the city university of new york...

D. Mynbaev, EET 2140 Module 11, Spring 2008 1

NEW YORK CITY COLLEGE of TECHNOLOGYTHE CITY UNIVERSITY OF NEW YORK

DEPARTMENT OF ELECTRICAL ENGINEERING AND

TELECOMMUNICATIONS TECHNOLOGIES

Course : EET 2140 Communications ElectronicsModule 11: Noise

Prepared by: Dr. Djafar K. Mynbaev

Spring 2008


Module 11: Noise.• Introduction

– Review of Quiz # 5 (AM).

– Term project third report is due next week.

• Noise:

– Two meanings: interference and the result

– Definition, sources and classification

– External noise

– Internal noise: thermal, shot and flicker

– Power spectral density

– Signal-to-noise ratio and Shannon’s theorem

– Noise figure and noise ratio

Key words

• Noise

• Noise sources

• External noise

• Internal noise: thermal,

shot and flicker

• Power spectral density

• Signal-to-noise ratio

• Shannon’s theorem

• Noise figure and noise

ratio


Noise is the stream of an unwanted energy that interferes

with the useful signal. This interference of a transmitting signal by

an external signal (noise!) causes a signal disturbance. We also refer

to noise as to the result of such an interference, that is, the signal

distortion itself.

Examples of noise: 1. Voices of other people as you are talking to someone in the

same room. 2. Disturbances of a radio signal by lightening during a thunderstorm,

which is the example everybody is familiar with. 3. White flecks seen on a

television picture. (Find more examples for yourself.)

Therefore, the term noise, as used in telecommunications, is defined

in two ways: (1) It’s the interference of a transmitting signal by an

external signal causing a signal disturbance and (2) it’s the result of a

signal disturbance, that is a signal distortion.

Remember, this term applies to any type of signal disturbance, not

just to voice or video transmission.

Noise - introduction


Tx Rx

Information Information

Transmitter ReceiverTransmission link

External

source

Interference

(noise)


Transmitted signal + Noise = Received signal

Eye Diagram after 160 Km on SM fiber

x10-10

Time (s)

0 1 2

x10-6

Sig

na

l (A

)

0

1

2

3

4


x10-10

Time (s)

0 1 2

x10-5

Sig

na

l (A

)

0

1

2

3

Eye Diagram after 1Km on SM fiber

x10-10

Time (s)

0 1 2

Sig

na

l (A

)

0.006

0.008

0.010

0.012

0.014

+ =



x10-10

Time (s)

0 1 2

x10-5

Sig

na

l (A

)

0

1

2

3


x10-10

Time (s)

0 1 2

x10-6

Sig

na

l (A

)

0

1

2

3

4


x10-10

Time (s)

0 1 2

x10-4

Sig

na

l (A

)

1

2

3

Eye Diagram after 1Km on SM fiber

x10-10

Time (s)

0 1 2

Sig

na

l (A

)

0.006

0.008

0.010

0.012

0.014

Transmitted signal

Received signals

Signal power is

more than noise

power


Noise puts the limit on the minimum

power of received signals. Below this

limit, correct information cannot be

extracted from a received signal.

Signal power is

comparable with

noise power

Signal power is

less than noise

power


A harmful signal (noise!) that disturbs the information signal

originates from two different sources:

1. An external to a transmission system source, such as natural or

man-made source.

2. Internal sources such as electronic circuits and devices that

themselves make up the transmission system.

This is why we distinguish between external and internal noise.

Noise – external and internal


Noise

External noise Internal noise

Tx Rx


Transmitter Receiver

Transmission link

External

source

Interference (noise)

noise


Transmitter ReceiverTransmission link

noisenoise

Noise – external and internal


External noise: a primer Everybody knows that lightning results in the

disturbance of radio transmission, which we hear as noise. Also, lightning generates

noise in voice transmission when you use a cordless or cellular phone. Why?

Lightning produces powerful electrical signals that interfere with radio, or wireless,

voice transmission. From the early days of radio, the term noise has been used to

describe any interference with a transmitting signal that results in signal distortion.

