## Input Characteristic Impedance

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On: 16 Jun, 2019

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The description of sensors by means of their static and dynamic characteristics is in no way complete. To illustrate why, let us consider the following situations: To prevent the wiper in a potentiometer (Section 2.1) from losing contact with the ...

The description of sensors by means of their static and dynamic characteristics is in no way complete. To illustrate why, let us consider the following situations: To prevent the wiper in a potentiometer (Section 2.1) from losing contact with the resistive element, it is necessary for the wiper to exert a force on it. What would happen if we desired to measure the movement of an element unable to overcome the friction between the wiper and the resistive element? When we use a thermometer having a considerable mass to measure the temperature reached by a transistor, upon contact, wouldn't the thermometer cool the transistor and give a lower reading than the initial transistor temperature?

It turns out that neither the static nor the dynamic characteristics of sensors that we have defined allow us to describe the real behavior of the combined sensor-measured system. The explanation is that the description of a sensor or a measurement system by means of block diagrams does not take into account the extraction of a certain amount of power from the measured system. When this extraction of power modifies the value of the measured variable, it is said that there is a loading error. Block diagrams can only be applied when there is no energy interaction between blocks. The concept of input impedance allows us to determine when there will be a loading error. When measuring a variable x1 , there is always another variable x2 involved, such that the product xr - xz has the dimensions of power. For example, when measuring a force, there is always a velocity; when measuring flow, there is a drop in pressure; when measuring temperatuie, there is a heat flow; when measuring an electric current, there is a drop in voltage, and so on.

Nonmechanical variables are designated as effort variables if they are measured between two points or regions in the space (voltage, pressure, temperature), and they are designed as flow variables if they are measured at a point or region in the space (electric current, volume flow). For mechanical variables the converse definitions are used, with effort variables measured at a point (force, torque) and flow variables between two points (linear velocity, angular velocity). For an element that can be described by means of linear relations, the input impedance Z(s) is defined as the quotient between the Laplace transforms of an input effort variable and the associated flow variable [7]. The input admittance I(s) is deflned as the reciprocal of Z(s). The values of both usually change with frequency. When very low frequencies are considered, stiffness and compliance are used instead of impeoance and admittance.

To have a minimal loading error, it is necessary for the input impedance to be very high when measuring an effort variable. If x1 is an effort variable

and if it is to be kept at minimum, x2 must be as small as possible. Therefore the input impedance must be high. To keep P very low when measuring a flow variable, it is necessa'y for x1 to be very small, and that calls for a low input impedance (i.e., a high input admittance). To obtain high-valued input impedances, it may be necessary to modify the value of components or to redesign the system and use active elements. For active elements most of the power comes from an auxiliary power supply, and not from the measured system. Another option is to measure,by using a balancing method because there is only a significant power drain when the input variable changes its value.

Finally, there are other errors that may not be caused by a loading effect but by the measurement method itself. For example, there will be error if, in

measuring a flow, the insertion of the flowmeter causes an appreciable obstruction of the conduit section. Thus no sensor should be applied without

first considering its effect on the system from which it obtains the information.

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