Using Quarter-Wavelength Resonator Filters in Modern Wireless Communication

Cadence System Analysis

Key Takeaways

The main drawback of half-wavelength resonator filters is their large circuit area and spurious passbands.
A folded quarter-wavelength stepped-impedance 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 half-wavelength and quarter-wavelength resonators, are used as microstrip filter structures to remove noise. The compactness of quarter-wavelength resonators is a major advantage that makes them popular for use in filtering structures.

Using Quarter-Wavelength Resonators in Filter Structures

The main drawback of half-wavelength resonator filters is their large circuit area and spurious passbands around nf₀, where f₀is the passband center frequency. A filter made of a quarter-wavelength resonator requires only a small footprint area. A quarter-wavelength resonator provides excellent stopband rejection with spurious passbands around (2n+1) f₀.

The two major types of quarter-wavelength resonator filters are interdigital filters and combline filters. Compared to half-wavelength resonators, interdigital and combline quarter-wavelength resonator filters provide higher spurious resonant frequencies.

Quarter-wavelength resonator filters can also be folded to give sharp passband selectivity without degrading the passband insertion loss. These types of resonators are called folded quarter-wavelength resonator filters, and they are designed with a reduced footprint area and circuit size. Applying the stepped-impedance resonator concept to a quarter-wavelength resonator filter creates a quarter-wavelength stepped-impedance resonator filter. These are more efficient than conventional quarter-wavelength resonator filters and they have a wider stop-band. Let’s take a closer look at the characteristics of folded quarter-wavelength stepped-impedance resonator filters.

Folded Quarter-Wavelength Stepped-Impedance Resonator Filters

A folded quarter-wavelength stepped-impedance 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 coupled-resonator filter from a quarter-wavelength stepped-impedance resonator, an open stub is inserted between the high impedance Z_b and low impedance Z_a sections. This creates a cross-coupled path and reduces the resonant frequency of the quarter-wavelength resonator.

A Concurrent Dual-Band Filter Using a Quarter-Wavelength Resonator

Switchable filters are often used in multiband communication equipment and are of two different types. The first type is switchable dual-band 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 dual-band filters, switching circuits are added to enable and disable the designated passband.

Concurrent dual-band filter design uses hybrid coupling paths and two quarter-wavelength resonators in its construction. The dual-band filter is designed to operate at two uncorrelated frequencies, f_L and f_H. The frequencies of operation are achieved using two speeded impedance quarter-wavelength resonators R₁ and R₂, which resonate at frequencies f_L and f_H, respectively. The resonators R₁ and R₂ constitute a second-order filter that allows the lower band signal from R₁ to pass through R₂. The higher band signal is blocked by the introduction of coupling length L between resonators R₁ and R₂. The coupling length is of quarter-wavelength at higher frequency f_H. The resonator R_H resonates at frequency f_H and forms a third-order 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 two-section dual-band 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 quarter-wavelength 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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