# Microstrip Impedance

PCB Microstrip Impedance Calculator

## Microstrip Impedance Calculator

### Inputs

Trace Thickness
T
Substrate Height
H
Trace Width
W
Substrate Dielectric
Er

### Output

Impedance (Z):

#### Introduction

The microstrip is a very simple yet useful way to create a transmission line with a PCB. There are some advantages to using a microstrip transmission line over other alternatives. Modeling approximation can be used to design the microstrip trace. By understanding the microstrip transmission line, designers can properly build these structures to meet their needs.

#### Description

A microstrip is constructed with a flat conductor suspended over a ground plane. The conductor and ground plane are seperated by a dielectric. The suface microstrip transmission line also has free space (air) as the dielectric above the conductor. This structure can be built in materials other than printed circuit boards, but will always consist of a conductor seperted from a ground plane by some dielectric material.

#### Microstrip Transmission Line Models

Models have been created to approximate the characteristics of the 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}}+.04\left ( 1-\frac{w}{h} \right )^{2} \right \}

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

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

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

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

\Large Where

\Large x_{1}=4\cdot \left ( \frac{h}{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}{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}}

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

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