Stability Analysis of Superluminal Metamaterial Transmission Line with Realistic Non-Foster Negative Capacitors

Abstract

Original scientific paperRecently, it has been shown possible to go around basic dispersion energy constraints that limit bandwidth of every passive metamaterial and construct a broadband active Epsilon-Near-Zero superluminal transmission line. A basic building block of this unusual transmission line is an active 'tank circuit' that contains both conventional (positive) capacitor and non-Foster negative capacitor. Published theoretical studies revealed that such a 'tank circuit' is stable if an overall capacitance is positive. These studies assumed lossless host transmission line periodically loaded with ideal dispersionless negative capacitors. However, a possible influence of the imperfections of a realistic negative capacitor (its dispersion and loss/gain) on the stability has not been investigated so far. Here, stability analysis of realistic superluminal transmission line is performed in Laplace domain. The obtained results are in a good agreement with those obtained in recent experiments on active transmission line developed at University of Zagreb.Key words: Non-Foster Element, Negative Capacitor, Stability, Metamaterial, Superluminal Propagation Analiza stabilnosti superluminalne prijenosne linije temeljene na metamaterijalu s neidalnim neFosterovim negativnim kondenzatorima. Nedavno je pokazano da je moguće zaobići temeljne energetskodisperzijske uvjete koji ograničavaju širinu frekvencijskog pojasa svakog pasivnog metamaterijala. Takoîer je pokazano da je moguće konstruirati širokopojasnu aktivnu superluminalnu prijenosnu liniju s približno nultom permitivnosti (ENZ). Osnovni gradivni element ove neuobičajne linije je aktivni "titrajni krug" koji se sastoji od klasičnog (pozitivnog) i ne-Fosterovog negativnog kondenzatora. Do sada objavljene teorijske studije pokazale su da je ovakav "titrajni krug" stabilan ako je ekvivalentni ukupni kapacitet pozitivan. Meîutim, stvarni (neidalni) negativni kondenzator uvijek ima gubitke (ili pojačanje) i disperziju. Utjecaj ovih nesavršenosti na stabilnost superluminalne linije je nejasan i do sada nije istraživan. Stoga je u ovomečlanku načinjena analiza stabilnosti neidealne superluminalne prijenosne u Laplaceovoj domeni. Rezultati analize su u vrlo dobrom suglasju s nedavno objavljenim rezultatima mjerenja na aktivnoj superluminalnoj prijenosnoj liniji koja je razvijena na Sveučilištu u Zagrebu.

Active Reconfigurable Metamaterial Unit Cell Based on Non-Foster Elements

“…We have also developed an entire three-cell 1D active ENZ metamaterial that has a fractional dispersion bandwidth of 200% (more than four octaves). In addition, this line supports counter-intuitive superluminal phase and group velocities [73,80,81]. All of the prototypes were 'hand-crafted' and based on low-cost FET, BJT and OPAMP components.…”

“…The isotropic versions of the above mentioned active metamaterials are simply constructed by selecting identical values of the inductances in the x and y branches. It is worth mentioning that the results published in our previous report [73], and subsequent publications [74][75][76][77][78][79][80][81][82][83], significantly enhanced the interest in this new field. Now, there are several research groups that actively work in the field of non-Foster metamaterials with proposals of novel applications such as squint-free leaky-wave antennas [100], broadband PMC surfaces [99] and many others.…”

“…The basic element of any broadband non-Foster metamaterial is a non-Foster element itself (i.e, a negative capacitor or a negative inductor). Practical non-Foster metamaterials developed so far were predominantly based on negative capacitors [65][66][67][68][73][74][75][76][77][78][79][80][81][82][83]. A negative capacitor C n ( Figure 3-1 (a)), briefly explained in Chapter 1, is a hypothetical network element, capacitance of which has the sign opposite to the sign of an ordinary (positive) capacitor C p with equal capacitance:…”