Introduction

Flex and flex-rigid PCB fabricators have long requested a practical method of predicting the impedance of stripline and microstrip PCB traces when crosshatching return paths are deployed, rather than the solid copper return paths of traditional rigid PCBs. Whilst RF purists may feel discomfort at the thought of using crosshatch as a high-frequency return path with all the implications of lengthened return path, etc., in practical terms, using crosshatched planes on flex and flex-rigid PCBs is a practical and realistic method of keeping impedance-controlled traces at a manufacturable dimension, and also retaining the desired flexibility of the assembly. Whilst this technique is in widespread use in circuits up to around 2GHz, further research is needed for suitable techniques at higher frequencies where line losses and ultimately signal integrity effects of the crosshatch itself may come into play.

Algebraic Equations

Prior to the widespread use of field solvers, closed form equations were widely used for the calculation of impedance; an example below is shown from Wadell [1]. Whilst a wide number of structures are described in Waddell, the closed form equations had limitations when addressing small geometries and their inability to take into account etch taper often encountered on fine line traces. Furthermore, Wadell does not cite any closed form equations for the handling of structures using crosshatched ground planes. The flexible circuits community has often requested a solution, but the market space is usually deemed too small for an economic approach. Modelling is possible, however, with the resort to high-cost 3-D field solvers requiring skilled operation [2]. An example closed form equation for a solid ground plane is shown in Figure 1.



Figure 1: Surface microstrip.

Parameter w' is the equivalent width of a track of zero w.