Smaller is often wiser in this age of electronic mobility and portability, and the choice of circuit material when starting a design has much to do with attempts to create smaller RF and microwave circuits. Circuit materials with higher dielectric constant (Dk) typically yield circuits with smaller features and dimensions for a given frequency range. But the higher Dk values can also result in increased insertion loss and other performance tradeoffs. The Dk value of a circuit material will also impact such circuit parameters as radiation loss, dispersion, and coupling. As a compromise, smaller circuits can be achieved with minimal tradeoffs by combining different circuit materials with low and high Dk values into composite multilayer printed circuit boards (PCBs) capable of good performance for the cost.
The wavelength of a given frequency shrinks with increasing Dk, resulting in smaller circuits fabricated on circuit materials with high Dk values than on circuit materials with lower Dk values. The circuit materials with higher Dk values also result in slower phase velocities for the electromagnetic (EM) waves traveling through circuits on those materials. The Dk of a circuit material is typically measured through the thickness or z-axis of the material at 10 GHz. The z-axis Dk values for commercial circuit materials can be as high as 10 or more and as low as 2 (compared to the Dk of air which is equal to 1). While the characterization is objective, Dk values of 6 or more are considered high.
Transmission lines on circuit materials with lower Dk values will have faster phase velocity than the same transmission lines on circuit materials with higher Dk values, a consideration when attempting to miniaturize phase-sensitive circuits such as phased-array antennas. In addition, circuit materials with higher Dk values tend to exhibit more dispersion than circuit materials with lower Dk values. Circuit materials with higher Dk values are used for directional couplers and other circuits requiring higher coupling coefficients.
Circuit materials are typically anisotropic in terms of Dk behavior, with different Dk values in all three axes, although materials are usually compared according to their z-axis Dk values. Dk differences in circuit dimensions tend to be greater between the z-axis and the x-y plane for materials with higher Dk values than for materials with lower Dk values. The Dk values in all three dimensions of a circuit material will determine the performance of transmission lines, such as microstrip, fabricated on that material. The anisotropic Dk nature of circuit materials is not often a consideration for many high frequency circuits but it can be a concern, especially if the Dk values for the x-y plane are much different than in the z axis. Such differences can result in unexpected performance for edge-coupled circuits in which coupling is highly dependent upon the Dk value in the x-y plane.
When attempting to miniaturize a circuit, an initial thought may be to minimize the thickness of the circuit material, but circuit material thickness affects several performance parameters for high frequency circuits. While the radiation loss of a high frequency circuit tends to increase with increasing frequency, a thicker circuit material will also exhibit higher radiation loss than a thinner circuit material with the same Dk value. The choice of Dk also influences the amount of radiation loss for a given circuit layout and design since circuit materials with higher Dk values will have lower radiation loss than circuit materials with lower Dk values.
Thinner circuits can be beneficial for circuit designs where excessive resonances may be a concern, such as between circuits in a multilayer PCB. The amount of resonances will usually depend on the type of transmission line in a circuit. For example, microstrip transmission lines tend to be more susceptible to resonances and propagation issues than other types of RF/microwave transmission lines, such as stripline and coplanar-waveguide (CPW) transmission lines. Thinner circuit materials can help shrink a PCB’s volume while limiting radiation loss and transmission-line propagation problems, such as resonances and moding. A rule of thumb was once to use a circuit material that is thinner than one-quarter wavelength of the highest operating frequency of a circuit, but a safer approach is to select a circuit material thickness that is thinner than one-eighth wavelength of the highest operating frequency.
To complicate matters, the dimensions of a transmission line, such as microstrip, will depend on the thickness of the circuit material, such as a circuit laminate or prepreg material. Circuits using thicker substrates have wider conductor widths, which exhibit lower insertion loss than more narrow conductor widths although they can suffer propagation problems compared to circuits with narrower conductors. In keeping with the choice of circuit material thickness for a high frequency design, the conductor width should also be narrower than one-eighth wavelength of the highest operating frequency.
In addition, the circuit material Dk plays a role in determining the transmission-line conductor width, since conductors fabricated on high-Dk circuit materials will exhibit lower impedance than the same type and size conductors fabricated on low-Dk circuit materials. To maintain the impedance of the conductors in a 50-Ω environment, for example, narrower conductors must be used on a circuit material with higher Dk value than on a circuit material with lower Dk value.
Tradeoffs in using circuit materials with different Dk values are numerous but circuit size can be saved when using higher-Dk circuit materials and miniaturization can be achieved with high performance by combining high-Dk and low-Dk circuit materials into composite assemblies. The size of bandpass filters formed of resonant elements is dependent upon circuit material Dk since the space between each filter element determines the amount of coupling in the circuit which is influenced by the circuit material Dk. Circuit materials with high Dk provide greater coupling and allow more space between filter resonant elements than the same filter fabricated on circuit materials with low Dk.
To demonstrate the advantages of using circuit materials with different Dk values or even combining the different materials into a composite assembly, bandpass filters were assembled on high-Dk and low-Dk circuit materials (see Microwave Journal article, September 2012, “Harmonic Suppression of Edge Coupled Filters using Composite Substrates”). The high-Dk material was RT/duroid® 6010.2LM circuit laminate with a Dk of 10.7 and 2929 bondply material with Dk of 2.9, both materials from Rogers Corp. (www.rogerscorp.com). Due to the differences in circuit behavior brought about by the circuit materials with different Dk values, computer modeling was performed to determine the required ratio of the two different materials’ thicknesses. The modeling helped to create a composite filter design with size comparable to a filter fabricated on the high-Dk material alone but with improved electrical performance, such as significant reduction in harmonic resonances and improved stopband characteristics. As the study showed, smaller circuits are often possible without sacrificing performance, by considering more than one circuit material for the final circuit design.
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