1_230 Lab Manual Winter2016.pdf

The current flow on the shieldednloop resonator is

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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 input terminal of the shieldedNloop resonator and propagates down the interior of the transmission line to the slit 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. The openNcircuited stub provides a capacitance which resonates with the loop’s inductance. Here, the shieldedNloops are constructed from stripline transmission lines, which have a planar cross section. The center conductor is the signal line. The top and bottom conductor make up the ground plane.
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75 Fig. 4.6. The behavior of currents on a shieldedUloop resonator. The current at the input propagates down the interior of the feedline. Upon encountering the slit, the current (red) on the interior of the outer conductor wraps around to the exterior of the loop. This current (blue), loops back around to the split, where it returns to the interior, ending at the openUcircuited stub. Modeling ShieldedOLoops Due to the current behavior shown in Fig. 4.6, the shieldedNloop resonators can be modeled as an inductor in series with an openNcircuited stub (a capacitance). However, there is also a feedline that must 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 a resonant circuit. From transmissionNline theory, we know that an openNcircuited transmissionNline stub shorter than a quarter wavelength ( ! ! 1 ) acts as a capacitor: ! !" = ! ! ! cot ! ! ! ! ! ! !" = ! ! ! ! ! = ! ! ! ! ! ! ! ! ! ! ! = ! 1 ! ! ! ! ! = ! ! ! ( 4 . 3 )
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