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There is an example in OrCad PSPICE which calculates noise figure for an RF amplifier.

I know the following formula for noise figure:

$$\text{NF}_\text{dB}=10\log\frac{P_{no}}{G_aP_{ni}}$$

But in this example the software uses another formula:

10*Log10(V(inoise)*V(inoise)/8.28e-19)

Where V(inoise) is the equivalent input voltage noise.

I don't understand why this formula should be true and where does 8.28e-19 come from? Is it a general formula that can be used in every simulation?

Here is the result enter image description here

and the circuit

enter image description here

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Where does 8.28e-19 come from?

Thermal noise of a 50 ohm resistor in a 1 Hz bandwidth at 27 degC is 9.1e-10 volts

To convert this to an equivalent power it needs squaring and this produces a number of 8.28e-19.

Thermal noise calculator.

The formula also reduces to 20 log\$_{10}(\frac{V_{NOISE}}{9.1e-10}\$) i.e. it compares actual RMS noise against 1Hz-limited voltage noise from a 50 ohm resistor.

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    \$\begingroup\$ And that 50 ohm resistor is R5 in your circuit, it is the output impedance of your source. So if your output impedance was 100 ohm, you would need a different value ! \$\endgroup\$
    – Bimpelrekkie
    Commented Oct 1, 2015 at 14:06
  • \$\begingroup\$ @FakeMoustache Is the source required to be matched to use this formula? \$\endgroup\$
    – SMA.D
    Commented Oct 1, 2015 at 17:37
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    \$\begingroup\$ No, a mismatch in source impedance will result in a different gain from input to output. So the noise figure will change but that will be because the output power will be lower (because of the mismatch). \$\endgroup\$
    – Bimpelrekkie
    Commented Oct 1, 2015 at 17:40

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