The Lock-in Technique

The Lock-in technique is used to detect and measure very small ac signals. A Lock-in amplifier can make accurate measurements of small signals even when the signals are obscured by noise sources which may be a thousand times larger. Essentially, a lock-in is a filter with an arbitrarily narrow bandwidth which is tuned to the frequency of the signal. Such a filter will reject most unwanted noise to allow the signal to be measured. A typical lock-in application may require a center frequency of 10 KHz and a bandwidth of 0.01 Hz. This 'filter' has a Q of 106 - well beyond the capabilities of passive electronic filters.

In addition to filtering, a lock-in also provides gain. For example, a 10 nanovolt signal can be amplified to produce a 10 V output--a gain of one billion.

All lock-in measurements share a few basic principles. The technique requires that the experiment be excited at a fixed frequency in a relatively quiet part of the noise spectrum. The lock-in then detects the response from the experiment in a very narrow bandwidth at the excitation frequency.

Applications include low level light detection, Hall probe and strain gauge measurement, micro-ohm meters, C-V testing in semiconductor research, electron spin and nuclear magnetic resonance studies, as well as a host of other situations which require the detection of small ac signals.

A Measurement Example

Suppose we wish to measure the resistance of a material, and we have the restriction that we must not dissipate very much power in the sample. If the resistance is about 0.1Ω and the current is restricted to 1 ∝ A, then we would expect a 100 nV signal from the resistor. There are many noise signals which would obscure this small signal -- 60Hz noise could easily be 1000 times larger, and dc potentials from dissimilar metal junctions could be larger still.

In the block diagram shown below we use a 1Vrms sine wave generator at a frequency wr as

our reference source. This source is current limited by the 1 MΩ resistor to provide a 1 ∝ A ac excitation to our 0.1Ω sample.

Two signals are provided to the lock-in. The 1VAC reference is used to tell the lock-in the exact frequency of the signal of interest. The lock-in's Phase-Lock Loop (PLL) circuits will track this input signal frequency without any adjustment by the user. The PLL output may be phase shifted to provide an output of cos(wrt+Ø).

The signal from the sample under test is amplified by a high gain ac coupled differential amplifier. The output of this amplifier is multiplied by the PLL output in the Phase-Sensitive Detector (PSD). This multiplication shifts each frequency component of the input signal, ws, by the

reference frequency, wr, so that the output of the PSD is given by:

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