One thing I didn't ask is how many pulses you're delivering per echo, and how far apart they are. You have to account for the discharging and recharging of the 100μF capacitor.
I think I understand your circuit, it is basically the same as my original one but replacing the transformer with a single inductor, and instead of the secondary pin of the transformer providing the voltage, that is instead coming off the bottom of the inductor through a diode to the transducer.
Well, not exactly. Instead of a pulse transformer (where you can say you have a 10:1 transformer x 5V = 50V) you are actually using the inductor as a kind of spring, building up energy and releasing it suddenly. Inductors resist changes in current (like capacitors resist changes in voltage); when you interrupt the input current flow, the voltage rises to maintain the same current. Since you have a high impedance load, that voltage can rise pretty high.
And the reason for the diode is to prevent any echos coming back on the transducer from being sunk by the inductor/transistor?
Partly. And to ensure that you get just a single pulse. Of course, if you want more than one pulse you can add a diode in series between the transistor and the inductor (cathode to transistor), thereby letting the inductor "ring". Replace the output diode between the transistor and the transducer with a capacitor which will resonate with the inductor at 40Khz.
Hopefully I have understood that correct. Is there a specific calculation for the collapsing field of an inductor and its charge as to the voltage spike, so I can calculate a specific voltage?
It may be easier to breadboard this. Get some inductors and high-voltage FETs and sit down with an oscilloscope and a pulse generator and see what you get.
The problem here is that what limits your voltage tends to be things that aren't necessarily specified in the component data sheet.
For one thing, your transducer is more complicated than a simple capacitor; it takes energy to wiggle it mechanically (there are some interesting academic papers on modeling piezo transducers, by the way). Some transducers go seriously non-linear at a high enough voltage, suddenly conducting current instead of acting like a capacitor.
Then there's the "parasitic" properties of the inductor: parallel capacitance (which you can typically get close to by using the "self resonant frequency" of the inductor if it's given; the higher the SRF, the lower the capacitance).
And there's also the question of how much current you can flow through the inductor before it goes into "saturation"; this depends mostly on the specific core material and is often not well specified, though if you stay well below the maximum current given by the manufacturer you probably won't go into saturation. And if you power the inductor's field from a capacitor as in the diagram I posted, the parasitic "equivalent series resistance" and "equivalent series inductance" parameters are interesting, as they determine how fast the inductor can charge. As can the inductor's series resistance.
I've attached my SPICE model; you can run it using Linear Technology's excellent LTSpice http://www.linear.com/designtools/software/ltspice.jsp
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