Basics of Electrical and Electronic Measurements

First of all, why do we need to learn this subject?

If the measurement is not there in our universe what will happen?

If the measurement is not there we don't know how to measure any unknown quantities.

Now again the question arises.

What is a quantity?

Quantity is nothing but which has magnitude and direction.

In general, quantities are classified as Electrical and Non-electrical.

So to measure any electrical and electronic quantity, we use meters.

To measure non-electrical quantity we need to convert that to electrical quantity using transducers.

Electrical quantity is generally higher in magnitude as kilo, mega, and Giga, and electronic quantity is lower in magnitude as in milli, micro, and nano.

Only one electrical quantity is low, the frequency, whereas in electronics we have a higher frequency.

Kindly note that we cannot use a multimeter to measure the voltage in the transmission lines and also we cannot use PMMC to measure low voltage such as 0.0001V whereas the pointer never shows deflection.

Take a battery, where a 1.5 V battery can be measured using a multimeter, potentiometer, Permanent magnet moving coil, Cathode ray oscilloscope (CRO), and Moving Iron.

Kindly make a note that we use a lot of meters to measure a 2.5V battery but we won't get all the values the same in all of the meters all the time. When I take 100 readings in one of the meters I won't get all the time the same value as 2.5V sometimes I may get 2.4V or sometimes I may even get 2.3V. So which value should I take?

Now to clear this doubt Gauss introduced a curve called Gauss Distribution Curve.

He gave a solution that in this universe we have infinite quantities and in that take one quantity to measure using the meter. If we measure the reading n times we don't get the same reading all the time also we don't get the different readings all the time but one answer must be repeated most of the time which is the precise value to take.

Gaussian distribution curve

As the battery voltage is 2.5 we can mark it as the true value whereas the curve has all the possible values and it is the measured value.

At = true value

Am = measured value

Here in this graph, 2.5 V is the most repeated one and it is a precise value.

Except for the true value, all the other values deviate from the true value of 2.5V in the graph. Hence that deviation is known as the error.

What is an error?

An error is defined as the deviation of the measured quantity from the true value.

E = Am -  At

Error = measured value - true value

The error may be positive or negative.

If Am >  At, then the error will be positive.

If Am <  At, then the error will be negative.

The error can be classified in two ways:

• Static error
• Dynamic error

Static Characteristics:

1. Static error

i) Static correction/Correction factor

ii) Percentage Static Error / Relative static error

2. Accuracy

3. Precision

i) Repeatability

ii) Reproducibility

4. Sensitivity

5. Resolution

6. Dead time and dead zone

7. Drift

8. Linearity

Static error:

The static error is one in which it is independent of time.

Dynamic error:

The dynamic error is one that depends on time. This error can be found only in the laboratory.

All instruments follow the Gaussian Distribution curve.

All instruments are error instruments as it has deviation.

Therefore in order to reduce these errors, we use the correction factor.

Now, what is the correction factor?

The value which we are adding or subtracting from measured quantity in order to get the true value.

                                    Correction factor ±  Am =  At

The correction factor may be positive or negative.

Correction factor =  - Error

Relative static error:

It is defined as the ratio of the error to the true value.

This error decides the quality of the instrument.

If the error percentage has a very less value then the meter has very good accuracy. 

If the error percentage has a very high value then the meter hasn't had good accuracy. 

Limitting error or Tolerance or Uncertainty:

The limitting error is decided by the manufacturer which is based on the instrument.

Limitting error gives the range of the error.

This error is always concerning the true value.

Limitting error is a variable error as the At is variable.

As the deviation is increasing the number of samples is decreasing.

When the Gaussian distribution curve becomes narrow then it is more probable when compared to the larger one.

Example question:

This question is asked in the IES exam.

Take an ammeter with a range of (0-10)A. The true value is 2A. Give me the best instrument from the %Limitting error as follows.

A ----> ± 3%

B ----> ± 1%

C ----> ± 0.5%

D ----> ± 0.0%

When we take A ,  ± 3%,

2 * ± 3/100 = ± 0.06

Therefore we do 2 ± 0.06

adding to the true value we get, 2.06

subtracting the true value we get, 1.94

Here the curve is wider as the deviations from the true value are more.

When we take B,  ± 1%,

2 * ± 1/100 = ± 0.02

Therefore we do 2 ± 0.02

adding to the true value we get, 2.02

subtracting the true value we get, 1.98

Here the deviation is less when compared to the previous one.

When we take C,  ± 0.5%,

2 * ± 0.5/100 = ± 0.01

Therefore we do 2 ± 0.01

adding to the true value we get, 2.01

subtracting the true value we get, 1.99

Here the deviation is narrow when compared to the previous one.

When we take D,  ± 0.00%,

2 * ± 0/100 = ± 0.00

Therefore we do 2 ± 0.00

we get, 2

This is not a Gaussian distribution curve.

Therefore this doesn't exist as no one can design an instrument without error.

Hence from this C is the best instrument as the Gaussian distribution curve is narrow which means the measured value is close to the true value and also when the limitting error is less, then that instrument is a good ammeter.