Lock-in amplifier

A lock-in amplifier ( also phase-sensitive rectifier or carrier amplifier ( TFV ) ) is an amplifier for measuring a weak alternating electric signal which is modulated at a known frequency and phase reference signal. The device represents an extremely narrow band-pass filter, thereby improving the signal -to-noise ratio ( SNR Signal to Noise Ratio). The advantage is that DC voltages, AC voltages other frequency and noise can be efficiently filtered.

Design and operation

A lock-in amplifier requires the following functional elements:

• Signal input for the modulated measurement signal.
• Signal input for the sinusoidal (sometimes rectangular ) reference signal.
• Input amplifier for input signals, possibly with the input filter.
• Phase shifter for matching between reference and measurement signal.
• Mixers ( multipliers ) for multiplying the input signal with the reference signal.
• Low pass in order to perform a time averaging over several signal periods.
• Optionally: a built-in oscillator to modulate the measurement signal.

The two input signals are multiplied together in a mixer and then incorporated into a low-pass. Thus, the lock-in amplifier calculates the cross correlation between the measuring and the reference signal for a fixed phase shift. The cross-correlation of signals of different frequency is zero. Therefore, the frequency of the reference signal from the measurement signal of the different lock-in is not supplied by the output signal. Only for the same frequencies, the cross-correlation provides a finite value and the lock-in so that a finite output signal. By choosing the appropriate frequency of the reference, therefore, the corresponding component in the measurement signal can be filtered out. The reference signal is lured to the measurement signal.

More simply mixed into the lock-in amplifier, the measurement signal with the reference signal from this composite signal, and evaluates the difference frequency. It is ideally zero. For filtering at this DC signal ranges from a low-pass, which needs to be interpreted only as wide to desired changes in the signal pass. All other frequencies, especially high frequency noise, hum or other interference signals are filtered by the low pass.

The output signal, the lock-in amplifier, ideally a DC voltage. It is proportional to:

• Input voltage;
• Cosine of the phase shift between the input signal and reference signal.

The output is as follows:

If the input signal is also modulated sinusoidally, the result for the output signal for a sufficiently large integration time:

Are the reference signal and the measurement signal in phase ( ), then the output signal generated from the lock-in amplifier at a maximum. The phase shift is 90 °, then the output signal is zero.

Looking at the lock-in amplifier in the frequency domain, so it corresponds to a band-pass to the reference frequency, the bandwidth is inversely proportional to the integration time. Noise in the measurement channel with frequencies that lie within this range, leading to a beat at the output.

This formulation is valid for a sinusoidal reference signal. In the practical application (see optical modulators ) but you often have to do it with square-wave reference signals, where the output signal then looks different. Square-wave reference signals cause the odd harmonics of the signal make a contribution to the output signal, as well as interfering signals in the corresponding bands.

The phase between the measurement and reference signal is therefore extremely important and stands as a measurement result on a par with the amplitude of the measuring signal. Some measurements may provide valuable information. For example, when using a / is made ​​of - amplitude-modulated light, which causes on a sample photo line, the measured current of the excitation is lagging somewhat, since various effects within the sample time delay effect, which is reflected in a phase shift. So you can draw conclusions about the nature and extent of these effects in the sample from the degree of phase shift.

There are single phase lock-in and dual-phase lock-in amplifier. The latter determine the output signal for two different phase shifts, which differ by 90 °. By Pythagorean addition of the two resulting outputs is the final result of the measurement independent of the phase, which both simpler, and more precise measurements allows (See links).

Digital lock-in amplifier

The best signal sensitivity can be achieved with the help of digital lock-in amplifier based on digital signal processors ( DSP). In this case, first, the input signal and the reference signal is digitized (ADC). The further steps such as preparation of the reference signal, phase shift, multiplication and low pass filtering, then be purely digital. The result is optionally converted back to an analog signal (DAC, digital -to- analog converter, digital-to- analog converter ). Lock -ins based on DSP also allow a more accurate determination of the phase angle between the input signal and the reference signal. Due to the purely digital data processing, it is possible to use more than just a demodulator for each channel. This expands the possibilities of evaluation.