# 4.8: Multimoding Considerations for Stripline

• • Michael Steer
• Lampe Distinguished Professor (Electrical and Computer Engineering) at North Carolina State University

A stripline transmission line is shown in Figure 4.7.3. Being a homogeneous line, stripline does not have a frequency-dependent permittivity until molecular effects become important at hundreds of gigahertz (depending on the substrate). Stripline has the frequency-dependent line resistance

$\label{eq:1}R(f)=\left\{\begin{array}{ll}{R(0)}&{f\text{ such that }t\leq 3\delta_{s}}\\{R(0)+R_{\text{skin}}(f)}&{f\text{ such that }t>3\delta{s}}\end{array}\right.$

where $$R(0) = R_{\text{strip}}(0) + R_{\text{ground}}(0)$$ is the resistance of the line at low frequencies. $$R(f)$$ describes the frequency-dependent line resistance, which is due to both the skin effect and current bunching. Approximately,

$\label{eq:2}R_{\text{skin}}(f)=R(0)k\sqrt{f}$

where $$k$$ is a constant.

As with microstrip, EM simulations are recommended to determine line loss. However, provided that regular vias are used between the ground planes (and eliminating the TEM parallel plate mode), attenuation due to radiation loss is minimal.

The moding that is of most concern with stripline is the parallel plate waveguide mode that can be excited at stripline discontinuities. The simplest parallel plate waveguide mode has no variation of the fields in the transverse direction, so there is a uniform electric field from the top plate to the bottom plate. This mode can propagate down to DC. In normal operation a stripline has an $$E$$ field directed from the strip to the top ground plane and an oppositely directed $$E$$ field from the strip to the bottom ground plane. Thus excitation of the parallel plate waveguide mode can be suppressed by making sure that the two ground planes are at the same potential. This is done by periodically shorting the two ground planes together using through-substrate vias. Apart from this consideration, the multimoding considerations presented for the microstrip should also be considered.