Hi Les - Here is a solid-state 12 VDC power supply I built for my A.R.C. Type 12 VHF aircraft set.  It also works with HF Command Set receivers.  Altho it is built around a junk box ferrite core (3B9 material versus iron) the basic design Kludge is pretty simple and works great. 
I like your description of "trapezoidal drive" which does describe a real-world square wave with its finite rise and fall times.  hihi.  Anyway, take a look here for maybe some ideas to use.
https://www.n6cc.com/solid-state-dynamotor/

73, Tim
N6CC

On Tue, Oct 25, 2022 at 6:11 PM Leslie Smith <lnsmith99@gmail.com> wrote:

Hello all:

I wish to build a lead-acid battery to B+ inverter using (probably) a conventional iron-core transformer.  Two configurations are generally seen in typical circuits.  I will describe these as "H" bridge and solid-state vibrator replacement.  The "H" bridge uses an untapped low-voltage winding; the vibrator circuits use a transformer with a center-tapped primary winding.

Since I can choose the switching frequency, and a higher frequency has some advantages, what limits the operating frequency?  Assume a conventional EI (or perhaps toroidal) core using common transformer iron.  (I assume the 'iron' used in most power transformer share a 'common' quality.)

I intend to feed 'the beast' with a trapezoidal wave-form not a sharp square wave.

Thanks for observations.

Leslie
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