### June 28, 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.

Planar resistors can be fabricated along with circuit patterns on selected high-frequency laminate materials. By executing processing steps not unlike those that form circuits on printed-circuit boards (PCBs), embedded planar resistors can be added to a high-frequency PCB. They can be made with precise values, with tight tolerances, and with reasonable power-handling capabilities. They can replace discrete resistors with their associated assembly and reliability issues, in many high-frequency applications. Planar resistors are well suited to compact designs, including in multilayer circuits where they can minimize or eliminate plated through holes for resistors.

Planar resistors on PCBs are fabricated from resistive films embedded into special high-frequency laminates, such as low-loss RT/duroid® 6202PR and RO4000® laminates from Rogers Corporation (www.rogerscorp.com). RT/duroid 6202PR incorporates OhmegaPly® resistive film foils from Ohmega Technologies (www.ohmega.com) while

RO4000 laminates feature Ticer™ TCR® thin film resistor foils from Ticer Technologies (www.ticertechnologies.com). As part of the laminates, the resistive foil layer lies between the dielectric layer and the conductive copper layer. Resistors are formed by etching away selected portions of the copper layer to expose precise areas of the resistive layer.

For some time, engineers were reluctant to design and fabricate high-frequency circuits with embedded planar resistors. The process of forming planar resistors was thought to be limited in achieving accurate resistor values with tight tolerances. However, in recent years resistive foils and the laminates that employ them have improved dramatically, to where planar resistors can now be fabricated with tolerances as tight as ±5%.

Working with a laminate with resistive foil is simple. When selecting RO4000 materials with resistive foil, for example, a user has a choice of RO4003™ laminate, with process dielectric constant (Dk) of 3.38 in the z-axis at 10 GHz, and RO4350B™ laminate, with process Dk of 3.48 in the z-axis at 10 GHz. As was noted in the last blog, for design purposes, a design Dk value for each material provides better results when used in modern software design tools. For RO4003 and RO4350B laminates, the design Dk values are 3.55 and 3.66, respectively, in the z-axis at 10 GHz. Both laminates are available with embedded resistive foils, with different thicknesses and resistance levels. Resistive foils are specified in terms of ohms per square (Ω/sq) of material, such as 25, 50, 100 Ω/sq, and higher, depending upon which resistor values are needed.

To form a planar resistor, the circuit is formed by imaging and etching away unneeded copper, leaving the desired transmission lines and circuit structures. Where the copper has been removed, the resistive foil layer beneath it is now exposed. The resistive layer can be chemically removed, except for the areas required for planar resistors. This is done by protecting all required copper circuitry with photoresist, but leaving openings in the photoresist to define the desired planar resistors. The copper will be etched away in the openings, exposing the resistive layer beneath and forming resistors in conjunction with the copper conductors. With this subtractive processing approach, it is actually the precision in etching the copper that dictates the accuracy in achieving precise resistor values and tolerances.

The resistor value of a planar resistor is a function of the length of a planar resistor divided by its width and then multiplied by the surface resistance of the resistive material. Suppliers of resistive films offer free calculators and technical assistance on their web sites to help designers determine the size of a planar resistor based on the type of resistive foil, the desired resistor value and tolerance, and the power-handling capability. In general, larger planar resistors allow tighter resistance tolerances, with tight tolerances more difficult to achieve with smaller planar resistors.

Online calculators and design guides are based on simple formulas to calculate resistor dimensions. They start with a choice of resistive foil resistance value, such as 50 Ω/sq, and then prompt a user for additional inputs, such as the desired resistance of the resistor to be fabricated, the resistor tolerance, and the power dissipation.

Tolerance typically dominates calculations of planar resistor size, since resistor tolerance is less controlled for smaller resistors. For example, a 50-Ω resistor formed on 50 Ω/sq resistive material with 100-mW power dissipation will measure 1000 x 1000 mils for ±5% tolerance. But if the allowable tolerance is raised to ±10%, with all other conditions the same, the size of the 50-Ω resistor is only 27 x 27 mils (the calculator provides resistor sizes in terms of mils, or thousandths of an inch). If the power dissipation for this resistor is dropped to only 50 mW, the size of a ±10%, 50-Ω resistor shrinks further, to 20 x 20 mils. (Note that because this is a 50-Ω resistor formed on 50 Ω/sq resistive foil, both dimensions are equal. For any other resistance value using this material, the dimensions are unequal. Also, resistive foils with higher resistance values will provide more resistance in smaller unit sizes.)

Power dissipation also impacts the size of a planar resistor. For example, in the case of a 50-Ω resistor formed on 50 Ω/sq material at ±10% tolerance, the size jumps from 20 x 20 mils for 50 mW power dissipation to 341 x 341 mils for 1000 mW (1 W) power dissipation. For the same resistance value and power rating, but with improved tolerance of ±5%, the size of the planar resistor increases to 1000 x 1000 mils, although that same size resistor will also handle 2000 mW (2 W). As the required power dissipation increases beyond 2 W, a 50-Ω, ±10% planar resistor on 50 Ω/sq material grows to 1578 x 1578 mils for 4 W, 2019 x 2019 mils for 5 W, and 4345 x 4345 mils for 10 W. A designer must make tradeoffs between using large planar resistors or discrete resistors, based on the required size of the final circuit.

For many smaller-signal circuits, however, planar resistors, and laminates with integrated resistive thin films, can provide compact and reliable circuit solutions, especially for multilayer designs. Because they can be formed with a wide range of resistor values (depending on resistive material, Ticer films are available with resistance values as high as 1000 Ω/sq) and tolerances to ±5%, planar resistors are useful in a variety of high-frequency circuit applications, from antennas to power dividers.