This tool allows to caluclate the quality factor and first-order frequency corrections to coplanar waveguide (CPW) resonators coupled to a CPW transmission line.
If you are interested in how this works or wish to refer to this webpage, see the article "Quality factor of a transmission line coupled coplanar waveguide resonator"
cite as: Besedin, I. & Menushenkov, A.P. EPJ Quantum Technol. (2018) 5: 2. https://doi.org/10.1140/epjqt/s40507-018-0066-3
(arxiv preprint: arXiv:1710.01998).
The actual implementation used here is based on javascript, complatible with node.js and web browsers. You can download this webpage and use it offline.
Alternatively, you can use a python implementation available on github.
For a short tutorial on how to use this page, visit youtube.
(c) Ilya Besedin, 2018. Creative Commons Attribution-NonCommercial-ShareAlike terms apply. Other licensing options are available upon request. Estimates done with this tool are usually slightly higher than true quality factors due to spurious couplings.
Conductor geometry (view)
This is a cross-section and top down view of the coplanar coupler.
The geometry is defined by "branching points" (red and green).
Each conductor is either "ground" (gray), "feedline" (blue) or "resonator" (yellow).
Click a conductor on the image to toggle its class.
Conductor geometry (edit)
Define geometry by "branching point" coordinates
Name
Position
Name
Position
A
B
C
D
Enter gap and conductor widths in any units: μm, nm, mils, ...
Gap
Conductor
AB
BC
CD
Material properties
The upper half-plane is vacuum (ε=1, μ=1).
Substrate permittivity (ε):
Substrate permeability (μ):
Calculation precision
The higher the numbers, the higher the precision.
Gauss-Chebyshev quadrature order:
Gauss-Newton iterations:
Impedances, Ohms
Termination impedances affect the quality factor of the coupled resonator. Complex impedances are supported (for example '50+50i').
Zo
Zi
Zr
Zt1
Zt2
Section lengths, mm
Coupler
l1
l2
Per-unit-length effective inductance, nH/m:
Feedline
Resonator
Feedline
Resonator
Per-unit-length effective capacitance, pF/m:
These value can be used to estimate the capacitance of interdigital capacitors.
Feedline
Resonator
Feedline
Resonator
Full per-unit-length inductance, nH/m:
BC
Full per-unit-length capacitance, pF/m:
BC
Resonances
First-order corrected resonance frequencies in the "resonator" (yellow) conductors and TLs 1 and 2.