Usually wires are shorter than the wavelength of the signal they are carrying (e.g. your 60Hz wall outlet has a wavelength of 5000km), but when the wire’s length is on the same order of magnitude as the signal’s wavelength, reflections from the signal become significant and may even cancel out the original signal entirely. This can happen if the wire length is very long (transcontinental power transmission lines) or if the signal frequency is very high (WiFi, Bluetooth, 5G/mmWave).

Analogy

Consider shaking a rope that is tied to a wall at 1 end. When the wave reaches the wall, all of it is reflected back.

Source: https://www.putaiao.nz/12phy/as91523/assets/wave-in-a-string.gif

If the rope were instead tied to a second thicker rope, part of the wave would be transmitted to the thicker section and the rest would be reflected. The thicker the second rope, the more of the wave is reflected. (The wall can be viewed as a rope of infinite thickness, reflecting 100% of the original wave.)

What IS a transmission line?

Tl;dr a pair of “wires” that are a constant distance apart, one of which carries the signal and one of which is “ground”, specifically at a reference voltage. It is very important for the wires to be at the same distance apart throughout the length of the line, since discrepancies will manifest as parasitic inductance/capacitance, resulting in “suckouts” at certain frequencies.

Some examples:

• Twisted pair: literally a pair of thin wires twisted together. The twisting maintains a constant distance between the wires, and it cancels out the magnetic fields induced by the currents through the wires. This is a good “homebrew” solution and is useful up to _ MHz, but for higher frequencies we need
  • Used in cars to carry CAN bus signals
• Coaxial cable: thin copper cable surrounded by aluminum foil sheathing. Has 50ohm resistance as a tradeoff between low attenuation/loss (lowest at 77.5ohm, cable TV uses 75ohm) and maximum power (33ohm).

Source: https://emersongokecarr.blogspot.com/2022/09/coaxial-cable-cross-section.html

• Stripline/Microstrip: used in PCBs. Like a patch antenna, the line runs coplanar to a large reference plane.

• Rectangular waveguide: sometimes this is not considered a transmission line (page 4) because there is only 1 “wire”, but these have very low loss and can handle high power. Usually seen in high-power radar or satellite systems

VSWR, reflection coefficient, and return loss

Similarly, signals sent over a transmission line also experience reflection when the impedance of the transmission line does not match the impedance of the target (usually an antenna). The twice-reflected signal is then added to the transmitted signal, distorting the phase and amplitude of the transmitted signal and producing a standing wave. In the extreme cases, a short or open circuit, all of the transmitted signal is reflected, resulting in 0 ($s(t) - s(t-\pi) = 0$). To quantify how much of the signal is reflected, we examine the Voltage-Standing Wave Ratio (VSWR):

$$ \mathrm{VSWR} = \frac{V_{\max}}{V_{\min}} = \frac{|V_i|+|V_r|}{|V_i|-|V_r|} = \frac{1 + \rho}{1-\rho} $$

where $V_i$ is the amplitude of the incident (transmitted) wave, $V_r$ is the amplitude of the reflected wave, and $\rho = \frac{|V_r|}{|V_i|} = |\Gamma|$ is called the scalar reflection coefficient. If instead we use phasors $\mathbb{V}_i, \mathbb{V}_r$, the more general reflection coefficient is the phasor