Lightning is just one source of stray electrical signals. Other natural sources of such

disturbances can be found in outer space: the Sun and other cosmic objects generate

electrical signals that may interfere with a signal being transmitted.

The main sources of interfering signals, however, are not natural but man-made. For

example, signals radiated by radio and TV stations interfere with other signals being

transmitted. The electrical motors in elevator systems and even the electronic

equipment in your college’s science laboratory generate their own interfering signals.

You can no doubt come up with your own list of troublesome sources. All you need

do is look around you. Noise originating from manufactured equipment is truly a

problem in transmission. This is because these sources are close to transmission lines

and their signals can therefore distort transmitting signals significantly. In addition,

most of these sources are in continuous operation and, as a result, generate noise

without letup.


Transmission

Mag

nit

ude

(V)

Mag

nit

ude

(V)

Mag

nit

ude

(V)

Mag

nit

ude

(V)

Time (s)

Time (s) Time (s)

Time (s)

Transmission

1 1 10 0 0 1 0 1 1 0 0

External

source

Interference

(noise)

Interference(noise)

External noise distorts both analog and digital signal in transmission.

Noise – external


External noise can be theoretically eliminated by a careful design,

for instance, by screening of a device or link. Examples of screening

include coaxial cable and metallic case of any measuring devices, such as

oscilloscopes, function generators, etc.

Another means to struggle with noise is turning to digital rather

than analog transmission.

An external source generates electromagnetic waves that interfere

with an analog signal being transmitted; the result is that an analog signal

arriving at the receiver end is distorted. The same is true for a digital

signal. However, digital signal is being distorted during the transmission

in the same way as an analog but it still delivers correct information.

This is because of in analog transmission, any change in signal

parameters causes errors. In contrast to analog transmission, digital

transmission allows for signal distortion within specific margins still

preserving the correct meaning of the information being delivered.

Noise – external


Noise –internal

IshotIthermal IflickerPD

RjCin

R2

Rload

Internal noise is generated by electronic circuits themselves. These

circuits include passive (conductors and resistors) and active (diodes, transistors,

ICs, and vacuum tubes) devices. Ideal reactive components (L and C) do not

generate noise. In contrast to external noise, the internal noise cannot be simply

eliminated by system design . However, careful circuit design helps to reduce

internal noise essentially.

The above circuit shows that a photodiode itself, which is the front-end element of a

receiver in a fiber-optic communications system, generates different types of noise. Don’t forget that

the input signal that enters a photodiode is weak and distorted by external noise. Thus, distortions

caused by external and internal noises will be added at the photodiode output.

Generalized equivalent circuit of a photodiode (PD) that includes ideal PD and

sources of internal noise (thermal, shot and flicker) [2].


We distinguish among three main types of internal noise: thermal, shot and flicker.

Thermal noise: The deviations of an instantaneous number of electrons

from their average value because of temperature change is called thermal noise [5].

Thus, any conductor, including resistors and semiconductor devices, are the sources

of thermal noise. Thermal noise is also referred to as Johnson or white noise.

The physical cause of thermal noise is as follows: Flowing electrons (that constitute current) interact with

lattice atoms of a conductor material. This interaction results in variation of an instantaneous value of

electrons crossing a given cross section of the conductor, that is, in variation of instantaneous value of

current (or voltage). The higher the temperature the more motion of lattice atoms, which impedes the

electron flow and increases variation of instantaneous number of electrons. Therefore, thermal noise (1) is

a random process by its very nature and (2) it will increase with the increase of temperature.

Internal noise - thermal

Time (s)

Instantaneous

noise voltage

Instantaneous voltage of thermal noise [4].


The average power of thermal noise, Pth, is given by

Pth (W) = k T BW,

where k = 1.38 x 10-23 (W/(K•Hz) or (J/K) is the Boltzmann’s constant; T is

absolute temperature in kelvins, K [T (K) = 2730C + X0C];BW is the bandwidth in

which the measurement is made (Hz) [3].

