Noise Figure&

Noise Floor(Understanding Noise Figure)

as Receiver NoiseBy: Mostafa Ali

• One of the most frequently discussed forms of noise is known as One of the most frequently discussed forms of noise is known as Thermal Noise.Thermal noise is a random fluctuation in voltage Thermal Noise.Thermal noise is a random fluctuation in voltage caused by the random motion of charge carriers in any conducting caused by the random motion of charge carriers in any conducting medium at a temperature above absolute zero (K=273 + medium at a temperature above absolute zero (K=273 + Celsius).This cannot exist at absolute zero because charge carriers Celsius).This cannot exist at absolute zero because charge carriers cannot move at absolute zero. As the name implies, the amount of cannot move at absolute zero. As the name implies, the amount of the thermal noise is to imagine a simple resistor at a temperature the thermal noise is to imagine a simple resistor at a temperature above absolute zero. If we'll use a very sensitive oscilloscope across above absolute zero. If we'll use a very sensitive oscilloscope across the resistor, we'll see a very small AC noise being generated by the the resistor, we'll see a very small AC noise being generated by the resistor.resistor.

• The RMS voltage is proportional to the temperature of the resistor The RMS voltage is proportional to the temperature of the resistor and how resistive it is.and how resistive it is.

• · Larger resistances and higher temperatures generate more noise.· Larger resistances and higher temperatures generate more noise.• The formula to find the RMS thermal noise voltage of a resistor is:The formula to find the RMS thermal noise voltage of a resistor is:

• VnVn = ( = (4kTRB)^4kTRB)^1/21/2• k = Boltzman constant (1.38*10^-23 Joules/Kelvin)k = Boltzman constant (1.38*10^-23 Joules/Kelvin)• T = Temperature in degrees Kelvin (K= +273 Celsius)T = Temperature in degrees Kelvin (K= +273 Celsius)• R = Resistance in ohmsR = Resistance in ohms• B = Bandwidth in Hz in which the noise is observedB = Bandwidth in Hz in which the noise is observed

Thermal Noise Of The ReceiverThermal Noise Of The Receiver

• In RF applications, we usually deal with circuits In RF applications, we usually deal with circuits having matched input and output impedances, and having matched input and output impedances, and are therefore more concerned with the power are therefore more concerned with the power available from a device than the voltage.available from a device than the voltage.

• In this case, it is common to express the noise of a In this case, it is common to express the noise of a device in terms of the available noise power.device in terms of the available noise power.

• P = (Voc/2)P = (Voc/2)^2^2 /R = kTB = Noise at input of receiver /R = kTB = Noise at input of receiver• Using this formula it is possible to determine that Using this formula it is possible to determine that

the minimum equivalent input noise for a receiver the minimum equivalent input noise for a receiver at room temperature (290K) is -174 dBm / Hz.at room temperature (290K) is -174 dBm / Hz.

Thermal Noise (cont’d)Thermal Noise (cont’d)

• To characterize the receiver alone,To characterize the receiver alone, the Noise Figure the Noise Figure (NF) (NF) concept which characterized the degradation in concept which characterized the degradation in Signal to Noise Ratio (SNR) by the receiver.Signal to Noise Ratio (SNR) by the receiver.

• Noise Figure (NF) is a measure of how much a device Noise Figure (NF) is a measure of how much a device (such an amplifier) degrades the Signal to Noise ratio (such an amplifier) degrades the Signal to Noise ratio (SNR).(SNR).

• · Noise Factor (linear not dB) of a receiver is the ratio · Noise Factor (linear not dB) of a receiver is the ratio of the SNR at its input to the ratio of the SNR at its of the SNR at its input to the ratio of the SNR at its output.output.

• NoiseFactor_F(linear) = SNR_input[linear] / NoiseFactor_F(linear) = SNR_input[linear] / SNR_output[linear]SNR_output[linear]

• NoiseFactor_F[dB] = SNR_input[dB] - SNR_output[dB]NoiseFactor_F[dB] = SNR_input[dB] - SNR_output[dB]• NoiseFigure_NF[dB] = NoiseFigure_NF[dB] = SNR_input[dB]SNR_input[dB]--SNR_output[dBSNR_output[dB]]

Noise FigureNoise Figure

Note that Note that SNR at the output will always be smaller SNR at the output will always be smaller than the SNR at the input, due to than the SNR at the input, due to the fact that the fact that circuits always add to the noise in a system.circuits always add to the noise in a system.this means that the noise factor is always greater than this means that the noise factor is always greater than one.one.

• It’s the sensitivity of the input of the It’s the sensitivity of the input of the receiver and this Input sensitivity is receiver and this Input sensitivity is evaluated by referring the output noise Nevaluated by referring the output noise NOO, , to the receiver’s input gainto the receiver’s input gain

• So that, Noise Floor =So that, Noise Floor =

Noise FloorNoise Floor

• NNOiOi(dBm) = KT(dBm) = KTOO(dBm/MHz)+ NF(dB)(dBm/MHz)+ NF(dB) + 10 Log B(MHz) + 10 Log B(MHz) • Noise floor     =     -174   +   NF Noise floor     =     -174   +   NF +   10 log Bandwidth+   10 log BandwidthThe concept of noise floor is valuable in many radio The concept of noise floor is valuable in many radio

communications systems and enables the radio communications systems and enables the radio receiver design and performance to be matched receiver design and performance to be matched to the requirements of the overall system.to the requirements of the overall system.

Noise Floor(cont’d)Noise Floor(cont’d)

• (1) Mohr on Receiver Noise (1) Mohr on Receiver Noise Characterization, Insights & Surprises Characterization, Insights & Surprises Richard J. Mohr Richard J. Mohr of the IEEE long islandof the IEEE long island

• (2) http://www.radi(2) http://www.radio-electronics.como-electronics.com• (3)http://en.wikibooks.org/wiki/(3)http://en.wikibooks.org/wiki/

Communication_Systems/Noise_FigureCommunication_Systems/Noise_Figure

ReferencesReferences