## 5. 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} =KT_{0}B

Substituting the values in the above formula,

F=[G*N_{in} + N_{dut]}/[GN_{in}] =
[T_{0} + Te]/T0

Or Te = T_{0}(F-1)

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

F dB = 10logF