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)

# Conductor geometry (edit)

# Material properties

# Calculation precision

# Impedances, Ohms

# Section lengths, mm

# Per-unit-length effective inductance, nH/m:

# Per-unit-length effective capacitance, pF/m:

# Full per-unit-length inductance, nH/m:

# Full per-unit-length capacitance, pF/m:

# Resonances

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.

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.

Enter gap and conductor widths in any units: μm, nm, mils, ...

Gap | Conductor | ||
---|---|---|---|

AB | BC | ||

CD |

The upper half-plane is vacuum (ε=1, μ=1).

Substrate permittivity (ε):

Substrate permeability (μ):

The higher the numbers, the higher the precision.

Gauss-Chebyshev quadrature order:

Gauss-Newton iterations:

Termination impedances affect the quality factor of the coupled resonator.

Complex impedances are supported (for example '50+50i').

Complex impedances are supported (for example '50+50i').

Zo | Zi | Zr | Zt1 | Zt2 |
---|---|---|---|---|

Coupler | l1 | l2 |
---|---|---|

Feedline | Resonator | |
---|---|---|

Feedline | ||

Resonator |

These value can be used to estimate the capacitance of interdigital capacitors.

Feedline | Resonator | |
---|---|---|

Feedline | ||

Resonator |

BC |
---|

BC |
---|

First-order corrected resonance frequencies in the "resonator" (yellow) conductors and TLs 1 and 2.

n | Frequency, GHz | Linewidth, MHz | Decay time, μs | Quality factor |
---|---|---|---|---|

1 | ||||

2 | ||||

3 | ||||

4 | ||||