Frequency / Wavelength Converter

In a dielectric medium, the electric field polarizes the molecules, which retards the wave propagation. The phase velocity is reduced to v = c/√(εr × μr), where εr is relative permittivity and μr is relative permeability. For non-magnetic materials (μr ≈ 1), v = c/√εr. The wavelength in the medium is shorter than in free space: λ_medium = λ_freespace × VF = λ_freespace / √εr.

In coaxial cable, the electrical length of a section is determined by its physical length divided by the wavelength in the cable. Cable sections that are λ/4 long act as impedance transformers; λ/2 sections repeat the input impedance. This is critical for phasing harnesses in antenna arrays, matching stubs, and delay lines. Using the free-space wavelength instead of the cable wavelength causes significant errors in these calculations.

Most practical antenna dimensions are expressed as fractions of the wavelength: λ/4 for quarter-wave monopoles, λ/2 for dipoles, λ for full-wave loops. This means antenna dimensions scale inversely with frequency. A 100 MHz VHF antenna is 10 times larger than a 1 GHz antenna performing the same function. This scaling is why satellite dishes for Ku-band (12 GHz) are much smaller than those for C-band (4 GHz).

ITU designates radio bands by number: Band 4 = VLF (3–30 kHz, λ = 10–100 km), Band 5 = LF (30–300 kHz, λ = 1–10 km), Band 6 = MF (300 kHz–3 MHz, λ = 100 m–1 km), Band 7 = HF (3–30 MHz, λ = 10–100 m), Band 8 = VHF (30–300 MHz, λ = 1–10 m), Band 9 = UHF (300 MHz–3 GHz, λ = 10 cm–1 m), Band 10 = SHF (3–30 GHz, λ = 1–10 cm), Band 11 = EHF (30–300 GHz, λ = 1–10 mm).

Water has a very high relative permittivity (dielectric constant) — approximately 80 at low frequencies, dropping to about 79 at 1 GHz and continuing to decrease at higher frequencies. This gives water a refractive index of about 8.9 at 1 GHz, meaning the wavelength is about 8.9 times shorter than in free space. This is why underwater communications at standard radio frequencies is extremely difficult — antennas would need to be impractically small, and attenuation is enormous.

In high-speed digital design, signal integrity problems arise when PCB trace lengths become significant fractions of the signal's wavelength. As a rule of thumb, transmission line effects become important when trace length exceeds λ/10 (about 1/10 of the wavelength in the PCB medium). For a 1 GHz digital signal on FR4 (λ ≈ 14.3 cm), traces longer than about 14 mm need careful impedance control and termination. This calculator helps quickly determine these critical length thresholds.

Visible light has frequencies from about 430 THz (red, 700 nm) to 750 THz (violet, 400 nm). These extremely high frequencies result in wavelengths in the nanometer range — far too small to build conventional wire antennas, which is why optical antennas use entirely different technologies (plasmonic nanostructures, photonic crystals). The same λ = c/f formula applies, but the domain of application is entirely different.