Embedded Microstrip Impedance

PCB Embedded Microstrip Impedance Calculator

Introduction

The embedded microstrip is a similar in construction to the microstrip transmission line. Modeling approximation can be used to design the embedded microstrip trace. By understanding the embedded microstrip transmission line, designers can properly build these structures to meet their needs.

Description

An embedded microstrip is constructed with a flat conductor suspended over a ground plane. The conductor and ground plane are seperated by a dielectric. There is also a layer of dielectric material above the conductor. One case of an embedded microstrip transmision line is a microstrip trace with soldermask.

Embedded Microstrip Transmission Line Models

Models have been created to approximate the characteristics of the embedded microstrip transmission line.

\Large When \frac{w}{h_{1}}

\Large er_{eff}=\frac{er+1}{2}+\frac{er-1}{2}\cdot \left \{ \sqrt{\frac{w}{w+12h_{1}}}+.04\left ( 1-\frac{w}{h_{1}} \right )^{2} \right \}


\Large When \frac{w}{h_{1}}\geq 1


\Large er_{eff}=\frac{er+1}{2}+\frac{er-1}{2}\cdot \left \{ \sqrt{\frac{w}{w+12h_{1}}} \right \}


\Large w_{eff}=w+\left ( \frac{t}{\pi } \right )\cdot \ln \left \{ \frac{4e}{\sqrt{\left ( \frac{t}{h_{1}} \right )^{2}+\left ( \frac{t}{w\pi +1.1t\pi } \right )^{2}}} \right \}\cdot \frac{er_{eff}+1}{2\cdot er_{eff}}


\Large zo_{embed}=zo\cdot \left \{ \frac{1}{\sqrt{e^{\frac{-2b}{h_{1}}}+\frac{er}{zo_{surf}\cdot er_{eff}}\cdot \left ( 1-e^{\frac{-2b}{h_{1}}} \right )}} \right \}


\Large Where


\Large zo=\frac{\eta_{o}}{2\pi \sqrt{2}\sqrt{er_{eff}+1}}\cdot \ln \left ( 1+4\cdot \left ( \frac{h_{1}}{w_{eff}} \right )\cdot \left ( x_{1}+x_{2} \right ) \right )


\Large x_{1}=4\cdot \left ( \frac{h_{1}}{w_{eff}} \right )\cdot \left ( \frac{14\cdot er_{eff}+8}{11\cdot er_{eff}} \right )


\Large x_{2}=\sqrt{16\cdot \left ( \frac{h_{1}}{w_{eff}} \right )^{2}\cdot \left ( \frac{14\cdot er_{eff}+8}{11\cdot er_{eff}} \right )^{2}+\left ( \frac{er_{eff}+1}{2\cdot er_{eff}} \right )\cdot \pi ^{2}}


\Large b=h_{1}-h_{2}

The source for these formulas are found in the IPC-2141A (2004) ?￠????Design Guide for High-Speed Controlled Impedance Circuit Boards?￠????