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?

 

You might be referring to the inverse square law - http://en.wikipedia.org/wiki/Inverse-square_law

 

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.

 

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.

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

 

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

 

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

 

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.

Nice post, never thought of that.

 

hey tht is gud explanation.thank u..

 

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?

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.