### May 26, 2011

John Coonrod is a Market Development Engineer for Rogers Corporation, Advanced Circuit Materials Division. John has 23 years of experience in the Printed Circuit Board industry. About half of this time was spent in the Flexible Printed Circuit Board industry doing circuit design, applications, processing and materials engineering. The past ten years have been spent supporting circuit fabrication, providing application support and conducting electrical characterization studies of High Frequency Rigid Printed Circuit Board materials made by Rogers. John has a Bachelor of Science, Electrical Engineering degree from Arizona State University. www.rogerscorp.com/acm. This blog is part of Microwave Journal's guest blog series.

Circuit designers select laminates for printed-circuit boards (PCBs) by merit of relative dielectric constant (Dk), among other parameters. Suppliers of laminates furnish Dk values on their data sheets and web sites, but designers often prefer the reassurance of knowing the Dk value as it relates to their specific application. The last blog explored the way that materials manufacturers typically use four techniques to evaluate the Dk of a dielectric material in its “raw” form, meaning without circuits. This blog will explore some common methods that materials users employ for determining a laminate’s Dk value and focus on a practical method.

Compared to the techniques used by materials manufacturers, RF/microwave circuit designers who use laminates typically rely on fabricating and measuring well-characterized circuits and structures on a material, using circuits and structures with behavior closely matched to the desired application. These test results can then be compared with the values computed by microstrip design equations, which relate the physical dimensions of transmission lines to electrical parameters, such as frequency and phase.

Some of the more common microwave evaluation circuits include microstrip ring resonators, strip resonators, highly selective filters, and phase delay circuits. Of course, many options are available and one test method proven to be a good indicator of the performance of a microstrip transmission line is the differential phase-length method. It is a relatively simple approach and can provide results of Dk performance over a wide range of frequencies.

The microstrip differential phase-length method is based on two transmission-line circuits fabricated on the same material and ideally in close proximity of each other. The circuits should be identical in every way except physical length. Typically, a long and a short circuit are used, with the difference in length a ratio of 3:1 or greater as a general guideline. The connectors on both circuits should be identical. Ideally, a pressure contact connector should be used so the same connectors can be used on both circuits. Whenever possible, a low-reflection fixture should be used for the signal launch.

The basic concept for the differential phase-length method is relatively simple. Two circuits of different physical lengths are measured for their phase responses at a discrete frequency. The microstrip phase-response formula is then used to calculate the effective dielectric constant (ε_{eff}) of the circuit, using the differential length between the two circuits (ΔL) and the differential phase angle (ΔΦ) between the two circuits. The formula can be used to calculate the effective Dk with the given measured data and at that specific frequency:

Once ε_{eff} is known, a software routine which also takes into account the circuit geometry can determine the Dk value of the circuit by an iterative process. When this is determined for one frequency, the process is repeated at the next higher frequency, and so on, ultimately producing a graph of Dk vs. frequency over a wide range of frequencies, as shown in the plot.

A plot of Dk vs. frequency can be a good reference for the Dk value of the material at many different frequencies as well as an indicator as to the dispersive property of the material. It can be seen in the above graph that this material has very good dispersion. For some materials, the slope of the curve is significantly negative, implying more dispersion; dispersion is a change in Dk relative to a change in frequency.

Each Dk test method has its benefits and shortcoming. The differential phase-length method is a transmission/reflection method which is typically less accurate than resonator methods. However the differential phase-length method provides Dk values over a wide range of frequencies whereas the resonator methods typically yield Dk results at one or more discrete frequencies.

Regardless of the chosen evaluation circuit or Dk test method, the designer should try to best match the type of circuit/method in the test to the type of circuit in their application, to obtain the best approximation of the laminate’s Dk for that application. To assist designers, the next blog will discuss a realistic value of relative dielectric constant known as “design Dk.” It is a value developed for circuit designers, to provide more reliable and accurate results when designing RF/microwave circuits with modern circuit and electromagnetic (EM) software simulation tools.