k is Boltzmann's constant (1.38 × 10−23 J K−1), B is the noise bandwidth, and T is the temperature in Kelvin. Note that the available noise power does not depend upon the impedance of the source. From the definition in Eq. (1.57) it is clear that if the temperature of the source impedance changes, then the noise figure of the amplifier using this definition would change as well. Therefore, by convention, a fixed value for the temperature is presumed, and this value, known as T0, is 290 K.
This is the noise power that would be delivered to a conjugately matched load. Alternatively, the noise power can be represented as a noise wave, much like a signal, and one can define an incident noise (sometimes called the effective noise power), which is defined as the noise delivered to a nonreflecting nonradiating load and is found as
which is consistent with the definition of Eq. (1.47). Since the available noise at the output of a network doesn't depend upon the load impedance, the available gain from a network similarly doesn't depend upon the load impedance, and the available noise at the input of the network can be computed as Eq. (1.58), the measurement of noise figure defined in this way is not dependent upon the match of the noise receiver. One way to understand this is to note that the available gain is the maximum gain that can be delivered to a load. If the load is not conjugately matched to Γ2, both the available gain and the available noise power at the output would be reduced by equal amounts, leaving the noise figure unchanged and independent of the noise receiver load impedance. Thus, for the case of noise measurements, the available noise power and available gain have been the important terms of use historically.
Recently more advanced techniques have been developed and made practical based on incident noise power and gain. If the impedance is known, the incident noise power can be computed as in Eq. (1.59); and if the output incident noise power NOE can be measured, then one can compute the output available noise as
(1.60)
Substituting into Eq. (1.57) to find
When the source is a matched source, this simplifies to
(1.62)
Thus, for a simple system of an amplifier sourced with a Z0 impedance and terminated with a Z0 load, the noise factor can be computed simply from the noise power measured in the load and the S21 gain. However, Eq. (1.61) defines the noise figure of the amplifier in terms of the source impedance, and this is a key point. In general, although the 50 Ω noise figure is the most commonly quoted, it is measured only when the source impedance provided is exactly 50 Ω. In the case where the source impedance is not 50 Ω, the 50‐Ω noise figure cannot be simply determined.
1.5.1 Noise Temperature
Because of the common factor of temperature in many noise figure computations, the noise power is sometimes redefined as available noise temperature.
(1.63)
From this definition, the noise factor becomes
(1.64)
where TRNA is the relative available noise temperature, expressed in Kelvin above 290 K.
1.5.2 Effective or Excess Input Noise Temperature
For very low noise figure devices, it is often convenient to express their noise factor or noise figure in terms of the excess power that would be at the input due to a higher temperature generator termination, which would result in the same available noise temperature at the output. This can be computed as
(1.65)
Thus, an ideal noiseless network would have a zero input noise temperature, and a 3 dB noise figure amplifier would have a 290 K excess input noise temperature, or 290 K above the reference temperature.
1.5.3 Excess Noise Power and Operating Temperature
For an amplifier under test, the noise power at the output, relative to the kTB noise power, is called the excess noise power, PNE, and is computed as
(1.66)
For a matched source and load, it is the excess noise, above kTB, that is measured in the terminating resistor and can be computed as
(1.67)
which is sometimes called the incident relative noise or RNPI (as opposed to available, or RNP). Errors in noise figure measurement are often the result of not accounting properly for the fact that the source or load impedances are not exactly Z0. A related parameter is the operating temperature, which is analogous to the input noise temperature at the amplifier output, and is computed as
(1.68)
While the effect of load impedance may be overcome with the use of available gain, which is independent of load impedance, the effect of source impedance mismatch must be dealt with a much more complicated way, as shown next.
1.5.4 Noise Power Density
The excess noise is measured relative to the kTB noise floor and is expressed in dBc relative to the T0 noise floor. However, the noise power could also be expressed in absolute terms such as dBm. But the measured noise power depends upon the bandwidth of the detector, and so the noise power density provides a reference value with a bandwidth equivalent to 1 Hz. Thus, the noise power density is the related to the excess noise by
(1.69)
1.5.5 Noise Parameters
The formal definition of noise figure for an amplifier defines the noise figure only for the impedance or reflection coefficient of current source termination, but this noise figure is not the 50‐Ω noise figure. Rather, it is the noise figure of the amplifier for the impedance of the source. In general, one cannot compute the 50 Ω noise figure from this value without additional information about the amplifier. If one considers the amplifier in Figure