Linking Electromagnetism to Transmission Line Theory with Telegraphers Equations

Personally, one of the most fascinating topics to me in RF is the link between electromagnetism and transmission line theory. It's the intersection between physics and practical RF engineering. Electromagnetism starts with Maxwell's equations which describe how electric and magnetic fields behave, interact, and propagate through space.

However, when you start analyzing electrical signals traveling along transmission lines, solving Maxwell's Equations can become unnecessarily complicated. Instead of analyzing the full electromagnetic field distribution, you can describe wave propagation using voltage and current along a transmission line using a distributed model.

Unlike analog-based transmission lines, RF-based transmission lines use a distributed model instead of a lumped model. This means the resistance, inductance, conductance, and shunt capacitance is represented in terms of unit length. This introduces us to Telegrapher's Equations which describe how voltage and current vary along a transmission line as a function of distance and time, accounting for the distributed resistance, inductance, conductance, and capacitance.

The first equation describes voltage variation. The equation describes how voltage changes along the transmission line due to conductor resistance and the electric field induced by a changing magnetic field.

The second equation describes current variation. The equation describes how current changes along the transmission line due to dielectric leakage and a changing electric field.

For a lossless transmission line without resistance or conductance, the equations simplify and reveal something pretty important: A changing current produces a changing magnetic field, which induces an electric field and a changing voltage corresponds to a changing electric field, which is associated with displacement current and magnetic-field behavior. This coupling between electric and magnetic fields is what allows EM waves to propagate.

In a TEM transmission line, the Telegrapher's Equations describe that propagation in terms of voltage and current rather than explicitly solving for the electric and magnetic field distributions. This is what makes RF engineering possible.