Looking for the Square Law region (II)

After the experience in Looking for the Square Law region (I) it was clear the only way to find the Square Law region was to find a way to measure microvolts. The first idea was to use an operational amplifier in a DC non-inverting amplifier with a gain of 1000 (actually 1001). This will allow me to measure microvolts as millivolts. My first try was a OP07, but input bias currents were too high, so I ended using a JFET operational amplifier, a TL081.

The circuit worked very well, but has a terrific temperature response. Without input signal, output voltage varies some dozens of millivolts up and down because the thermal variations.

Working in a closed room, without any kind of wind and taking the average of several measurements, with the help of a voltmeter with relative measurement function some significant data could be obtained.

As RF source I used the FT-817 transceiver, working at 1.85 MHz, to minimize frequency response errors, and a bunch of fixed attenuators that allowed me to test input power between +15 and -53 dBm.

Raw data looks promising:

The relationship looks quite linear, and looking in the values some very interested things can be observed:

-50 dBm	0.9 uV
-40 dBm	8.9 uV
-30 dBm	89.9 uV
-20 dBm	899 uV

This is the Square Law region in all its glory: Ten times more power produces exactly ten times more voltage. With the actual diode (1N5711) and actual load (1Mohm) this relation is almost 90uV / uW. But with higher power levels the relation is lost:

-10 dBm	10900 uV (should be 8990 uV)
0 dBm	131000 uV (should be 89900 uV)
+10 dBm	680000 uV (should be 899000 uV)

So to see exactly what the diode does with all these power levels, I decided to plot the deviation from the theoretical Square Law, taking -30dBm as the reference. This is what I get:

Now it is pretty clear: The Square Law region goes from... somewhere under -53 dBm up to -20 dBm in perfect concordance to theory. Above -20 dBm (10 uW) the diode response becomes irregular, at least from the Square Law point of view.

Conclusion

It is wonderful to have a sensing device where output voltage goes 10 times higher when input power is 10 times higher, or half output voltage when input power goes down by 3 dB. But when that voltage is in the range of microvolts, measurements are quite difficult.

To amplify DC signals is not an easy task, at least not with common devices. Temperature drift is the main problem. Anyway, although the Square Law region in a diode seems to be the perfect solution for accurate power measurements, there are still other problems: Does the Square Law proportion varies with temperature? Does the Square Law proportion varies with frequency?

I'm sure the answer is yes, so the Square Law property of a diode does not seems to be a practical way to measure accurate power levels for the average ham radio operator.