This kind of noise is called “thermal noise” because its average power depends on

temperature; i.e., Pth (W) is directly proportional to T. Note that the thermal noise

power is independent of resistance.

Example:

Problem: What is the noise power generated by a resistor at room temperature

(270C) if BW = 1 MHz? At 600C?

Solution: Pth = k T BW = 1.38 x 10-23 (W/(K•Hz) x (273 + 27) (K) x 106 (Hz) =

0.0041 x 10-12 W = 0.0041 pW. This is indeed a very small power. At 600C we

obtain Pth = 0.0046 pW.

Note: Room temperature is usually considered as 170C. Manufacturers of electronic devices use 250C

as a reference point. In calculations of noise parameters, it is customary to use 270C to obtain 300 K.




In general, P = E2/R. Thus, we could measure noise voltage across a

resistor. A resistor as a generator of thermal noise can be represented by the

following equivalent circuit. En is noise generator, R is the ideal resistance and

Rload is a load resistor. If R = Rload, then En will split equally between R and Road.

Therefore,

PR = (En/2)2/R = kTBW and En2/4 = kTBWR

and the rms noise voltage measured across the resistor R is equal to:

En = √(4kTBWR)

En/2

En

R

Rload


If we refer to the graph of instantaneous noise voltage shown above, we can easily see

that the average noise voltage across the conductor is zero. However, the rms (root-

mean-square) value is finite and can be calculated, as shown above, and measured.

You will recall the concept of rms value: Erms = √(area (e2(t))/period).

(Remind yourself about a cosine wave and its rms value.)

Example: Problem: What is the noise voltage generated by a 1-kΩ resistor at room

temperature (270C) if BW = 1 MHz?

Solution: En = √(4kTBWR) = √ (4 x 1.38 x 10-23 (W/(K•Hz) x (300) (K) x 106 (Hz) x

103 (Ω)) = 4.1 x 10-6 V = 4.1 µV. This is not a large value; however, this voltage is quite

measurable and comparable with the rms voltage of received signals.

Time (s)

Instantaneous

noise voltage,

e(t)

Instantaneous voltage of thermal noise [4].




There is the other important parameter describing noise: power spectral density, S(f),

which is equal to average noise power divided by bandwidth, Pnoise/BW (W/Hz).

Power spectral density of thermal noise is equal to:

Sth(f) = Pth/BW = k T (W/Hz)

When refer to mean-square voltage, spectral density is given by

Sth(f) = E2/BW (V2 /Hz) = 4 k T R (V2/Hz),

where R (Ώ) is a resistor on which the noise power is dissipated. Note that spectral

density of thermal noise doesn’t depend on frequency (bandwidth). Observe the units

of Sth(f) in both cases. In electronics we mostly use V2/Hz. or A2/Hz.

Example (See Example 4-2, Part 1, Page 121,

[3].) Problem: What is the spectral density of

thermal noise generated by a 20-kΩ resistor at

room temperature (270C)?

Solution: Sth(f) =En2/BW = 4kTR = 4 x (1.38

x 10-23 (W/(K•Hz) x (300) (K) x 20 x 103 (Ω)

= 3.312 x 10-16 V2/Hz.

Sth(f) (V2/Hz)

f (Hz)


Shot noise: Deviation of the actual number of generated

electrons from the average number is known as shot noise [5]. Shot

noise is generated by active devices such as diodes, transistors, ICs, and

vacuum tubes. Shot noise is “rain on a tin roof.” (See [7].)

The physical cause of shot noise is simply the finiteness of the charge quantum, which

results in statistical fluctuation of the current. For example, a 1-A dc current actually

has 57-nA rms fluctuations measured in 10-kHz bandwidth, which means this current

fluctuates by approximately 0.000006% [7]. The shot noise model assumes that charge

carriers making up the current act independently as they cross a potential barrier (p-n

junction). Therefore, shot noise (1) is a random process by its very nature, (2) it will

increase with the increase of the bias current and (3) it is flat over frequency spectrum,

that is, it is white like thermal noise.

