Option 4 : Resolution

__Resolution__:

- Resolution is the ability of the instrument or measurement system to detect and faithfully indicate the small changes in the characteristics of the measurement result.
- Let’s assume the resolution is denoted by ‘δ’. ∴ A small δ implies good resolution and a large δ implies poor resolution.
- Since Resolution is the smallest output that we can detect in the scale with clarity, we need high-resolution instruments, so that they can’t lose accuracy.

__Important Notes__:

Accuracy: It is the degree of closeness with which the reading approaches the true value of the quantity to be measured.

Precision: It is the measure of reproducibility i.e., given a fixed value of a quantity, precision is a measure of the degree of agreement within a group of measurements.

- The precision of an instrument does not guarantee accuracy.
- An instrument with more significant figures has more precision.
- The deflection factor is reciprocal of sensitivity.

Sensitivity: It is defined as the ratio of the changes in the output of an instrument to a change in the value of the quantity being measured. It denotes the smallest change in the measured variable to which the instrument responds.

Deflection factor or inverse sensitivity is the reciprocal of sensitivity.

Option 4 : 4.9 kΩ

Concept:

To increase the range of a voltmeter, we need to the series resistance and it is given by

\({R_{se}} = {R_m}\left( {\frac{V}{{{V_m}}} - 1} \right)\)

Where V is the required voltmeter range

Vm is the voltmeter range

Rm is the meter internal resistance

Calculation:

Given that,

Meter full scale current reading (Im) = 10 mA

Internal resistance (Rm) = 100 Ω

Voltmeter range (Vm) = I m Rm = 10 × 10-3 × 100 = 1.0 V

Required voltmeter range (V) = 50 V

\({R_{se}} = 100\left( {\frac{{50}}{1} - 1} \right) = 4.9k\;{\rm{Ω }}\)

Option 3 : 1 milli V

__Concept__:

The resolution (R) in an N bit DVM is given by:

\(R= \frac{1}{{{{10}^N}}} \times range\;of\;voltage\)

Where N is the number of full digits.

In a DVM, a full digit counts 0 to 9 and a half digit counts from 0 to 1.

__Calculation__:

The full-scale reading = 9.999 V

It is a 4-digit voltmeter i.e. N = 4.

Range of voltmeter = 10 V

Resolution for the given DVM is

\(= \frac{1}{{{{10}^4}}} \times 10 = 1 \ mV\)

Find the vertical and horizontal resolutions, respectively, used in a TV system in USA where NT = 525, NL = 42

Option 2 : 338, 451

- NTSC is an abbreviation for National Television Standards Committee, named for the group that originally developed the black & white and subsequently color television system that is used in the United States, Japan, and many other countries.
- An NTSC picture is made up of 525 interlaced lines and is displayed at a rate of 29.97 frames per second.

- The vertical resolution would be equal to the number of active lines per frame. This would happen if the scanning lines were centered on the picture details.
- However, the scanning lines cannot be assumed to occupy a fixed position relative to vertical detail at all times. Complete loss of vertical resolution will occur when the scanning spot straddles picture details.
- From subjective data, obtained with progressive (non-interlaced) scanning, it has been found that the vertical resolution is equal to 70 percent (the Kell factor) of the number of active lines.
- In the NTSC standard, there is a total of 525 lines per frame, of which about 40 are blanked, leaving, typically, about 485 active lines per frame. Given a Kell factor of 0.7, the effective vertical resolution is:

** NV = 0.7 × 485 ≈ 338 LPH**

- The horizontal resolution defines the capability of the system to resolve vertical lines. It depends on the camera and display capabilities, as well as the bandwidth and the high-frequency amplitude and phase response of the transmission medium.
- In a 4:3 aspect ratio television system, it is expressed as the number of distinct vertical lines, alternately black and white, which can be satisfactorily resolved in three-quarters of the width of a television screen.
- In the NTSC system, this results in
**339 × 4/3 ≈ 451**horizontal details to be resolved.

Hence **option (2)** is the correct answer.

Option 3 : \(V_{fs}=V_{ref}\left(1-\dfrac{1}{2^n}\right)\)

__Concept__**:**

Output voltage = Resolution × Decimal equivalent of binary Data.

\({V_0} = K\;\mathop \sum \limits_{i = 0}^{M - 1} {2^i}{b_i}\)

K = Proportionality factor i.e. Resolution

b_{n} = 1: if n^{th} bit of digital input is 1

0 = If n^{th} bit of digital input is 0

** Resolution:** It is a change in the analog voltage corresponding to the LSB bit increment at the input.

\(R=\dfrac{V_r}{2^n-1}\)

\(\% \;R = \frac{{Resolution}}{{{V_{fc}}}} \times 100\)

\(\% \;R = \frac{1}{{{2^n} - 1}} \times 100\)

__Explanation: __

Refrence voltage (V_{ref}):

\({V_{ref}} = \frac{{{2^n}\left[ {{V_{FC}}(full\;save\;voltage} \right]}}{{\left( {{2^n} - 1} \right)}}\)

\({V_{FC}} = \frac{{{2^n} - 1}}{{{2^n}}}{V_{ref}}\)

^{\({V_{FC}} = {V_{ref}}\left[ {1 - \frac{1}{{{2^n}}}} \right]\)}

**Option 3 correct.**

__More information:__

** Error/Accuracy:** Maximum error acceptance in ADC/DAC is 1 LSB bit which is equal to the resolution

Error ≤ resolution.

Full-scale voltage V_{FC} = Resolution × maximum decimal.

