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46 The PCB Design Magazine • March 2017 roughness parameter can be applied to finally estimate effective Dkeff due to roughness. Final- ly, I tested the method via case studies. In his book "Transmission Line Design Hand- book," Brian C. Wadell defines D keff as the ratio of the actual structure's capacitance to the capaci- tance when the dielectric is replaced by air. [2] D keff is highly dependent on the test appara- tus and conditions of how it is measured. There are several methods used in the industry. One method that is commonly used by many lami- nate suppliers is called the clamped stripline resonator test method. It is described by IPC- TM-650, section, Rev C. [3] In short, this method rapidly tests dielectric material for permittivity and loss tangent, over an X-band frequency range of 8-12.4 GHz, in a production environment. It does not guarantee the values are accurate for design applications. Here's why: The measurements are made under stripline conditions, using a carefully designed resonant element pattern card, made out of the same di- electric material to be tested. The card is sand- wiched between two sheets of unclad dielectric material under test. The whole structure is then clamped between two large plates, lined with copper foils that are grounded. Since the resonant element pattern card and material under test are not physically bonded together, there are small air gaps between the various layers affecting measured results. These air gaps are caused in part by: • Removing the copper from the material under test, leaving the bare substrate, com- plete with the micro void imprint of the copper roughness. • The air gap between resonant element pat- tern card and material under test, due to the copper thickness of the etch pattern. • The roughness profile of the copper, on the resonant element pattern card and fixture's grounded foil reference planes, are different than would be in practice, unless the same foil type is used. If D keff and R z roughness parameters from the manufacturers' data sheets are known, then the effective D k due to roughness (D keff_rough ) of the fabricated core laminate can now be easily esti- mated by: Equation 1 Where: H smooth is the thickness of dielectric from data sheet; Rz is 10-point mean roughness from data sheet; and D keff is the D k from data sheet. OBSESSING OVER CONDUCTOR SURFACE ROUGHNESS: WHAT'S THE EFFECT ON DK? Figure 2: Effective D k due to roughness model. Using D keff with rough copper model (left) is equivalent to using D keff_rough with smooth copper model (right).

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