Measurement noise and signal processing

 5.5.6 Signal integration

Connected in the configuration shown in Figure 5.15, an operational amplifier is able to integrate the input signal V_i such that the output signal V₀ is given by:

                                          V0 = - 1/RC

This circuit is used whenever there is a requirement to integrate the output signal from a transducer.
5.5.7 Voltage follower (pre-amplifier)

The voltage follower, also known as a pre-amplifier, is a unity gain amplifier circuit with a short circuit in the feedback path, as shown in Figure 5.16, such that:

                                                                       V0 = Vi

It has a very high input impedance and its main application is to reduce the load on the measured system. It also has a very low output impedance that is very useful in some impedance-matching applications.

5.5.8 Voltage comparator

The output of a voltage comparator switches between positive and negative values according to whether the difference between the two input signals to it is positive or negative. An operational amplifier connected as shown in Figure 5.17 gives an output that switches between positive and negative saturation levels according to whether V1  V2 is greater than or less than zero. Alternatively, the voltage of a single input

signal can be compared against positive and negative reference levels with the circuit shown in Figure 5.18.

In practice, operational amplifiers have drawbacks as voltage comparators for several reasons. These include non-compatibility between output voltage levels and industry[1]standard logic circuits, propagation delays and slow recovery. In consequence, various other special-purpose integrated circuits have been developed for voltage comparison.

In practice, operational amplifiers have drawbacks as voltage comparators for several reasons. These include non-compatibility between output voltage levels and industry[1]standard logic circuits, propagation delays and slow recovery. In consequence, various other special-purpose integrated circuits have been developed for voltage comparison.

5.5.9 Phase-sensitive detector

One function of a phase-sensitive detector is to measure the phase difference between two signals that have the same frequency. For two input signals of amplitude V₁ and V₂ and frequency f, the output is given by V₁V₂ cos 0, where ­0 is the phase difference between the signals. In many cases, the phase difference is adjusted to zero (cos ­0 = 1) so that the output is a maximum.

 A phase-sensitive detector can also be used as a cross-correlator to enhance the quality of measurement signals that have a poor signal-to-noise ratio. This ability is also exploited in the use of phase-sensitive detectors to demodulate amplitude-modulated (AM) signals. For these roles, the detector requires firstly a clean reference voltage at the same frequency as the measurement signal and secondly, phase-control circuits to make the phases of the reference and measurement signals coincide. Commercial instruments known as lock-in amplifiers (see next section) are available that combine a phase-sensitive detector with the other components required to provide the demodu[1]lation function.

Phase-sensitive detectors are known by several alternative names, two examples of which are synchronous demodulator and synchronous detector. They can also exist physically in a number of alternative forms that include both transformer-based and fully electronic circuits (see Olsen, 1974, pp. 431–435).