Before any equation, the frequency map. Microwave engineers carve the spectrum into letter bands, mostly inherited from World War II radar work where the original letters were code names so the enemy could not tell which radar was running where. The names stuck.
| Band | Frequency | Wavelength | What lives there |
|---|---|---|---|
| L | 1–2 GHz | 30–15 cm | GPS L1 (1.575 GHz), GSM, mobile telemetry, air-traffic-control secondary radar |
| S | 2–4 GHz | 15–7.5 cm | Wi-Fi 2.4 GHz, Bluetooth, weather radar (NEXRAD), microwave ovens (2.45 GHz) |
| C | 4–8 GHz | 7.5–3.75 cm | Satellite uplink, Wi-Fi 5/6 (5 GHz), some long-range radar |
| X | 8–12 GHz | 3.75–2.5 cm | Military radar, deep-space comms (8.4 GHz), marine radar |
| Ku | 12–18 GHz | 2.5–1.67 cm | Satellite TV downlink, VSAT, police radar (13.45 GHz in some regions) |
| K | 18–27 GHz | 1.67–1.11 cm | Police radar (24 GHz), some 5G; mostly avoided due to water absorption |
| Ka | 27–40 GHz | 11.1–7.5 mm | High-throughput satellite, automotive radar, 5G mm-wave |
| V | 40–75 GHz | 7.5–4 mm | 60 GHz unlicensed (WiGig), 5G; oxygen absorption peak at 60 GHz |
| W | 75–110 GHz | 4–2.7 mm | 77 GHz automotive radar, mm-wave imaging, scientific radar |
| mm-wave | 110–300 GHz | 2.7–1 mm | Radio astronomy, security imaging, 6G research |
The wavelengths drawn out are critical because they tell you immediately how big a half-wave dipole would be at that frequency. At 10 GHz, cm, so a antenna is 1.5 cm; at 77 GHz it is two millimeters. This is why automotive radar antennas can fit inside a fender plate while AM broadcast antennas need a 100-meter tower. Wavelength shrinks linearly with frequency, and the entire mechanical scale of the hardware shrinks with it.
1.1 Atmospheric absorption
Above about 22 GHz the atmosphere begins to misbehave. Water vapor has a strong absorption resonance near 22 GHz, oxygen has a series of overlapping resonances around 60 GHz, and beyond 100 GHz the atmosphere becomes a soup of absorption lines. Plot attenuation versus frequency and you see two windows where propagation is decent (around 35 GHz and 90 GHz) separated by walls where the air itself drinks your signal.
This has practical consequences that drive entire system architectures. The 60 GHz unlicensed band exists because oxygen absorbs the signal in a few hundred meters; spectrum can be reused on the next block without interference, which is great for short-range high-bandwidth links and terrible for long-haul comms. Conversely, 35 and 94 GHz radar systems exploit the local windows for high-resolution imaging despite the heavy general background absorption.
Everyday analogy. The atmosphere is an FM-radio-friendly door curtain at low frequencies, an X-ray-transparent thin window in the middle, and an oven-door-mesh screen at millimeter wave. The frequency you choose determines whether the air is trying to cooperate or actively swallowing your photons.
1.2 Why "microwave" is special
At low frequency, a wire is a wire. Push voltage in one end, the same voltage shows up at the other, and Kirchhoff's laws apply. At microwave, this picture fails. The voltage at one end of a 5-cm trace at 10 GHz can be V while the voltage at the other end is V simultaneously, because half a wavelength fits between them. The "wire" is now a transmission line.
Lumped components also stop being lumped. A 1 pF capacitor at DC is a capacitor. At 10 GHz the same part has lead inductance that resonates with its capacitance, so above its self-resonant frequency it behaves as an inductor. A 100 nH wire-wound inductor might be a fine inductor up to 1 GHz, then become a capacitor at 1.5 GHz because parasitic capacitance dominates. RF datasheets always specify SRF for exactly this reason.
This is what makes the field its own subject. You need new ways to guide energy (waveguides), new ways to generate it (klystrons, magnetrons, Gunn diodes), new components (microstrip, ferrite circulators), and a new measurement language (-parameters).