Transmission Lines

TEM (transverse electromagnetic) wave

- Wave propagation direction: +z

- E_z = 0 and H_z = 0

Line length Δz << λ (wavelength)

- The sinusoidal signal does not change much while the wave travels over Δz

- The transmission line appears to exist at one point.

A small section of a transmission line is represented as an equivalent

circuit shown above.

R, L: Series elements. Resistance and inductance per unit length (one meter). They are due to metal wires or traces.

G, C: Parallel elements. Conductance and capacitance per unit length. They are due to material filling the line.

Apply KVL and KCL to obtain the two equations.

Take a limit as Δz → 0 and divide both sides with Δz to otain a system of partial differential equations for V(z) and I(z).

Finding solutions to the telegrapher's equation.

γ : complex proagation constant

α : attenuation constant

β : phase constant

Waves on a transmission line can travel in +z and –z directions.

Characteristic impedance: Remember the definition.

The current wave can be expressed using V(z) and Z₀.

Z_L : load impedance

: either one determined by Z_L and Z₀.

Reflection coefficient: Remember the definition and its formula.\

Load impedance can be found from the reflection coefficient:

Some special cases:

Short (단락, 단락회로)

Open (개방, 개방회로)

Load (정합, 정합부하)