3 Phase Energy Meter Working,Construction,Uses

Three phase energy meter  working,construction 

An energy meter is used to measure the energy consumed in the kilowatt hours. This is used in each and every house and industry for calculating the energy consumed by them. A 3-phase energy meter has same elements as in case of a single-phase energy meter. We see each of them in detail in this post.

Construction of three phase energy meter:

A 3-phase energy meter has following systems. This systems are same for both single phase and three phase energy meters. They are:

1. Driving System.

2. Moving System.

3. Breaking System.

4.Registering or Counting System.

Driving System:

This consists of a coil wounded on central limb of a shunt electro magnet which acts as pressure coil also known as voltage coil. This coil should have high inductance which means that inductance to resistance ratio of this coil is very high. Because of this inductive nature the current , flux will lag behind supply voltage by 90° approximately. 

        

Copper shading bands are provided on the shunt magnet's central limb to get 90° phase angle displacement between magnetic field set up by the shunt magnet and supply voltage. We have another series electro magnet on which current coil is wounded. This current coil is in series with the load so load current will flow through this.The flux produced by series magnet is proportional to and in phase with the load current. The driving system of 3-phase energy meter comprises of these elements.

Moving system:

On a vertical spindle or shaft a light rotating aluminium disc is attached. With the help of a gear arrangement aluminum disc is attached to the clock mechanism on front side of meter which helps to measure the energy consumed by load.

Eddy currents are induced due to time varying flux produced by series and shunt magnets. A driving torque is set up due to interaction between these two magnetic fields and eddy currents.

Therefore  number of rotations of the disk is  proportional to the energy consumed by the load in a certain time interval and is measured in kilowatt-hours (Kwh).

Breaking system:

To damp aluminium disc we keep a small permanent magnet diametrically opposite to both the ac magnets(parallel,series). Now this disc moves in the magnet field crossing air gap. When this happens eddy currents are induced in aluminium disc which interacts with the magnetic field and produces breaking torque.

The speed of the rotating disc can be controlled by changing the position of the brake magnet or diverting some of the flux. 

Counting system:

It has a gear system to which pointer is attached. This is connected to aluminium disc which drives this pointer. This pointer moves on the dial and gives number of times the is disc rotated.

These can be seen in the diagram given below:

A 3-phase induction motor has same four systems but they are arranged in a different way as shown in the figure given below.

This is a two element 3-phase energy meter. On a common spindle two discs are mounted and each disc has its own break magnet. Moving system drives a gear  Each unit is provided with its own copper shading ring, shading band, friction compensator, etc., to make adjustments for obtaining correct reading.

This gives construction of a 3 phase energy meter.

Working of three phase energy meter:

Now let us see how a 3 phase energy meter works.

For same power/energy the driving torque should be equal in both elements. For adjusting torque in both the elements we have two current coils connected in phase opposition and two potential coils connected in parallel. Full load current passes through current coil and this arrangement causes two torques to be in opposition and the disc doesn't move if torques are equal. Magnetic shunt is adjusted if there is inequality in torques to make the disc to stand still. Before testing a 3 phase energy meter torque balance is obtained in this way. 

            

                  Aluminium discs are acted upon by the two coils one is voltage coil and the other is current coil. Voltage coil produces magnetic flux proportional to voltage and current coil produces magnetic flux proportional to current. The voltage coil field lags by 90 degrees by using a lag coil.

                     Due to this two torques eddy currents are produced in the aluminium discs and discs rotate on a common shaft. Force exerted on the aluminium disc is proportional to product of instantaneous current and voltage. To this shaft a gear arrangement is made and a needle is attached to this gear so when discs rotates this needle moves on dial and counts the number of rotations of the disc.

                    A permanent magnet is used to produce a force in opposition and proportional to the speed of disc. When power is switched off this acts as break and makes the disc to stop rotating instead of rotating faster. Disc rotates at a speed proportional to power consumed.

Instantaneous power can be calculated by using below formula

Pi = (3600 * N) / (T * R)

where

Pi = Real power being used at that point in time in kW

T = Time (in seconds) for the disc to rotate through the N rotations or part of a rotation

N = The Number of full rotations counted.  

R = The number of revolutions per Kilowatt hour (rev/kWh) of the meter being used. 

In this way we use a three phase energy meter to calculate the energy consumed by the load.

