Lock-in amplifiers find the signal in the noise

05 May 2004

If you want to extract a signal from a huge amount of noise, a lock-in amplifier is the ideal tool. But when it comes to buying one, doing your homework first can avoid a costly mistake, advises Richard Burdett.

From Opto & Laser Europe May 2004.

In many optical experiments it is necessary to isolate and measure a weak electrical signal that is buried in noise. A good example is the characterization of a photodiode's response to light at a particular wavelength where any noise due to stray light needs to be eliminated.

In such cases, a lock-in amplifier is a highly effective measurement system. These popular laboratory instruments can reject huge amounts of noise surrounding a signal by using a frequency-selective measurement technique. Put simply, lock-in amplifiers work by ensuring that the signal to be measured is modulated at a known frequency, then using a detection system that is precisely tuned to this reference frequency (see Further information). In optical experiments, the modulation often involves placing an optical chopper in the path of a light beam or controlling the drive current to a laser diode.

In common with many other instruments, the performance of lock-in amplifiers has significantly improved over the past decade. Today there are models available to suit virtually every application and budget. However, their specialized nature means that their operation is often poorly understood, leading to ill informed purchasing decisions.

The secret of success The heart of the lock-in amplifier is the demodulator which multiplies the signal to be measured by a signal that is generated from the supplied reference frequency. Instruments can be categorized by their type of demodulator. Some lock-in amplifiers use analogue technology, while others use digital signal processing (DSP) techniques.

The cheapest lock-in amplifiers use an analogue switching demodulator. This has the advantage of linear operation over a high input dynamic range, but suffers because it responds not only to signals at the reference frequency but also to those at odd harmonics of it. Adding a bandpass filter in the signal channel can reduce such responses, but this is usually at the expense of the overall accuracy. The best analogue lock-ins therefore use a Walsh function switching demodulator, which has no response at the third and fifth harmonics of the reference, and a relatively wide bandpass filter around the signal channel. Such instruments offer dynamic reserves of up to 130 dB, which allow signals of 1 µV, for instance, to be measured in the presence of interfering signals of up to 3 V.

In a DSP lock-in amplifier, the input signal and accompanying noise are amplified and then digitized using a 14-18 bit sampling analogue-to-digital converter (ADC). The DSP multiplies the digital representation of the input signal by a digital representation of the reference frequency. A low-pass filter then removes the noise around the signal. The result of the measurement is displayed as a number on a display or its analogue voltage representation generated by a digital-to-analogue converter (DAC).

The digital difference The major advantage that these digital lock-ins offer is that DSP electronics are not subject to the drift with time and temperature that can occur in analogue units. DSP technology also allows some models to offer extended features, such as the ability to simultaneously measure two signals at different frequencies.

Beyond the analogue or digital choice there are a number of other factors to consider when making a purchase. The first is whether you want an instrument that is single or dual phase. Single-phase instruments use a single demodulator, so the phase of the reference signal needs to be adjusted for maximum output before each measurement. Dual-phase instruments use two demodulators and can directly measure signal magnitude without phase adjustments. Another benefit of dual-phase models is that they can measure phase shifts.

Dual-phase lock-in amplifiers should not be confused with dual-channel instruments, which can measure two signals simultaneously. However, if these two signals are at the same frequency then two instruments will generally be needed.

The frequency range of the reference signal is also important. This is the range of frequencies over which the instrument operates and typically runs from 1 mHz (0.001 Hz) to 2 MHz or even greater. Most optics applications can use instruments that cover the range from 0.5 Hz to 100 or 250 kHz.

The sensitivity of lock-in amplifiers is usually quoted as a value for a full-scale indication. If, for example, the scale is set to 100 µV and a 50 µV rms sinusoid signal at the reference frequency is applied, the instrument will display 50%. Modern units also give the option of displaying the calibrated value, which would be 50 µV in this example.

Another key specification is the time constant, which controls the cut-off frequency of the lock-in's low-pass filter. Longer time constants give better rejection of interfering signals and improve measurement accuracy, but result in longer measurement times.

Dynamic reserve describes the ratio of the measurable signal level to that of the noise and interference. This is typically quoted in decibels (dB), and a value of 100 dB implies that a signal of 10 µV can be measured in the presence of 1 V (i.e. 10⁵ times larger) of interfering signal.

For DSP-based devices, a final specification to consider is the internal sampling frequency at which the input signal is digitized and processed. Sampling frequency is limited by the performance of ADCs - the higher the frequency, the poorer the performance. But it also has to comply with Nyquist's sampling criteria, which state that the sampling must be at least twice the upper cut-off frequency of the input low-pass anti-aliasing filter. So an instrument capable of working to 100 kHz might have a sampling frequency of 250 kHz.

Some manufacturers take advantage of the fact that, unlike most other sampled-data systems, the lock-in "knows" the frequency of the signal that is being measured.

The conventional low-pass anti-aliasing filter is replaced by a bandpass stage with bandwidth of a few tens of kilohertz, continuously tuned to this same frequency. Since it is the signal bandwidth that defines the minimum sampling frequency under Nyquist (rather than the maximum frequency), this allows the instrument to operate to frequencies higher than the sampling frequency. For example, typical lock-ins that operate at reference frequencies up to 250 kHz use sampling frequencies of around 170 kHz.

Do the research In conclusion, modern lock-in amplifiers offer excellent signal-recovery performance and many extra features that make them an invaluable addition to any optics laboratory. Suppliers offer plenty of advice to help you choose the most appropriate model. This is usually in the form of applications notes and product information, most of which can be obtained from their websites. It is certainly worth studying these before making a purchasing decision, and in case there is any doubt, contact the suppliers first to discuss your options.

Further information

Lock-in amplifiers explained A lock-in amplifier multiplies the input signal (i.e. the signal to be measured) by an internal signal generated at the reference frequency.

Figure 1 illustrates an example in which the input signal (signal in) is a noise-free sinusoid that is multiplied by a phase-locked sinusoidal signal, which is internally generated by the instrument. The output from the demodulator is a signal at twice the reference frequency with a DC component (the mean positive output level). This DC level directly correlates with the amplitude of the input signal and is isolated by a low-pass filter and measured. Unfortunately the DC value depends on the phase angle between the input signal and the internal reference signal.

Figure 2 shows the same situation, except that the signal phase is now delayed by 90° with respect to the internal reference frequency. In this situation, although the output still contains a signal at twice the reference frequency, the DC level is now zero.

If the reference signal amplitude is kept at a fixed value, and the reference phase adjusted to ensure a relative phase shift of 0°, the input signal amplitude can then be determined by measuring the mean level.

In most real applications the signal will be accompanied by noise. This noise is also multiplied by the reference signal in the demodulator but has no fixed frequency or phase relationship to the reference, so it does not result in any change to the mean DC level. The combination of a demodulator and a low-pass filter therefore allows the measurement of a signal even when there is significant noise.