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OCTOBER 2021 I DESIGN007 MAGAZINE 55 Microstrip resonator structures are widely used for determining the dielectric constant of substrate materials at high frequency. e results are applied to the design of controlled impedance interconnects, microwave, and RF circuit elements. By measuring the response of resonators that have been covered with and without no-clean flux, the change in effective dielectric constant (Dk) and dielectric dissipation (Df ) caused by the presence of residues can be deduced and incorporated in the design. e frequency response of a typical T-resonator con- sists of a series of resonant dips (Figure 1), measured at the input port S 12 , the first of which occurs when the stub length (l stub) equals one- quarter wavelength (when the impedance of the stub tends towards zero). Subsequent resonant dips occur at the odd harmonics of the fundamen- tal frequency. e resonant frequency of the T-resonator depends on the length of the stub (l stub) and the effective dielectric constant (eeff)— where eeff is a combination of the material Dk and that of the flux (eflux). e pres- ence of flux residue reduces the resonant frequency over the entire bandwidth but has its greatest impact at higher harmonics. W h e n t h e f l u x r e s i - due is deposited around a microstrip signal conduc- tor, it also contributes to the effective dielectric constant of the structure. Figure 2 illustrates the results for dif- ferent values of thickness and dielectric constant of the flux residue lay- ers. It can be clearly seen that increased values of eflux also increase the effective dielectric constant. e dielectric constant of a laminate is an important electrical property needed to accu- Figure 1: Typical T-resonator insertion loss (with/without residue) 1 . Figure 2: Effective dielectric constant vs. residue flux 1 .

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