Dielectric constant (Dk or relative permittivity) is an important starting point for many circuit designers, whether specifying a printed circuit board (PCB) material for a design or with a material in hand and using its Dk in computer circuit simulations. Especially at higher, mmWave frequencies where wavelengths are short and circuit dimensions must be precise, according to a substrate’s Dk, the accuracy of a circuit material’s Dk can impact the success of a prototype. Circuit material Dk is determined by measurements and derivations based on known physical parameters of the circuit material and any test circuits and fixtures used in the measurement procedure.
There is no perfect Dk measurement method. Because of this, there are many different Dk test techniques that attempt to achieve the highest accuracy possible. The methods have various levels of difficulty and accuracy and can yield different Dk values when testing the same material at the same frequency and temperature. As electronic circuits are required more and more for mmWave applications, variations in Dk values can lead to delays in the design process. When a material’s Dk is not as published, prototype circuits built on that material must start with the most accurate Dk value possible, especially in achieving the electromagnetic (EM) characteristics required for electronic designs with the fine features of mmWave circuits. Differences in Dk test methods can deliver different Dk measurement results, so a basic understanding in how different Dk test methods work can help when specifying a circuit material for mmWave circuits.
As circuits and applications climb in frequency, different test methods have been developed to determine essential material parameters such as Dk and dissipation factor (Df). Measurement techniques to determine Dk typically are material- or circuit-based approaches. Material-based Dk test methods place a material in a test fixture while circuit-based test methods fabricate a reference circuit or structure on the material and derive Dk from measurements made on the circuit or structure. Most material-based Dk test methods measure unclad material, without conductive metal lamination, while circuit-based material measurements include the contributions of the conductors.
Material-based Dk test methods typically determine Dk at a single frequency and temperature, while circuit-based Dk test methods can be performed over a range of frequencies, depending upon the type of test circuit. Test circuits based on transmission-line structures, such as microstrip and stripline, for example, can be evaluated with continuous swept-frequency measurements. Test circuits using resonators are fabricated and tuned to a single frequency.
Many Dk measurement methods are standardized, according to electronics industry organizations such as IPC (www.ipc.org). IPC TM-650, for example, is a collection of test methods for characterizing PCBs for Dk, dissipation factor (Df), and other essential material parameters. Still, even with standardization and clear guidelines for performing a measurement, different Dk measurement methods will yield different Dk values for the same material simply because of the variables involved in each measurement. Knowledge of how Dk test methods differ can provide insight to designers when comparing materials and Dk values, especially if those values have been determined by different test methods.
Because different Dk test methods can yield different Dk values, some material suppliers such as Rogers Corporation provide several Dk values for a material: “process” and “design” Dk. For Rogers, process Dk values are based on specific standardized measurements, such as the test method detailed in IPC-TM-650 2.5-5.5, at a single frequency and temperature. Design Dk values, on the other hand, apply to a range of frequencies; the values may be based on data from multiple test methods, such as material- and circuit-based Dk test methods. For most designers, design Dk values provide a more practical idea of a material’s Dk, especially if the specified frequency range applies to their area of interest. When it does not, such as at mmWave frequencies (30 to 300 GHz), a designer may want to characterize the material’s Dk across the frequency of interest and perform their own Dk measurements. By understanding that different Dk test methods yield different Dk results, they can be better prepared for different Dk values they achieve when performing different Dk measurement approaches.
Comparing Dk Test Methods
The accuracy of each Dk test method is affected by numerous factors, such as the calibration accuracy of the test equipment, often a vector network analyzer (VNA), variations in the test fixtures used for material-based measurements, and variations in the fabrication of the transmission-line or resonant structures used for circuit-based Dk measurements. Most circuit materials are anisotropic and Dk varies along the different axes of a sheet of material, through its x (length), y (width), and z (thickness) axes. While test methods that determine Dk through the x and y axes are useful, measurements that determine Dk through the z axis are usually of most interest because this is the Dk of the dielectric layer between most circuits’ transmission lines.
