Mercury Pressure Sensor

Pressure measurement history was primarily based on the pioneering work of Evangelista Torricelli,who, for a short time,was a student of Galileo. During his experiments with mercury-filled dishes, in 1643, he realized that the atmosphere exerts pressure on Earth. Another great experimenter, Blaise Pascal, in 1647, conducted an experiment, with the help of his brother-in-law Perier, on the top of the mountain Puyde Dome and at its base. He observed that pressure exerted on the column of mercury depends on elevation. He named the mercury-in-vacuum instrument they used in the experiment a barometer.

In 1660, Robert Boyle stated his famous relationship: The product of the measures of  pressure and volume is constant for a given mass of air at fixed temperature. In 1738, Daniel Bernoulli developed an impact theory of gas pressure to the point where Boyle’s law could be deducted analytically. Bernoulli also anticipated the Charles–Gay–Lussac law by stating that pressure is increased by heating gas at a constant volume.

In general terms, matter can be classified into solids and fluids. The word fluid describes something which can flow. That includes liquids and gases. The distinction between liquids and gases are not quite definite. By varying pressure, it is possible to change liquid into gas and vice versa.

Concepts of Pressure

For a fluid at rest, pressure can be defined as the force F exerted perpendicularly on a unit area A of a boundary surface.

       p = dF/dA

Pressure vary with elevation as:

       dp = − w.dh

where w is the specific weight of the medium and h represents the vertical height.

The kinetic theory of gases states that pressure can be viewed as a measure of the total kinetic energy of the molecules:

       p = (2/3).KE/V = (1/3) ρ.C² = NRT

where KE is the kinetic energy, V is the volume, C² is an average value of the square of the molecular velocities, ρ is the density, N is the number of molecules per unit volume, R is a specific gas constant, and T is the absolute temperature.

Units of Pressure

The SI unit of pressure is the pascal:

       1 Pa = 1 N/m²

that is, one pascal is equal to one newton of force uniformly distributed over 1 squaremeter of surface.

Sometimes, in technical systems, atmosphere is used, which is denoted 1 atm. One atmosphere is the pressure exerted on 1 square centimeter by a column of water having a height of 1 meter at a temperature of +4^oC and normal gravitational acceleration. 

A pascal can be converted into other units by the use of  the following relationships:

       1 Pa = 1.45 × 10^-4  lb/in² = 9.869 × 10^-6 atm = 7.5 × 10^-4 cmHg

For practical estimation, it is useful to remember that 0.1 mm H₂O is roughly equal to 1 Pa. In industry, another unit of pressure is often used. It is defined as pressure exerted by a 1-mm column of mercury at 0^oC at normal atmospheric pressure and normal gravity. This unit is named after Torricelli and is called the torr.

The ideal pressure of the Earth’s atmosphere is 760 torr and is called the physical atmosphere:

       1 atm = 760 torr= 101,325 Pa

The U.S. Customary System of units defines pressure as a pound per square inch

        (lb/sq in.) or psi

Conversion into SI systems is the following:

       1 psi = 6.89 × 103 Pa = 0.0703 atm

A simple yet efficient sensor is based on the communicating vessels principle. Its prime use is for the measurement of gas pressure. A U-shaped wire is immersed into mercury, which shorts its resistance in proportion with the height of mercury in each column. The resistors are connected into a Wheatstone bridge circuit, which remains in balance as long as the differential pressure in the tube is zero.

Pressure is applied to one of the arms of the tube and disbalances the bridge, which results in the output signal. The higher the pressure in the left tube, the higher the resistance of the corresponding arm is and the lower the resistance of the opposite arm is. The output voltage is proportional to a difference in resistances ΔR of the wire arms which are not shunted by mercury:

       Vout = V.(ΔR/R) = V.β.Δp

The sensor can be directly calibrated in units of torr. Although simple, this sensor suffers from several drawbacks, such as necessity of precision leveling, susceptibility to shocks and vibration, large size, and contamination of gas by mercury vapors.

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Pressure Sensor

Ashcroft Indust Digital 4-1/2" Pressure Gauge

Pressure is force per unit area. Sensing it follows the same principle as the sensing of force that is measuring the displacement of an appropriate member of the sensor in response to pressure. The range of methods is quite large and includes thermal, optical as well as magnetic and electrical principles. Earliest sensors were purely mechanical.

