Designing Half-Wavelength Resonator Bandpass Filters
Key Takeaways
-
In end-coupled, half-wavelength resonator filters, each resonator length is made approximately half of the guided wavelength corresponding to the mid-band frequency f0 of the bandpass filter.
-
The steps to designing a half-wavelength 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, cut-off 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 quasi-lumped element resonators are formed by inductors and capacitors.
-
Distributed-line resonators have two types: quarter-wavelength and half-wavelength resonators. These resonators are
long, where
is the guided wavelength corresponding to the fundamental resonant frequency, f0. A half-wavelength resonator can oscillate at nf0 frequency, where n=2,3. These line resonators can be shaped into different configurations for filter designs. In bandpass filters, half-wavelength resonators are used in the form of end-coupled, half-wavelength resonator bandpass filters and parallel-coupled bandpass filters.
In this discussion, we will focus on the different types of half-wavelength resonator bandpass filters.
End-Coupled, Half-Wavelength Resonator Bandpass Filters
In end-coupled, half-wavelength resonator filters, each resonator length is made approximately half of the guided wavelength corresponding to the mid-band frequency f0 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 half-wavelength resonator. End-coupled, half-wavelength resonators exhibit shunt-type resonance, so the filters designed from them operate like shunt-resonators.
Designing a Half-Wavelength Resonator Bandpass Filter
The steps to designing a half-wavelength 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, cut-off frequency, frequency bandwidth, and guided wavelength. The filter approximation should be selected so the ripple pass-band and stopband requirements are met.
Parallel-Coupled, Half-Wavelength Resonator Bandpass Filters
Parallel coupled, half-wavelength resonator (also called edge-coupled, half-wavelength resonator) filters utilize half-wavelength line resonators. These resonator filters are placed so that the adjacent resonators are parallel to each other from the half-length of the immediate-resonator above it. This arrangement creates a large coupling between the resonators in the given space. The structure of a parallel, half-wavelength resonator makes it well-suited for filters with a wider bandwidth.
Hairpin-Line Bandpass Filters
When a parallel-coupled, half-wavelength resonator filter is folded into a “U” shape, it forms a compact structure called a hairpin-line bandpass filter. The design procedure of a hairpin-line bandpass filter is similar to that of a parallel-coupled half-wavelength resonator filter. However, due to folding, a reduction of the coupled-line length exists in hairpin-line filters. This reduces coupling between the resonators.
Half-wavelength 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 half-wavelength resonator filters, desirable filter properties such as passband, stopband, center frequency, cut-off frequency, and bandwidth can be obtained.
If you’d like to keep up-to-date with our System Analysis content, sign-up for our newsletter curating resources on current trends and innovations. If you’re looking to learn more about how Cadence has the solution for you, talk to us and our team of experts.