portion of the outer conductor is removed to form a slit.The current flow on the shieldedNloop resonator is depicted in Fig. 4.6. The current enters the inputterminal of the shieldedNloop resonator and propagates down the interior of the transmission line to theslit in the outer conductor. It then traverses the exterior of the loop to the opposite side of the slit and,finally, enters the openNcircuited stub. Therefore, the loop and openNcircuited stub appear in series. TheopenNcircuited stub provides a capacitance which resonates with the loop’s inductance. Here, theshieldedNloops are constructed from stripline transmission lines, which have a planar cross section. Thecenter conductor is the signal line. The top and bottom conductor make up the ground plane.
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75Fig. 4.6. The behavior of currents on a shieldedUloop resonator. The current at the input propagates down the interior of thefeedline. Upon encountering the slit, the current (red) on the interior of the outer conductor wraps around to the exterior of theloop. This current (blue), loops back around to the split, where it returns to the interior, ending at the openUcircuited stub.Modeling ShieldedOLoopsDue to the current behavior shown in Fig. 4.6, the shieldedNloop resonators can be modeled as aninductor in series with an openNcircuited stub (a capacitance). However, there is also a feedline thatmust be included, as shown in Fig. 4.7.Fig. 4.7. A model of the shieldedUloop resonator shown in Fig. 4.4. The openUcircuited stub acts as a capacitance, forming aresonant circuit.From transmissionNline theory, we know that an openNcircuited transmissionNline stub shorter than aquarter wavelength (!!≪1) acts as a capacitor:!!"=−!!!cot!!!!≪!!!"=−!!!!!=−!!!!!!!!!!!=−!1!!!!!=!!!(4.3)