A 3-D Smith Chart Based on the Riemann Sphere for Active and Passive Microwave Circuits

Müller, Andres; Soto, Pablo; Dascǎlu, D.; Neculoiu, D.; Boria, Vicente E.

doi:10.1109/lmwc.2011.2132697

Cited by 24 publications

(42 citation statements)

References 8 publications

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“…The transmission parameter is plotted onto the 3-D Smith chart, to give a curve of S 213D (ω) as frequency changes on the surface of the Riemann sphere [9], [10] using the following mapping function [9, eq. (3)], written here in Cartesian vector form:…”

Section: A Differential-phase Group Delay Based On Homothetymentioning

confidence: 99%

“…The 3-D Smith chart (impedance version) was recently introduced by Muller et al [9]- [13] in 2011. This visualization platform represents the response of passive components/networks, active devices/ circuits, and mixed topology subsystems, by exploiting the unity radius Riemann sphere, using the conformal mapping illustrated in Fig.…”

mentioning

confidence: 99%

“…The Eastern hemisphere represents inductance and West capacitance-separated by the prime meridian that represents pure resistance (positive and negative in the Northern and Southern hemispheres, respectively). Therefore, the origin of the 2-D Smith chart is mapped to the North Pole of the 3-D Smith chart, while infinite is just as conveniently mapped to the South Pole [9], [10].…”

mentioning

confidence: 99%

“…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%

See 3 more Smart Citations

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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Section: A Differential-phase Group Delay Based On Homothetymentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

See 2 more Smart Citations

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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“…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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Review of Telecommunication Aspects for Power Amplifier Design

Božanić

Sinha

2015

Signals and Communication Technology

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A 3-D Smith Chart Based on the Riemann Sphere for Active and Passive Microwave Circuits

Cited by 24 publications

References 8 publications

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

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

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

Review of Telecommunication Aspects for Power Amplifier Design

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