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January 29, 2017 at 07:38PM by EEE, ADBU

HRC Fuse Operation,Types And Characteristics

Operation,Types And Characteristics Of HRC Fuse

Fuse is a common switch gear device which we see even at our homes. It is used to protect a device or circuit from over currents.  For household purpose usage of HRC fuse is more economical than usage of circuit breakers. Let see a clear picture about what is fuse? , how a fuse works?

What Is Meant By HRC Fuse?

HRC fuse means high rupturing capacity fuse which is a modern type fuse. It interrupts current flow and protects from over current.  It is used to provide protection from short circuit damages in low voltages and medium level voltages.

Construction Of HRC Fuse:

The body of HRC fuse is made of ceramic which is highly heat resistant. It has two end caps to this caps a silver current carrying element is welded. The internal space of fuse is filled with powder material such as plaster of paris, marble, chalk, cooling media etc. as shown in the following diagram.

The above diagram shows the cross-sectional diagram of a HRC fuse.

Working Of HRC Fuse:

The fuse wire inside the HRC fuse conducts the short circuit current for a period of time safely. During this time if the fault is removed the fuse doesn't blow off. But if the fault is not removed the fuse will melt and isolates the circuit from the electrical supply as shown in the below figure.

This is how a fuse works

Controlling Of Arc In HRC Fuse:

The inner portion of HRC fuse consists of cooling medium which helps to carry normal current by the fuse wire without heating. When over current flows then heat is produced in the current carrying fuse wire because of high I2Rf loss. This heat vaporizes the silver metal element and a chemical reaction takes place between this silver metal and filling powder which produces a high resistance substance. This high resistance substance helps in arc quenching.

Characteristics Of HRC Fuse:

As discussed for normal current the fuse wire doesn't melt but when over current flows due to high I2Rf loss the fuse wire melts.So fuse wire melts faster for higher fault currents and takes more time to melt for lower fault currents. This gives the time-current characteristics of HRC fuse. This is shown in the following figure.

Types Of HRC Fuse:

We have different types of HRC fuse. They are:

1.Semi- enclosed or rewireble type.

2.Totally enclosed or cartridge type.  

3. Current limiting fuse link. 

4. Drop-out fuse.

5. Explosion fuse.

6. Striker fuse.

7. Switch fuse.

Now let us see each of them in detail.

1. Semi- enclosed Or Rewireble Type Fuse:

In this type of fuse the carrier of fuse can be pulled out and the melted fuse wire can be replaced with the new wire. Carrier has to be replaced in the fuse base. This type of fuse is used in our houses. Its diagram is shown below.

2. Totally Enclosed Or Cartridge Type Fuse:

In this type we have a fuse wire inside a totally closed container and it has metal contacts on either sides. This is further divided into two types.

1. Bolted type 2. D-type.

The above diagram is cartridge type fuse. 

3. Current Limiting Fuse Link:

This fuse link brings the current to a value lower than a prospective value.

4. Drop Out Fuse:

After fault current flows,fuse-carrier drops out. Now there will be isolation between the terminals. This diagram is shown below.

5. Explosion Fuse:

In this type of fuse the arc is quenched when produced arc produces heat which vaporizes the metal and chemical reaction is established between this vapors and powdered filling. This produces a high resistance substance which helps the produced arc to quench.

6. Striker Fuse:

This type of fuse consists of combination of a fuse and a mechanical device. This fuse releases a striker after fuse operation with a certain displacement and pressure. The following figure shows diagram of striker fuse before and after fuse operation.

7. Switch Fuse:

This is a fuse which contains both switch and fuse. This is shown in following figure.

                                            

In this post we have discussed about the operation, types and characteristics of HRC fuse.

January 29, 2017 at 07:36PM by EEE, ADBU

Differences between electrical degree and mechanical degree

Differences between electrical degree and mechanical degree

Many people get confused about what is electrical degree and mechanical degree. Well, to get a clear idea about this we have provided the following post.

We consider an alternator with two poles once and four poles once to clearly understand about electrical degree and mechanical degree.An alternator consists of conductors on stator and poles on rotor. But for understanding purpose we consider conductors are rotating and poles are stationary. Because of relative motion between conductors and poles emf is induced inside the conductor.

Two pole alternator:

Consider a two pole alternator with a conductor as shown in the following figure.

Position 1 :At this point velocity vector V is parallel to magnetic flux lines of poles(indicated by dotted line). So at this position conductors do not cut the flux lines, there will not be change in flux so emf induced inside the conductor is zero.

