Table of Contents
A sensor measures a variable by converting information about that variable into a dependent signal of either electrical or pneumatic nature. To develop such transducers, we take advantage of fortuitous circumstances in nature where a dynamic variable influences some characteristic of a material. Consequently, there is little choice of the type or extent of such proportionality. For example, once we have researched nature and found that cadmium sulfide resistance varies inversely and nonlinearly with light intensity, we must then learn to employ this device for light measurement within the confines of that dependence. Analog signal conditioning provides the operations necessary to transform a sensor output into a form necessary to interface with other elements of the process-control loop. We will confine our attention to electrical transformations.
We often describe the effect of the signal conditioning by the term transfer function. By this term we mean the effect of the signal conditioning on the input signal. Thus, a simple voltage amplifier has a transfer function of some constant that, when multiplied by the input voltage, gives the output voltage.
It is possible to categorize signal conditioning into several general types.
The simplest method of signal conditioning is to change the level of a signal. The most common example is the necessity to either amplify or attenuate a voltage level. Generally, process-control applications result in slowly varying signals where dc or low-frequency response amplifiers can be employed. An important factor in the selection of an amplifier is the input impedance that the amplifier offers to the sensor (or any other element that serves as an input). In process control, the signals are always representative of a process variable, and any loading effects obscure the correspondence between the measured signal and the variable value. In some cases, such as accelerometers and optical detectors, the frequency response of the amplifier is very important.
As pointed out earlier, the process-control designer has little choice of the characteristics of a sensor output versus process variable. Often, the dependence that exists between input and output is nonlinear. Even those devices that are approximately linear may present problems when precise measurements of the variable are required.
Historically, specialized analog circuits were devised to linearize signals. For example, suppose a sensor output varied nonlinearly with a process variable, as shown in Figure 2.1a. A linearization circuit, indicated symbolically in Figure 2.1b, would ideally be one that conditioned the sensor output so that a voltage was produced which was linear with the process variable, as shown in Figure 2.1c. Such circuits are difficult to design and usually operate only within narrow limits.
The modern approach to this problem is to provide the nonlinear signal as input to a computer and perform the linearization using software. Virtually any nonlinearity can be handled in this manner and, with the speed of modern computers, in nearly real time.
FIGURE 2.1 The purpose of linearization is to provide an output that varies linearly with some variable even if the sensor output does not.
An important type of conversion is associated with the process-control standard of transmitting signals as 4-20 mA current levels in wire. This gives rise to the need for converting resistance and voltage levels to an appropriate current level at the transmitting end and for converting the current back to voltage at the receiving end. Of course, current transmission is used because such a signal is independent of load variations other than accidental shunt conditions that may draw off some current. Thus, voltage-to-current and current-to-voltage converters are often required.
The use of computers in process control requires conversion of analog data into a digital format by integrated circuit devices called analog-to-digital converters (ADCs). Analog signal conversion is usually required to adjust the analog measurement signal to match the input requirements of the ADC. For example, the ADC may need a voltage that varies between 0 and 5 volts, but the sensor provides a signal that varies from 30 to 80 mV. Signal conversion circuits can be developed to interface the output to the required ADC input.
Filtering and Impedance Matching
Two other common signal conditioning requirements are filtering and matching impedance.
Often, spurious signals of considerable strength are present in the industrial environment, such as the 60-Hz line frequency signals. Motor start transients also may cause pulses and other unwanted signals in the process-control loop. In many cases, it is necessary to use high-pass, low-pass, or notch filters to eliminate unwanted signals from the loop. Such filtering can be accomplished by passive filters using only resistors, capacitors, and inductors; or active filters, using gain and feedback.
Impedance matching is an important element of signal conditioning when transducer internal impedance or line impedance can cause errors in measurement of a dynamic variable. Both active and passive networks are employed to provide such matching.
Concept of Loading
One of the most important concerns in analog signal conditioning is the loading of one circuit by another. This introduces uncertainty in the amplitude of a voltage as it is passed through the measurement process. If this voltage represents some process variable, then we have uncertainty in the value of the variable.
Qualitatively, loading can be described as follows. Suppose the open circuit output of some element is a voltage, say Vx, when the element input is some variable of value x. Open circuit means that nothing is connected to the output. Loading occurs when we do connect something, a load, across the output, and the output voltage of the element drops to some value, Vy < Vx. Different loads will result in different drops.
Quantitatively, we can evaluate loading as follows. Thevenin's theorem tells us that the output terminals of any element can be defined as a voltage source in series with an output impedance. Let's assume this is a resistance (the output resistance) to make the description easier to follow. This is often called the Thevenin equivalent circuit model of the element.
FIGURE 2.2 The Thovenin equivalent circuit of a sensor allows easy visualization of how loading occurs
Figure 2.2 shows such an element modeled as a voltage Vx and a resistance Rx. Now suppose a load, RL, is connected across the output of the element as shown in Figure 2.2. This could be the input resistance of an amplifier, for example. A current will flow and voltage will be dropped across Rx. It is easy to calculate that the loaded output voltage will thus be given by
This equation shows how the effects of loading can be reduced. Clearly, the objective will be to make RL much larger than RX, that is, RL > RX. The following example shows how the effects of loading can compromise our measurements.
An amplifier outputs a voltage that is ten times the voltage on its input terminals. It has an input resistance of 10 kW. A sensor outputs a voltage proportional to temperature with a transfer function of 20 mV/°C. The sensor has an output resistance of 5 kW. If the temperature is 50°C, find the amplifier output.
The naive solution is represented by Figure 2.3a. The unloaded output of the sensor is simply VT = (20 mV/°C)50°C = 1.0 V. Since the amplifier has a gain of 10, the output of the amplifier appears to be Vout = 10Vin = (10)1.0 V = 10 V. But this is wrong, because of loading!
Figure 2.3b shows the correct analysis. Here we see that there will be a voltage dropped across the output resistance of the sensor. The actual amplifier input voltage will be given by Equation (2.1),
where VT = 1.0 volts, so that Vin = 0.67 volts. Thus, the output of the amplifier is actually Vout = 10(0.67 V) = 6.7 V.
This concept plays an important role in analog signal conditioning and will be referred to many times in this and later chapters.
FIGURE 2.3 If loading is ignored, serious errors can occur in expected outputs of circuits and gains of amplifiers.
If the electrical quantity of interest is frequency or a digital signal, then loading is not such a problem. That is, if there is enough signal left after loading to measure the frequency or to distinguish ones from zeros, there will be no error. Loading is important mostly when signal amplitudes are important.
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