Consider an RF source with output resistance of driving a resistive load as shown in Figure 1.
RF source is directly driving the load, input and output nodes are the same. Therefore the power gain =1
Noise factor is now given by the ratio of noise power at the output to the noise power due to source.
Alternatively, consider the input as current source and taking output as voltage across . The Norton equivalent of the circuit is shown in Figure 1.
Power gain from input to output is
Noise factor is given by,
If the load impedance() is power matched for source resistance(), then . Its conversion gain is -6dB.
To minimize noise factor should me as high as possible, but for maximum power transfer from source to load. Therefore a tradeoff comes into picture between noise figure and maximum power transfer.
For example a 6dB RF attenuator or pad has noise figure of 6dB and conversion gain of -6dB. If a signal enters into a attenuator or pad, then the signal is attenuated by 6dB while the noise floor remains constant. Therefore the signal to noise ratio through the pad is degraded by 6dB.
The Noise figure of a passive device is same as that of the conversion gain(in dB sense).