Effective permittivity and attenuation coefficient of microstrip transmission line determined by 1-port and 2-port measuring methods

Abstract

Both 1-port and 2-port measuring methods have been demonstrated and compared to determine the real part of the frequency-dependent effective relative permittivity, re(f), of microstrip lines fabricated on an alumina substrate. Signal flow diagram analysis has been used to derive equations from which re(f) was calculated at discrete frequencies for the substrate with a known dielectric constant, r = 9.5. Both methods gave similar results for re(f) from 45 MHz to 50 GHz. In addition, the measured frequency dependence of re(f) was in agreement with the Kirschning-Jansen dispersion model within better than 2%. From the measured S-parameter data it was also possible to determine approximately the attenuation coefficient of the microstrips. Measured values obtained by the 2-port method were about 1.5-2 times the calculated values whereas the 1-port method suffered from radiation loss at the open end of the microstrips in the millimetre wave region. Both 1-port and 2-port methods can be used, for example, for quality checking purposes to verify how well the r value of the substrate material employed is within the specified range in a broad frequency band. However, the 1-port method can be more easily used to determine r of the substrate material at low microwave frequencies because it is faster than the 2-port method, the test structure is simpler and the calibration routine is easier to perform.