Circuit traces on microstrip printed circuit boards (PCBs) form the interconnections between components in addition to the components themselves. These controlled-impedance lines are typically designed with a characteristic impedance of 50 Ω for RF/microwave circuits or 75 Ω for cable television (CATV). The equations commonly associated with calculating the geometry of microstrip lines based on a desired impedance are quite complex and not easy to handle. Fortunately, a set of simplified equations has been developed based on well-known publications from IPC (www.ipg.org).

In these simplified equations, the dimensions for thickness, T, must be expressed in microns (µm), although the values for height, H, and width, W, can have any measurement unit congruent with one another. The plots shown throughout the article assume a copper thickness of 35 µm with the errors are calculated as:

where:

Z_cal = the calculated impedance and Z_theor = the expected value (i.e., 50 or 75 Ω

Figure 1 shows a cutaway view of a typical microstrip circuit with the three dimensions and the relative dielectric constant (e_r). In the IPC's publication IPC-2141, the impedance of a microstrip line is given by:

This relationship can be rearranged to show width, W, explicitly as:

When W is determined for characteristic impedance (Z₀ of 50 Ω or 75 Ω the calculations can be performed by means of:

Plots of errors based on circuit-board materials with several different dielectric constants were determined by using the previous equations. The results are shown in Fig. 2.

To simplify the microstrip dimensional formula, the exponential term can be linearized. This linear series expansion leads to:

Assuming a range of dielectric constants (e_r) from 3 to 10 as in the original formula, the value of x₀ = 2.6 for a characteristic impedance (Z₀) of 50 Ω and the value of x₀ = 5.9 for a characteristic impedance of 75 Ω so that: