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I stumbled across this line in this datasheet (page 10):

Serial Data Output Pin. Internal N-Ch FET with open-drain output that requires external pull-up resistor. It shifts out the previous eight SDI bits that allow daisy-chain operation of multiple packages.

Could somebody briefly explain what this means? Specifically, if I'm not planning on using the daisy-chain functionality, can I leave this pin unconnected or do I need to connect it to an external pull-up resistor regardless?

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If you are not using the serial daisy chain then you can leave the SDO pin open and not have to install a pullup resistor on this pin.

The AD5290 part is designed to allow its use in analog circuits that have power supplies up to and including +/- 15V. This allows the "digital pot" terminals to connect into OpAmp circuits (and other similar types) that operate on voltage rails of this magnitude.

The main reason that the SDO pin on this part is open drain is that it allows the device to be built into a package of 10 pins and eliminates a need for a digital logic level supply pin. If the SDO pin (the only digital output on the part) was designed with a push-pull output then the extra digital supply pin would be required.

As others have stated the open drain nature of the pin is such that the pin could be be tied together with multiple other open drain outputs but that has very little utility in the use of this particular part. Instead it can have a role in the daisy chain operation when the digital supply levels are other than a 5V supply. A close look at the VIH and VIL specifications for the part will show that the inputs to this device can be driven equally well from a digital realm of 5V or from 3.3V.The open drain SDO can be externally wired up to a 5V or a 3.3V pullup with equal utility depending on which digital rail is used in the system.

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The data that you shift in on SDI will be shifted out on SDO. You can optionally connect multiple of these devices in series:

schematic

simulate this circuit – Schematic created using CircuitLab

This means you only need a single data pin and a clock pin on your microcontroller to access all these device, all you need to do is apply enough clock pulses to get the data to/from all the devices.

The open drain means that the output can only pull low, pull to ground. It cannot by itself make a high signal, it needs help for that from an external resistor. The transistor pulls the output low and when the transistor is 'released' the resistor will pull the output up to Vcc.

schematic

simulate this circuit

The advantage of open drain (or open collector when using a BJT) is that you can tie multiple outputs together without problems.

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See page 16. SDO is only used if devices are daisy-chained.

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SDO is an open-drain output-only pin. It needs a pullup resistor in order to drive a logic 1 out, otherwise the SDO pin will remain at ground. The internal NFET drives a "0". Open drain pins allow multiple devices to be tied together w/o fighting, since there's no active pullup.

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