I want to make a simple device that causes my cellphone to vibrate for 30 seconds when my phone is 10 feet away from it. How would I go about doing that. How small could I make the device?
Program a Bluetooth 4 BLE transmitter to send a burst of short data every n seconds. Choose n to balance cell life and response time. Small n, less cell life. The data is dummy data as we need the signal strength only. Use shortest data length to save cell life.
Older transmitter is MCU and BLE chip. Seem newer chip is one chip doing both.
Program a cell phone app to read RSSI signal strength to estimate distance with reasonable accuracy.
With mass production factory grade tools, facility and know how, size can be 1.2 diameter of coin cell and 3 times height of coin cell, being 1 time for cell, 1 time for electronic and PCB and 1 time for plastic and misc.
Google "child monitor bracelet" to see examples of real commercial products
Hope this helps