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I am fairly new to half bridge drivers and understand the concept of a full bridge. I was looking at building a basic full bridge using 2 half bridge drivers, the driver IC's I was going to use were the international rectifier IRS2004 (datasheet can be found here http://www.irf.com/product-info/datasheets/data/irs2004pbf.pdf).

However the college will have issues ordering them due to USA stock so extra carriage, so I have been looking at the IRS2003 (datasheet can be found here http://www.irf.com/product-info/datasheets/data/irs2003pbf.pdf)

This seems like it will do the task, but I am struggling to understand the timing diagram and the benefit of having the LIN input out of phase by what looks like 180 degrees.

The datasheet states:

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My understanding is that if I want to use the irs2003 in a similar fashion to the irs2004 (minus the ShutDown input) , I Feed the same PWM signal into both the HIN and LIN pins?

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Your analysis appears to be correct. Tying the IRS2003 inputs together and driving them with a single PWM signal should provide similar functionality to the IRS2004 single input device, per the hyperlinked datasheets.

The discrete inputs on the IRS2003 gives you the flexibility to manually adjust the deadtimes higher than what's provided by the IC itself, and give you complete phase control over the outputs.

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