Ultracompact Planar Filter Design Based on Pixelated Configurations

In this article, a design method for ultracompact planar filters based on pixelated configurations is proposed. This design framework discretizes the transmission lines and resonant structures of microstrip filters into pixel units. Under the premise of introducing a novel concept of circuit miniaturization, the presented methodology achieves size reduction by optimizing the layout and parameters of these pixel units. Each pattern of the upper metallic layer in these microstrip filters is defined by an <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$M \times $ </tex-math></inline-formula> N model matrix. Within this binary matrix, matrix elements with a value of “1” correspond to metal, while those with a value of “0” correspond to vacuum or air. To validate the presented method, both microstrip low-pass and bandpass filters have been designed, fabricated, and measured. Both the sizes of the presented low-pass and bandpass filters are <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$0.0935\lambda _{g} \times 0.0935\lambda _{g}$ </tex-math></inline-formula>. Measurement results show that the low-pass filter exhibits an insertion loss of 0.3 dB and an out-of-band suppression of greater than 20 dB. Meanwhile, the bandpass filter demonstrates an insertion loss of 1.6- and 3-dB fractional bandwidth of 12.9%. Compared to conventional circuit layouts, the area of the low-pass filter is only 17.2% of its original, while the area of the bandpass filter is only 36.3% of its original. Additionally, the presented example demonstrates the design of a 3-dB coupler with a center frequency of 2.4 GHz using this method, where the coupler’s area is reduced to only 24% of its original size. This indicates that the method has the potential to be extended to other planar circuits designed based on transmission line theory to enable ultracompact implementations.