## 1. Introduction

[2] The effective antenna noise figure *F*_{a} is one of several parameters that are used to characterize radio noise. It is a measure of the noise power received by an antenna from sources external to the antenna [*International Radio Consultative Committee* (*CCIR*), 1964, 1982, 1988; *Spaulding and Hagn*, 1978; *Spaulding and Washburn*, 1985], and it is the ratio measured either in dB(*kT*_{0}) or dB(*kT*_{0}*b*) of the received noise power available from an equivalent lossless antenna (i.e., the power available after corrections for the antenna losses [*CCIR*, 1964, 1988; *Lauber and Bertrand*, 1994]) to the thermal, or Johnson, noise power available in the same bandwidth from a resistor at room temperature. As suggested by the wording of this definition, *F*_{a} values tend to be closely linked to the antennas used for their measurement, and this linking sets *F*_{a} apart from other radio noise parameters, which usually have little or no dependence on the antennas used for their measurement. In practice, the dependence means that an antenna-dependent numerical factor appears in the expressions relating *F*_{a} to the amplitudes of the electric or magnetic field strengths of the noise. This is not a fundamental problem, but the antennas traditionally used for the measurement of *F*_{a} have been electric field antennas, and the expressions that have been derived to convert the electric field measurements to *F*_{a} values have all been specific to electric field antennas. As a result, the survey of extremely low frequency (ELF)/very low frequency (VLF) radio noise being made by my Stanford University research group [*Fraser-Smith and Helliwell*, 1985; *Fraser-Smith et al.*, 1988, 1991; *Fraser-Smith*, 1995], which involves measurements of the magnetic field of the noise by means of loop antennas, has until now been limited to the derivation of noise parameters other than *F*_{a}. In addition, since magnetic field loop antennas are conventionally used to make measurements on ELF/VLF radio signals and noise, and not electric field antennas, there have been few actual measurements of *F*_{a} for ELF/VLF radio noise. To remedy this situation, an expression for *F*_{a} as measured with a small vertical loop antenna has been derived, and the twofold purpose of this paper is (1) to document this derivation and (2) to provide representative measurements of *F*_{a} for the ELF/VLF radio noise occurring at a number of locations around the world and compare them with CCIR predictions.

[3] *F*_{a}, the effective antenna noise figure, is derived from the effective antenna noise power factor *f*_{a}, which, for any antenna, is given by

where *p*_{n} is the mean noise power available from an equivalent loss-free antenna (W), *k* is the Boltzmann constant (1.38 × 10^{−23} J/K), *T*_{0} is a reference temperature (K), and *b* is the effective receiver noise bandwidth (Hz). The antenna noise figure is then defined by *F*_{a} = 10log_{10}*f*_{a}, with units of dB(*kT*_{0}) or dB(*kT*_{0}*b*). If we define *P*_{n} = 10log_{10}*p*_{n} (dB), we can further write *F*_{a} in the form

for a temperature *T*_{0} that is conventionally taken to be 288 K (15°C).

[4] The noise power (in W) available from a loss-free antenna must equate to the power flux density (in W/m^{2}) of the electromagnetic radiation illuminating the antenna multiplied by the antenna's effective aperture. Thus we can write

where an impedance of 120*π* (ohms) is assumed for free space and where *e* is the root mean square (RMS) electric field strength (in V/m) of the noise (for a bandwidth *b*), *g* is the antenna gain relative to an isotropic radiator, and *λ* is the wavelength (in m) at the center of the bandwidth of the receiver. Typically, the ratio of this center frequency to the bandwidth is large; for the measurements we report below, the ratio is 20. Considering that one of the goals of this work is to derive an expression for *F*_{a} in terms of measurements made on the magnetic field of the radio noise illuminating an electrically small loop antenna, we could as well have written the power flux density (i.e., Poynting flux) in equation (3) in terms of the magnetic field strength of the radiation instead of the electric field strength *e*. To facilitate comparison with earlier work, we have, at this stage, retained the traditional electric field approach, but it is important to note that no additional assumptions or simplifications are involved when we finally convert from *e* to the corresponding magnetic field. If we now write *G* = 10log_{10}*g*, *E* = 10log_{10}*e*^{2}, and the wavelength *λ* = 300/*F* (in m), where *e* is measured in *μ*V/m and *F* is the center frequency measured in MHz, we have

where *P*_{n} is measured in dBW (dB above 1 W). Then, from equation (2)

and

The antenna dependence of the above two expressions linking *F*_{a} and *E* comes from the presence of the antenna gain factor *G*. Given a particular antenna, the gain factor is usually combined with the constant 96.79 to give an antenna-dependent constant. For example, for a short vertical monopole above a perfectly conducting ground plane, the gain *G* is −1.25 dB and (−*G* − 96.79) in equation (4b) is replaced by the new constant 1.25 − 96.79 = −95.54. A list of these constants for a variety of electric field antennas is provided in the study by *Hagn and Shepherd* [1984], but no constants are available for magnetic field antennas.