ESL electronics 101 for the electronics challenged

[oshifis]

Check also Quad ESL Dummy Load

[bolserst]

Originally Posted by markusA

Very cool spreadsheet.
The model for a transformer driven ESL sounds interesting.

Ok. I'll see if I can dig it up tonight, or tomorrow.

[bolserst]

Originally Posted by markusA

Very cool spreadsheet.
The model for a transformer driven ESL sounds interesting.

Attached is a *.zip file containing an Excel 2004 compatible and Excel 2007+ compatible spreadsheet for modeling impedance and response of an ESL connected to a step-up transformer. Also attached is the specification sheet for the Plitron 4314 transformer which I will post a couple sample calculations for.

Lower left plot shows impedance magnitude and phase.
Lower right plot shows normalized output response of voltage applied to ESL stators.
Upper right plot shows the impedance vector diagram for marker frequency.

Note that Rc(core losses) and Lp(primary inductance) are in reality a function of input voltage magnitude and frequency. In this spreadsheet they are constants. So not perfect modeling, but pretty good. Rc is not specified in the Plitron data. I estimated it at 500 ohm. This sets the peak magnitude of the impedance peak for the parallel resonance between Lp and (Cw + Cesl)*N^2.

Pic #1: Plitron 4314 with 1000pF ESL and recommended Rdamp = 0.8 ohm
You can see that the impedance and response match well with page 2 of the Plitron data sheet.

Pic #2: Plitron 4314 with 1000pF ESL and Rdamp = 0.2 ohm
The recommend value of 0.8 ohm gives you a maximally flat HF electrical response(stator voltages). If a lower value is chosen for Rdamp, the under-damped series resonance between LL and (Cw + Cesl)*N^2 causes a peak in the HF response. Also note that HF impedance drops and the phase angle gets even more negative (ie capacitive) in the top two octaves.

Pic #3: Plitron 4314 with 1000pF ESL and Rdamp = 1.5 ohm
If a higher value is chosen (Rdamp = 1.5 ohm) the HF electrical response droops a bit. But, since the native response of an ESL is a rising response (+3dB/oct for line source, +6dB/oct for point source) this is actually closer to the value needed for a flat acoustic response. Not that the minimum impedance has risen and the phase angle is reduced.

Pic #4: Plitron 4314 with 1000pF ESL and Rdamp = 1.5 ohm, Rshunt = 16 ohm
Adding a shunt resistance before Rdamp does not change the response. But, it does make the impedance load the amplifier sees more resistive. If used, this resistor would need to be able to dissipate considerable power/heat.

Like before, the spreadsheet does use complex variable functions, so you will need to load the Analysis Toolpak Addin before it will work properly.