Model

The electrostatic loudspeaker simulator tries to find a numerical solution to the following expression:



This is the general form of Peter Walker's equation which predicts the far field frequency response. For it's derivation see chapter 22 of the work of Frank Verwaal (theory section).

What is accounted for in this expression is interference between contribution of different locations of the diaphragm, the angle w.r.t the axis of the speaker and the proximity effect.

Limitations

Like Dirty Harry used to say: "A man's got to know his limitations". The program assumes rectangular shaped, unbaffled, flat panels. It does not account for diaphragm mass or suspension, hence does not know about resonances or high frequency roll off due to diaphragm mass. Nor does it incorporate the effect of the room. To simulate a line source that is tall compared to the height of the room, you have to enter a very large value for the height, for example 10 meters, and you'll get the expected 3dB/oct slope.

For some values the simulation may take a while to finish. Please be patient and wait for the graph to load.

In the future I'd like to add support for segmented or curved panels.

   

How to use it

You specify the physical attributes of the speaker, e.g. width, height, diaphragm-stator spacing, polarization voltage etc.
All dimensions are in SI (kg/m/s) units. The units involved here are meter, Farad, Ohm, Volt, Ampere and Henry. You can use scientific (exponential) notation or you can use the symbols M(ega), K(ilo), m(illi), n(ano), p(ico) etc. See also SI units. So for a stator spacing of 1 millimeter you could write 1mm, 1e-3 or 0.001, whichever you like best.
The program can calculate the frequency response for voltage as well as for current drive. The output for voltage drive is calculated by estimating the drive current by steady state circuit analysis. Constant current drive is the current at the stator plates.
Finally you have to specify the location of the observer (listener) and the frequency range of interest.

Electrical circuit

I added the parameters 'series resistance' and 'series inductance' so you can account for real-world step-up transformer behavior. Series resistance would be the resistance of the secondary and the reflected resistance of the primary. Series inductance would be the leakage inductance and shunt capacitance is the shunt capacitance of the step up plus the dead capacitance in the ESL panel. Note: shunt capacitance is currently disabled. You should be able to see high frequency loss and resonance. You can also use the series resistance parameter to play with frequency response shaping (shift from voltage to current drive). These parameter only have effect for voltage drive!

Calculation

The parameter 'points per decade' determines the roughness of the graph. If it looks rough increase this value. The parameter 'integration points' determines the step size of the numerical calculation. Precision might suffer if chosen too low, and if chosen too high you might have to wait a very long time for the program to finish.
Tip:You can save your result by right-clicking the graph and select 'export as image'.