1 Noise Analysis Electrical Noise Electrical noise is defined as any undesirable electrical energy. Figure 57 shows the effect of noise on an electrical signal. Figure 57: Effect of noise on a signal. (a) Without noise (b) With noise

2 Noise Analysis Noise can be categorised into two general categories: Correlated Uncorrelated Correlated Noise: Correlated noise is noise that is correlated (mutually related) to the signal and cannot present in a circuit unless there is an input signal. No signal means no noise!. Correlated noise is produced by nonlinear amplification or mixing and includes harmonic and IMD.

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5 Noise Analysis Uncorrelated Noise Uncorrelated noise present regardless of whether there is a signal present or not. Uncorrelated noise can be subdivided into two general categories: External Internal External Noise. External noise is noise that is generated outside the circuit or device. There are three primary sources: Atmospheric Extraterrestrial Man-made

6 Noise Analysis Atmospheric Noise Is naturally occurring electrical disturbances that originate within Earth’s atmosphere. The source of the atmospheric noise is from the natural source such as lightning and insignificant above 30 MHz. Extraterrestrial noise It consists of electrical signals that originate from outside Earth’s atmosphere and sometime called deep space noise. Extraterrestrial noise originates from the Milky Way, other galaxies and the sun. Extraterrestrial noise can be sub divided into two categories: solar and cosmic noise. Solar noise generated directly from the sun’s heat in two parts, quiet condition when a constant radiation intensity exists and high intensity caused by sun spot activity and solar flare up repeats every 11 years.

7 Noise Analysis Cosmic noise sources are continuously distributed throughout the galaxies and the source of the noise is located quiet far from the sun and therefore their intensity is relatively small. Cosmic noise is often called black body noise distributed fairly evenly throughout the sky. Man Made Noise Man made noise is simply noise that is produced by man. The predominant sources of man-made noise are spark-producing mechanisms such as electric motors, automobile ignition system, fluorescent lights and switching equipment. Man made noise is impulsive in nature and contains a wide range of frequencies that are propagated through space in the same manner as radio wave. Man made noise is most intense in the industrial area and sometime called industrial noise.

8 Noise Analysis Internal Noise Internal noise is electrical interference generated within a device or circuit and there are three primary kinds of internally generated noise: Thermal Noise Shot Noise Transit Noise Thermal Noise is associated with the rapid and random movement of electrons within a conductor due to thermal agitation. Electrons within the conductor carry a unit negative charge and the mean-square velocity of an electron is proportional to the absolute temperature. Each flight of an electron between collisions with molecules constitutes a short pulse of current that develops a small voltage across the resistive component of the conductor.

9 Noise Analysis Because this type of electron movement is totally random and in all directions, the average voltage in the substance due to this movement is 0 V dc. However such a random movement does produce an ac component. The ac component produced from thermal agitation has several names including thermal noise because it is temperature dependent, Johnson noise after the man who related particle movement of electron movement and white noise because the random movement is at all frequencies. Johnson proved that thermal noise power is proportional to the product of bandwidth and temperature. Noise power can be expressed mathematically as: N = KTB (1)

10 Noise Analysis Where N = noise power (watts) B = bandwidth (hertz) K = Boltzmann’s proportionality constant (1.38×10-23 joules per kelvin) T = absolute temperature (kelvin) (room temperature = 17 ºC or 290 K) Noise power in dBm is: To convert  C to kelvin, simply add 273 , thus T =  C .

11 Noise Analysis Shot Noise is caused by the random arrival of carriers (holes and electrons) at the output element of an electronic devices, such as diode, field-effect transistor or bipolar transistor. Shot noise is randomly varying and superimposed onto any signal present. Transit-time noise is any modification to a stream of carriers as they pass from the input to the output of a device (such as from the emitter to the collector of a transistor produces an irregular and random variation). Transit time noise in transistors is determined by carrier mobility, bias voltage and transistor construction. Carriers travelling from emitter to collector suffer from emitter time delays and base transit-time delays.

12 Noise Analysis Noise source equivalent circuit. Noise Voltage. Figure below shows the equivalent circuit for a thermal noise source where the internal resistance of the source R I is in series with the rms noise voltage V N.

