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Application of Symmetry Properties to Common-Mode Suppressed Differential Transmission Lines

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Symmetry Properties in Transmission Lines Loaded with Electrically Small Resonators

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Abstract

The selective mode suppression inspired by the alignment of symmetry planes described in Sect. 4.2 can be useful for the design of microwave differential circuits and components.

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Notes

  1. 1.

    Balanced is the microwave term for differential [1].

  2. 2.

    In the absence of a common ground plane, the differential transmission line becomes a two-conductor propagative structure where common-mode signals cannot be supported. For instance, coplanar strips (CPS) support only differential-mode signals.

  3. 3.

    The common-mode rejection ratio (CMRR) may also be used as a figure of merit [5].

  4. 4.

    In CPW-based structures with asymmetric topologies, the rejection of the parasitic differential mode while remaining the common mode unaltered is of general interest. As was mentioned in Sect. 4.1, slot-mode rejection is usually and efficiently achieved using air bridges to short-circuit this mode [23].

  5. 5.

    A balanced line carries balanced signals, that is, the two conductors carry signals with the same amplitude but with 180\(^\circ \) phase shift; the signal on one conductor is referenced to the other one.

  6. 6.

    There are two possible alignments. Particularly, the slits of the inner rings are lined up with the line axis, as shown in Fig. 5.9a. This orientation is aimed at obtaining a coupling dominantly electric through a chain of DS-CSRRs.

  7. 7.

    Note, however, that the circuit model for the CSRR is approximate, since the line-to-resonator magnetic coupling is ignored.

  8. 8.

    Using CSRRs, the transmission zero frequency also depends on the line-to-resonator magnetic coupling, but its contribution is neglected.

  9. 9.

    The transmission zero frequency for an isolated unit cell provides a reasonable estimate of the central filter frequency.

  10. 10.

    This comparison is meaningful for a large number of cells. A discussion on whether the bandwidth inferred from the dispersion relation (\(FBW_{max}\)) is related to the \(-20\) dB bandwidth of a structure with a large number of cells (FBW) is given in Appendix E.

  11. 11.

    As explained in Sect. 3.2.1, the inter-resonator capacitance at input and output ports are left opened, and the equivalent circuit reduces to a two-port network.

  12. 12.

    The reported approach allows us to infer the maximum achievable common-mode rejection bandwidth, rather than specifying the bandwidth to a particular value.

  13. 13.

    For a particular transmission zero frequency, the accuracy of the circuit model does not depend exclusively on the physical size, but also on the ring width and inter-ring distance. It is for this reason that, despite the fact that the DS-CSRR is physically larger than the CSRR, the circuit model is more accurate for the former.

  14. 14.

    The proposed differential filter is a second-order Chebyshev bandpass filter with a central frequency of 1.37 GHz, a fractional bandwidth of 10 %, and 0.1 dB ripple. The design of the filter is done following the procedure described in [28].

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  1. School of Engineering, Autonomous University of Barcelona, Barcelona, Spain

    Jordi Naqui

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Naqui, J. (2016). Application of Symmetry Properties to Common-Mode Suppressed Differential Transmission Lines. In: Symmetry Properties in Transmission Lines Loaded with Electrically Small Resonators. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-319-24566-9_5

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  • DOI: https://doi.org/10.1007/978-3-319-24566-9_5

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