Position 2: Now conductor rotates to position 2.Velocity vector V is perpendicular to magnetic flux lines of poles. So at this position maximum amount of flux is cut by conductors, there will be maximum amount of change in flux so emf induced is maximum at this point.

Position 3: Now conductor rotates to position 3.At this point velocity vector V is parallel to magnetic flux lines of poles.So at this position conductors do not cut the flux lines, there will not be change in flux so emf induced inside the conductor is zero.

Position 4: Now conductor rotates to position 4.Velocity vector V is perpendicular to magnetic flux lines of poles. So at this position maximum amount of flux is cut by conductors, there will be maximum amount of change in flux so emf induced is maximum at this point.

So for one complete rotation of a conductor i.e, 360 degrees there will be two maximum positions of emf this is indicated in the following figure.

Induced emf inside the alternator is sinusoidal in nature.Two maximum peaks is 360 degrees.Conductor rotation angle is mechanical degree and emf wave cycle degree for one complete rotation of conductor gives electrical degree.

Here mechanical degree is equal to electrical degree which is 360 degrees. Since for one complete rotation of conductor one complete emf cycle is produced.

Four pole alternator:

Consider a four pole alternator with a conductor as shown in the following figure.

Position 1 :At this point velocity vector V is parallel to magnetic flux lines of poles(indicated by dotted line). So at this position conductors do not cut the flux lines, there will not be change in flux so emf induced inside the conductor is zero.

Position 2: Now conductor rotates to position 2.Velocity vector V is perpendicular to magnetic flux lines of poles. So at this position maximum amount of flux is cut by conductors, there will be maximum amount of change in flux so emf induced is maximum at this point.

Position 3: Now conductor rotates to position 3.At this point velocity vector V is parallel to magnetic flux lines of poles.So at this position conductors do not cut the flux lines, there will not be change in flux so emf induced inside the conductor is zero.

Position 4: Now conductor rotates to position 4.Velocity vector V is perpendicular to magnetic flux lines of poles. So at this position maximum amount of flux is cut by conductors, there will be maximum amount of change in flux so emf induced is maximum at this point.

Position 5: Now conductor rotates to position 5.At this point velocity vector V is parallel to magnetic flux lines of poles.So at this position conductors do not cut the flux lines, there will not be change in flux so emf induced inside the conductor is zero.

Position 6: Now conductor rotates to position 6.Velocity vector V is perpendicular to magnetic flux lines of poles. So at this position maximum amount of flux is cut by conductors, there will be maximum amount of change in flux so emf induced is maximum at this point.

Position 7: Now conductor rotates to position 7.At this point velocity vector V is parallel to magnetic flux lines of poles.So at this position conductors do not cut the flux lines, there will not be change in flux so emf induced inside the conductor is zero.

Position 8: Now conductor rotates to position 8.Velocity vector V is perpendicular to magnetic flux lines of poles. So at this position maximum amount of flux is cut by conductors, there will be maximum amount of change in flux so emf induced is maximum at this point.

So for one complete rotation of a conductor i.e, 360 degrees there will be four maximum positions of emf this is indicated in the following figure.

°

Induced emf inside the alternator is sinusoidal in nature.Four maximum peaks is 720 degrees.Conductor rotation angle is mechanical degree and emf wave cycle degree for one complete rotation of conductor gives electrical degree.

Here mechanical degree is 360 degrees and electrical degree is 720 degrees.  Since for one complete rotation of conductor two complete emf cycles are produced.

This says that electrical degree depends on number poles inside the alternator. Now we can obtain relation between mechanical degree and electrical degree as

360° mechanical = 360° ✕ P/2 electrical

P = number of poles

1° mechanical = (P/2)° electrical.

In this post we have discussed about difference between mechanical degree and electrical degree.

To download this post on difference between mechanical degree and electrical degree as PDF click here.

January 29, 2017 at 04:16PM by EEE, ADBU

Generation of electrical energy

GENERATION OF ELECTRICAL ENERGY

Energy exists in different forms in nature but the most important form is the electrical energy.Now a days usage of electricity is very high it has become a basic need for everyone. 

Why electrical energy why not other energy sources?

Well, the simple answer to this is the modern technology has developed in such a way that electrical energy can be easily converted into all other energy forms. It also has other advantages  as mentioned below.

