Synthesis of Transmission Line Resonators for Harmonic Suppression

Abstract

The problem of synthesis of stepped impedance resonators (SIRs) and resonators with stubs, which contain transmission line segments of the same length and suppress harmonics of the main signal, is solved. It is established that SIR with <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$N$</tex> composite segments allows us to continuously suppress <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$(\boldsymbol{N}-1)$</tex> harmonics <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$2\boldsymbol{f}0,\ 3\boldsymbol{f}_{0},\ \ldots,\ \boldsymbol{Nf}_{0}$</tex> of the main signal with a frequency <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\boldsymbol{f}_{0}$</tex> . To do this, it is necessary to coincide the anti-resonant frequencies of SIR with the specified harmonic frequencies. Simple expressions are established to determine the characteristic impedances of SIRs with four composed segments. It is shown that the transition from SIR to stub resonators improves their practical feasibility. Using the circuit simulator, the reliability of the presented solution was confirmed.