Designing HalfWavelength Resonator Bandpass Filters
Key Takeaways

In endcoupled, halfwavelength resonator filters, each resonator length is made approximately half of the guided wavelength corresponding to the midband frequency f_{0 }of the bandpass filter.

The steps to designing a halfwavelength resonator bandpass filter are:

Select the appropriate bandpass prototype.

Find a microstrip realization that approximates the lumped element filter.

Bandpass design specifications include center frequency, dielectric permittivity, substrate thickness, loss tangent, passband ripple, input/output load impedance, cutoff frequency, frequency bandwidth, and guided wavelength.
In microwave and RF circuits, microstrip resonators are structures used for filtering purposes. They are characterized by resonant frequency and contain at least one oscillating electromagnetic field.
Microstrip resonator filters are classified as the following:

Lumped element resonators or quasilumped element resonators are formed by inductors and capacitors.

Distributedline resonators have two types: quarterwavelength and halfwavelength resonators. These resonators are long, where is the guided wavelength corresponding to the fundamental resonant frequency, f_{0}. A halfwavelength resonator can oscillate at nf_{0} frequency, where n=2,3. These line resonators can be shaped into different configurations for filter designs. In bandpass filters, halfwavelength resonators are used in the form of endcoupled, halfwavelength resonator bandpass filters and parallelcoupled bandpass filters.
In this discussion, we will focus on the different types of halfwavelength resonator bandpass filters.
EndCoupled, HalfWavelength Resonator Bandpass Filters
In endcoupled, halfwavelength resonator filters, each resonator length is made approximately half of the guided wavelength corresponding to the midband frequency f_{0 }of the bandpass filter. The coupling between the resonator is through the gap between the open ends of the resonators, and the setup is capacitive. Gaps reflect high impedance levels to open ends of the halfwavelength resonator. Endcoupled, halfwavelength resonators exhibit shunttype resonance, so the filters designed from them operate like shuntresonators.
Designing a HalfWavelength Resonator Bandpass Filter
The steps to designing a halfwavelength resonator bandpass filter are:

Select the appropriate bandpass prototype.

Find a microstrip realization that approximates the lumped element filter.
Bandpass design specifications include center frequency, dielectric permittivity, substrate thickness, loss tangent, passband ripple, input/output load impedance, cutoff frequency, frequency bandwidth, and guided wavelength. The filter approximation should be selected so the ripple passband and stopband requirements are met.
ParallelCoupled, HalfWavelength Resonator Bandpass Filters
Parallel coupled, halfwavelength resonator (also called edgecoupled, halfwavelength resonator) filters utilize halfwavelength line resonators. These resonator filters are placed so that the adjacent resonators are parallel to each other from the halflength of the immediateresonator above it. This arrangement creates a large coupling between the resonators in the given space. The structure of a parallel, halfwavelength resonator makes it wellsuited for filters with a wider bandwidth.
HairpinLine Bandpass Filters
When a parallelcoupled, halfwavelength resonator filter is folded into a “U” shape, it forms a compact structure called a hairpinline bandpass filter. The design procedure of a hairpinline bandpass filter is similar to that of a parallelcoupled halfwavelength resonator filter. However, due to folding, a reduction of the coupledline length exists in hairpinline filters. This reduces coupling between the resonators.
Halfwavelength resonator filters are used in modern microwave and RF communication circuits. They can be designed to match any lumped element filter through microstrip realization. By properly designing halfwavelength resonator filters, desirable filter properties such as passband, stopband, center frequency, cutoff frequency, and bandwidth can be obtained.
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