The best-laid plans can sometimes go awry—in the case of predicting the performance of high frequency circuit designs, by normal circuit fabrication process variations. Modern computer-aided-engineering (CAE) software design tools based on electromagnetic (EM) simulation are quite good at predicting circuit performance using different models. But even the best simulation software can fall short of predicting the effects of some normal circuit fabrication process variations, specifically, deviations in copper plating thickness and how it can affect how conductors are shaped and the resulting performance of edge-coupled circuits.
Printed circuit board (PCB) materials normally will have some amount of variation in the thickness of the copper plated on the dielectric substrate material, variations within the same panel of material and variations from panel to panel. The variations in copper plating thickness can be enough to affect the performance of even a single small circuit fabricated on one small area of a panel of circuit material or the repeatability of multiple circuits fabricated on multiple panels of PCB material.
Plated-through-hole (PTH) viaholes are commonly used to make electrical connections through the thickness or z-axis of dielectric circuit materials, from one side of a PCB to the other or between conductive layers in a multilayer circuit board. The side walls of the viaholes are plated with copper to improve their conductivity. Unfortunately, the processes for plating copper over PTHs are not routine or simple and can suffer many variations in thickness. One approach for plating copper in viaholes is by electrolytically plating copper in the hole and on the copper surfaces of a PCB. This adds to the thickness of the copper laminate and introduces variations in the copper thickness throughout a panel of material. The copper thickness variations within a single panel result in variations among the circuits fabricated on the same panel. Similarly, variations can occur from panel to panel, degrading the repeatability of the same circuit fabricated in volume across multiple panels of material.
Due to the shrinking sizes of signal wavelengths at higher frequencies, variations in copper plating thickness will have greater impact on circuits at millimeter-wave circuits than on circuits at lower frequencies with their larger features. And not all transmission lines are affected the same way. For example, the performance of RF/microwave microstrip transmission lines, such as variations in amplitude and phase along the lines, are only minimally influenced by variations in PCB copper plating thickness. But circuits with edge-coupled features, including those based on grounded coplanar waveguide (GCPW) transmission lines as well as microstrip transmission lines, can suffer significant variations in RF performance as a result of excess variations in copper plating thickness. And unless accounted for, even the best EM simulation software tools will not properly predict the effects of PCB copper plating thickness on RF performance, such as insertion loss and return loss.
Edge coupled circuits achieve tight coupling by means of very narrow gaps between the coupled conductors. Because of the microscopic dimensions of the gap, the gap spacing between the coupled sidewalls can be altered by variations in the copper plating thickness. Loosely coupled circuits (with wider gaps) feel less of the effects of variations in copper plating thickness: as the gap between the coupled lines becomes narrower and the coupling becomes tighter, the dimensional tolerances can become more affected by variations in copper plating thickness. An edge coupled circuit with thicker copper will have taller sidewalls than the same edge coupled circuit design fabricated on a PCB with thinner copper. A difference in sidewall height results in a difference in coupling coefficient and a difference in the effective dielectric constant (Dk) perceived by circuits with different copper plating thicknesses.
Variations in copper plating thickness can also affect the physical form of a high frequency circuit’s conductors. For modeling purposes, electrical conductors are usually presumed to be rectangular in shape, maintaining consistent width along the length of the conductor as seen from a cross-sectional view. But such a rectangular shape is ideal and real conductors often take on a trapezoidal shape, with the widest dimensions at the base of the conductor, at the interface of the conductor and the circuit substrate. For circuits with thicker copper, the trapezoidal shape tends to become more exaggerated. Variations in a conductor’s dimensions result in variations in the current density through the conductor and variations in the performance of a high frequency circuit.
The amount of such variations will depend on the circuit design and transmission-line technology. Standard microstrip transmission-line circuits will experience little variation in electrical performance due to the trapezoidal effects of conductors but circuits with edge-coupled features can be significantly affected by trapezoidal-shaped conductors, especially as the trapezoidal shapes become more pronounced with thicker copper.
For edge-coupled circuits with tightly coupled features, computer modeling based on rectangular-shaped conductors will show a relatively high current density on the sidewalls of the coupled conductors. But if the computer model is modified and based on trapezoidal-shaped conductors, a greater amount of current density will be found at the base of the conductor, with current density increasing as a function of the conductor thickness.
With the change in current density comes a corresponding change in the electric field intensity as a result of the trapezoidal-shaped conductors. For edge-coupled conductors with rectangular-shaped conductors, the current density is high along the coupled sidewalls of the conductors and a significant portion of the electric field around the conductors will be found in the air between the conductors. For edge-coupled conductors with trapezoidal shape, the current density is lower on the conductor sidewalls, with less of the electric fields occupying the air between the coupled conductors. Having more of the electric fields in air, which has a Dk which is the same as in a vacuum, approximately 1, will result in a lower effective Dk for edge-coupled circuits with rectangular-shaped conductors than for circuits with trapezoidal-shaped conductors where more of the electric fields are found around the conductors and in the dielectric material than in air with its lower Dk value.
Because the copper plating thickness on PCBs can vary within a single circuit panel as a result of standard circuit fabrication processes, the electrical performance of circuits experiencing those copper thickness variations will vary as well, depending upon the circuit topology and frequency. Due to the smaller dimensions/wavelengths of circuits at millimeter-wave frequencies, the variations can be especially pronounced and require forethought and planning when using circuit simulation software to predict the performance for a given circuit material, no matter how well controlled its Dk performance.
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