![]() ![]() The filter has a footprint of only 0.084 The measured results show a tuning range of more than 19%, a low insertion loss in the neighboring frequency bands (below 2 dB at 20 GHz and 40 GHz in on/off-states) while a maximum rejection level close to 18 dB in off-state, limited by the no RF-ideal CMOS compatible substrate. The filter is designed to work in K a band with tunable central frequencies ranging from 28.2 GHz to 35 GHz. The tunable filter is fabricated on a high-resistivity Silicon substrate (HR-Si) based on a CMOS compatible technology using a 1 μ m ×10 μ m long and 300 nm thick Vanadium Oxide (VO2) switch by exploiting its insulator to metal transition (IMT). This paper proposes and validates a new principle in coplanar waveguide (CPW) bandstop filter tuning by shortcutting defected ground plane (DGS) inductor shaped spirals to modify the resonant frequency. Escher, in some of his best known illustrations, as well as being closely related to original Smith's chart (Gupta, 2006). This is not the only possible generalization, in this work we present other possibilities using hyperbolic geometry. ![]() In addition, these authors developed a CAD tool (com ) toįacilitate the measurements and graphics in it. This new model unifies the design of the circuits, keeping unchanged all the properties of the original Smith chart. In Müller et al., 2011, the authors proposed a generalization of Smith's chart in space: the Smith 3D chart, where they use the stereographic projection of the sphere in the plane. Problems and, although its usefulness has survived to this day, it has some drawbacks that have been alleviated by successive generalizations. One of its main advantages is that it provides an excellent visual approach to highfrequency Smith's chart is a graphical tool, classically used in the analysis and design of microwave circuits, based on the mathematical idea of inverting the positive semi-plane to the unit circle through the transformation of Mobius M(z) = (z-1)/(z+1). The image of the infinite magnitude constant reflection coefficient circle |í µí¼| = ∞ unimaginable to represent even on a generalized 2D Smith chart becomes the contour of the new chart |í µí¼ ℎ | = 1. The 1 < |í µí¼| < ∞ constant circles (which are exterior to the 2D Smith chart or in the South hemisphere on the 3D Smith chart) and which are important in active circuit design are contained in limited region of the hyperbolic reflection coefficients plane with 0.414 < |í µí¼ ℎ | < 1, as shown in Figure 9, and their circular forms is unaltered. ![]() Further, as seen from (16), the constant reflection coefficients circles 0 ≤ |í µí¼| ≤ 1 of the 2D Smith chart are projected onto circles with 0 ≤ |í µí¼ ℎ | ≤ 0.414 in the hyperbolic reflection coefficients plane. The Hyperbolic Smith chart contains the circuits with inductive reactance above the horizontal (real line) of the ρ h-plane and the circuits with capacitive reactance below the real line of the hyperbolic reflection plane, like in the Smith chart. Circuits with the magnitude of the voltage reflection coefficient below 1 are mapped into the interior of the 0.414 hyperbolic circle in ρ h (the circuits with blue normalized resistance r and with red normalized reactance x) while the circuits with negative normalized resistance (green) are mapped in between the 0.414 radius circle and the unit circle (in this the constant normalized reactance circle are coloured in orange). In this case, there is no substantial difference in bandwidth between the two solutions. 92 pF π fZ 2 0 There are two solutions for the matching networks. Then for a frequency at f = 500 MHz, we have b C = 0. Step 2: Move the load impedance to the impedance circle of 1+ jx (done in admittance Smith Chart) - add j 0.3 in Step 4: Move to the center of the Smith Chart by adding an series inductor susceptance ELEC344, Kevin Chen, HKUST 1 ELEC344, Kevin Chen, HKUST 2 Step 4 Step 3 Therefore we have b = 0.3, x = 1.2 (check this result with the analytic solution). Step 1 Step 2 Solution: Step 1: Convert the load impedance to admittance by drawing the SWR circle through the load, and a straight line from the load through the center of the Smith Chart. 13: Impedance Matching (2) Smith Chart Solution 2 (not using combined ZY Smith Chart) Example 5.1 on of Pozar Design an L section matching network to match a series RC load with an impedance Z L = 200 - j 100 Ω, to a 100 Ω line, at a frequency of 500 MHz. ![]()
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