[sdiy] [synth-diy] lock-in amplifiers

cheater00 . cheater00 at gmail.com
Sun Jan 26 16:50:10 CET 2014

Hi guys,
I've recently stumbled upon the concept of a lock-in amplifier.
Basically, it is a way to recover an AM signal from a carrier, even if
the carrier is buried deep in noise.

This app note from Stanford Research extols the virtues:


For one thing it's got much narrower bandwidth than a even a very high Q filter.

You can also read about them here:

The basic idea is like this: you have a carrier wave which is being
amplitude modulated by the signal you want to recover in the end. This
carrier wave comes with noise and other signals all of which make up

You multiply (mix) Vin by a reference sine wave which is at exactly
the same frequency as the carrier wave. Call that frequency f0.

For every frequency f inside Vin, this will obviously create two new
frequencies in the mixer output: f+f0, f-f0. We only care about the
f-f0 part. If f0 is more than f (that is, noise above the carrier
frequency), then f-f0 will be positive. If f0 is less than f, then
f-f0 will be negative, but that just means it'll be positive but
flipped in phase. If f0 is exactly f, then f-f0 will be 0, that is you
get a DC signal. Well... almost. It's not exactly constant. As the
amplitude of the carrier frequency slowly changes (over many, many
cycles of the carrier frequency f), the level of this "DC" signal also
changes. So what you do is you use a low-pass filter which will pass
any of this "DC" (that is, the modulator waveform), and which will
reject the parts where f0 != 0. Apparently it somehow adds up that
those parts will mostly produce (f-f0) much higher than the modulator
frequency, but I haven't worked out the numbers for that yet. Anyways,
what you get is something like a filter that's got a Q of about 10000.
A normal band pass of Q=100 is considered absurdly steep.

This helps in two ways. For one thing, you can uncover this carrier
frequency from within a huge amount of noise.

The other thing is that you can amplify signals which, if amplified
normally, would bring a lot of noise with themselves. Take your
extremely weak signal, do amplitude modulation with a sine wave. That
can go through a very noisy line. Then use a lock-in amp to recover
the weak signal again. So maybe it's a good idea for microphones.

Also, it's much easier to build a precise oscillator than it is to
build a precise high-Q filter. You can do it in digital without being
penalized by terrible things like aliasing or decimation.


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