Using QuarterWavelength Resonator Filters in Modern Wireless Communication
Key Takeaways

The main drawback of halfwavelength resonator filters is their large circuit area and spurious passbands.

A folded quarterwavelength steppedimpedance resonator consists of two transmission line sections of different line widths and different characteristic impedances.

Switchable filters are often used in multiband communication equipment.
Filter structures are used in wireless communication systems to improve system performance
Filter structures are often used in wireless communication systems to improve system performance. Uniform distributed element resonators, such as halfwavelength and quarterwavelength resonators, are used as microstrip filter structures to remove noise. The compactness of quarterwavelength resonators is a major advantage that makes them popular for use in filtering structures.
Using QuarterWavelength Resonators in Filter Structures
The main drawback of halfwavelength resonator filters is their large circuit area and spurious passbands around nf_{0}, where f_{0 }is the passband center frequency. A filter made of a quarterwavelength resonator requires only a small footprint area. A quarterwavelength resonator provides excellent stopband rejection with spurious passbands around (2n+1) f_{0}.
The two major types of quarterwavelength resonator filters are interdigital filters and combline filters. Compared to halfwavelength resonators, interdigital and combline quarterwavelength resonator filters provide higher spurious resonant frequencies.
Quarterwavelength resonator filters can also be folded to give sharp passband selectivity without degrading the passband insertion loss. These types of resonators are called folded quarterwavelength resonator filters, and they are designed with a reduced footprint area and circuit size. Applying the steppedimpedance resonator concept to a quarterwavelength resonator filter creates a quarterwavelength steppedimpedance resonator filter. These are more efficient than conventional quarterwavelength resonator filters and they have a wider stopband. Let’s take a closer look at the characteristics of folded quarterwavelength steppedimpedance resonator filters.
Folded QuarterWavelength SteppedImpedance Resonator Filters
A folded quarterwavelength steppedimpedance resonator consists of two transmission line sections of different line widths and different characteristic impedances. The width W_{b} and characteristic impedance Z_{b} form the first section of length Lb. The second section of width W_{a} and characteristic impedance Z_{a} is of length L_{a}. The input admittance Y_{in} of the resonator can be given by equation (1):
The parallel resonance occurs in this resonator when the input admittance Y_{in}=0. This gives the resonant condition given by equation (2):
The size of the resonator is minimized for the given impedance rate, R_{Z} =Z_{b} /Z_{a}, by choosing the electrical length, 𝜃_{a} and 𝜃_{b} , as shown in equation (3):
To build a coupledresonator filter from a quarterwavelength steppedimpedance resonator, an open stub is inserted between the high impedance Z_{b} and low impedance Z_{a} sections. This creates a crosscoupled path and reduces the resonant frequency of the quarterwavelength resonator.
A Concurrent DualBand Filter Using a QuarterWavelength Resonator
Switchable filters are often used in multiband communication equipment and are of two different types. The first type is switchable dualband filters working on one operating band at a time. The second type of switchable filter uses two bands, and each band can be enabled and disabled independently. In concurrent dualband filters, switching circuits are added to enable and disable the designated passband.
Concurrent dualband filter design uses hybrid coupling paths and two quarterwavelength resonators in its construction. The dualband filter is designed to operate at two uncorrelated frequencies, f_{L} and f_{H}. The frequencies of operation are achieved using two speeded impedance quarterwavelength resonators R_{1} and R_{2}, which resonate at frequencies f_{L} and f_{H}, respectively. The resonators R_{1} and R_{2} constitute a secondorder filter that allows the lower band signal from R_{1} to pass through R_{2}. The higher band signal is blocked by the introduction of coupling length L between resonators R_{1} and R_{2}. The coupling length is of quarterwavelength at higher frequency f_{H}. The resonator R_{H} resonates at frequency f_{H} and forms a thirdorder filter. The lower band coupling coefficient is controlled by gap g_{L} and the higher band coupling coefficient is controlled by gap g_{H}. A twosection dualband impedance transformer is applied to the construction to provide the required external quality factor to the dual bands simultaneously.
Based on these desirable characteristics, the quarterwavelength resonator filter is becoming increasingly important to wireless communication systems due to its excellent filter performance, short length, and small footprint area.
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