Understanding Noise Figure

1. Noise Figure
&
Noise Floor
(Understanding Noise Figure)
as Receiver Noise
By: Mostafa Ali

2. • One of the most frequently discussed forms of noise is known as ThermalOne of the most frequently discussed forms of noise is known as Thermal
Noise.Thermal noise is a random fluctuation in voltage caused by theNoise.Thermal noise is a random fluctuation in voltage caused by the
random motion of charge carriers in any conducting medium at arandom motion of charge carriers in any conducting medium at a
temperature above absolute zero (K=273 + Celsius).This cannot exist attemperature above absolute zero (K=273 + Celsius).This cannot exist at
absolute zero because charge carriers cannot move at absolute zero. Asabsolute zero because charge carriers cannot move at absolute zero. As
the name implies, the amount of the thermal noise is to imagine a simplethe name implies, the amount of the thermal noise is to imagine a simple
resistor at a temperature above absolute zero. If we'll use a very sensitiveresistor at a temperature above absolute zero. If we'll use a very sensitive
oscilloscope across the resistor, we'll see a very small AC noise beingoscilloscope across the resistor, we'll see a very small AC noise being
generated by the resistor.generated by the resistor.
• The RMS voltage is proportional to the temperature of the resistor and howThe RMS voltage is proportional to the temperature of the resistor and how
resistive it is.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 observed
Thermal Noise Of The ReceiverThermal Noise Of The Receiver

3. • In RF applications, we usually deal with circuitsIn RF applications, we usually deal with circuits
having matched input and output impedances, andhaving matched input and output impedances, and
are therefore more concerned with the powerare 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 aIn 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 theUsing this formula it is possible to determine that the
minimum equivalent input noise for a receiver atminimum equivalent input noise for a receiver at
room temperature (290K) is -174 dBm / Hz.room temperature (290K) is -174 dBm / Hz.
Thermal Noise (cont’d)Thermal Noise (cont’d)

4. • To characterize the receiver alone,To characterize the receiver alone, the Noise Figurethe Noise Figure
(NF)(NF) concept which characterized the degradation inconcept 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 deviceNoise 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 of· 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 output.the SNR at its input to the ratio of the SNR at its 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

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

6. • It’s the sensitivity of the input of the receiver andIt’s the sensitivity of the input of the receiver and
this Input sensitivity is evaluated by referring thethis Input sensitivity is evaluated by referring the
output noise Noutput noise NOO, to the receiver’s input gain, to the receiver’s input gain
• So that, Noise Floor =So that, Noise Floor =
Noise FloorNoise Floor

7. • NNOiOi(dBm) = KT(dBm) = KTOO(dBm/MHz)+ NF(dB)(dBm/MHz)+ NF(dB)
+ 10 Log B(MHz)+ 10 Log B(MHz)
• Noise floor = -174 + NFNoise floor = -174 + NF
+ 10 log Bandwidth+ 10 log Bandwidth
The concept of noise floor is valuable in many radioThe concept of noise floor is valuable in many radio
communications systems and enables the radiocommunications systems and enables the radio
receiver design and performance to be matched toreceiver design and performance to be matched to
the requirements of the overall system.the requirements of the overall system.
Noise Floor(cont’d)Noise Floor(cont’d)

8. • (1) Mohr on Receiver Noise Characterization,(1) Mohr on Receiver Noise Characterization,
Insights & SurprisesInsights & Surprises Richard J. MohrRichard J. Mohr of theof the
IEEE long islandIEEE long island
• (2) http://www.radi(2) http://www.radio-electronics.como-electronics.com
• (3)http://en.wikibooks.org/wiki/Communicatio(3)http://en.wikibooks.org/wiki/Communicatio
n_Systems/Noise_Figuren_Systems/Noise_Figure
ReferencesReferences