Every instrument has at least one *input *and one *output*. For a pressure sensor, the input would be some fluid pressure and the output would (most likely) be an electronic signal. For a loop indicator, the input would be a 4-20 mA current signal and the output would be a human-readable display. For a variable-speed motor drive, the input would be an electronic signal and the output would be electric power to the motor.

*Calibration *and *ranging *are two tasks associated with establishing an accurate correspondence between any instrument’s input signal and its output signal. Simply defined, *calibration *assures the instrument accurately senses the real-world variable it is supposed to measure or control. Simply defined, *ranging *establishes the desired relationship between an instrument’s input and its output.

### 18.1 Calibration versus re-ranging

To *calibrate *an instrument means to check and adjust (if necessary) its response so the output accurately corresponds to its input throughout a specified range. In order to do this, one must expose the instrument to an actual input stimulus of precisely known quantity. For a pressure gauge, indicator, or transmitter, this would mean subjecting the pressure instrument to known fluid pressures and comparing the instrument response against those known pressure quantities. One cannot perform a true calibration without comparing an instrument’s response to known, physical stimuli.

To *range *an instrument means to set the lower and upper range values so it responds with the desired sensitivity to changes in input. For example, a pressure transmitter set to a range of 0 to 200 PSI (0 PSI = 4 mA output ; 200 PSI = 20 mA output) could be re-ranged to respond on a scale of 0 to 150 PSI (0 PSI = 4 mA ; 150 PSI = 20 mA).

In analog instruments, re-ranging could (usually) only be accomplished by re-calibration, since the same adjustments were used to achieve both purposes. In digital instruments, calibration and ranging are typically separate adjustments (i.e. it is possible to re-range a digital transmitter without having to perform a complete recalibration), so it is important to understand the difference.

### 18.2 Zero and span adjustments (analog instruments)

The purpose of *calibration *is to ensure the input and output of an instrument reliably correspond to one another throughout the entire range of operation. We may express this expectation in the form of a graph, showing how the input and output of an instrument should relate. For the vast majority of industrial instruments this graph will be linear:

This graph shows how any given percentage of input should correspond to the same percentage of output, all the way from 0% to 100%.

Things become more complicated when the input and output axes are represented by units of measurement other than “percent.” Take for instance a pressure *transmitter*, a device designed to sense a fluid pressure and output an electronic signal corresponding to that pressure. Here is a graph for a pressure transmitter with an input range of 0 to 100 pounds per square inch (PSI) and an electronic output signal range of 4 to 20 milliamps (mA) electric current:

Although the graph is still linear, zero pressure does not equate to zero current. This is called a *live* *zero*, because the 0% point of measurement (0 PSI fluid pressure) corresponds to a non-zero (“live”) electronic signal. 0 PSI pressure may be the LRV (Lower Range Value) of the transmitter’s input, but the LRV of the transmitter’s output is 4 mA, not 0 mA.

Any linear, mathematical function may be expressed in “slope-intercept” equation form:

Where,

*y *= Vertical position on graph

*x *= Horizontal position on graph

*m *= Slope of line

*b *= Point of intersection between the line and the vertical (*y*) axis

This instrument’s calibration is no different. If we let *x *represent the input pressure in units of PSI and *y *represent the output current in units of milliamps, we may write an equation for this instrument as follows:

On the actual instrument (the pressure transmitter), there are two adjustments which let us match the instrument’s behavior to the ideal equation. One adjustment is called the *zero *while the other is called the *span*. These two adjustments correspond exactly to the *b *and *m *terms of the linear function, respectively: the “zero” adjustment shifts the instrument’s function vertically on the graph (*b*), while the “span” adjustment changes the slope of the function on the graph (*m*). By adjusting both zero and span, we may set the instrument for any range of measurement within the manufacturer’s limits.

The relation of the slope-intercept line equation to an instrument’s zero and span adjustments reveals something about how those adjustments are actually achieved in any instrument. A “zero” adjustment is always achieved by *adding *or *subtracting *some quantity, just like the *y*-intercept term *b *adds or subtracts to the product *mx*. A “span” adjustment is always achieved by *multiplying *or *dividing *some quantity, just like the slope *m *forms a product with our input variable *x*.

Zero adjustments typically take one or more of the following forms in an instrument:

- Bias force (spring or mass force applied to a mechanism)
- Mechanical offset (adding or subtracting a certain amount of motion)
- Bias voltage (adding or subtracting a certain amount of potential)

Span adjustments typically take one of these forms:

- Fulcrum position for a lever (changing the force or motion multiplication)
- Amplifier gain (multiplying or dividing a voltage signal)
- Spring rate (changing the force per unit distance of stretch)

It should be noted that for most analog instruments, zero and span adjustments are *interactive*. That is, adjusting one has an effect on the other. Specifically, changes made to the span adjustment almost always alter the instrument’s zero point^{1} . An instrument with interactive zero and span adjustments requires much more effort to accurately calibrate, as one must switch back and forth between the lower- and upper-range points repeatedly to adjust for accuracy.