The channels on this Phidget are switch-to-ground relays
Ok. That helps.
This device does support PWM, so you should be able to set duty cycle. I'm not sure if I understand your oscilloscope circuit, it looks like you're putting both probes in series? Are you measuring voltage or current?
I am trying to measure voltage. Closing the relay in the circuit, I should see a voltage on my oscilloscope. This works using the SetState() function. If I call SetState(1), I see a voltage (of the source). I was expecting to see the voltage oscillate using the SetDutyCylce() function. But I don't see anything. Can I check the duty cycle or state of the relay on the software side?