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# ROG Blog

# Ring Resonators Help Characterize PCB Materials

Circuit designers often reach for a particular printed-circuit-board (PCB) material based on what they know of its essential material properties, such as dielectric constant (Dk) and dissipation factor (Df). At lower frequencies, having accurate material parameters may be helpful but not crucial whereas, at higher frequencies, knowing such circuit-material parameters as Dk and Df can be critical to the success of a circuit design. For those who need to know, fortunately, a number of different methods have been developed over the years for measuring and calculating a PCB material’s Dk at different frequencies, perhaps other than what is provided on the data sheets by a circuit-material’s manufacturer. One of the most reliable methods for determining a PCB material’s Dk and Df values is through the use of microstrip ring resonator circuit elements, due to the relationship of the resonant frequency of these circuit elements to the permittivity of the PCB material.

Ring resonators represent one method for determining the Dk of a PCB material. Resonance measurement techniques are narrowband and an alternative approach to more broadband transmission-reflection techniques for determining PCB material Dk. A major difference in the two approaches is that resonance measurement methods, which fabricate ring resonator circuit structures on a PCB, work at one frequency at a time, while transmission-reflection approaches can be used for swept-frequency measurements, to determine a circuit-material’s dielectric constant across a range of frequencies.

Especially as available higher frequencies are being used more and more for communications applications, there is a greater need for accurate characterization of the PCB materials used to fabricate those higher-frequency circuits. Ring resonators have often been used to measure the Dk of PCB materials, although they must be used with knowledge and with care. Ring resonators can be formed on a PCB material of interest using standard circuit-fabrication techniques. They can be constructed as single-port or two-port ring resonator structures. The simpler, single-port structure can be used to determine Dk but not Df. The two-port ring resonator, which is a thru-type circuit design with transmission lines leading to and from the resonant circuit, includes feed lines to and from the resonator structure, a closed microstrip transmission-line structure, and coupling gaps between the resonator and the feed lines. The method is well established and proven, and is typically the resonator structure of choice for measurements of PCB material Dk and Df.

This type of resonator structure typically suffers minimal radiation losses, rendering additional calculations or measurements of radiation losses unnecessary. For high-loss PCB materials, calculations of conductor losses can have minimal impact on estimations of Df. Conductor losses are more pertinent for low-loss materials, where those losses may play a more dominant role in the total loss behavior of the PCB material.

The frequency response of the two-port ring resonator structure can be measured with an RF/microwave vector network analyzer (VNA). The unwanted effects of connector interfaces of the ring resonator structure must be eliminated, which can be done through the use of a thru-reflect-line (TRL) calibration of the VNA with appropriate TRL calibration standards.

What are the PCB parameters of interest when using ring resonators to determine dielectric constant? Some pertain to the material itself, such as the thickness of the substrate material and the thickness of the conductor metal. For thinner circuit materials (less than 5 mils in thickness), a ring resonator may not represent the optimum method for measuring PCB material Dk, since it can be difficult to develop a clean resonant peak from the material and ring resonator for a measurement. Some of the PCB parameters of interest are related to the ring resonator structure, such as the fundamental resonant frequency, the line width of the ring resonator, the length of the feed lines, and the length of the coupling gaps.

A microstrip ring resonator is coupled through gaps to the microstrip feed lines for a two-port ring resonator (and single microstrip feed line for a single-port ring resonator). The operation of a two-port ring resonator is based on satisfying a simple condition for resonance defined by the equation:

2πR = nλ_{g} for n = 1, 2, 3…

where

R = the mean radius of the resonator’s ring;

n = the harmonic order of the resonance; and

λ_{g} = the wavelength of the resonance.

Based on the measured frequency response of the ring resonator, the PCB material’s Dk value can be calculated by determining the frequency-dependent value of the effective permittivity for that resonant frequency. The PCB material’s measured frequency response can also reveal other details about the material, including Df, dielectric material losses, and/or conductor losses. Of course, the surface roughness of PCB conductors can also contribute to conductor losses, with increased surface roughness resulting in higher conductor losses.

Rogers offers “design Dk” values of dielectric constant for its PCB materials, optimized for use in modern computer simulation programs. These dielectric constant values are determined by careful measurements, using ring resonator approaches as well as a microstrip differential phase-length technique. It is based on fabricating two microstrip transmission-line segments on a PCB material of interest. The transmission lines are identical in every way except for length. As characterized on an RF/microwave VNA, this difference in length will result in a difference in phase for the two transmission lines. The phase responses of the two transmission lines also depend on the Dk characteristics of the PCB material upon which the transmission lines have been fabricated.

The electrical contributions of the associated coaxial connectors and test fixtures, such as the reactances at the signal launches, must be minimized when using the microstrip differential phase-length approach, in order to produce results that reveal the PCB materials properties based on those two transmission lines. Further details on the microstrip differential phase-length technique can be found at the Rogers Corp. website, at http://www.rogerscorp.com/articles/index.aspx.The method can be used in combination with the ring resonator method when determining a PCB material’s Dk, with the combination helping to minimize issues with gap coupling for the ring resonator circuits.

Do you have a design or fabrication question? John Coonrod and Joe Davis are available to help. Log in to the Rogers Technology Support Hub and “Ask an Engineer” today.