Application of barium titanate to microwave parametric amplification

This paper investigates the usefulness of barium titanate rods as the non-linear element of an S-band resonant cavity parametric amplifier, the pump power being at X-band. An analysis is made of the variation of reactance of a small diameter loss free rod as a function of diameter (d) and relative permittivity (¿¿r). This shows that there is a large change in the resonant frequency of the cavity for a small change in the permittivity of the rod at a number of values of ¿d/¿¿¿¿r. Taking the loss into account removes all except the smallest optimum value of ¿d/¿¿¿r, and this is about unity. For solid polycrystalline barium titanate (¿¿r ¿ 5000) the optimum diameter becomes impractically small. This paper therefore deals particularly with the application of composition rods 0.2 cm diameter made of various percentages of powdered barium titanate and powdered polythene. Microwave measurements at X- and S-bands have shown that relative permittivity values between 10 and 65 can be obtained quite easily, but that these values change only by one or two percent with a d.c. biasing field of 7 kV/cm. A quality factor for these rods is defined analogously to that for varactor diodes, but the measured values compare very unfavourably with that for a typical diode. Based on one of these composition rods a resonant cavity parametric amplifier was built for a signal frequency at S-band and the pump power at X-band but no evidence of gain was detected.