>## Ell301 Summery 1
> ### Arvind Kumar .
> measurement is aspect of our daily life , we have to measure quantities in order to control , analyse and compare so, for measuring we use diffrent type of measuring devises .

#### what is an Instrument:-
a device used to sense the quantity and to represent a number or measure corrosponidng to the amount of the quantity .
Electrical & Electronic instrumentations can be devided in two parts **
1. Analog instrumentation
2. Digital instrumentation
### measurment in history and need of instruments
in historical time we use length , weight these properties as standerd to measure other objects and to compare quantities . this is artefact based measuring . but with time there may be some changes to length , weight of objects , so we can't use them as a standerd . that's why we need a universal measuring units . we took some fundamental constants and we relate units to these constant . like one metre is the length of the path travelled by light in vacuum during a time interval with duration of 1/299 792 458 of a second.
here this number is a fixed constant .

## catagarisation of instruments **
#### on the basis of energy
1. Active Transducer:-
2. this doesn't uses external energy , . like multimeter .
3. Passive Transducer:- it uses external energy like thermometer . uses energy of measurand

#### according to mode of operation
1. Digital:- Instrument which gives final reading as a numerical value and generally in degits
2. Analog:- reading cover all value in a range diffrence between values can be infintly small .

**characteristics **
###### a. Static
Factors or Properties that affect the measurement from an
instrument. But, they don't affect an individual measurement
###### b. Dynamic
here we see mathematical depandency between input and output. like zero order, first order and sencond order etc. we study some specific terms Rise time, Delay/lag, fidelity and speed to analyze input output curve of the instrument.
a mathematical Model is
$$ a_n \frac{d^nq_o}{dt^n}+...+a_2\frac{d^2q_o}{dt^2}+a_1\frac{dq_o}{dt}+a_0q_o = b_0q_i+b_1\frac{dq_i}{dt}+b_2\frac{d^2q_i}{dt^2}+...+b_n\frac{d^nq_i}{dt^n} $$
Here $q_i$ = input
$q_o$ = reading of instrument
So in case of current and voltage they are linearly related so zero order . heat/ temperature instrument are of first order instrument .
Second order Instrumentation which uses charging of a capacitor and spring position and force applied where position is changes by some force are 2nd order device .
Mathematical model for second order
$$ J\frac{d^2q_o}{dt^2}+D\frac{dq_o}{dt}+Kq_o = b_0q_i$$

$$ w_n = \sqrt{\frac{K}{J}}$$
$$ \zeta = \frac{D}{2\sqrt{JK}}$$
based on the above constant related to input output curve we can defince damping of curve

Analog Instrumentation works based on some principle and it uses this principle to deflect needle according to the input given

###### Permanent Magnet Moving Coil(PMMC)

works on the principal of Fleming's left hand rule which says tht a current carring conductor experiences force when placed in a magnatic field . fixed U shaped permanent magnet is used here.
##### working of PMMC
accoring to flaming's left hand rule wire experiences force in the direction perpendicular to both current and field . pointer will move due to this force . to balance restoring torque of spring is used here .
Force exerted by megnatic field on current carring conductor
$$ F = BINlSin(\alpha)$$
here

instrument in this PMMC also some pros and cons like it can only uses for DC it is little bit expensive in comarre to others and good point is No hysteresis loss becouse of constants magnatic field and as the resistance of the coil is low so there is low power consumption.
###### Moving Iron
These type of Instrument uses for both AC and DC measurment in this there is a Fixed coil and a moving plate made up of soft iron. it work on the perincipal that when we fed out signal to the fixed coil excited then it work as an electromagnet then the plate move to sustain equlibirium.

## Electrodynamometer

### Working principle -
a current carrying wire will feel force if placed in a magnetic flux this fact is used in electrodynamometer .

### basic design -
* have two parts moving coil and fixed coil .
* in electrodynamometer both moving and fixed coils carry current.
* fluxed generated in fix coils is used to rotate another coil(moving ).
* control torque is given by spring attached
### operation -
* damping to slow down is given by air friction

both current values are rms values here .
* in DC case theta =
* in AC theta =
* here dm/dtheta is not constant but we will make is constant by suitable design.

### Use

* we can use it as ammeter
for low current both coils are connected in series and in case of large current , coils arw connected in parallel with shunt and swamping resistance .

* we can also use it as a voltmeter
for this purpose a high resistance is connected in series with the colils .

## note -
in both the cases of ammeter and voltmeter deflection in meter is proportional to square of quantity measured .

### Errors
there are mainly three type of error.
* Low Torque/Weight ratio : because of air cored , so frictional losses may happen .
* Frequency : impedence here is not independent of frequency . it might generate some error .
* Stray magnetic field : Magnetic fields
are produced by small current so field is weak . and the system may affect due to stray magnetic fields.
so here we can use shielding .

## how good this meter is
Pros
* Less hysteresis or eddy
currents
* Very accurate in low
frequencies and can be used in
frequencies > MI instruments
* using astatic system to 10KHz also
* Caliberation can be transferred from AC to DC
* Gives true RMS value
irrespective of wave shape.

Cons
* air cored so low torque /weight . friction losses .
* Less sensitive
* not much solid and stable
* much expensive
* need high power
* Non uniform scale
* can't be used for reading for low frequencies

## use of electrodynamometer as a wattmeter .

formely we can define it as
an instrument which works depends on the reaction between the magnetic field of moving and fixed coils is known as the Electrodynamo-meter Wattmeter
Instantenous power is equal to vi.

### construction
* Fixed coil is connected in series with the load so current flowing is
proportional to load current . this coil is called Current coil(CC).
* Moving coil is connected in parallel with the load so current is
proportional to load voltage. this coil is called Pressure Coil(PC).
#### Concept -
we know that we can measure product of both these current by deflection in meter so indirectly we are measuring iv that is power.

## Induction type instruments

### wroking principal
#### induction -
the phenomena of generation of electromotive force across an electrical conductor when placed in varaying magnetic field is called induction and this is used in induction type instruments

* instantaneous torque is directly proportional to the instantaneous eddy current and the flux.

### Shaded pole induction type instruments -

* Control torque is exerted by
control spring attached .
* Damping torque is provided by the
eddy current produced because of interaction between permanent magnet with the moving disc . * can be used as both ammeter and voltmeter but the scale is not linear in both the cases

#### pros and cons
pros
* Lower friction
* Higher torque/weight ratio
* Robust against stray magnetic
fields
* damping is good .

cons
* High power consumption
* Costly
* Sensitive to frequency
* can be used for only AC
* Non uniform scale
* Not a good choice for Voltage
or Current measurement

## induction type energymeter

* this is used to measure energy
* no. of rotation is the measure of energy and the speed of rotation is the measure of power

### Structure

* Driving System- genrates force to drive
* Moving System- part which moves
* Braking System- used to make the speed constant so we can measure energy
* Registering System- which measures the rotations
made up of gears