Measurement noise and signal processing

5.5 Other analogue signal processing operations

To complete the discussion on analogue signal processing techniques, mention must also be made of certain other special-purpose devices and circuits used to manipulate signals. These are listed below.

5.5.1 Signal amplification

Signal amplification is carried out when the typical signal output level of a measure[1]ment transducer is considered to be too low. Amplification by analogue means is carried out by an operational amplifier. This is normally required to have a high input impedance so that its loading effect on the transducer output signal is minimized. In some circumstances, such as when amplifying the output signal from accelerometers and some optical detectors, the amplifier must also have a high-frequency response, to avoid distortion of the output reading.

The operational amplifier is an electronic device that has two input terminals and one output terminal, the two inputs being known as the inverting input and non-inverting input respectively. When connected as shown in Figure 5.9. The raw (unprocessed) signal V_i is connected to the inverting input through a resistor R₁ and the non-inverting input is connected to ground. A feedback path is provided from the output terminal through a resistor R₂ to the inverting input terminal. Assuming ideal operational ampli[1]fier characteristics, the processed signal V₀ at the output terminal is then related to the voltage V_i at the input terminal by the expression:

                                     V₀ = R₂V_i/R1                                                (5.3)

The amount of signal amplification is therefore defined by the relative values of R₁ and R₂. This ratio between R₁ and R₂ in the amplifier configuration is often known as the amplifier gain or closed-loop gain. If, for instance, R₁ = 1 MΩ and R₂ = 10 MΩ, an amplification factor of 10 is obtained (i.e. gain = 10). It is important to note that, in this standard way of connecting the operational amplifier (often known as the inverting configuration), the sign of the processed signal is inverted. This can be corrected for if necessary by feeding the signal through a further amplifier set up for unity gain (R₁ = R₂). This inverts the signal again and returns it to its original sign.

Instrumentation amplifier

For some applications requiring the amplification of very low level signals, a special type of amplifier known as an instrumentation amplifier is used. This consists of a circuit containing three standard operational amplifiers, as shown in Figure 5.10. The advantage of the instrumentation amplifier compared with a standard operational amplifier is that its differential input impedance is much higher. In consequence, its

 common mode rejection capabilityŁ is much better. This means that, if a twisted wire pair is used to connect a transducer to the differential inputs of the amplifier, any induced noise will contaminate each wire equally and will be rejected by the common mode rejection capacity of the amplifier. The mechanism of common mode noise rejection is explained more fully in section 5.5.3.