## Sunday, October 7, 2012

### Looking for the Square Law region (I)

One of the basic tasks in RF work is to measure power. There are many ways to measure power but the simplest ones use a diode as peak rectifier. Peak voltage (over a known impedance) is a measure of power, because P = (Veff)/ R and Veff = Vpeak x √2. Combining both expressions you get P = (Vpeak)2 / 2R, where R is usually 50 ohms.

The problem here is the relationship between the diode's output (Vpeak) and P is not linear, so if you want to use a microampmeter to display results, you need to draw a new scale on it. Of course, forget any digital meter unless it is microcontrolled, I mean unless it is specifically designed to calculate power from peak voltage, generally using a microcontroller.

But diode theory says there is an area in the diode's transfer curve where output voltage is proportional not to input voltage peak, but to input power, hence the Square Law name. This means the output from the diode can be feed to a linear display (analogic or digital) and measure directly power. This seems very attractive, so I decided to test it.

But theory also says this area of the transfer curve occurs at around -20 dBm and down, this is with levels of  10 microwatts or lower, so special care must be taken to realize the measures. To minimize errors, I used a RF signal at 1.85 MHz, with a series of fixed and variable attenuators, an oscilloscope to measure level just at the load resistor and a milivoltmeter to measure rectified voltage.

Four diodes where tested: 1N4148 (silicon), 1N5711 (schottky), 1N60 (germanium) and 0A79 (really old germanium diode):

Results are quite interesting. It is easy to see two areas: Under 1 mW and over 1 mW. Slopes change at around 0.9 mW, but there seems to be a good relationship between input power and rectified output between 1 and 5 mW. Let's see the 0 - 1 mW area in detail:

Except for the 1N4148, there is clearly no direct relationship between input power and rectified output. What does this means? This means the Square Law region is at even lower input values:

Well, displaying input power in dBm it is clear where the Square Law ends. Between -22 and -20 dBm, but measure levels there is difficult with my actual setup.

## Conclusion

The Square Law region is not useful unless you have a DC microvoltmeter (yes, micro, not milli). To amplify such small DC voltages is not a easy task, even with operational amplifiers. Anyway, I'll try.

From all the diodes tested, the universal 1N4148 seems to be the one with best linearity in each segment. This is something to explore in detail in the future.