Noise Figure Measurement - A Practical Approach

V. What is Noise Figure:

            Noise Figure is defined as the ratio of signal to noise ratio at the output to that at the input. In other words,

NF= (s/n)i/(s/n)o

Where (s/n)I is the signal to noise ratio at the input, and (s/n)o is the signal to noise ratio at the output of the device under test. Note that s/n at the output will always be smaller than the s/n at the input, due to the fact that any circuit will only add to the noise, but never reduces the noise present in the system.

 (S/N)_in=(signal power) _in /(noise power) _in

            =  S _in /N _in

(S/N)out=(Signal Power)out/(Noise Power)out

         =S_out/N_out            = [S _in *G]/[G*N_in + N_dut]

N_dut is the noise power due to the device.

 (S/N)_in/(S/N) _out

= [S _in /Nin]/[S _in *G/[ G*N_in + N_dut]

             = [G*N_in + N_dut]/[ GN_in]

 Effective Noise Temperature:

 Let us assume that Te (called Effective Noise Temperature) is the noise temperature that results in N_dut. Then Te is related to the N_dut as follows:

N_dut = KGB*Te

or

Te= N_dut /[KGB]

Also we know at room temperature, N_in =KT₀B

Substituting the values in the above formula,

F=[G*N_in + N_dut]/[GN_in] = [T₀ + Te]/T0

Or Te = T₀(F-1)

F expressed in linear terms is called Noise Factor. In log terms, F is called Noise Figure.

F dB = 10logF

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