Nonlinear Dielectric Responses of Glasses and Glass-Ceramics in the Microwave Range
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Abstract
The ever-increasing data traffic by a growing number of communicating wireless devices
calls for a larger bandwidth and for its efficient use in the fifth (5G) and sixth (6G)
mobile communication generations. The bandwidth is extended by utilizing higher
frequencies. However, a phenomenon that troubles the efficient use of bandwidth is
passive intermodulation (PIM). PIM leads to channel cross talk and has its origin in
any kind of nonlinear response. One such source is the nonlinear electric susceptibility
of dielectrics in microwave devices.
This work deals with the characterization of the nonlinear electric susceptibility of
glasses and glass-ceramics at microwave frequencies. Glasses and glass-ceramics exhibit
advantageous properties for microwave devices compared to classically employed sintered
ceramics or PTFE compounds, such as better metal adhesion and higher homogeneity.
The nonlinear susceptibility of a Ba 4 Al 2 Ti 10 O 27 glass-ceramic was determined to
|χ 3 | = (4 ± 2) × 10 −16 m 2 /V 2 at 1GHz . The intermodulation level observed during this
measurement cannot be adequately described by a classical power-law representation of
the nonlinearity. While the power-law description is only applicable within its radius
of convergence, an alternative approach based on Fourier coefficient integrals allows
accurate description of the dependency of intermodulation levels on input power over
a wider range. Using established physical nonlinear response models, this description
additionally allows determining previously inaccessible model parameters, such as the
linear contribution of the nonlinear mechanism (χ 1 = 10 −8 ).
The experimental setup was extended to also characterize materials with lower permit-
tivity, including a glass. SiO 2 immiscibilities in the glass were found to increase the
nonlinear microwave response significantly without having a measurable impact on the
linear dielectric properties.
For comparison, the nonlinear susceptibility of the Ba 4 Al 2 Ti 10 O 27 glass-ceramic was
measured with a 1kHz ultra-high precision capacitance bridge under a high DC voltage
bias, resulting in a nonlinear susceptibility, which is higher by three orders of magnitude
than in the GHz range. The kHz nonlinear susceptibility was shown to increase with
the crystallite size in the glass-ceramic.
In summary, both the experimental method as well as the theoretical description of
intermodulation open new prospects in understanding dielectrics and nonlinear responses
in general and thus laying a foundation for higher performance microwave devices.