Pressure Units

The basic SI unit is pascal, where 1 pascal (Pa) = 1 (N/m2). Other often units are:

• bar: 1 bar = 0.1 Mpa
• torr: 1 torr = 133Pa
• millibar: 1 millibar = 100Pa = 1.333 torr
• microbar: 1 microbar = 0.1 Pa

Types of Pressure Sensor

Pressure sensors come in four basic types :

• Absolute pressure sensors: pressure sensed relative to absolute vacuum.
• Differential pressure sensors: the difference between two pressures on two ports of the sensor is sensed
• Gage pressure sensors: the pressure relative to ambient pressure is sensed. (Most common)
• Sealed gage pressure sensor: the pressure relative to a sealed pressure chamber (usually 1atm at sea level or 14.7 psi) is sensed.

How Does Pressure Sensors Work

Pressure metrology is the technology of transducing pressure into an electrical quantity. Normally, a diaphragm construction is used with strain gauges either bonded to , or diffused into it, acting as resistive elements. Under the pressure-induced strain,the resistive values change.

In capacitive technology, the pressure diaphragm is one plate of a capacitor that changes its value under pressure-induced displacement.

Figure 1. Pressure sensing using diaphragm technology

Pressure sensing using diaphragm technology measures the difference in pressure of the two sides of the diaphragm. Depending upon the relevant pressure, we use the terms ABSOLUTE, where the reference is vacuum (1st picture), GAUGE, where the reference is atmospheric pressure (2nd picture), or DIFFERENTIAL, where the sensor has two ports for the measure of two different pressure.

The piezoresistive pressure sensor, or silicon cell

Figure 2. Pressure sensor consists of a micro-machined silicon diaphragm with piezoresistive strain gauges

This type of pressure sensor consists of a micro-machined silicon diaphragm with piezoresistive strain gauges diffused into it, fused to a silicon or glass backplate. The resistors have a value of approx. 3.5 kOhm. Pressure induced strain increases the value of the radial resistors (r), and decreases the value of the resistors (t) transverse to the radius. This resistance change can be high as 30%. The resistors are connected as a Wheatstone Bridge, the output of which is directly proportional to the pressure.

Figure 3. The resistors are connected as a Wheatstone Bridge

Leadouts from the bridge

Figure 4. Leadout from the bridge

1. Gold or aluminium wires are welded to the aluminium contacts on the chip and to the glass feed-through, pins of the header.
2. TAB (Tape Automated Bonding). The contacts on the chip have a gold dot.

A pretinned felxible printed circuit is directly soldered to these gold dots and the other end to a PC-board, or the header. In the first method, the sensor must be fixed on the header. The TAB printed circuit, however, holds the sensor in place itself.

Low cost sensors

Figure 5. Low cost sensors

Low cost sensors are devices where the they are exposed to the media without protection. The glass feed-through and the silicon cell is mounted in a plastic housing with pressure ports for positive and negative pressure (1st picture). The silicon sensor with the TAB print is fixed between two plastic mouldings with pressure ports (2nd picture). The silicon sensor is bonded to a brass pressure port. The contacts are made either by gold wires to soldering pins, or by TAB flexible printed circuit (3rd picture).

Piezoresistive OEM Pressure Transducer

Figure 6. Piezoresistive OEM Pressure Transducer

The silicon sensor on the glass feed-through is mounted in a stainless steel housing, isolated by a thin stainless steel diaphragm and filled with silcone oil. The pressure acts on the diaphragm and is transfered through the oil onto the sensor. These transducers are fully tested for temperature and linearity and the compensation resistor values given on the individual test sheets.

  Pressure Transducers

Figure 7. Pressure transducer

Pressure transducers are pressure measuring instruments, ready to use. It is an OEM transducer with pressure port, integrated compensation resistors and a cable or connector. Transducers give an unamplified signal into a separate instrumentation amplifier or indicator. They can be considered as passive bridges, being interchangeable between different manufacturers.

Pressure Transmitters.

Figure 8. Pressure transmitter

In pressure transmitters, the full signal conditioning circuitry is integrated in the housing. The sensor signal is conditioned into standard output signals of 0...100mV, 0...10V, 0.5...4.5V,and 4-20mA. Normally, the signal is independent from the excitation (i.e. 8...28V), but in ratiometric transmitters, the signal is proportional to the excitation. The accuracy of a transmitter is best described by an error band. This band covers all errors over the full pressure and temperature range. Typical errors are also given. The typical error describes the accuracy which can normally be expected in a measurement.

More Information

Handbook of Modern Sensors: Physics, Designs, and Applications

SENSOR CHARACTERISTICS (1)

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 characteristics, 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 = a₀ + a₁s^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, s₀, 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_b⁴ - T_s⁴ )          (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 = ∂V / ∂T_b = 4GT_b³        (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 sensors 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:

       1 dB = 10 log ( P₂  / P₁)         (8)

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

       1 dB = 20 log ( S₂ / S₁ )         (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.

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