The clamped stripline resonator test described by standard IPC-TM-650 2.5-5.5 is used by Rogers Corp. to determine process Dk values for its circuit materials; it can also be used to measure Df, with both parameters determined through the thickness or z-axis of the material. This Dk test method is accurate and repeatable but provides a Dk value at a single frequency, such as 10 GHz. It characterizes unclad dielectric material, without conductive metal. To perform the material-based test, a material under test is clamped in a test fixture surrounding a resonator card typically holding a stripline resonator. The metal clamps securing the test fixture also serve as ground planes for the resonator. For repeatable, accurate measurements, the test fixture must be assembled with care since any air (with a Dk of 1) trapped inside the fixture with the material under test will become part of the test and lower the value of the Dk that is determined for the material.
Test fixtures are essential components in any material based Dk test setup. The fixture typically uses some form of resonator and the measurements of frequency combined with knowledge of the material’s physical parameters, such as thickness, help determine the material’s Dk. The repeatability and accuracy of material-based Dk test techniques depend on high-quality fabrication of the test fixture, just as the repeatability and accuracy of circuit-based Dk measurement methods depend on the fabrication quality of the test circuits.
Several types of resonant structures are used in test methods to determine circuit material Dk values, including the split-post dielectric resonator (SPDR) test, the full sheet resonance (FSR) test, and the split cylinder resonator test, all defined by test methods in the IPC-TM-650 series of measurements. SPDR measurements compare a resonant cavity filled with air (an empty cavity) to the same cavity filled with the material under test to extract the difference in Dk. The accuracy of this approach depends on precise measurement of material thickness and the resonant cavity dimensions. It provides Dk results in the x-y plane but not in the z-axis. FSR measurements use a full copper clad panel of material, with swept-frequency measurements to search for standing waves or resonant peaks. The copper clad panel behaves as an open-walled parallel plate waveguide and the standing waves along the length of the panel are measured. Material dimensions along with the resonant frequency can provide enough detail to derive the material’s Dk at that resonant frequency. This method works well for longer wavelengths and lower frequencies but is not accurate when evaluating thinner circuits.
The split cylinder resonator test is based on placing a material sample between two halves of a cylindrical resonant cavity. One half is fixed in place and the other half is movable, with an adjustable gap between the two cylinder halves to accommodate different thicknesses of material to be evaluated. Small coupling loops are added to holes in the side of each cylinder half to measure the electric field that is tangential to the x-y plane of the material under test to determine the Dk.
Circuit-based Dk measurement methods are also different in how they are applied and the results they produce. These test approaches may depend on measuring the transmission and reflection characteristics of transmission-line circuits or structures or in measuring the frequency and phase of a resonant circuit. Transmission-line types include microstrip, stripline, and coplanar waveguide (CPW) while resonant circuits include ring resonators and sometimes structures that use resonators such as bandpass filters.
High accuracy depends on precise measurement of material and circuit physical dimensions, such as transmission-line widths, copper conductor thickness, and dielectric thickness, and such measurements become especially challenging at the dimensions of mmWave circuits and structures. Variations in dielectric material thickness as well as the roughness of a copper conductor can result in deviations in a transmission-line signal path that are more noticeable at mmWave frequencies and result in loss of accuracy when determining Dk. Smoother copper conductors form shorter transmission paths and different Dk values from measurements. Such physical circuit deviations are also important for resonator circuits in which precise measurements of frequency and phase are critical.
Many test methods have been developed to determine circuit material Dk with many different approaches. While a single material may yield consistent Dk values when characterized with the same test method in the same way each time, different Dk test methods will yield different Dk values for that same material. Quite simply, variations in test circuits and fixtures result in variations in Dk values. The variations can be minimized by using the same Dk test method each time, but that test method may not provide a Dk value under the conditions (such as frequency) required to support an application of interest, such as at higher, mmWave frequencies. By better understanding how the Dk test methods vary, it may not be possible to find the perfect Dk test, but at least the optimum Dk measurement approach can be followed for an application of interest.
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