BEE3413 Noise

1FKEE NorizamMay 3, 2023

CHAPTER 6

NOISE


Chapter 6 Noise – Defination It is a random signal without specific

amplitude.

It may come from various source such as environment, electrical devices and so on.

It disturb the system performance. All electrical & electronics systems are

affected by noise.

It often expressed in term of decibel, dB.


Chapter 6 Noise – Defination 1. An undesired disturbance within the frequency

band of interest; the summation of unwanted or disturbing energy introduced into a communications system from man-made and natural sources.

2. A disturbance that affects a signal and that may distort the information carried by the signal.

3. Random variations of one or more characteristics of any entity such as voltage, current, or data.

4. A random signal of known statistical properties of amplitude, distribution, and spectral density.

5. Loosely, any disturbance tending to interfere with the normal operation of a device or system.


Chapter 6Noise - Type of Noise The are several types of noise, among them are: 1. Thermal Noise 2. White Noise 3. Shot Noise 3. Quantization Noise 4. Signal to Noise Ratio (SNR)


Chapter 6Noise - Thermal Noise In any object with electrical resistance the thermal

fluctuations of the electrons in the object will generate noise.

The noise generated by thermal agitation of electrons in a conductor. The noise power, P , in watts, is given by P = kTB , where k is Boltzmann's constant in joules per kelvin, T is the conductor temperature in kelvins, and B is the bandwidth in hertz.

In dB, it is defined as: NdBm = 10log(KTB/0.001)

N = KTB

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Chapter 6Noise - Thermal Noise

EXAMPLE 1 : A receiver has a noise power bandwidth of 10 kHz. A resistor

that matches the receiver input impedance is connected across its antenna terminals. Determine the Noise Power if the resistor has temperature of 27 oC.

SOLUTION : 1. Use Noise Power formula

2. N = (1.38 x 10-23 J/K)(273o + 27oK)(10000 Hz) = 4.14 x 10-17 W. 3. in dB, N(dB) = 10log[(4.14 x 10-17 W) / 0.001] = -133.8

N = KTB


Chapter 6 Noise - White Noise It is generated from random motion of molecules that

occurred in any materials that affected by environment’s temperature change.


Chapter 6 Noise - Shot Noise Shot noise – This noise is generated by

current flowing across a P-N junction and is a function of the bias current and the electron charge. The impulse of charge q depected as a single shot event in the time domain can be Fourier transformed into the frequency domain as a wideband noise.

The noise caused by random fluctuations in the motion of charge carriers in a conductor.


Chapter 6 Noise - Quantization Noise Noise caused by the error of approximation in quantization

. signal.

error: 1. The difference between a computed, estimated, or measured value and the true, specified, or theoretically correct value.

2. A deviation from a correct value caused by a malfunction in a system or a functional unit. Note: An example of an error is the occurrence of a wrong bit caused by an equipment malfunction.

A process in which the continuous range of values of an analog signal is sampled and divided into nonoverlapping (but not necessarily equal) subranges, and a discrete, unique value is assigned to each subrange. Note: An application of quantization is its use in pulse-code modulation. If the sampled signal value falls within a given subrange, the sample is assigned the corresponding discrete value for purposes of modulation and transmission.












Chapter 6 Noise - Quantization Noise• Example of Quantization Noise


Chapter 6 Noise - Signal to Noise Ratio (SNR) The ratio of the amplitude of the desired signal

to the amplitude of noise signals at a given point in time.

SNR is expressed as 20 times the logarithm of the amplitude ratio, or 10 times the logarithm of the power ratio.

SNR is usually expressed in dB and in terms of peak values for impulse noise and root-mean-square values for random noise. In defining or specifying the SNR, both the signal and noise should be characterized, e.g., peak-signal-to-peak-noise ratio, in order to avoid ambiguity.









Chapter 6 Noise - Bit Error Rate It occurred in digital communication.

It is a function of the carrier to noise power ratio (the average energy per bit to noise power density ratio and the number of possible encoding conditions used (M-ary).

The carrier power is defined as below: CdBm = 10log(Cwatts / 0.01).

The carrier to the noise power ratio is: C/N = C/KTB


Chapter 6 Noise - Bit Error Rate The carrier to Noise power in dB is:

C/N (dB) = log (C/N) = CdBm - NdBm

The enery per bit is simply the energy of a single bit of information.

It is defined as below: Eb = CTb (J/bit) in dBJ, Eb(dBJ) = 10 log Eb

Since Tb = 1/fb, Eb(dBJ) = 10 log (C/fb )


Chapter 6 Noise - Bit Error Rate The Noise power density is No = N/B (W/Hz)

= 10log(N/0.001) – log B

Energy per bit to the noise power density is defined as:

Eb / No = C/N x B/fb

Energy per bit-to-noise power density ratio is simply the ratio of the energy of a single bit to the noise power present in 1 Hz of bandwidth.


