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Tuesday, December 7, 2021

Measurement noise and signal processing

 

5.5.10 Lock-in amplifier

A lock-in amplifier is used to demodulate small signals and extract them from noise when they are transmitted on an a.c. carrier. As shown in Figure 5.19, it consists of a phase-sensitive detector, an element to generate a square-wave reference signal at the same frequency as the a.c. carrier, a tuned narrow-band amplifier, a phase-control circuit, and a low-pass filter at the output. The role of the phase-sensitive detector is to selectively rectify only signals that are in phase with the a.c. carrier transmitting the measurement signal. This is achieved by using the phase-control circuit to lock the reference square-wave signal in phase with the carrier. Because any noise will be of random phase and generally out of phase with the measurement signal, it is rejected by the phase-sensitive detector because this only transmits in-phase signals. The phase[1]detector produces positive and negative outputs in response to noise that randomly lag and lead the measurement signal on the carrier, and therefore the noise component in the output goes to zero if the output is averaged over a period of time by a low-pass filter. Finally, the low-pass filter acts as a demodulator that regenerates the original measurement signal by extracting it from the carrier.

5.5.11 Signal addition

The most common mechanism for summing two or more input signals is the use of an operational amplifier connected in signal-inversion mode, as shown in Figure 5.20. For input signal voltages V1, V2 and V3, the output voltage V0 is given by:

                                                   V0 = - (V1 + V2 + V3





5.5.12 Signal multiplication
Great care must be taken when choosing a signal multiplier because, whilst many circuits exist for multiplying two analogue signals together, most of them are two[1]quadrant types that only work for signals of a single polarity, i.e. both positive or both negative. Such schemes are unsuitable for general analogue signal processing, where the signals to be multiplied may be of changing polarity.

For analogue signal processing, a four-quadrant multiplier is required. Two forms of such a multiplier are easily available, the Hall-effect multiplier and the translinear multiplier.


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