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# ROG Blog

# Prime Material Parameters For Impedance Matching

#### Impedance matching, Part 2

Successful high-frequency circuit design requires achieving an impedance match among a wide range of transmission-line features, circuit elements, and active and passive components. High-frequency circuits typically operate at a characteristic impedance of 50 Ω, and matching the different parts of the circuit and its components to that impedance helps maximize the transfer of power from a source to a load, such as from a transmitter to an antenna. In the previous blog, some of the challenges in achieving good impedance match at RF/microwave frequencies were detailed, including the importance of a printed-circuit-board (PCB) material with stable and consistent effective dielectric constant. To further explore the impact of a circuit substrate on high-frequency impedance matching, two popular PCB materials from Rogers Corp. (www.rogerscorp.com), RO3010™ and RO3035™ circuit materials will serve as examples to show how circuit-material parameters can be translated into solutions for high-frequency impedance-matching issues.

Both RO3010 and RO3035 laminates are ceramic-filled PTFE-based circuit materials with consistent mechanical properties, although with different values of dielectric constant. Both are designed to provide stable dielectric constant versus temperature and frequency with a dielectric constant that does not vary across the width, length, and thickness of the materials. This consistency is instrumental in achieving a good impedance match for all parts of a circuit, without having to “customize” impedance tuners or quarter-wave transformers because of changes in the dielectric constant of the material.

The RO3010 laminate, suitable for microstrip and stripline circuits through 77 GHz, is defined by a “process” dielectric constant of 10.2 at 10 GHz, held to a tolerance of ±0.3 in the z-direction (thickness of the material). The material’s data sheet also lists a second value of dielectric constant of 11.2 in the z-direction, from 8 to 40 GHz. This is referred to as the “design” dielectric constant, recommended for use in commercial simulation software.

Why two different values for dielectric constant? And what is the significance of having two difference values of dielectric constant to impedance matching with this material? For the case of RO3010 material, and in fact for many circuit laminates, values of dielectric constant are determined by standardized test methods. The “process” value is the result of a clamped stripline test method in which a stripline resonator is formed using two sheets of RO3010 laminate and a clamping fixture with a thin resonator circuit. The frequency of the resonator is measured and used to determine the dielectric constant. A potential problem with this method is any air entrapped between the two sheets. As noted in the last blog, air has a dielectric constant of 1.0. If it is mixed in with materials being evaluated, and if electromagnetic (EM) waves propagate through the air, the determination of dielectric constant can be altered.

The clamped stripline test method is also sensitive to the anisotropic nature of most PCB materials—that is, the dielectric constant is typically different in the x and y directions than in the z direction. The stripline resonator method can be more sensitive to the influence of the material’s dielectric constant in the x and y directions than in the z direction.

The “design” dielectric constant value for RO3010 laminate results from the differential phase-length method, which is based on measurements using microstrip transmission lines. In this method, two microstrip circuits of different lengths are fabricated on a material under test and phase angle differences are evaluated using the same connectors or test fixture and an appropriate test instrument, such as a vector network analyzer (VNA). From the lengths of the circuits and their differences in phase angles, the influence of the PCB material on the wave propagation of the two circuits can be used to determine the dielectric constant of the material at a specific frequency. This method is relatively accurate in gauging the dielectric constant in a material’s z-direction and is less affected by a material’s anisotropic effects. But it is relatively slow and not well suited for high-volume production.

A simple example may help to understand the importance of the “design” dielectric constant, or Design Dk as it is known, to impedance matching. This example consists of a circuit application at 2 GHz, using 25-mil-thick RO3010 laminate, and it requires a main line impedance of 50 Ω and a load with 30-Ω resistance and -40-Ω reactance. If the process Dk of 10.2 is used to calculate the circuit dimensions, a quarter-wavelength transformer section would have a length of 0.542 in., a width of 0.055 in., and would be placed 0.271 in. from the load. If the same transformer width is assumed, and the same laminate, but the circuit dimensions are now based on a Design Dk value of 11.2, the quarter-wavelength transformer section would have a length of 0.518 in. and would be placed 0.259 in. from the load. The two different Dk values yield quite different results in terms of transformer length and location from the load.

The RO3035 circuit material also features very consistent electrical properties but with much lower dielectric constant values, with a “process” dielectric constant of 3.50 ± 0.05 in the z-direction at 10 GHz, measured by the clamped stripline method, and 3.6 in the z-direction from 8 to 40 GHz as measured by the differential phase length method. It also exhibits stable dielectric constant with frequency and temperature to minimize performance variations when pursuing impedance-matched circuits. Because a number of material properties contribute to impedance and impedance matching, including dielectric thickness and conductor thickness, the RO3010 and RO3035 materials are available with a number of different dielectric thicknesses and electrodeposited copper foil thicknesses, allowing designers to select the mechanical parameters that can best suit their efforts to control impedance.

Impedance matching of RF/microwave circuits can be challenging enough without dealing with unexpected variations in material parameters, such as inconsistent copper cladding and dielectric thickness. The key parameters for the RO3010 and RO3035 circuit laminates are tightly controlled to help make impedance matching more straightforward and based on the expected impedances of circuit dimensions for a specific effective dielectric constant. In general, material properties that are critical to impedance matching and maintaining a desired impedance include tight control of the dielectric constant, control of conductor thickness, and control of dielectric thickness. For example, for achieving impedance-matched circuits, dielectric materials maintained to thickness tolerance of ±10% or better can help achieve impedance matches that are consistent and predictable.

The next blog will take a close look at designing RF/microwave bandpass filters, and why RT/duroid® 6010 PCB material provides the right features for filters.

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.