Design strategy of tunable matching network and prototype verification

Abstract

A set of design strategies for the tunable matching network are proposed, which are performed on the impedance domain rather than the reflection coefficient domain (Smith Chart). Moreover, the bandwidth and parasitic parameters of the network are discussed. The proposed methods guarantee the finding of optimal point and accelerate the convergence speed from O(N) to O(log N).

3D Smith Chart Constant Quality Factor Semi-Circles Contours for Positive and Negative Resistance Circuits

“…The quality factor of an impedance Z or admittance Y can be defined as (1) [12][13][14][15][16][17], (this is denoted also as nodal quality factor in [15][16][17]) where X represents its reactance, B its susceptance, R resistance and G conductance as defined in (1) where Z and Y can be related through (2). Other authors skip the absolute value sign in (1) [8][9][10][11], however this doesn't change anything in respect to their geometry, only to the sign labelling convention.…”

“…Other authors skip the absolute value sign in (1) [8][9][10][11], however this doesn't change anything in respect to their geometry, only to the sign labelling convention. Using the sign conventions [12][13][14][15][16][17] (as for example at p.102 in [13]), we do not allow negative Q values for passive circuits with positive resistances.…”

“…1 (b) shows the family of the radial lines obtained for various values of ≠ 0. Imposing now Q constant and positive in (3) one gets the contours obtained in [8][9][10][11][12][13][14][15][16][17] irrespective of the presence of the absolute value in (1). However, by using inversive geometry [18], it can be proven that imposing (5) in (3), the set of radial constant Q lines is proven to generate a family of coaxal circles as r and x are swept from -∞ to +∞.…”

“…At resonance the imaginary part is zero and (15) is fulfilled where ω0 is the angular resonance frequency, while f0 the resonance frequency. The input admittance at resonance 110 becomes (16) and Q defined in (13) becomes (17).…”

“…The Smith chart [1][2], proposed by Philip Hagar Smith in 1939, survived the passing of years, becoming an icon of microwave engineering [3], being nowadays still used in the design and measurement stage of various radio frequency or microwave range devices [4][5][6][7], for plotting a variety of frequency dependent parameters. Constant quality factor (Q) representations on the Smith chart are a visual way to determine the quality factor of various passive microwave circuits, being mostly known in the microwave frequency range community [8][9][10][11][12][13][14][15][16][17]. These constant Q shapes are often denoted as contours or curves, [8][9][10][11][12] while extremely seldom as circles [11].…”