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hbridge basic question

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The small, single IC H-bridges you'll see in common use here only require positive and ground. Take a look at the L293D, this is probably the most common H-bridge IC in use by hobbyists.
Many of the basic BJT and MOSFET home-built H-bridges also only use positive and ground for simplicity, but some of the improved MOSFET H-bridges require positive ground and negative. Many of the IC MOSFET H-bridges that need an additional higher or lower 3rd voltage are capable of generating it internally, so you only need to supply 2 voltage levels for power.
so does a h-bridge in general requires a ground, positive, and negative?? or just a positive and ground?

Linear amplifiers are not a common choice for driving motors as they're usually more complex than an H-bridge, and most small linear amp ICs are only capable of currents <100mA. Most small motors need at least a few hundred mA to start under stall conditions. If efficiency is a major factor in motor drive selection, it's worth looking into buying or building a FET based H-bridge instead of a linear amp.

I was just asking it in general
That depends on the exact arrangement; different H-bridges and linear amps will have significantly varied efficiencies in differing situations. Do you have something in mind?
Also is the H-Bridge much cooler (i.e. is more power efficient) than an equivalent sized linear amplifier if I have a PWM/HBridge combination?
There are many H-bridge designs out there, and although I'm sure there will be at least one that requires all 3 rails, most H-bridges just use positive and ground.