An Observation of the Challenges of Cross-couplings and Frequency-dependent Couplings

Design of microwave filters with finite transmission zeros are crucial and indispensable to achieve stringent selectivity requirements. Methods of producing transmission zeros had been one of the greatest research interests in the field such as cross-couplings, frequency dependent couplings, non-resonating node etc.

Cross-coupling for Transmission Zeroes

Cross coupling has been the most popular technique to realize transmission zeros as it requires no additional resonator element. The physical realization of cross-coupling is achieved by placing non-adjacent resonators close enough and hence field coupling is exhibited.

The strength of the cross-coupling is determined from the coupling matrices based on the synthesized filter topology. The sign of the coupling will decide the placement of transmission zeros either below or above the passband of a bandpass filter. Theoretically N-2 transmission zeros can be produced by N order filter without the presence of source-load coupling. The most common network representation of such network can be shown as a transversal array network where N resonators are all connected in parallel between source and load. The bypass of each resonator is shown to be feasible in producing transmission zero and hence resulting in the realization of maximum of N-2 transmission zeros due to the minimum path rule.

When the source-load coupling exist, N transmission zeros for N-order filter becomes possible. Such network representation is shown to be impractical for physical realization. In most cases a transversal array network is mathematically represented by coupling matrices where both self and cross-couplings are described. Matrix rotation technique is commonly applied on the coupling matrices in achieving alternative topology network for physical realization without changing the inherent properties of the transversal filter network.

Frequency-dependent couplings

The disadvantages associated with the cross-coupling method includes the non-optimum layout space due to the accommodation of non-adjacent physical gap for cross-couplings and spurious frequency components.

In the last decade, other methods such as frequency-dependent couplings have been introduced where in-line filter topology has been shown feasible. In-line filter network is a network comprising of only adjacent resonator coupling without cross-couplings. Following the minimum path rule, it is impossible to exhibit transmission zeros without cross-coupled network due to the additional path (resonator bypass) for signal cancellation.

Therefore the transmission zeros are now achieved with the aid of frequency-dependant components between adjacent resonator. However the frequency-dependant coupling is practically difficult for realization as it requires additional opposite sign of couplings in parallel with main-line coupling between adjacent resonator.

As a result of the complexity, the design is more sensitive to manufacturing tolerance and temperature shift. An alternate method of inline topology was also shown with the introduction of non-resonating node. The non-resonating node is shunted with resonator element as to produce anti-resonance effect for transmission zero realization. It is evident that additional element or complicated and unique resonator structure is required for the realization of non-resonating node.

A Novel Alternative

In this year International Microwave Symposium (IMS) 2023, FILPAL will be presenting a novel synthesis technique for in-line microwave filter with transmission zeros. For the first time ever, FILPAL introduces an unprecedented method to unlock novel in-line topologies based on non-Chebyshev function which is no longer restricted by the minimum-path rule.

A more generalized transversal array is proposed for the first time where novel technique of eigenvalue reconfiguration will be presented.

FILPAL will be attending IMS 2023 and presenting on a novel alternative for achieving finite transmission zeroes. Join us for our presentation on the 14th of June 2023 3pm (IF-9) if you are in San Diego. The findings in this paper will be published later on at IEEE MTT-S International Microwave Symposium Digest

Originally published at http://filpal.wordpress.com on June 14, 2023.