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I want to control an 8-port Sainsmart relay from a Raspberry Pi (via the GPIO pins) and I'm trying to understand a couple of things about the suggested circuit for integrating the two. Here is the circuit:

enter image description here

As the explanatory text says, the relay is "active low" but, for a number of reasons, I want to control it from the RPi as an "active high" device (i.e. raise a GPIO pin to high to activate the relay, and lower it to zero to deactivate it).

I have it working and I sort of understand what it does, but I have a couple of questions:

  1. How is the sizing of the resistor(s) determined?
  2. What is the purpose of the 10K resistor?
  3. This design implies to me that the RPi and the relay must share a common ground. Is this true? Does it mean they must also share the same power supply?
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As the explanatory text says, the relay is "active low" but, for a number of reasons, I want to control it from the RPi as an "active high" device (i.e. raise a GPIO pin to high to activate the relay, and lower it to zero to deactivate it).

The accompanying text is explaining to you that the GPIO high (3.3 V) will turn on the transistor connecting the collector to the emitter thus pulling the relay low. This gives your desired behaviour.

How is the sizing of the resistor(s) determined?

The transistor base-emitter junction behaves rather like a diode and will have a 0.7 V drop across it when current is flowing through it. That leaves 3.3 - 0.7 = 2.6 V across the base resistor.

The 2.2 kΩ base resistor is chosen to give enough base current to turn the transistor on in "saturation". i.e. The collector-emitter voltage drop has gone as low as it can. In the example the base current will be given by \$ I = \frac V R = \frac {2.6}{2k2} = 1.2 \ \text {mA} \$. If the transistor has a high current gain this may be enough.

What is the purpose of the 10K resistor?

It helps keep the transistor off when your microcontroller is powering up and the GPIO isn't in output mode because the program hasn't booted yet.

This design implies to me that the RPi and the relay must share a common ground. Is this true?

Correct.

Does it mean they must also share the same power supply?

No. The relays can and often are powered from a higher voltage supply. This is one of the reasons the open-collector design is so popular as it provides a means of doing voltage translation between circuits.

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  1. It is determined by GPIO output voltage, transistor base voltage, and required base drive current.

  2. 10k resistor is to keep transistor off when GPIO pin is not an output for some reason, like booting up or misconfigured as input.

  3. Yes, transistor emitter must be connected together with Raspberry Pi ground, otherwise there is no loop for the current to flow. They don't need to share a power supply, they can have different voltages, as long as grounds are common.

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This design implies to me that the RPi and the relay must share a common ground. Is this true?

The relay coil needs to have a shared ground. The relay contacts - not at all :)

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