Lumped-Distributed Resonators Providing N or 2N Transmission Zeros at Real Frequencies in Bandpass Filters Without Cross and Mixed Couplings

This article deals with lumped-distributed resonators, in which one or two antiresonant frequency are adjustable and can be located close to the main resonant frequency. By antiresonant frequencies, we mean the poles of input admittance
$Y_{\text {in}}$
of resonator. The use of such resonators in
$N$
-order bandpass filters (BPFs) with parallel-type resonators and admittance inverters (J-inverters) results in
$N$
or
$2N$
transmission zeros (TZs) located at real frequencies and close to the passband. These TZs are a means to improve the filter’s performance. TZs improve the filter selectivity, including one-side selectivity, and also provide specified frequency bands with an increased attenuation level, which makes it possible to effectively suppress spurious signals. Moreover, these TZs are implemented without cross and mixed couplings. The resonators under consideration are half-wave (
$\lambda $
/2) transmission line segments, in which a capacitance
$C$
or inductance
$L$
is connected in series, or
$C$
and
$L$
at the same time. The main properties of these resonators are established. If BPF uses
$k$
such resonators with identical values of lumped elements, then we obtain a pair of TZs of
$k$
degree. Increasing the degree of TZs located closest to the passband improves BPF selectivity. A prototype of a microstrip second-order BPF, which has four TZs, center frequency
$f_{0}$
= 2 GHz, and bandwidth BW = 120 MHz, is considered.