13 Noise Analysis For the maximum power transfer of noise power, the load resistance R is made equal to R I. So that, the noise voltage dropped across R is equal to half of the noise source. From equation 1 the noise power (N) developed across the load resistor is equal to KTB. Thus V N can be mathematically expressed as follows: Thus: (2) (3)

14 Noise Analysis Example: For an electronic device operating at 17º C with a bandwidth of 10 kHz, determine: a)Thermal noise power in watts and dBm b)Rms noise voltage for a 100  internal resistance and a 100  load resistance. Solution a)Thermal noise power is: N = KTB T(kelvin) = 17º C + 273º = 290 K B = 1×10 4 Hz  N = (1.38× )(290)(1×10 4 ) = 4× W. In miliwatt: N(mW) = 4× /1×10 -3 = 4× mW In dBm : N(dBm) = 10logN(mW) = -134 dBm. b)

15 Noise Analysis Signal-to-Noise Power Ratio Signal-to-noise power ratio (S/N) is the ratio of the signal power level to the noise power level. S/N can be expressed as: or Where:

16 Noise Analysis Example: For an amplifier with an output signal power of 10 W and an output noise power of 0.01 W, determine the S/N Solution:

17 Noise Analysis Signal-to-noise power ratio can also be expressed in terms of voltage and resistances: Where: S/N = signal-to-noise power ratio (decibels) R in = input resistance (ohms) R out = output resistance (ohms) V s = signal voltage (volts) V n = noise voltage (volts)

18 Noise Analysis If the input and output resistances of the amplifier, receiver or network being evaluated are equal, the previous equation reduces to:

19 Noise Analysis Example: For an amplifier with an output signal voltage of 4 V, an output noise voltage of V, and an input and output resistance of 50 , determine the signal-to-noise ratio: Solution:

20 Noise Factor and Noise Figure Noise Factor (F) and Noise Figure (NF) are figure of merits used to indicate how much the S/N deteriorates as a signal passes through a circuit or series of circuits. Noise factor is a ratio of input S/N to the output S/N. Mathematically: Noise figure is simply the noise factor in dB:

21 Noise Factor and Noise Figure Example: For a nonideal amplifier and the following parameters, determine: Input signal power = 2  W Input noise power = 2  W Power gain = 1,000,000 Internal noise (N d ) = 6  W (a) Input S/N ratio in dB (b) Output S/N ratio in dB (c) Noise factor and noise figure

22 Noise Factor and Noise Figure Solution (a) The input S/N ratio is: (b) Output S/N ratio is the sum of the internal noise and the amplified noise:

23 Noise Factor and Noise Figure The output signal power is simply the product of the input power and the power gain: The output S/N is:

24 Noise Factor and Noise Figure Solution (c) The noise factor is: The noise figure is:

25 Cascaded Noise Figure When two or more amplifiers are cascaded as shown below, the total noise factor is the accumulation of the individual noise factors. Friiss’ equation can be used to calculate the overall noise figure of the cascaded amplifier:

26 Cascaded Noise Figure For passive component with loss L, we have: Previous equation allows for the calculation of the noise figure of a general cascaded system and it is clear that the gain and noise figure in the first stage are critical in achieving a low overall noise figure. Therefore, it is very desirable to have a low noise figure and high gain in the first stage.

27 Cascaded Noise Figure Example: For three cascaded amplifier stages, each amplifier has a noise figure of 3dB and power gain of 10 dB, determine the total noise figure. Solution: Convert To absolute Value first!!! Common mistake

28 Noise Temperature Equivalent noise temperature (T e ) is a hypothetical value that cannot be directly measured. T e is a convenient parameter often used rather than noise figure in VHF, UHF, microwave and satellite receivers. The lower the equivalent noise temperature is, the better the quality of a receiver.Mathematically, T e at the input of the receiver can be expressed as:

29 Noise Temperature Example: (a) Noise figure for an equivalent noise temperature of 75 K (b) Equivalent noise temperature for a noise figure of 6 dB. Solution: (a) (b)