Internal noise - shot

Time

Current

Idc

Shot noise [4]


The shot-noise power, Psn, in semiconductor components is proportional to dc

bias current (except of MOSFET devices [1]), that is, Psn ~ Idc.

Specifically, shot-noise power represented by the square of rms value of average

noise current, Isn, is given by ([3], Formula 4-3, Page 118)

I2sn = 2 q Idc BW,

where q = 1.6 x 10-19 (Coulombs) is the charge of an electron, Idc – bias current

in amperes, BW – the bandwidth in which the measurement is made (Hz).

Example (See [3], Example 4-1, Page 118.)

Problem: Determine the rms value of noise current for a diode with Idc = 1 mA

measured in 10-MHz bandwidth.

Solution: Isn = √(2 q Idc BW) = √(2 x 1.6 x 10-19 (C) x 1 x 10-3 (A) x 10 x 106

(Hz)) = 56.6 x 10-9 A = 56.6 nA.



Spectral density of shot noise is given by:

Ssn(f) = Psn/BW

Applying this formula to the equation describing the

shot-noise current, we obtain:

Ssn(f) = I2sn/BW = 2 q Idc,

which clearly shows that shot-noise spectral density is

flat over frequency (white noise).


Ssn(f) (A2/Hz)

f (Hz)

Example (See [3], Example 4-2, Part 2, Page 121.) Problem: Determine

the spectral density of noise generated by a silicon diode if Vcc = 10V

and R = 20-kΩ .

Solution: Thermal noise plays almost no role here since resistance of a

forward-biased diode is few ohms only.

Spectral density of shot noise is given by Ssn(f) = I2sn/BW = 2 q Idc.

Plugging the given numbers, we obtain I dc = (Vcc – 0.7V)/R = (10 –

0.7) V/ 20 kΩ = 0.465 mA.

Ssn(f) = 2 q Idc = (2 x 1.6 x 10-19 (C ) x 0.465 (mA) = 1.488 x 10-22

(A2/Hz).

R

20kohm

D

Silicon

10V

VCC


Thermal and shot noises are generated by electronic components according to

physical principles. We cannot reduce these noises by design or better manufacturing the

devices and conductors. In addition, real devices are the sources of “excess noise.” This noise is

caused by imperfections in electronic devices such as fluctuations in resistance of resistors and

bias current in transistors. Despite the variety of sources, this noise is always inversely

proportional to frequency. Its essential power is concentrated in low-frequency (< 1 kHz

typically) range. This excess noise is also refer to as flicker or pink or 1/f noise.

Internal noise - flicker

The flicker-noise power is proportional to bias current and

decreases with frequency. There is no precise formula for noise

power since this noise is a device-specific [1]. However, if we

represent the noise power by square of rms average value of the

current in the device, Irms2, then the general formula is given by

[6]:

Irms2 = (k Im BW)/fn,

where I is the current in the device, k – constant (specific for a

particular device), BW – bandwidth and f –frequency, m

(between 0.5 and 2) and n (near 1) are the coefficients. Power

spectral density of flicker noise, Sfl(f), is given by:

Sfl(f) = Pfl/BW = (k Im )/fn 1/f

S(f) (V2/Hz)

f (Hz)


Internal noise – spectral density

S(f) (V2/Hz)

f (Hz)

1/f noise

White noise

(thermal and shot)

General noise spectrum ([1] and [6]).

Transit-time

noise

fC ≈ 1kHz fhC

Legend: fC – critical frequency (≈ 1kHz), fhC - high-frequency cutoff (device specific)

The power of flicker noise is concentrated at lower frequencies; its spectral density is

inversely proportional to frequency as 1/f. The power of white noise is spread

uniformly across the spectrum (theoretically, from 0 to infinity). At high frequencies

the power of noise rises again because of transit-time effect (when transit time of

charge carriers crossing p-n junction becomes comparable to the signal period [1]).

White noise


How we can reduce the harmful effect of noise? We can filter it.

Filtering the noise

Band-pass filter can increase

signal-to-noise ratio in a specific

band. Generally, signal-to-noise power ratio is

taken across the entire bandwidth (from

zero to infinity). Using a band-pass filter,

we can reject the most harmful noise

components, such as flicker noise, and

improve S/N within a specific band..

