Applied Electronics and Instrumentation 3(2+1)

LESSON 25. Basic input circuits-Active and passive transducer-Error-types-calibration.

The manipulating unit consists mainly of a conversion circuit (a bridge circuit), an amplifier, if necessary an impedance matching circuit, for transmission a modulation circuit and a detector fro display.  All units are not always necessary and sometimes some more and different units are needed.

The present day trend is to convert the sensor output into an electrical signal first whatever be the form of its original output as conditioning and data processing are much more convenient by electrical means.

Basic input circuits (Interfacing circuits)

Interfacing circuit or input circuit is an electrical circuit that interfaces the sensor/transducer (where electrical output is available) with the more demanding signal conditioning equipment like amplifier, modulator, processor, etc.  There are a number of such circuits performing appropriate functions in the interfacing stage.  One major reason of such circuits is that the transducer may be a passive type and requires an auxiliary source of energy for giving a signal in voltage or in current.  As mentioned earlier, bridge circuit is a very common interfacing circuit.  There are others like ballast circuits current sensitive circuits, voltage divider circuits etc.

Current sensitive circuit

It is basically a series circuit of the voltage supply, a current indicating/recording device and the transducer of the resistance type.  The supply source has a internal resistance R_s.  The meter has a resistance R_m and the transducer resistance may vary between 0 and R (say) – let it be represented by kR when 0 £ k £1.  The circuit schematic is shown in Fig. 13.2.  The meter current at any stage is i with a maximum of i_x.

 Let R_m + R_s = R_T then the circuit current is given by

            

The maximum current occurs when k = 0, so that

                                   

giving the ratio

                                   

The output, I is a function of i_x i.e. of V_S and it should be maintained constant.  The sensitivity of the system increases with increasing R/R_T  i.e. system is nonlinear.

Ballast circuit

It is a voltage sensing circuit instead of the current sensing type.  The scheme is shown in Fig. 13.3.  V_s is the supply voltage, R_v is the supply or voltage source resistance, V₀ is the supply voltage, R_v is the supply or voltage source resistance, V_o is the voltage indicated or recorded for a variation in R again given as kR, R_i is a resistance introduced in the position as shown and R_i >> R_s.  The resistance R_i is known as the ballast resistance.

For the voltmeter having a very high resistance, current through R_i + R_s is

                                   

and the voltage across kR is also the output voltage V_o

                                   

or

                                   

With change in measurand k changes so that change in V_o with k is given by

                                   

There is, however, an optimum choice of R_i (or, R_i + R_s = R_b say) for which sensitivity can be made maximum.  By differentiating V_o with respect to R_b, this is obtained as

                                    R_b = kR

Obviously, this also varies with sensor output resistance

Loading Error

If the voltmeter draws a current, there is an error in measurement called the loading error.  If the meter has a resistance R_m then the total resistance seen by the source V_s is

                                   

and the current is now

                                   

so that the output voltage is now

                                    V_o = V_s - iR_b

                                         =

                                        =

By taking the difference one can show that

 

so that the % error is

                                   

                                    E% =

It is worthwhile to note that (percentage) error also is a function of k.

Bridge Circuits

The most common interfacing circuit between a passive sensor and the measurement system is the bridge circuit.  Wheatstone bridge is a circuit that is extensively used till today although it was devised as early as 1833.  A lot of variation has since been in operation of this bridge without altering the basic structure which is shown in Figure.

The resistance bridge supply is V_s and output V_o.  Solving for V_o = 0, the condition in terms of R₁, R₂, R₃ and R₄ is obtained as

                                   

This is called the null-balance bridge.  It is possible to take output V_o for different values of resistance.  It is initially balanced satisfying the above condition and subsequently the unbalanced voltage is measured b a voltmeter of very high impedance.  However, alternative to this, a current meter may also be connected and response observed.

For voltage detector scheme with very high impedance of the detector and R₄ as the sensor resistance that changes to R₄ + DR₄ and initially with R₁ = R₂ = R₃ = R₄ = R one derives.

                                   

which changes to

                           

for DR_s<<R.

If, instead, a galvanometer is used as a detector with its resistance R_g often chosen to be equal to R_v and, again with all R/s equal initially to R, one derives the incremental detecting current through the galvanometer   for an incremental change in R₁ equal to DR₁ say, and is given as

                       

where i_g is the current supplied by the source.

Bridge circuits have been used in ac operation for resistance, capacitance as well as inductance measurement. Impedance bridges, as they are called, are listed in figure

Active and passive transducers

To perform all the general functions, a physical component may act as an active transducer or a passive transducer.

A component whose output energy is supplied entirely or almost entirely by its input signal is commonly called a passive transducer. The output and input signals may involve energy of the same from or there may be an energy conversion from one form to another farm.

An active transducer has an auxillary source of power which supplies a major part of the output while the input signal supplies only an insignificant portion.

Error Analysis

Types of Errors

a) Gross errors- largely human errors, among them misreading of instruments, incorrect adjustment and improper application of instruments and computational mistakes.

b) Random errors –those errors that cannot be directly established because of random variations in the parameter or the system of measurement.

c) Systematic errors- Shortcomings of the instruments such as defective or worn parts and effects of the environment on the equipment or the user.

 Types of systemic errors

• Instrumental errors

• Environmental errors

• Static errors

• Dynamic errors

The uncertainty in the final result is due to the uncertainties in the primary measurements. This may be done by a commonsense analysis of the data which may take many forms. One rule of thumb that could be used that the error in the result is equal to the maximum error in any parameter used to calculate the result. Another commonsense analysis would combine all the errors in the most detrimental way in order to determine the maximum error in the final result. Consider the calculation of electric power from

P=EI

Where E and I are measured as

E=100V±2V

I=10A±0.2A

The nominal value of the power is 100*10=1000W.by taking the worst possible variations in the voltage and current, we could calculate

P_max= (100+2) (10+0.2) =1040.4W

P_min= (100-2) (10-0.2) =960.4W

Thus, using this method of calculation, the uncertainty in the power is +4.04 percent,-3.96%.it is quite unlikely that the power would be in the error by these amounts because the voltmeter variations would probably not correspond with the ammeter variations. when the voltmeters reads an extreme “ high” there is no reason that the ammeter must also read an extreme “high” at that particular instant, indeed, this combination is most unlikely.

 Calibration

Calibration: To check the instrument against a known standard and subsequently to reduce errors in accuracy

Calibration procedures involve a comparison of the particular instrument with either a primary standard or a known input source.

NIST-This institute defines the standard for length, mass, time, temperature and force.

Static calibration -All the static performance characteristics are obtained in one form or another by a process called static calibration. All working instruments must be calibrated against some reference instruments which have a higher accuracy.

Error calibration-Error calibration means that an instrument has been calibrated against a suitable standard.