Dielectric Modulation: Motion Sensor, 200V Containment Field, 100mV Modulation

[Calvin Cox]

We have recently developed a motion sensor that introduces charge into an electric field. From the 200V (containment field) we derive a modulation of 100mV. Although the sensor has passed pre-production tests we are struggling to come up with a simple formula to describe the operation. Can anyone help?. Regards - Calvin

 

[Bob S]

I think you are referring to deriving a voltage modulation by modulating the capacitance C while holding charge Q constant:

V = Q/C

C = εε₀A/x for parallel plate capacitor with area A, separation x, dielectric constant ε, and ε₀ = 8.85 x 10^-12 Farads per meter.

So V = Qx/(εε₀A)

So dV/dt = Q[1/(εε₀A)·dx/dt - x/(εε₀A²)·dA/dt - x/(ε²ε₀A)·dε/dt]
= [Q/C]·[1/x ·dx/dt -1/A ·dA/dt - 1/ε ·dε/dt]

Bob S

 

[Calvin Cox]

Thanks you for that, Bob.
It is not quite as you have assumed from my crude description: the capacitor is fixed and we utilise the charge congregated on the edges of the blades of a plastic impeller wheel to modulate the dielectric field. We were thinking perhaps of 'field displacement' ?