Chapter 6 Noise - Bit Error Rate EXAMPLE 2: A QPSK system has the following

specification: C = 10-12 W, fb = 60 kbps, N = 1.2x10-14 W &

B = 120 kHz Determine the following: (i) Carrier power in dBm (ii) Noise power in dBm (iii) Noise power density in dBm (iv) Energy per bit in dBJ (v) Carrier to noise power ratio in dB (vi) Eb / No ratio


Chapter 6 Noise - Bit Error Rate SOLUTION TO EXAMPLE 2: (i) Carrier power 10log[C/0.001] = 10log[(10-12/0.001] = -90 dB (ii) Noise power 10log[N/0.001] = 10log[(1.2x10-14/0.001] = -109.2 dB

(iii) Noise power density No = N/B = 10log[N/0.001] – 10logB = 10log[(1.2x10-14/0.001)]-10log(120k) = -109.2 – (50.79) = -160 dB


Chapter 6 Noise - Bit Error Rate SOLUTION TO EXAMPLE 2 (Continued):

(iv) Energy per bit in dBJ Eb(dBJ) = 10 log (C/fb ) = 10log[(10-12 / 60 kbps) = -167.8 dB (v) Carrier to Noise power ratio in dB 10log[C/N] = CdBm - NdBm = -90 – (-109.2) = 19.2 dB (vi) Eb / No = 10logEb + 10logNo = 19.2 + 10log[(120kHz/60kbps) = 19.2 + 3.0 = 22.2 dB


Chapter 6 Noise - Noise Factor & Noise Figure Noise factor (F) It simply a ratio of [input signal-to-noise-power

ratio] to [output signal to noise-power ratio] as shown below:

F = Signal-to-Noise ratio at input of cct Signal-to-Noise ratio at the output of cct.

Signal-to-Noise ratio (SNR) = Signal Power / Noise Power

SNR (dB) = 10log(Ps / Pn) Noise figure (NF) is the Noise factor stated in

dB. NF = 10logF


Chapter 6 Noise - Noise Factor & Noise Figure Noise factor (F) It simply a ratio of [input signal-to-noise-power

ratio] to [output signal to noise-power ratio] as shown below:

F = Signal-to-Noise ratio at input of cct Signal-to-Noise ratio at the output of cct.

Signal-to-Noise ratio (SNR) = Signal Power / Noise Power

Noise figure (NF) is the Noise factor stated in

dB. NF = 10logF


Chapter 6 Noise - Noise Factor & Noise Figure EXAMPLE 3: The signal power at the input to an amplifier is 100

µW and noise power is 1 µW. The signal power at the output of an amplifier is 1 W with noise power of 30 mW. Determine the Noise Figure of the Amplifier.

SOLUTION : 1. SNR at Input of Amplifier = 100 µW / 1 µW = 100 2. SNR at Output of Amplifier = 1 W / 0.03 W = 33.3 3. The Noise Factor, F = 100 / 33.3 = 3 4. Noise Figure, NF = 10logF = 10log(3) =4.8


Chapter 6 Noise - Noise Factor & Noise Figure Noise factor (F) for cascaded Amplifier circuit F = F1 + (F2 – 1)/G1 + (F3 – 1)/G1G2 + (F4 – 1)/G1 G2G3 + …

Signal-to-Noise ratio (SNR) = Signal Power / Noise Power EXAMPLE 4: FOR 3 CASCADED AMPLIFIER STAGES, EACH

WITH NOISE FIGURES OF 3 dB, POWER GAIN OF 10 dB, DETERMINE THE TOTAL FACTOR & FIGURE:

NOISE FACTOR : FT = 2 + [(2-1)/10] + [(2-1)/100] = 2.11 NOISE FIGURE : NFT = 10log(2.11) = 3.24 dB


Chapter 6 Noise - Equivalent Noise Temperature It is defined as below:

Te = T(F – 1) or F = 1 + Te / T

EXAMPLE 5: Determine the Noise Figure where the temperature is 75 K

(reference 290 K) and equivalent noise temperature with noise figure of 6 dB

SOLUTION :

1. F = 1 + 75/290 = 1.258 2. NF = 10log(1.258) = 1 dB. 3. F = antilog(NF/10) = antilog(6/10) = 4

4. Te = T(F-1) = 290(4-1) = 870 K


Chapter 6 Noise - Noise Figure FM systems are far better at rejecting noise than AM

systems. Noise generally is spread uniformly across the spectrum (the so-called white noise, meaning wide spectrum).

The amplitude of the noise varies randomly at these frequencies. The change in amplitude can actually modulate the signal and be picked up in the AM system.

As a result, AM systems are very sensitive to random noise. An example might be ignition system noise in your car. Special filters need to be installed to keep the interference out of your car radio.


Chapter 6 Noise - Noise Figure FM systems are inherently immune to random

noise. In order for the noise to interfere, it would have to modulate the frequency somehow. But the noise is distributed uniformly in frequency and varies mostly in amplitude. As a result, there is virtually no interference picked up in the FM receiver.

FM is sometimes called "static free, " referring to its superior immunity to random noise.


Chapter 6 Noise - Noise in Digital Communication BPSK & QPSK Error Performance The bit error rate for PSK is directly related to the

distance between point on a signal state-space diagram (constellation or phasor diagram).

In BPSK, the signal poitns (logic “1” & logic “0”) have maximum separation of d for a given power level, D. For this the noise vector, VN combined with the signal vector, Vs shifts the phase of the signaling element, VSE .

If the phase shift exceed 90o (shifted beyond its threshold points) , it will enter the error region.

The threshold points, TP = (/M), M is the number of signal states.


Chapter 6 Noise - Noise in Digital Communication BPSK & QPSK Error Performance The distance d, is defined as:

d = 2 sin (180o / M) x D M number of phase

QAM Error Performance The error distance is defined as: d = [sqrt (2)/(L-1)]xD, L is number of level on each axis. Refer to

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