High-pass filter can filter flicker

(1/f) noise.

S(f) (V2/Hz)

f (Hz) fC passed

S(f) (V2/Hz)

f (Hz) fC

1/f noise dominant

passedrejected

High-pass filter


Spectral density - more

As you noticed, noise power depends on

frequency; that is, noise power can be

different over the different bands of a

spectrum. This is why we introduced

power spectral density. Power spectral

density of a signal, S(f), is the average

power carried by the signal in a one-hertz

bandwidth around frequency f. Small

rectangle at the right figure represents S(f1)

at frequency f1. The entire graph of S(f) is

built with the sequence of these rectangles.

It is the power of a signal (noise) per unit frequency:

S(f) = P/BW (W/Hz) or S(f) = E2/BW (V2 /Hz) or S(f) = I2/BW (A2 /Hz),

where E (I) is the noise rms magnitude in volts (amperes). Here we can represent power in

V2 (I2) because we can disregard the resistor. What’s more, we usually don’t need to refer to a resistor

because we are interested in power ratio of signal and noise signals; thus, resistor value will be

cancelled.

S(f) (V2/Hz)

f (Hz)

S(f1)

f1

1 Hz



Why do we need spectral density? To

compute noise power. Elementary power δP1

concentrated in δf1 bandwidth around

frequency f1 is equal to the area of the

shadowed rectangle, that is, δP1 = δf1 x S(f1).

If we add all these rectangles δP1 + δP2 +

δP3 +…, we obtain approximate total area

under the curve S(f), which is noise power.

In other words, P ≈ ∑ δPi .

To accurately compute the noise power, we

need to decrease δfi and move to integration

(rather than summation) of elementary

powers δPi . Thus,

Pnoise (W) = ∫ δP = ∫ S(f) df

We can simplify our consideration by introducing the

average noise power, Pnoise. Then, power spectral

density, S(f) can be defined as

S(f) = Pnoise/BW (V2/Hz).

This is the formula we used in our previous discussion.

S(f) (V2/Hz)

f (Hz) f1 f2

δP1

δP2

S(f1)

δf1


Noise spectrum:

As we distinguish between two main types of noise: white noise and flicker

(“pink”) noise, we can conclude that the power of white noise is spread uniformly

across the spectrum (theoretically, from 0 to infinity) while the power of flicker

noise is concentrated at lower frequencies, so that its average power is inversely

proportional to frequency as 1/f.

S(f) (V2/Hz)

f (Hz)

S(f) (V2/Hz)

f (Hz)

White noise Flicker (1/f) noise

Spectral density and noise power



x10-10

Time (s)

0 1 2

x10-6

Sig

na

l (A

)

0

1

2

3

4

f (Hz)

A(V)

1 Hz

f 1

Square the output

obtain E2 (V2).

Calculate the average

power over long time

obtain S(f1).

Repeat these measurements

for filters with different

central frequencies

Obtain S(f) (V2/Hz)Noise waveform Band-pass filter with center

frequency f1 and a 1-Hz

bandwidth

Measurement and calculation of power spectral density [6].



Signal-to-noise ratio

Why do we need to know noise power? To calculate signal-to-noise power ratio.

We need to understand that the quality of received signal is determined by the ratio

of signal power to noise power and not by the noise itself. (Refer to Slide 5.) This

ratio is called signal-to-noise ratio, S/N or SNR:

S/N = Signal power ((W)/Noise power (W)

As any ratio in communications, we commonly express it in decibels:

S/N (dB) = 10 log10(Signal power ((W)/Noise power (W)).

Now we can appreciate why we represented signal power through E2 (V2) or I2 (A2).

Since in reality we are interested in signal-to-noise power ratio, we always can

neglect the value of a resistor across which the both power are dissipated.

Example: Problems: 1. Signal power is 1 W and noise power is 1 µW. What is S/N?

