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I am trying to just use the voltage from 4 Alkaline AA batteries in series (6v nominal) to power a motor with the TI drv8830 IC.

My question is, will this circuit (specifically just pulling the sda and scl pins to 3.3v) work reliably? The datasheet says at maximum of 6.8v vcc the chip will still recognize 3.3v i2c lines (minimum 3.13V at that vcc voltage) but will the varying voltage of the battery cause the communication to be unstable? There is a 10uf capacitor between vbat and gnd (not shown).

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will the varying voltage of the battery cause the communication to be unstable?

No. As the battery voltage drops the input HIGH threshold (which is a function of VCC) also drops. If anything as the battery voltage drops the communication becomes more stable.

Since I2C is an open drain protocol the voltage makes no different for sending data - that voltage is set by the pull-up resistors to 3.3V.

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