From the input to the output, a

**sensor**may have several conversion steps before it produces an electrical signal. For instance, pressure inflicted on the**fiber-optic sensor**first results in strain in the fiber, which, in turn, causes deflection in its refractive index,which, in turn, results in an overall change in optical transmission and modulation of photon density. Finally, photon flux is detected and converted into electric current.In this article, we discuss the overall

**sensor characteristic**s, regardless of its physical nature or steps required to make a conversion. We regard a**sensor**as a “black box” where we are concerned only with relationships between its output signal and input stimulus.**The characteristics we discuss are:**

Transfer Function

Span (Full-Scale Input)

Full-Scale Output

Accuracy

Calibration

Calibration Error

Hysteresis

Nonlinearity

Saturation

Repeatability

Dead Band

Resolution

**1. Transfer Function**

An ideal or theoretical output–stimulus relationship exists for every sensor. If the

**sensor**is ideally designed and fabricated with ideal materials by ideal workers using ideal tools, the output of such a

**sensor**would always represent the true value of the stimulus. The ideal function may be stated in the form of a table of values, a graph, or a mathematical equation. An ideal (theoretical) output–stimulus relationship is characterized by the so-called transfer function. This function establishes dependence between the electrical signal S produced by the

**sensor**and the stimulus s :

S = f(s).

That function may be a simple linear connection or a nonlinear dependence, (e.g., logarithmic, exponential, or power function). In many cases, the relationship is unidimensional (i.e., the output versus one input stimulus). A unidimensional linear relationship is represented by the equation:

S = a + bs (1)

where a is the intercept (i.e., the output signal at zero input signal) and b is the slope, which is sometimes called sensitivity. S is one of the characteristics of the output electric signal used by the data acquisition devices as the sensor’s output. It may be amplitude, frequency, or phase, depending on the

**sensor**properties.Logarithmic function:

S = a + b ln s (2)

Exponential function:

S = a e

^{ks}(3)

Power function:

S = a

_{0}+ a

_{1}s

^{k}(4)

where k is a constant number.

A

**sensor**may have such a transfer function that none of the above approximations fits sufficiently well. In that case, a higher-order polynomial approximation is often employed. For a nonlinear transfer function, the sensitivity b is not a fixed number as for the linear relationship [Eq. (1)]. At any particular input value, s_{0}, it can be defined as:b = dS

_{(s0) }/ dS (5)

In many cases, a nonlinear

**sensor**may be considered linear over a limited range. Over the extended range, a nonlinear transfer function may be modeled by several straight lines. This is called a piecewise approximation. To determine whether a function can be represented by a linear model, the incremental variables are introduced for the input while observing the output.Adifference between the actual response and a liner model is compared with the specified accuracy limits.A transfer function may have more than one dimension when the

**sensor**’s output is influenced by more than one input stimuli. An example is the transfer function of a thermal radiation (infrared)**sensor**. The function connects two temperatures (Tb, the absolute temperature of an object of measurement, and Ts , the absolute temperature of the**sensor**’s surface) and the output voltage V :V = G ( T

_{b}

^{4}- T

_{s}

^{4}) (6)

where G is a constant. Clearly, the relationship between the object’s temperature and the output voltage (transfer function) is not only nonlinear (the fourth-order parabola) but also depends on the

**sensor**’s surface temperature. To determine the sensitivity of the**sensor**with respect to the object’s temperature, a partial derivative will be calculated as:_{b}= 4GT

_{b}

^{3}(7)

**2. Span (Full-Scale Input)**

A dynamic range of stimuli which may be converted by a

**sensor**is called a span or an input full scale (FS). It represents the highest possible input value that can be applied to the

**sensor**without causing an unacceptably large inaccuracy. For the

**sensor**s with a very broad and nonlinear response characteristic, a dynamic range of the input stimuli is often expressed in decibels, which is a logarithmic measure of ratios of either power or force (voltage). It should be emphasized that decibels do not measure absolute values, but a ratio of values only. A decibel scale represents signal magnitudes by much smaller numbers, which, in many cases, is far more convenient.

Being a nonlinear scale, it may represent low-level signals with high resolution while compressing the high-level numbers. In other words, the logarithmic scale for small objects works as a microscope, and for the large objects, it works as a telescope. By definition, decibels are equal to 10 times the log of the ratio of powers:

_{2 }/ P

_{1}) (8)

In a similar manner, decibels are equal to 20 times the log of the force, current, or voltage:

1 dB = 20 log ( S

_{2}/ S

_{1 }) (9)

**3. Full-Scale Output**

Full-scale output (FSO) is the algebraic difference between the electrical output signals measured with maximum input stimulus and the lowest input stimulus applied. This must include all deviations from the ideal transfer function. For instance, the FSO output in Fig. 1 is represented by SFS.

## 5 comments:

nanti kalau sudah semester 5 saya keliatannya akan dapat tugas bikin sensor.:D

February 19, 2010 at 7:46 PMSulit sekali ya kayaknya membuat sensor sensor ya.Terlalu rumit buatku

March 13, 2010 at 7:49 AMHello my friend, thank you very much for your visit, good weekend with happiness and peace. Hugs Valter.

March 13, 2010 at 6:23 PMkunjugan gan...

February 24, 2011 at 12:54 AMnice post my freinds...

February 24, 2011 at 1:02 AM## Post a Comment