2. The output of an amplifier is 1 mV and the noise is 0.465 mV. What is S/N?

Solutions: 1. Using the definitions, we obtain: S/N = Signal power (W)/Noise power (W) = 1 (W)/1x10-6

(W) = 106. And S/N (dB) = 10 log (106) = 60 dB.

2. S/N = (Vsig2/R)/(Vnoise2/R) = (Vsig2)/(Vnoise2) = 4.62 or 10log(4.62) = 6.65 dB. Another way to

solve this problem is using the dB formula for voltages: S/N (dB) = 20 log (Vsig/Vnoise). Indeed, S/N =

20 log (1/0.465) = 20 log 2.15 = 6.65 dB.


The real importance of signal-to-noise ratio can be revealed by examining

the Shannon’s theorem:

C = BW log2 (1 + S/N),

where C (bit/s) is the channel capacity, which is the maximum transmission speed a

channel can support; BW is the channel bandwidth and S/N is the signal-to-noise

ratio.

Example: Problem: The bandwidth of a telephone line is equal to 4 kHz. What is the capacity of this

channel if S/N is equal to 1000? 10,000?

Solution: Applying the Shannon’s formula, we obtain:

C = BW log2 (1 +S/N) = 4 x 103 (1/s) log2 (1001)

Since most calculators operate with a base-10 logarithm, we convert the base-2 logarithm as follows:

log2 N = log10 N/log10 2 = 3.32 log10 N.

Thus, we compute: C = 4 x 103 x 3.32 log10 (1001) = 4 x 103 x 3.32 x 3.0 = 39.8 x 103 bit/s = 39.8 kbit/s.

With a better signal-to-noise ratio, we can achieve:

C = 4 x 103 x 3.32 log10 (10001) = 4 x 103 x 3.32 x 4.0 = 53.1 kbit/s.

Shannon’s formula is often referred to as Shannon’s limit since the formula

puts the limit of transmission capacity of a given channel at a given S/N.

Signal-to-noise ratio – Shannon’s formula


Noise figure and noise ratio

Amplifiersignal

noise

+(S/N)in (S/N)out

When we present a signal with noise to an amplifier, we can expect that the output

will contain amplified signal-plus-noise combination. However, we need to

remember that every amplifier (even a single transistor, as we already know)

generates its own noise. As a result, the output will contain an amplified input signal-

plus-noise combination plus the amplifier’s noise. In other words, output signal-to-

noise ratio will degrade. In addition, we need to remember that an amplifier has its bandwidth too

and therefore will amplify different segments of input signal and noise differently.

To estimate the effect of an amplifier on signal-to-noise ratio, we introduce a

parameter called noise figure, NF.

NF (dB) = 10 log (S/N)in/(S/N)out,

where

NR = (S/N)in/(S/N)out

is called noise ratio, NR.


Example 1 [1]:

Problem: An amplifier has measured S/N power of 10 at its input and 5 at its output.

Calculate NR and NF.

Solution: NR = (S/N)in/(S/N)out = 10/5 = 2. And NF (dB) = 10 log (S/N)in/(S/N)out

= NF (dB) = 10 log NR = 10 log 2 = 3 dB.

If we use signal-to-noise ratio in dB, we can apply the simple formula for NF

calculations: NF (dB) = (S/N)in (dB) - (S/N)out (dB).

Example 2 [1]:

Problem: Verify the new formula for NF with data given in the above example.

Solution: To verify formula NF (dB) = (S/N)in (dB) - (S/N)out (dB), we need to

calculate every S/N in dB.

(S/N)in (dB) = 10 log (S/N)in = 10 log 10 = 10 dB

(S/N)out (dB) = 10 log (S/N)out = 10 log 5 = 7 dB.

Therefore, NF (dB) = (S/N)in (dB) - (S/N)out (dB) = 10 dB – 7 dB = 3 dB as above.

Bear in mind that (S/N)in (dB) = (S/N)out (dB) + NF (dB), which means that (S/N)in

is always greater (read, better!) than (S/N)out.

