# Why are "square law" devices important?

In the literature, I often see the notion of square law devices. Why are these devices important, to the extent that they have their own characterization as square law device?

In what context does this square law property become relevant, except the fact that it characterizes the relationship between an input and an output parameter for that device.

• Please give a link to an example of the literature of which you speak, or provide much more detail about your question. Feb 21, 2019 at 18:40
• It's just a common trait in a bunch of things so rather than explain them one-by-one piecemeal you just group them together so you can talk about them all at once. It's like asking "why the notion of circular motion so important to the extent that it has its own set of equations?" You can apply the same concepts to a bunch of different things, so you just group them together with a label. In that sense, there is nothing beyond it being relevant except for the fact that it characterizes a common input-output relationship. Feb 21, 2019 at 18:47
• The ability to convert a squiggly line on a graph to numbers/variables is invaluable in analyzing, characterizing, understanding, and simplifying the transfer function (aka output/input). For instance, when building more complicated circuits, would you rather combine a bunch of input/output graphs together to understand the final output or combine mathematical descriptions of it like (x-2)^2 and (y+2)^2 ? Feb 21, 2019 at 21:52

It's a particular classification of nonlinear behavior that has important applications.

In the same way as you can consider, say, a BJT as linear over a limited range, you can consider something like a diode as square law over a limited range. That simplification allows you to analyze functions such as RF detectors analytically.

See, for example, this Agilent paper "Square Law and Linear Detection".

• Similarly, the OP could have also replaced "square law devices" with "linear devices" into his question and the basic answer would essentially be the same. Feb 21, 2019 at 18:50
• That app note is still "in print" from Broadcom. Though they haven't bothered to re-badge it from Avago. (And HP versions of it are also out there on the net) Feb 21, 2019 at 19:25

Electronic things that follow square laws:

• power loss with distance over the air aka "Friis Loss" for RF due to power is spread by broadcast over beam width arc path at a distance is proportional to $$\r^2\$$

• the same is true with optical communication, sound and other signal sources like WiFi when there are no reflections of obstacles.
• power loss in conductors from Ohm's Law, $$\V=IR\$$ we get $$\Pd = VI = V^2/R = I^2R\$$

• diode impedance = voltage/current for small ac signals with Vdc bias before saturation at rated current, then it becomes linear
• reverse diode capacitance vs voltage. C is maxed at 0V and reduces by k*V² at rated reverse Vr and C(0V) is a function of rated power and 1/Rs the linear saturation resistance in forward bias. Varicaps are controlled diodes for specific square law VCO tuning with C ratios given at 2 voltages.
• because of diode square law when used in negative feedback can be used as "analog signal "multipliers" or converting the voltage to power.

Fundamentally, based on the geometry of a 2D circle $$\C=\pi R^2\$$ then we have cubic laws based on 3D geometry of a sphere and higher orders that describe laws of nature.

• TY @VolkerSiegel for edits Feb 22, 2019 at 2:42

Square Law devices make excellent RF mixers. A perfect square law device produces only the Sum and the Difference outputs.