A visual comparison between voltage and power wave reflection coefficients of microwave circuits

Müller, Andres; Soto, Pablo; Moldoveanu, Alin; Asavei, Victor; Boria, Vicente E.

doi:10.1109/apmc.2012.6421888

Cited by 4 publications

(5 citation statements)

References 7 publications

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“…Evaluation of already synthesized matching networks as well as other components can be made using boundaries in classic Smith chart analysis. But, both complex load and source impedance occurs often in the context of active circuits, in which case the use of a 3D Smith chart [17,22,23] could be considered, as it possess a unique way of 3D visualization.…”

Section: Disk Covering Problemmentioning

confidence: 99%

“…conjugate match. Since the classical approach with voltage and current traveling waves fail to deal with both complex load and source impedance in a satisfactorily way we use the concept of power waves as introduced by [13 -15], further described by [16,17], and used by [18]. The degree of matching (or rather mismatch) can be measured by the reflection coefficient for power waves, Γ p , as…”

Section: Finding An Expression For the Boundary Of Matchingmentioning

confidence: 99%

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Constant Mismatch Loss Boundary Circles and Their Application to Optimum State Distribution in Adaptive Matching Networks

Sjöblom

Sjöland

2014

IEEE Trans. Circuits Syst. II

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An adaptive matching network provides a number of states between which it can be reconfigured. At a certain frequency the matching network transforms a reference impedance to different impedances for the different states. The circuit will be able to match those impedances perfectly to the reference impedance, and impedances close to those will also be fairly well matched. The matching will however decline for impedances further away and eventually become too low. By defining the level of acceptable matching, a boundary can be formed that identifies an area of well enough matched impedances. In the same manner a boundary is possible to form for constant mismatch loss. It is shown that the boundaries are circular if plotted in a Smith chart, and that the sizes of the circles depend on the location of z L . With these results it is then investigated how the impedances should be distributed to minimize the number of states while still achieving the matching performance and coverage.Index Terms-Adaptive matching, antenna tuning unit, impedance matching, matching coverage, matching network, switched matching network.

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Section: Disk Covering Problemmentioning

confidence: 99%

Section: Finding An Expression For the Boundary Of Matchingmentioning

confidence: 99%

Constant Mismatch Loss Boundary Circles and Their Application to Optimum State Distribution in Adaptive Matching Networks

Sjöblom

Sjöland

2014

IEEE Trans. Circuits Syst. II

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“…On the 3D Smith chart these visualization problems never occur [1][2][3][4]. Mapping the new defined parameters (3) and (7) on the 3D Smith chart with the same stereographical projection used in [1], ensures that these will be always circles (since extended lines are mapped into circles on the Riemann sphere).We may actually see that plotting (3) and (7) on the 3D Smith chart for the symmetrical circuit presented in Fig.…”

Section: Circuits Examples On the 3d Smith Chartmentioning

confidence: 99%

“…In the recent years it was shown that elements of group theory present in geometry may bring to light new tools in microwave engineering [1][2][3][4] like the 3D Smith chart, while in [5][6] it was also lately demonstrated how new circle boundaries obtained by ingenious manipulation of different functions of the scattering parameters may still help in the microwave design. Nevertheless in [3] it was proved that the well known unilateral transducer power gain circles are a family of Apollonius circles recently introduced too in microwave engineering in [7].…”

Section: Introductionmentioning

confidence: 99%

On the sum of the reflection and transmission coefficient on the Smith chart and 3D Smith chart

Müller

Codesal

Moldoveanu

et al. 2015

2015 Asia-Pacific Microwave Conference (APMC)

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IEEEMüller, A.; Sanabria-Codesal, E.; Asavei, V.; Favennec, J. (2015). On the sum of the transmission and reflection coefficient on the Smith chart and 3D Smith chart. Asia-Pacific Microwave Conference (APMC 2015 Abstract-The paper presents in premiere a simple mapping property of the sum of the reflection and transmission parameters of reciprocal two port networks. It is proved that although the reflection and transmission parameter may have very complicated paths on the Smith chart, their sum will be always moving on the unit circle if the circuit is symmetric and lossless. Further once symmetrical losses at the ports occur their sum path will switch on a family of circles through one point. Using inversive geometry we construct a new function which maps this family of circles in lines on the extended Smith chart. The proposed method for checking the symmetry uses just two parameters and avoids testing the phase of the corresponding input and output parameters. By means of the 3D Smith chart we propose in the end an alternative approach to visualize the parameters.

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“…Until very recently, the main applications for the 3-D Smith chart included complex port matching, representing amplifier stability circles (originally at a single frequency, it will be shown in the Appendix that this can also be extended to cover a wide frequency range) and oscillator design, by projecting onto the surface only of the sphere [9]- [11], with computer-aided design (CAD) software now commercially available [12]. The basic geometrical framework employs a stereographical projection to map the generalized Smith chart onto the Riemann sphere.…”

mentioning

confidence: 99%

Extended Capabilities of the 3-D Smith Chart With Group Delay and Resonator Quality Factor

Müller¹,

Codesal²,

Moldoveanu

et al. 2017

IEEE Trans. Microwave Theory Techn.

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Abstract-This paper extends the capabilities of the 3-D Smith chart for representing positive and negative differential-phase group delay and the associated loaded resonator quality factor, displayed simultaneously with scattering (S)-parameters. Here, mathematical concepts, inspired from elementary differential geometry and topology, are used to implement 3-D projections. It is shown that a condition for a circuit to exploit negative differential-phase group delay is that its S-parameter winding number should be ≥ 0 (relative to its origin). Finally, exemplar network responses that exhibit both positive and negative differential-phase group delay and loaded resonator quality factor are shown with the 3-D Smith chart. The convenience of being able to simultaneously display a wider range of parameters on one visualization platform, with the 3-D Smith chart, may help to speed-up the design and analysis of microwave circuits by the user.Index Terms-Computer-aided design (CAD), differentialphase group delay, negative group delay (NGD), non-Foster, quality factor, Smith chart.

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A visual comparison between voltage and power wave reflection coefficients of microwave circuits

Cited by 4 publications

References 7 publications

Constant Mismatch Loss Boundary Circles and Their Application to Optimum State Distribution in Adaptive Matching Networks

Constant Mismatch Loss Boundary Circles and Their Application to Optimum State Distribution in Adaptive Matching Networks

On the sum of the reflection and transmission coefficient on the Smith chart and 3D Smith chart

Extended Capabilities of the 3-D Smith Chart With Group Delay and Resonator Quality Factor

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