Also, consider this reasoning: Ideally, Sout = Sin x A and Nout = Nin x A. Thus,

(S/N)idealout = (S/N)idealin. In reality, however, Nout = Nin x A + Namp, which results

in (S/(ANin +Namp))out < (S/N)in.




Example [Mynbaev/Scheiner, Page 538]:

Problem: Calculate the noise ratio and the noise figure if the input-signal power is 300

µW, the input-noise power is 30 nW in a 1-THz bandwidth, the output-signal power is

60 mW, and the output-noise power is 20 µW in a 1-THz bandwidth..

Solution: Input and output signal-to-noise ratios are equal to (S/N)in = 10 x 103 and

(S/N)out = 3 x 103, respectively. Hence, NR = 3.33 and NF = 5.2 dB.

NR = (S/N)in/(S/N)out = 10/3 = 3.33 and NF (dB) = 10 log (S/N)in/(S/N)out = = 10 log

NR = 10 log 3.33 = 5.2 dB.

Discussion: This example demonstrates a very important concept: An amplifier does

indeed decrease the signal-to-noise ratio. However, an amplifier also raises the signal

power to such a high level that we can tolerate this degradation of the SNR.

Assignment:

Answer the following question: What would be NF of an ideal amplifier?


Homework problems: (See also [1], [2], [3], and [4].)1. What is noise? How does it affect a transmitted signal?

2. Distinguish between external and internal noise. List the sources of the both types of noise.

3. Can we eliminate external noise? Can we eliminate its effect on an useful signal?

4. Can we eliminate internal noise? Can we eliminate its effect on an useful signal?

5. Can we predict the exact instantaneous value of noise power?

6. What is the average noise power and rms noise voltage generated by a 10-kΩ resistor at room

temperature (270C) if BW = 10 MHz?

7. What is spectral density of noise calculated in Problem 6?

8. Determine the rms noise current generated by a silicon diode if Vcc = 5V, R = 10-kΩ and BW = 20

MHz.

9. What is spectral density of noise calculated in Problem 8?

10. Qualitatively sketch the graph of a flicker-noise spectral density. How can we reduce the harmful effect

of flicker noise?

11. Define spectral density. How does noise spectral density relate to noise power?

12. Qualitatively sketch the general graph of noise spectral density of semiconductor devices versus

frequency. Distinguish among main segments of this graph and name them. Does this graph relate to

external or internal noise?

13. Signal power is 100 mW and noise power is 0.1 µW. What is S/N?

14. The input signal to an amplifier is 10 mV and the noise is 0.23 mV. What is S/N?

15. The bandwidth of an audio system is restricted to 20 kHz. What is the system’s capacity if S/N = 104?

If S/N = 105?

16. An amplifier has measured S/N power of 100 at its input. Will the value of the S/N at its output be

greater or smaller than this value? Explain.

17. An amplifier has measured S/N power of 20 at its input and 6 at its output. Calculate NR and NF.


Topic: Noise

You must be able to:

• Define noise and explain how it affects a transmitted signal;

• Distinguish between external and internal noise and list the sources of the both types of noise;

• Classify all types of noise you know;

• List all the the measures to eliminate noise or reduce its harmful effect;

• Explain what is an external noise and how we can reduce its effect.

• Explain what is an internal noise and how we can reduce its effect.

• Explain the specific types (thermal, shot and flicker) of internal noise.

• Explain the random nature of noise (e.g., can we predict the exact instantaneous value of noise power?)

• Compute the average noise power, rms noise voltage and power spectral density of thermal, shot and flicker noise;

• Define spectral density and explain how noise spectral density relates to noise power;

• Qualitatively sketch the graph of the power spectral density of flicker, thermal and shot noise;

• Qualitatively sketch the general graph of noise spectral density of semiconductor devices versus frequency, distinguish among main segments of this graph and name them and explain whether this graph relates to external or internal noise;

• Explain the concept and compute signal-to-noise ratio;

• Explain how signal-to-noise ratio affects the transmission capacity of a communications system and compute this capacity (Shannon’s formula);

• Explain the concept and compute noise figure and noise ratio.

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