Introduction to the NHMFL Pulsed Field Facility at LANL

Information on the physical set-up of pulsed field measurements

Read about lock-in amplifiers and their role in your measurements

Information about noise and ways to eliminate it from your measurements

How to collect and evaluate your measurement data

Information on optical spectroscopy

Information about time-resolved optics

Information on de Haas van Alphen Effect measurements

Information on Shubinkov de Haas Effect measurements

Information on Absolute Resistivity measurements

Information on Heat Capacity measurements

Information on RF Penetration Depth measurements

Lock-In Amplifiers

One of the biggest obstacles to overcome in the quest for accurate measurements is excess noise and interference that obstructs the signal from your sample. In other areas of this site, there are explanations of the many steps that can be taken during the experiment to reduce noise. Note, however, that the connections between the magnet and data acquisition devices are arranged to help reduce as much noise as possible. A central component of this arrangement is the Lock-In Amplifier.

Lock-In Amplifiers detect the signal and any noise associated with it (including thermal, shot and 1/f noise). Because of this, it is necessary to take noise into consideration when choosing a frequency for the measurement. There is substantial 1/f noise at zero frequency, making DC undesirable. Measuring at a higher frequency usually results in a less noisy environment. However, if you go too high in frequency, cable capacitance and inductance may obscure the signal. Therefore, it is best to test your system at chosen frequencies to determine the appropriate one for your particular sample and measurement.

Taking an average of the signal is the first way to eliminate noise and isolate the signal. Averaging over a time t enables you to measure noise over a bandwidth ~1/t, no matter what the excitation frequency is. The noise you will see is just

Where is the noise density at that frequency.

Once an excitation frequency is chosen, a mixer is used to isolate the signal. A mixer is an electronic gadget that multiplies, instantaneously, two voltages. The two common modes of operation of the mixer and related signals and excitation frequency are homodyne detection and heterodyne detection.

Heterodyne detection is when . This is better.
Homodyne detection is what lock-ins use and is when . If then

then


The mixer output has components at 2f. Also, at DC the amplitude of the DC component is dependent on the phase of the signal relative to the reference, and the size of the signal.

It is important to know that the averaging time determines the bandwidth. This is crucial if the signal is changing. For example, if the signal varies at 100 Hz, then the averaging time has to be less than 10ms.

Conversely, if there is an interference source at 60 Hz, and you want to measure at 200 Hz, while the signal varies at 10 Hz, then:

If you choose a filter time constant of 50 ms for averaging:

Then the filter bandwidth is