# The Properties of the TEM Mode of Propagation in a Lossless Medium

### Key Takeaways

• The TEM mode of propagation requires two conductors for propagation.

• The TEM mode of propagation is the mode of propagation in coaxial lines, two-open-wire lines, stripline transmission lines, and parallel plate lines.

• In a non-dispersive medium with TEM propagation, the characteristic impedance and phase velocity remain constant. However, multiple dielectrics in coax and striplines lead to non-pure TEM modes. In RF and microwave circuits, electromagnetic waves propagate in different modes, namely transverse electromagnetic (TEM) mode, transverse electric (TE) mode, and transverse magnetic (TM) mode.

To support TEM mode, a minimum of two conductors are required. Parallel plate and stripline transmission lines support only the TEM mode of wave propagation. However, with non-idealities in the conductors and dielectric, the characteristics of the wave propagation vary. The properties of TEM mode in a lossless medium are totally different from that of a lossy medium.

Let’s take a closer look at the TEM mode of wave propagation.

## The Transverse Electromagnetic Mode of Transmission

Consider a transmission line where the electric and magnetic field lines are transverse to the direction of propagation in the Z direction. This can be expressed as TEM mode and is characterized by EZ= HZ= 0.

TEM mode requires two conductors for propagation, and it is the mode of propagation in coaxial lines, two-open-wire lines, stripline transmission lines, and parallel plate lines. This mode doesn’t exist in hollow waveguides and cavities.

For the TEM mode of propagation, field lines need to exist within a homogenous medium. In ideal cases of coax and stripline transmission lines, the above condition is satisfied. In a non-dispersive medium with TEM propagation, the characteristic impedance and phase velocity remain constant. However, the multiple dielectrics in coax and striplines lead to non-pure TEM modes.

## TEM Propagation in Transmission Lines

A pure TEM mode of propagation in a transmission line requires several criteria:

1. The electric and magnetic fields should be confined to the homogenous dielectric material.
2. The basic requirement for supporting TEM mode is two conductors.
3. The electric field lines remain straight when the conductors have infinite conductivity.
4. The dielectric substrate needs to be lossless.
5. The cross-section of the transmission line should remain constant.

## Properties of the TEM Mode in a Lossless Medium

The electric and magnetic fields in the X and Y direction are given by general equations, where h2=Y2+k2,  y = α + jβ and  k=ω√με: In a lossless medium, the attenuation constant α = 0 and the propagation constant reduces to: For the TEM mode of propagation to exist in a lossless medium, the following condition should be satisfied: Rearranging the above equation, we can get the relationship between the propagation constant and wave number as: The TEM mode of propagation in a lossless medium satisfies the equation above. The phase velocity of TEM propagation is derived as: The phase velocity remains constant in an unbounded lossless dielectric. The wave impedance or intrinsic impedance is given by the following equation: We have seen the properties of the TEM mode in a lossless medium. However, there are no pure or ideal TEM modes in coax cables, striplines, or parallel plate transmission lines. Most of the transmission line fields spread in dielectric medium and air, and this makes the mode of wave propagation non-TEM.

Understanding the properties of the TEM mode in a lossless medium helps us understand wave propagation characteristics in general. This understanding can help when designing transmission lines with minimum losses. Cadence’s software also offers tools to support the design of transmission lines in RF circuits with comparatively fewer losses.