input will be generated by equivalent resistance such that Equivalent noise voltage at the input ( assuming all resistances as noiseless) R1

Vn1

R2

Vn2

R3

Vn3

Amplifier gain A1

Amplifier gain A2


Addition of noise due to amplifier in cascade

• It is important to note that high resistance at the output R3 have noise effect equal to a low resistance • Equivalent noise resistance Req is fictitious resistance, which generates total equivalent noise power at the input

of the device at room temperature while device is assumed to be noiseless. Req is fictitious resistance and does not contribute to the input impedance of the device and is used for noise calculations only.

Ex. Two amplifiers of voltage gain 10 and 15 are cascaded and applied to a load resistance of 1 M. A 100 resistance is applied to input of a first stage, while 200 resistance is connected to the input of second stage. Calculate equivalent noise resistance at the input. At room temperature (27 0C) calculate equivalent noise voltage at the input for measuring bandwidth of 100 KHz. What is equivalent noise resistance of load resistance at the inputSol:Equivalent noise resistance Req = R1+ + =100+ += 100+2 + = 146.44 Equivalent noise voltage = = 492.45 nVEquivalent load resistance at the input = = 44.44


Shot noise

• Shot noise is present in all active devices• Caused due to random arrival of charge carriers.• For diode shot noise is given as rms noise current Where is diode current in amperes, is charge of electron, is bandwidth of measurement• Equivalent noise resistance of shot noise is generally quoted in manufacturer

datasheet


Signal to noise ratio (SNR)

• Noise power alone is not sufficient for analysing noise performance of any system

• SNR is unit less quantity and is usually measured in dBEx. A 10 mV rms voltage is applied to 10 K noisy resistor at 27 0C. Calculate SNRdB of the resistor of measuring bandwidth is 10 MHz.Sol:Signal power Noise power pWSNR=241545.89Now


Noise figure

• Noise figure provides a measure of noise performance of receivers and amplifiers• = Where A is voltage gain of amplifier, Si signal power at the input,So signal power at the output,Ni noise power at the input,No noise power at the input,• A practical receiver adds noise power. So its noise figure is always greater than 1• For ideal recover (which does nor add noise) noise figure is 1


Calculation of Noise figure from equivalent resistance

• Receiver is fed from antenna of resistance Ra. It feeds signal Vs and generate noise Vn1.

• Receiver has input impedance Ri , Voltage gain A and output is taken at load RL.

• Equivalent noise resistance of amplifier is Req. • Let us define such that Signal input to amplifier Signal power at input of amplifier Signal power at output of amplifier

Ra

Vn1

Ri RL

Vs

VoVi

Antenna Amplifier with voltage gain A


Calculation of Noise figure from equivalent resistanceNoise at the input is due to antenna resistance and internal resistance of amplifier which are in parallelNoise power at the input of amplifier Output noise power is sum of noise generated at input and added by amplifier itself i.e output noise power will be due to equivalent noise resistance at input Noise voltage at the output Output noise power Noise figure Under matched conditions () ,


Calculation of Noise figure from equivalent resistance

Ex. Two receivers has input impedance and equivalent noise resistance as (50 and 100 ) and (250 and 100 ) respectively. Calculate the noise figure of both receivers if it is fed by an antenna of 50 impedance.

Sol. noise figure For first receiver , noise figure For second receiver , noise figure • Noise contribution at input is same in both amplifiers as their noise equivalent resistance are same.• Input impedance of Amplifier 2 is higher than Amplifier 1, it appears more noise will be generated

at input of amplifier 2.• From the noise figure it is evident that noise performance of amplifier 2 is better than amplifier 1.


Amplifier Input noise in terms of noise figure=

Total noise power at the output, Total Noise power at the input Contribution of amplifier in noise power at the input (so that amplifier can be assumed noiseless)


Amplifiers in cascadeNoise power fed from the source at the inputEquivalent noise power contributed by amplifier 2 at its input (assuming amplifier 2 noiseless) Total noise power at the input of second amplifier is sum of noise contributed by second amplifier and noise at the out put of first amplifier,

Total Noise power at the input of first amplifier

If F is the overall noise figurei.e. In general, Friss equation ++ ------ Amplifier

gain A2

Noise figure F2

Amplifier gain A1

Noise figure F1

Rs

Vn

Source

NfNoNi


Amplifiers in cascadeEx. Three amplifiers of voltage gain 10,20,40 and noise figure 2, 5, 20 are cascaded. Find overall noise figure. What is contribution of amplifier in input noise if measuring bandwidth is 10 KHz (room temperature is 300 0K), Calculate the noise figure if sequence of cascading is reversed. Sol:Noise figure +

Equivalent noise power contributed by amplifiers to its input (assuming amplifiers noiseless) Noise figure for reversed order cascadingNoise figure


Experimental determination of Noise figureR

Vn

In

Equivalent circuit for noise source generating shot noise

Noise generating

source

Amplifier gain ANoise

figure F

AC Wattmeter

Shot noise power Noise generating diode is applied to a resistance usually matched to input of amplifierThen as per maximum power transfer theorem, noise power at the input of amplifier

Noise power at the output due to amplifier itself,


Experimental determination of Noise figureTotal noise power at the output Let where Q is a constantThen Or Or or When the source does not generate noise and in the output noise is due to amplifier itself. Then is increased such that output noise power doubles i.e. Q=2Let T= 3000CSo


Equivalent noise temperatureNoise associated with the amplifier at the input can be represented by equivalent noise temperature such that

i.e. Noise equivalent temperature is an alternative of noise figure

In general, Friss equation ++ ------


White noiseIdealized form of noise which is independent of frequencyPower spectral density where =KT

𝜂2

𝑅𝑛 (𝜏 )

𝜏Auto correlation of white noisef

𝜂2

𝑆𝑤 ( 𝑓 )

Power spectral density function of white noise

Noise basics and its modelling

Engineering

Transcript of Noise basics and its modelling