How does a center fed dipole antenna for 40m work on 15m?

 It is common knowledge among radio amateurs that a 40m center-fed half wave dipole antenna will work very well on 15m. That is because center fed dipole antennas, whether it be a horizontal dipole or an inverted V, will resonate on all odd harmonics. Amateur band allocations are mostly as harmonics, for example, if you consider 3.5 MHz 80m band as a fundamental frequency, 7 MHz 40m band is its second harmonic, 14 MHz 20m fourth harmonic, 21 MHz 15 m band sixth harmonic, 28 MHz 10m band is 8th harmonic. This used to help in the days of homebrewed radios when the harmonics of a fundamental frequency oscillator could be amplified using corresponding tuned circuits to get on higher bands.

When crystals are used for the fundamental frequency, stability is also good, though it restricts operation to a single frequency. In case of antennas, as already mentioned, center-fed half wave dipole antennas resonate on odd multiples of fundamental frequency while end fed half wave dipole antenna (EFHW) resonate on all harmonics of the fundamental frequency. This helps in reducing the number of antennas needed, especially for portable operations where mounting more antennas may be difficult. A single 3.5 MHz or 80m EFHW can work on 80m, 40m, 20m, 15m, 10m and even 6m! EFHW has high feedpoint impedance and hence needs a matching transformer, typically 49:1.

For any dipole antenna, resonance occurs when its impedance has only resistive component and no reactive component on a given frequency. At resonance, inductive reactance is cancelled by an equal and opposite capacitive reactance. For a center fed dipole antenna, this occurs when the length of each arm is a quarter wavelength and total length equal to half wavelength. If it is shorter than half wave length, it has a higher capacitive reactance than inductive reactance. That is why loading coils are added to shortened dipoles to make them resonant by increasing inductive reactance.

The principle of third harmonic resonance is applicable not only to HF frequencies, but also to higher frequencies. That is how VHF amateur radio antennas have been used for UHF amateur radio band in low earth orbit (LEO) amateur satellite operations on a limited scale. Ideal way for satellite operations is to have two separate antennas for VHF and UHF, that too directional antennas like Yagi antennas, along with a rotator which can work in both azimuth and elevation. As an example, the uplink frequency of Space Station is 145.990 MHz, in the VHF band. Third harmonic of this will be 437.970 MHz in the UHF band. This is very close to the 437.800 MHz downlink frequency of the Space Station. Hence a transmitting antenna for the uplink can also receive the downlink fairly well. On uplink it acts as a 1/2 wavelength antenna and on downlink it acts as a 3/2 wavelength antenna for the downlink UHF frequency. A full duplex radio which can receive on UHF while it is transmitting on VHF is needed for this.