Lock-in Basics

Commercial lock-in amplifiers used in atomic physics laboratories will run up to \$4,000. Here we will build one for about \$60. While commercial lock-ins will detect nanovolt signals, we will be limited to millivolt signals here.

Lock-in amplifiers are used frequently in scientific experiments that require measuring small voltages in noisy environments. If the frequency of the desired signal is known, the instrument can "lock in" onto the signal using a matching reference frequency. Although unnecessary in constructing the circuit, it is useful to recognise the mathematical underpinnings that drive such a device. The time-averaged value of the product of two frequency-divergent sinusoidal functions is zero. However, if both functions have the same frequency, then the value is 1/2 of the product of the amplitudes.

Phase-Offset

Phase is central to a functional lock-in amplifier (the alternative name of a lock-in amplifier is a phase-sensitive detector). If the phase of the input signal does not match the phase of the reference signal, then the output is also zero. For the purposes of this instructable, I neglect consideration of a phase offset and focus only on locking into a signal of identical phase. For phase correction, I point your attention to adding a phase-shift oscillator to the reference signal.

Three Parts: Amplifier, Demodulator, Amplifier

We can break down the lock-in amplifier in this instructable into three parts: the input amplifier, a synchronous demodulator, and a final low-pass filter/amplifier that finally outputs our DC signal.

## Step 1: Basic Components

Three Parts: Amplifier, Demodulator, Amplifier

We can break down the lock-in amplifier in this instructable into three parts: the input amplifier, a synchronous demodulator, and a final low-pass filter/amplifier that finally outputs our DC signal.

The input amplifier (AD620) amplifies the input signal using a variable gain resistor. Keep in mind that the amplifier doesn't just amplify the desired signal, but the input signal as a whole i.e. noise is also amplified. This will be important to keep in mind when choosing an appropriate gain setting.

The synchronous demodulator (AD630) is the essential ingredient in the lock-in amplifier and is what does the actual signal mixing. This is where the reference signal is inputted.

The low-pass amplifier (OP27G) filters out any noise in the demodulated signal and outputs our desired DC signal that determines the strength of the lock-in.

For building the circuit, it is useful to build and test each component separately, as this will ease isolating any problems you may run into. I will break down the instructions

## Step 2: Supplies Needed

• OP27 Instrumentation Amplifier
• A function generator in the range of 10-100 KHz.
• A digital oscilloscope
• connecting wires
• soldering iron and solder
• 1 protobard
• 6 10µF electrolytic capacitors
• 1 0.47µF disc capacitor
• 1 100µF electrolytic capacitor
• 100µF-1000pF capacitor (for low-pass filter time constant)
• 7 10Ω resistors
• 1 1MΩ resistor
• 2 10KΩ resistor
• 1 1KΩ resistor
• 1 100KΩ resistor
• 10K potentiometer or resistor box for amplifier gain
• +/-15V power supply

## Step 3: The Input Amplifier

Our first step is constructing the input amplifier. This component will take in our input signal and amplify its voltage, depending on the variable gain resistor. The amplifier works simply through a non-inverting op-amp. For this component, we power it using our +/-15V power supply with low-pass filters attached to each source to filter out any circulating/unwanted noise. The disc capacitor functions to prevent any fluctuations in the signal when performing demodulations later down the road. Pin 6 will output to the demodulator for signal mixing.

This would be a good time to check to see if the amplifier does indeed work as desired. Play around with various gain resistors and the oscilloscope to see that the amplifier functions BEFORE moving onto the next step. This will save you a lot of headaches.

## Step 4: Synchronous Demodulator

Now the bread-and-butter of the instrument. The synchronous demodulator (AD630) will take the input amplifier output and multiply it with the reference input. If you wanted to account for phase, it would be ideal to place the phase-shift oscillator here. Again, test the output of the demodulator so that it does what you want it to do. Your demodulator output should look similar to the oscilloscope picture shown above.

## Step 5: The Low-Pass Instrumentation Amplifier (DC Out)

The final component of the lock-in amplifier is filtering out any unwanted signals and outputting a DC signal indicating lock-in strength. This is the OP27 component. By choosing the ideal capacitor, you can set the 3dB point to your choosing. I added two headers to allow quick swapping of capacitor.

## Step 6: Putting It All Together

Your final product should be a self-contained lock-in amplifier, capable of detecting millivolt signals embedded in noisy environments. Try playing around with various gain settings/time constants to get the appropriate response to signal changes. WARNING: If you see any odd behaviour with the voltage output readings from the demodulator/amplifier and you are noticing some clipping, this is probably because you have set your gain too high! Reduce the gain in your input amplifier or drop the amplitude of your reference signal. Remember, your gain resistor will amplify up to around 1000 times your input signal! If you have a 1V input, it is unlikely/impossible that your 15V-powered amplifier will output a 1000V signal. Thus, clipping will occur.

I leave the applications up to you. While you are probably not going to be using it to carry out atomic physics experiments, you can try putting an LED at some distance from a photodiode as your input signal. In a well-lit room, if you put the LED at, say, a 30KHz frequency, you should pick up the signal even in the noisy environment of 120Hz fluorescent noise!

This instructable was written up as part of completion of Pomona College Physics 128 final project assignment. Any questions, e-mail me at khatamidk@gmail.com

<p>it is quite informative</p>