a question about noise figure

Dear all,

Here is a question about noise figure. Assuming a three stage cascade amplifier system. Every stage has the same gain and noise figure characteristic(gain=10 dB, NF=10 dB).

Input conditions are: Si= -100 dBm Ni= -174 dBm.

We can calculate the output signal and noise level of each stage based on the SNR definition. The following are the output condition of each stage:

So1= -90 dBm
No1= -154 dBm

S02= -80 dBm
No2= -143.1 dBm

So3= -70 dBm
No3= -133.01 dBm

Let us focus on the second stage. Base on the definition of noise figure, it can be calculated as NF2= So1/No1/So2/No2= 64/63.1= 0.9dB.


Why the answer is 0.9 dB? Not 10 dB? I know the second stage's noise figure won't be 10 dB because of the first stage's gain[(10-1)/10]. But it's the mathmatical way. What happened in the physical or electrical point of view?

There are two noise figures involved. The first is of each stage in isolation and the other is of the system. What you calculated is probably the effects of the second stage upon the system. That is the second stage not having 0 dB causes the system to be 10.9 instead of the 10 of the first stage.

flatulent said:

There are two noise figures involved. The first is of each stage in isolation and the other is of the system. What you calculated is probably the effects of the second stage upon the system. That is the second stage not having 0 dB causes the system to be 10.9 instead of the 10 of the first stage.

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So you meant that it's a one-way calculation? the system one and the stand alone one? it sounds reasonable, but I still cannot get it.

Thanks for your help!

But there is still a question in my mind. The definition of noise figure is on one condition. That is the input noise power is assumed to be the noise power resulting from a matched resister at T0=290 K.

Does it mean you will not get the whole noise figure(10 dB, in the previous example) if the input noise power is not -174 dBm/Hz?

Is it the answer for why noise figure contributed at each stage in a cascade system is different?

Hi,

bagel520, you are right, the definition of noise figure is for an input equivalent temperature of 290K, or an input noise power density of -174 dBm/Hz.
This condition is not met at the input of your second amp, where the noise power is -154 dBm.

But the noise figure of a device actually shows how much noise is generated internally in this device. The definition is: NF= (available noise at the output) / (available noise at the output if the device was noiseless - that is, no added internal noise), also at 290K

The internal noise is a constant and is given by:
Ni = (F-1)*G*k*T0

You can try to calculate this value for the amps and check the noise levels along your chain. For example, at the output of the second amp you should have:
No1*G+Ni - in Watts, not dBm

I hope this helps