Complex permittivity and loss (Cole-Cole), two ways

The same calculation run twice, side by side. Change anything on either side and the difference is shown output by output. This page is a link: both sets of numbers are in the address bar.

Side A open alone

w Water

What is in the cell. Conductivity is the parameter that dominates here, and it is what most separates these.

f Frequency

kHz

The drive frequency.

Side B open alone

w Water

What is in the cell. Conductivity is the parameter that dominates here, and it is what most separates these.

f Frequency

kHz

The drive frequency.

Swap sides

What changed

The two sides are the same. Change something on either.

Output	A	B	B against A
δ Loss tangent	0.1234	0.1234	same
ε Real permittivity	80.1	80.1	same
κ Loss permittivity	9.887	9.887	same
λ Dipole loss alone	5.214e-5	5.214e-5	same
Q Effective Q of the dielectric	8.102	8.102	same

Side A, with its numbers

{80.1}^{*} = ε_{\infty} + \frac{ε_{s} - ε_{\infty}}{1 + {(j ω τ)}^{1 - α}} - j \frac{σ}{ω ε_{0}}

LaTeX

80.1^{*}(\omega) = \varepsilon_\infty + \frac{\varepsilon_s - \varepsilon_\infty}{1 + (j\omega\tau)^{1-\alpha}} - j\,\frac{\sigma}{\omega\varepsilon_0} \qquad \tan0.1234 = \frac{9.887}{80.1}

A loss tangent of 0.123 caps the circuit Q at about 8 before any copper or core losses are counted.

Side B, with its numbers

{80.1}^{*} = ε_{\infty} + \frac{ε_{s} - ε_{\infty}}{1 + {(j ω τ)}^{1 - α}} - j \frac{σ}{ω ε_{0}}

LaTeX

80.1^{*}(\omega) = \varepsilon_\infty + \frac{\varepsilon_s - \varepsilon_\infty}{1 + (j\omega\tau)^{1-\alpha}} - j\,\frac{\sigma}{\omega\varepsilon_0} \qquad \tan0.1234 = \frac{9.887}{80.1}

A loss tangent of 0.123 caps the circuit Q at about 8 before any copper or core losses are counted.