Ferroelectric Phase Shifters

A diagram of the microstrip ferroelectric phase shifter is shown in Fig. 1(a). The nominal thickness of the ferroelectric material is 10 mils. As the dielectric constant of the ferroelectric is very high, the impedance af the microstrip line (~15 mils wide) is comparatively low. For matching purposes quarter-wave transformers of Ti0/sub 2/ were used. A ceramic ferroelectric material containing 68.5 per cent SrTi0/sub 3/ and 31.5 per cent PbTi0/sub 3/ (PS 68.5) was used in the experiments. For a TEM-mode propagation the insertion phase of a transmission line of length 1 is given by /spl beta/1. Fig. 2 shows the insertion phase of one of the units as measured with a phase discriminator. The total insertion phase at 3.05 Gc/S is 4.434/spl lambda/. Substracting the insertion phase of the connectors and the quarter-wave transformers the insertion phase of the ferroelectric material alone is 3.486/spl lambda/. On the application of a biasing voltage, the differential phase shift is given by /spl Delta//ppl phi/= (/spl beta/1- /spl beta/2) where /spl beta/1 and /spl beta/2 are the phase constants without and with bias respectively. or /spl Delta//spl phi/= 2/spl pi/l / /spl lambda//sub o/ /spl radic//spl epsi//sub 1/ [1-/spl radic/ /spl epsi//sub 2/ / /spl epsi//sub 1/ ] where /spl lambda//sub o/. is the free-space wavelength and /spl epsi//sub 1/ and/spl epsi//sub 2/ are the values of the dielectric constant with zero bias and with a bias voltage respectively. The insertion loss is /spl alpha//sub d/= 27 tan /spl delta/ db/ /spl lambda/ where tan /spl delta/ is the loss tangent of the material.