# what is a square law device?

Discussion in 'Wireless & RF Design' started by scythe, Apr 14, 2010.

1. ### scythe Thread Starter Active Member

Mar 23, 2009
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Hey all, I've been studying up on mixers and stuff, but what exactly is a square law device and what is it useful for?

Apr 20, 2004
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3. ### Ghar Active Member

Mar 8, 2010
655
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A square law device is something where either current or voltage depends on the square of the other.

For example, a saturated MOSFET has I proportional to V^2.
A diode's characteristics also has a square but it's not as clean. It's exponential, and through a Taylor series you get linear, square, cubic terms....

Anyway, it's useful because you can use it as a modulator or mixer.

Adding voltages is easy (just use resistors or an op amp) but multiplying is hard. With a square law device like a MOSFET you can do this:

$I \propto V^2$
$I \propto (sin(w_ct) + m(t))^2$
$I \propto sin(w_ct)^2 + m(t)^2 + m(t)sin(w_ct)$

Now if you follow that with a bandpass filter centered on $w_c$ you just get $m(t)sin(w_ct)$
Amplitude modulation.

mik3 likes this.
4. ### KL7AJ AAC Fanatic!

Nov 4, 2008
2,053
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A plain old diode also has a square law characteristic right near the forward "turn on" point, which becomes more linear with more voltage. Any such device will act as a mixer to varying degrees of predictability.

Eric

5. ### KL7AJ AAC Fanatic!

Nov 4, 2008
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To be perfectly accurate, most diodes actually have a current curve which has a CONTINUOUSLY VARYING exponent, but it's square law over a useful region. Special diodes with an expanded true square law region are specially made.

Eric

6. ### Ghar Active Member

Mar 8, 2010
655
73
I did mention diodes but I didn't know they made ones specially for this purpose.
Good to know, thanks.

7. ### mik3 Senior Member

Feb 4, 2008
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Nice post, never thought of that.

8. ### surya137 New Member

Sep 16, 2012
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hey tht is gud explanation.thank u..

9. ### KL7AJ AAC Fanatic!

Nov 4, 2008
2,053
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Howdy:

A simple diode is a square law device over a small region of its operating point. In this region, the current through the diode is proportional to the SQUARE of the applied voltage.
Square law devices are crucial components of logarithmic amplifiers and analog computers.