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18 DESIGN007 MAGAZINE I DECEMBER 2023 waveguides. e microstrip line is the most common type of impedance structure: an external trace separated from a plane layer by a dielectric material. Microstrips are compact, allowing for greater design flexibility. ey are also easy to probe and measure, making them suitable for easy fabrication and a wide range of applications. Figure 1 shows a microstrip trace with width (w) and thickness (t). e dielectric material separating the trace from the plane has an over- all thickness of h and a dielectric constant of ε r . Key Calculations Involved in Microstrip Design Incorporating a microstrip line into a PCB requires calculations involving the analysis and design of transmission lines which are widely used in microwave and RF circuits. Characteristic impedance, the effective dielec- tric constant, and propagation are all criti- cal pieces of information for the designer to understand. Characteristic Impedance Characteristic impedance (Z 0 ) is the ratio of voltage to current in a transmission line and is an important parameter for determining the performance of microstrip circuits (Figure 2). Figure 2: Illustration of characteristic impedance. e characteristic impedance of a microstrip line can be approximated as: h is the height of the substrate w is the width of the trace t is the thickness of the trace Effective Dielectric Constant Effective dielectric constant (ε r ) is the rela- tive permittivity of the substrate material as seen by the signal on the microstrip line (Fig- ure 3). For a microstrip line, the dielectric of the material and the dielectric of the sur- rounding air are the two values that are used to understand the effective constant. Figure 3: Illustration of effective dielectric constant. εr1 is the permittivity of the substrate εr2 is the permittivity of the air above the substrate h is the height of the substrate w is the width of the trace Velocity of Propagation e velocity of propagation (vp) is the speed of a signal as it travels down the microstrip line—or through any transmission line. It is typically expressed as a fraction of the speed of light, due to the effective dielectric constant of the substrate material (Figure 4). Figure 4: Illustration of velocity of propagation. c is the speed of light in a vacuum: 300 million meters/second Propagation Delay Propagation delay (τ) is the time taken for a signal to travel down the microstrip line. is is a relatively straightforward equation using the velocity of propagation and the distance the signal must travel (Figure 5). Figure 1: Illustration of a microstrip trace.