Maximum Usable Frequencies

Figure 7. Radio waves of the same frequency, but radiated at different angles, behave somewhat as shown. The angle θ is the critical angle for the frequency used.

When a ray such as C of Fig. 7 strikes the earth, absorption of energy occurs; also, the wave is reflected, and the signal may reach point y. A wave is said¹ to reach point x by a single-hop path, and to reach point y by a double-hop path. Ray D sent out by the antenna reaches point y by a single-hop path. The signal voltage induced in the receiving antenna will be due to the combined effects of the two (or more) rays.

The effect of the angle of radiation on radio signals of the same frequency was considered in the preceding paragraphs. The effect of frequency on radio signals radiated at the same angle will now be considered, using Fig. 8. At some frequency f₁ the ray will not be reflected but will pass even through the F layer. At a lower frequency f₂ the ray will pass through the E layer, but reflection back to the earth will occur from the F layer. At a lower frequency f₃ the ray will be reflected by the E layer.

From phenomena just considered, it follows that there is a maximum usable frequency, defined¹ as "the highest frequency that can be used for radio transmission at a specified time between two points on the earth by reflection from the regular ionized layers of the ionosphere. Higher frequencies are transmitted only by sporadic and scattered reflections." For instance, suppose that the transmitting antenna of Fig. 7 is to provide a signal at point x. For a given ionosphere height (existing at that specific time), the signal can be provided by ray C which leaves the antenna at a critical angle for some

Figure 8. Radio waves of different frequencies, but radiated at the same angle θ, behave somewhat as shown.

frequency. A higher frequency at this angle will not be reflected, and, if sent at a lower angle so that it will be reflected, it will miss point x. The maximum usable frequency f_m is (neglecting the earth's curvature) approximately⁸

where d is the horizontal distance from the transmitting to the receiving antenna, h is the virtual height of the reflecting layer under consideration, and f_c is the penetration or critical frequency. The units d and h should be the same.