1.Greater flexibility: As it can be easily transported with the help of conductors from one place to other it has great flexibility.

2.Convenient : As it can be easily converted into other forms of energy it is very convenient form.  If we take the example of converting electrical energy into heat energy  all we need to do is just pass electricity through a resistor then electrical energy converts o heat energy. Similarly, all the others forms of energy like light,mechanical etc can be obtained easily from electrical energy.

3.Cheapness: When compared to other forms of energy electrical energy is much cheaper . Thus it is  economical to use for any purpose.

4.Cleanliness: Electrical energy doesn't produce  smoke,ash or poisonous  gases. So it maintains cleanliness.

5.Easy control: The electrically operated machines can be controlled easily by switching on or off the switch. For example we can turn off or on the fan by switching off or switching on the switch. And speed can also be easily controlled for example speed of fan can be adjusted by using a regulator. So it is easy to control.

6.High transmission efficiency:  Consumers of electrical energy are located away from the electricity generation stations generally.But with the help of over head line conductors and by using transformers and few other equipment's electricity can be supplied efficiently with less amount of losses.

The above mentioned advantages made usage of electrical energy popular than other energy forms.

Generation of electrical energy:

Converting  different forms of energy that are present in nature into electrical energy is known as generation of electrical energy.

To get the basic idea of generation of electrical energy observe the following figure. 

Energy from any of the sources like heat, wind, hydro, fossil etc can be given as input to the prime mover. For example take hydro energy, Water at certain head  when falls on the prime mover which is a rotating part rotates the prime mover in this way the potential energy exerted on it is converted to mechanical energy. This prime mover drives generator and the generator converts mechanical energy to electrical energy.

Sources of energy:

1. Fuels: Fuels like  coal,  oil and natural gas are the main sources of energy. The heat energy produced  by these fuels is converted into mechanical energy by certain type of  prime movers like steam engines, steam turbines etc. The prime mover drives the alternator which converts mechanical energy into electrical energy. Although these fuels play main role in the electrical energy production now a days we need to see other alternatives as there quantity is diminishing due to increase in the usage of electrical energy. The alternative to them is renewable energy sources likes solar, wind, hydel.

2.Solar energy:  Sun is the major source of energy. Electrical energy can be produced from sun by focusing the heat energy produced  by sun on reflectors and heating water which produces steam which in turn rotates the turbine which is coupled to the generator and this generator converts mechanical energy to electrical energy. As it has limitations like availability of solar energy is not possible all the time it can be used as alternative wherever other sources of energy are not available abundantly.

3.Water:  When water present at certain head falls down on turbine the potential energy possessed by water is converted into mechanical energy by a water turbine. This turbine drives the generator which converts mechanical energy to electrical energy.

4. Wind: To generate electrical energy from wind energy a wind mill is established. This runs the generator which produces electrical energy. Wind mills are generally placed at hilly areas.It is cheaper way to generate electrical energy.

5.Nuclear energy: Very large amount of heat can produced by nuclear fuels like uranium. This heat energy is utilized to produce steam. This stem rotates the steam turbine and runs the generator which can produce electrical energy.

This helps you to understand the basics of generation of electrical energy from different power plants.  

Efficiency:

Some energy is lost i.e converted to other form of energy other than electrical energy  while converting any input energy to output electrical energy. Efficiency gives you how efficiently the input energy given is converted to output electrical energy. Efficiency is generally calculated in percentage.

Efficiency of power plant =  output energy / input energy = output power / input power.

Power is rate of flow of energy.

In this post we have learnt about electrical energy importance and generation of electrical energy from different power plants.

To download this post on generation of electrical energy as PDF click here

January 28, 2017 at 01:46PM by EEE, ADBU

Electrical Machinery [ Electrical Machines ] By Ps Bimbhra Pdf Download

You all know we recently launched free electrical engineering pdf books to all. In this post we are sharing a very good book on electrical machines by ps bimbra , he is a very good author of so many electrical engineering books some of them are mentioned below,

1. Electrical Machinery by ps bimbhra

2. Power electronics by ps bimbhra

3. Generalised theory of electrical machines by ps bimbhra

Electrical Machines PS Bimbhra  PDF Free Download 

User Ratings: *****A Lecturer - Abhishek TiwariI have referred to this for many topics in Electrical Machines. This books gives a detailed explanation of design and working of electrical machines. It a good book to refer for undergraduate students.

