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The MCP4241 digital rheostat still responds to SPI data after Vdd is disconnected. Could someone please shed some light on why that is?

Data sheet: http://ww1.microchip.com/downloads/en/DeviceDoc/22059b.pdf

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There are ESD protection networks on each input or output pin that act as diodes to Vcc and Vss. So it's completely possible for a CMOS chip to be powered inadvertently by an input (or, in this case, one of the emulated pot pins).

Needless to say, this is not really kosher and you should not generally depend on this 'feature' as you're operating outside of the recommended operating conditions.

Here, from Fairchild, is a detailed application note AN-248 covering the ESD networks used on certain of their CMOS chips:

enter image description here

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Usually it is because the ESD diodes on the inputs will conduct and provide power to the device from the control signals.

A common way of protecting the device from ESD is to put two diodes on each input pin, one diode goes from the input to VDD the other to GND. The intent is that if the driving signal attempts to go beyond the supply rails, such as during an ESD strike, the diodes will conduct away the excess charge.

Many CMOS devices exhibit this behavior. The same effect can often be observed if device ground is missing.

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