Composing Capacitors and Inductors on PCB Materials
Circuit design engineers have long relied upon the basic physics of printed-circuit boards (PCBs) and how capacitors and inductors can be formed from simple patterns and structures on a PCB. For example, a PCB provides parasitic capacitance because the metal signal plane layer and the metal ground plane layer underneath are parallel to each other, separated by a dielectric material layer. Of course, the characteristics of the metal layers, such as the thickness and type of conductive metal used, and the mechanical and electrical traits of the dielectric material, including its relative permittivity or dielectric constant (Dk), can contribute quite a bit to the final performance levels and consistency that can be achieved for a particular circuit design. A number of PCB material traits, in particular the consistency of the dielectric constant, can go a long way towards achieving consistent and reliable PCB capacitors and inductors especially at RF and microwave frequencies.
Circuit designers are constantly being asked to make their circuits smaller, whether they are for commercial cellular telephones or for portable military radios. Integrated-circuit (IC) designers have been doing their part to contribute to the size reductions, packing more and more active components onto chips, including amplifiers, microprocessors, and oscillators. But when added to PCBs, even these tiny chips require the support of essential passive components, such as capacitors and inductors, for such functions as impedance matching to help transfer signals from the chips to other components. And circuit designers are constantly faced with the need to produce reliable capacitors and inductors on their circuits. Understanding the role of the PCB material in building those capacitors and inductors can be a huge help.
PCB material characteristics that strongly impact the performance and consistency of embedded capacitors and inductors include Dk and Dk consistency or tolerance. Because capacitors and inductors that are created from different structures using, for example, microstrip or stripline circuit traces, can occupy more than a small portion of a section of PCB, it is essential that a candidate circuit material for those passive components and their associated circuitry maintain good Dk control in order to achieve consistent capacitance and inductance from different circuit structures.
When working in microstrip, for example, the amount of transmission-line area above the ground plane will determine the amount of capacitance for a particular circuit structure. Even a 90-deg. change in a transmission line can add capacitance to a circuit. Such simple structures as meander lines have been used to add small amounts of inductance to a circuit. Spiral circuit patterns have long been used to add inductance to a circuit, with the inductance changed by varying the trace width and the spacing between the traces in the spiral circuit pattern. Such an inductor is characterized by a self-resonant frequency (SRF), which will increase when the inductor trace width is increased and the spacing between traces is decreased.
The amount of capacitance in an embedded capacitor will depend on such factors as the distance from the signal plane to the ground plane—essentially the thickness of the dielectric material between them—and the physical size of the capacitance structure. The coupling between arms on the signal plane can also add to a microstrip circuit’s capacitance. These embedded capacitors and inductors are typically referred to by designers as part of a circuit’s resistor-inductor-conductor-capacitor (RLGC) parameters and are included in computer circuit models to predict the performance and behavior of transmission-line circuits.
Computer models assume that such things as the dimensions of the various RLGC structures on a PCB that are entered into the software program are the same dimensions that have been fabricated on the actual PCB. Variations between the sets of values can result in variations in such things as capacitance and inductance values from computer-predicted expectations.
Of course, such computer models also consider the contributions of PCB materials when predicting such things as the capacitance in a 90-deg. bend in a circuit’s transmission line. Circuit computer models work with such circuit material parameters as Dk and even Dk tolerance, or the deviations in Dk with temperature and frequency. Models can focus on different parameters with some models, for example, ignoring the losses contributed by the PCB’s conductors and the dielectric material but concentrating on the Dk consistency to accurately predict the values and expected performance of circuit elements such as inductors and capacitors based on the physical dimensional tolerances of circuit structures.
Numerous reference guides are available for calculating the values of microstrip capacitors and inductors based on dimensions etched onto different PCBs, such as the ARRL Handbook from the American Radio Relay League (www.arrl.org). For microstrip inductors, for example, it provides calculations for microstrip inductors using such variables as transmission-line strip width, distance to the ground plane, and Dk of the PCB material.
The choice of PCB material can play a significant role in the performance levels to be expected from these etched capacitors and inductors, with the material properties impacting capacitance value and consistency and such inductor characteristics as quality factor (Q), SRF, and self-inductance factor. A PCB material’s Dk value will determine the size of different circuit structure for a desired operating frequency, but it is the tolerance to which the Dk value is held that greatly impacts the consistency and performance of capacitors and inductors etched onto the copper layer of the PCB material.
As an example, RO4835™ circuit material from Rogers Corp. is a glass-reinforced hydrocarbon and ceramic dielectric material with good z-axis (through the thickness) stability that makes it a candidate for multilayer circuits. It exhibits a z-axis Dk value of 3.48 at 10 GHz with impressive Dk tolerance within ±0.05 of 3.48 across the circuit board. In terms of fabricating passive circuit elements such as capacitors and inductors, this means that they will maintain their capacitance and inductance values with frequency and with temperature, with minimal variations in capacitance and inductance caused by changes in PCB Dk value.
As impressive as that Dk tolerance, Rogers Corporation offers even more tightly controlled circuit materials, such as its RO3003™ ceramic-filled polytetrafluoroethylene (PTFE) circuit material. Its Dk value of 3.00 at 10 GHz through its z-axis is held to a tolerance of ±0.04 across the material and from board to board. And RT/duroid® 5880 is a glass-microfiber-reinforced PTFE composite material with a Dk of 2.20 that is maintained to an extremely tight tolerance of ±0.02 across the material. This low-loss material supports circuit applications across a wide range of frequencies, well into the millimeter-wave frequency range.
Designers may choose a PCB material for a particular Dk value, but the Dk tolerance may not be known or may not be tightly controlled, resulting in etched circuit elements such as capacitors and inductors that may not provide the performance or consistency expected or predicted by commercial software circuit-design programs. A PCB material with tightly controlled Dk tolerance can provide the assurance of achieving the circuit values expected for such passive elements as capacitors and inductors and for maintaining circuit performance with frequency and time.
Do you have a design or fabrication question? Rogers Corporation’s experts are available to help. Log in to the Rogers Technology Support Hub and “Ask an Engineer” today.