Electronic – How to generate a -5V to +5V sine wave from one DC supply

You need to use Olin's idea of determining the zero crossings of the signals to get the time delay. Then plug the time delay into Scott's equation to get the phase delay.

The following is pseudo-code. I'll leave it up to you to implement each function since they should either be trivial to implement or you should already have something similar written.

reset_timer();    //reset timer to zero

while(get_amplitude(INPUT_CHANNEL) > 0.0)
{
    //do nothing until input channel crosses zero
}

start_timer();    //start timer counting

while(get_amplitude(OUTPUT_CHANNEL) > 0.0)
{
    //do nothing until output channel crosses zero
}

stop_timer();    //stop timer counting

time_delay_ticks = get_timer_ticks();    //get the number of timer ticks between zero crossings 
time_delay = ticks_to_time(time_delay_ticks);    //need to get timer ticks into time domain

period = 1 / frequency;    //get the period from the known frequency

phase_delay = (time_delay / period) * 360;    //calculate phase delay

It's important to read the documentation on the timer you will be using so that you know how to convert from timer ticks into time.

Bruno, Digital Pot DS1804 is very easy to control and has 100 ohm taps. Digital pot CAT5114VI-10-GT3 is bit harder to control as it is controlled via 3 wire serial interface, it has 32 ohm taps. Using DS1804 will get you the gains you need. Using zener diodes to limit voltages in you case is fine. Good luck.