# Inverter Design - What DC input voltage for most efficient DC to 120VAC inverter

I have seen several online circuit diagrams for a DC to AC inverter. Commonly many inverters use a transformer to step up 12V to 120V. I understand that inverting from DC to AC requires additional components, and that the transformer only induces 12V to 120V, so it doesn't make AC out of DC (that is done by the rest of the inverter circuitry).

The question is, given a choice of any possible voltage into an inverter without a transformer, what voltage would result in the inverter producing 120V RMS naturally? Is it 170VDC?

So once again, in an inverter design without a transformer, what DC input voltage would result in 120VAC naturally?

Ultimately, what I am trying to determine is what is the most efficient design for a DC to AC inverter. If by inputting a specific voltage, one can omit the transformer normally found in a DC to AC inverter design, then that reduces the number of components in the design (and naturally increases efficiency since the transformer isn't 100% efficient).

However my question isn't intrinsically about simply being able to remove specific components (such as the transformer) from the design. I am looking for the most efficient design, with or without any specific componentry.

What would the (DC) input voltage for that DC to AC inverter design be?

• Are we talking about square wave, modified sine or sine wave? Nov 10, 2015 at 20:43
• The reason a lot of designs us 12V is because 12V battery/sources are very common. Also note the transformer provides isolation. As well as the transformer is most likely not the least efficient step. You will most likely have an efficiency lost switching higher voltages. Nov 10, 2015 at 20:49
• A square wave would be fine for the application at hand.
– LCS
Nov 10, 2015 at 20:50
• electronics.stackexchange.com/questions/130069/…
– user16222
Nov 10, 2015 at 21:34

The fundamental RMS value of the output waveform for a square wave is given by:

Vrms = (4 X Vdc) / ( Sq-rt-2 X Pi)

However a square wave produces 33% 3rd harmonic, 20% 5th harmonic, 14% 7th harmonic in addition to the fundamental. If the positive and negative square pulses are only 120 degrees instead of 180 degrees, the fundamental will be about 86% of the value given by the above equation, the 3rd harmonic will be zero, the 5th will be 17 percent and the 7th will be 12%.

More specifically, you need only about 133 volts DC for a 120 volt RMS inverter output with a 180 degree square wave and 153 volts DC with a 120 degree square pulse output. That doesn't include the voltage drop in the switching devices. From Bedford & Hoft, Principles of Inverter Circuits, John Wiley & Sons, 1964

• Cool that takes me back a few years Nov 11, 2015 at 10:08

So once again, in an inverter design without a transformer, what DC input voltage would result in 120VAC naturally?

If you use a H bridge output then you need a DC supply capable of delivering the peak voltage of a 120 V AC sinewave. That's about 170 volts but you'll probably need a couple of volts more to account for volt drops.

• Thanks for your comment, but it seemingly conflicts with the formula answered above for the Vrms of a Square Wave. Is the H Bridge output a sine wave?
– LCS
Nov 11, 2015 at 16:17
• Yes it's for a sinewave. If you'd had mentioned that a square wave output was acceptable but only the primary the fundamental was to be considered then my answer would have lowered the dc level by 4/pi. If in fact you are considering filtering the sq wave to produce a sinwave then the magnetic components would probably be bigger than using a transformer and it would be marginally less efficient than my proposal. Nov 11, 2015 at 17:26