\(= \frac{{{V_r}}}{{{2^n} - 1}} \times {2^n} - 1\)

VOption 4 : Resolution

__Resolution__:

- Resolution is the ability of the instrument or measurement system to detect and faithfully indicate the small changes in the characteristics of the measurement result.
- Let’s assume the resolution is denoted by ‘δ’. ∴ A small δ implies good resolution and a large δ implies poor resolution.
- Since Resolution is the smallest output that we can detect in the scale with clarity, we need high-resolution instruments, so that they can’t lose accuracy.

__Important Notes__:

Accuracy: It is the degree of closeness with which the reading approaches the true value of the quantity to be measured.

Precision: It is the measure of reproducibility i.e., given a fixed value of a quantity, precision is a measure of the degree of agreement within a group of measurements.

- The precision of an instrument does not guarantee accuracy.
- An instrument with more significant figures has more precision.
- The deflection factor is reciprocal of sensitivity.

Sensitivity: It is defined as the ratio of the changes in the output of an instrument to a change in the value of the quantity being measured. It denotes the smallest change in the measured variable to which the instrument responds.

Deflection factor or inverse sensitivity is the reciprocal of sensitivity.

Option 4 : 4.9 kΩ

Concept:

To increase the range of a voltmeter, we need to the series resistance and it is given by

\({R_{se}} = {R_m}\left( {\frac{V}{{{V_m}}} - 1} \right)\)

Where V is the required voltmeter range

Vm is the voltmeter range

Rm is the meter internal resistance

Calculation:

Given that,

Meter full scale current reading (Im) = 10 mA

Internal resistance (Rm) = 100 Ω

Voltmeter range (Vm) = I m Rm = 10 × 10-3 × 100 = 1.0 V

Required voltmeter range (V) = 50 V

\({R_{se}} = 100\left( {\frac{{50}}{1} - 1} \right) = 4.9k\;{\rm{Ω }}\)

Option 3 : 1 milli V

__Concept__:

The resolution (R) in an N bit DVM is given by:

\(R= \frac{1}{{{{10}^N}}} \times range\;of\;voltage\)

Where N is the number of full digits.

In a DVM, a full digit counts 0 to 9 and a half digit counts from 0 to 1.

__Calculation__:

The full-scale reading = 9.999 V

It is a 4-digit voltmeter i.e. N = 4.

Range of voltmeter = 10 V

Resolution for the given DVM is

\(= \frac{1}{{{{10}^4}}} \times 10 = 1 \ mV\)

Find the vertical and horizontal resolutions, respectively, used in a TV system in USA where NT = 525, NL = 42

Option 2 : 338, 451

- NTSC is an abbreviation for National Television Standards Committee, named for the group that originally developed the black & white and subsequently color television system that is used in the United States, Japan, and many other countries.
- An NTSC picture is made up of 525 interlaced lines and is displayed at a rate of 29.97 frames per second.

- The vertical resolution would be equal to the number of active lines per frame. This would happen if the scanning lines were centered on the picture details.
- However, the scanning lines cannot be assumed to occupy a fixed position relative to vertical detail at all times. Complete loss of vertical resolution will occur when the scanning spot straddles picture details.
- From subjective data, obtained with progressive (non-interlaced) scanning, it has been found that the vertical resolution is equal to 70 percent (the Kell factor) of the number of active lines.
- In the NTSC standard, there is a total of 525 lines per frame, of which about 40 are blanked, leaving, typically, about 485 active lines per frame. Given a Kell factor of 0.7, the effective vertical resolution is:

** NV = 0.7 × 485 ≈ 338 LPH**

- The horizontal resolution defines the capability of the system to resolve vertical lines. It depends on the camera and display capabilities, as well as the bandwidth and the high-frequency amplitude and phase response of the transmission medium.
- In a 4:3 aspect ratio television system, it is expressed as the number of distinct vertical lines, alternately black and white, which can be satisfactorily resolved in three-quarters of the width of a television screen.
- In the NTSC system, this results in
**339 × 4/3 ≈ 451**horizontal details to be resolved.

Hence **option (2)** is the correct answer.

Option 3 : \(V_{fs}=V_{ref}\left(1-\dfrac{1}{2^n}\right)\)

__Concept__**:**

Output voltage = Resolution × Decimal equivalent of binary Data.

\({V_0} = K\;\mathop \sum \limits_{i = 0}^{M - 1} {2^i}{b_i}\)

K = Proportionality factor i.e. Resolution

b_{n} = 1: if n^{th} bit of digital input is 1

0 = If n^{th} bit of digital input is 0

** Resolution:** It is a change in the analog voltage corresponding to the LSB bit increment at the input.

\(R=\dfrac{V_r}{2^n-1}\)

\(\% \;R = \frac{{Resolution}}{{{V_{fc}}}} \times 100\)

\(\% \;R = \frac{1}{{{2^n} - 1}} \times 100\)

__Explanation: __

Refrence voltage (V_{ref}):

\({V_{ref}} = \frac{{{2^n}\left[ {{V_{FC}}(full\;save\;voltage} \right]}}{{\left( {{2^n} - 1} \right)}}\)

\({V_{FC}} = \frac{{{2^n} - 1}}{{{2^n}}}{V_{ref}}\)

^{\({V_{FC}} = {V_{ref}}\left[ {1 - \frac{1}{{{2^n}}}} \right]\)}

**Option 3 correct.**

__More information:__

** Error/Accuracy:** Maximum error acceptance in ADC/DAC is 1 LSB bit which is equal to the resolution

Error ≤ resolution.

Full-scale voltage V_{FC} = Resolution × maximum decimal.

\(= \frac{{{V_r}}}{{{2^n} - 1}} \times {2^n} - 1\)

V