question on RF field strength measurement of two signal souces

if I got two RF signal sources, one, which transmit at 2GHz 20mW/m2 at 1 meter distance and the other which transmit at 3GHz 10mW/m2 at a 1 meter distance. Should the RF field strength power meter show 30 mW/m2 at 1 meter distance from them? or just the 20mW/m2 (from the strongest signal source)?

for 2G, it's 20mW/m2; for 3G, it's 10mW/m2. That's electromagnetic's principles.

If they are uncorrelated signal sources (i.e. not locked to the same crystal reference frequency), then the powers simply add linearly. So, at 1 meter, you should show 30 mw/m2

They also add linearly if locked to the same reference. Signals of different frequency are always orthogonal and add by their power. Common harmonics, e.g. at 6 GHz, would show a correlation effect, however.

Yes, you are probably right. I was thinking that field strength indicator is usually ham speak for diode detector, so the envelope of the waveform would matter. But thinking more, locked or unlocked, you have basically the same envelope.

Actual experiment shows the signal level from the antenna attached to the RF power meter is about the same as the level from strongest signals source or just 2-3 db higher when two RF signal source is on at the same time. (it does not sum the two together). Looks like the two waves are combined together and sometimes they sum-up together, sometimes cancel each other (causes by phase different?)

Two equal power signals summing together linearly will indicate as 3 dB higher.

If you have two sources, and are radiating them and tying to measure 1 meter away, yes there can be higher and lower indications as you move the receiving power meter around. It is most likely because of the geometry of the two antennas, or reflections from nearby objects causing it.

Yes. You have to go to an antiechoic chamber or at least outdoor, with sufficient height above ground, for an undisturbed experiment.

Referring to the previously discussed detector problem. I was actually thinking of a true power meter, I guess, biff44's intuitive thought is right for an envelope detector. A simple averaging diode rectifier must be expect to show a higher reading, when superimposing two sources of different frequency and equal power somewhere above +3dB, but surely below +6dB. It's basically the same thing that happens when measuring a distorted mains voltage with a non-rms meter.

In so far, it's possible that you see this kind of effect in your antenna measurements. Only a true (thermal) power meter measures correct in this case.