Electrical machinery ps bimbhra will cost us around Rs.400 /- in india. To provide this book for students who can't afford we are sharing  "electrical machinery by ps bimbhra".you can download this pdf directly into your computer or mobile phone easily.You need to have any pdf reader to read this book.

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January 17, 2017 at 05:41PM by EEE, ADBU

Welding Transformer Working Principle and Applications

Welding Transformer Working Principle and Applications 

Now a days we have many ac power supplies. So the usage of welding transformer has significant role in welding compared to a motor generator set. When we need to use a motor generator set for welding we need to run it continuously which produces a lot of noise. With the help of welding transformer weld is done with a less noise. Now let us see in detail about welding transformer.

Construction of welding transformer:

1. Welding transformer is a step down transformer.

2. It has a magnetic core with primary winding which is thin and has large number of turns on one arm.

3. A secondary winding with less number of turns and high cross-sectional area on the other arm.

4. Due to this type of windings in primary and secondary it behaves as step down transformer.

5. So we get less voltage and high current from the secondary winding output. This is the construction of ac welding transformer. 

6.A dc welding transformer also has same type of winding the only difference is that we connect a rectifier(which converts ac to dc) at the secondary to get dc output. 

7.We also connect a inductor or filter to smooth the dc current. This will be construction of dc welding transformer. The diagrams are shown below.

Fig 1.DC welding transformer

Fig 2.AC welding transformer

Note:

Many people have a doubt which is primary winding and which is secondary winding. The winding which is connected to power supply is called primary winding and the winding to which load is connected is called secondary winding.

Working of welding transformer:

1.As it is a step down transformer we have less voltage at secondary which is nearly 15 to 45 volts and has high current values which is nearly 200 A to 600 A it can also be higher than this value.

2. For adjusting the voltage on secondary side there are tappings on secondary winding by this we can get required amount of secondary current for welding.

3. These tappings are connected to several high current switches.

4. Now one end of secondary winding is connected to the welding electrode and the other end is connected to the welding pieces as shown in fig 2. 

5.When a high current flows a large amount of  I2R heat is produced due to contact resistance between welding pieces and electrode. 

6.Because of this high heat the tip of electrode melts and fills the gap between the welding pieces.

This is how a welding transformer works.

Volt - ampere characteristics of welding transformer:

Figure given below shows the volt - ampere characteristics of welding transformer.

Arc control of welding transformer:

The impedance of welding transformer must be higher than the normal transformer to control arc and also to control current. 

We can use different reactors for controlling the arc. They are

1.Tapped reactor.

2.Moving coil reactor.

3.Magnetic shunt reactor.

4. Continuously variable reactor.

5. Saturable Reactor.

Now let us see each of this methods for arc control of welding transformer in detail.

1.Tapped reactor:

Below is the circuit for arc control using tapped reactor is given below.

  

With the help of taps we control the current. It has limited current control.

2. Moving coil reactor:

Below is the circuit for arc control using moving coil reactor.

The distance between primary and secondary decides the amount of current. If the distance between the primary and secondary is high then the current is less.

3. Magnetic shunt reactor:

Below is the circuit for arc control using magnetic shunt reactor.

By adjusting the central magnetic shunt flux is changed. By changing the flux current can be changed.

4. Continuously variable reactor:

Below is the circuit for arc control using continuously variable reactor.

By varying the height of reactor core insertion is changed. If core insertion is greater reactance is higher so output current will be less.

5. Saturable reactor:

Below is the circuit for arc control using saturable reactor.

The reactance of the reactor in this is adjusted by changing the value of d.c. excitation which is obtained from d.c. controlled transducer. Higher the d.c. currents, reactor approaches to saturation. This changes the reactance of reactor. By changing the reactance current can be changed.

By using above reactors current can be controlled which helps to control the arc.

In this post we have learnt about welding transformers.

To download this post on welding transformers as PDF click here.

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January 12, 2017 at 08:07PM by EEE, ADBU

Operational Amplifier as Integrator and Differentiator/OP Amp Differences between Integrator and Differentiator

Operational amplifier as integrator and differentiator

Operational amplifier which is called also called as op-amp has a key role in many electronic applications due to its special characteristics. Name itself indicates that it can perform operations. By using op-amp we can perform different operations like addition, subtraction, multiplication, differentiation and integration. Of these op-amp application as integrator and differentiator is very common.

                  Before going to see op-amp as integrator and differentiator let us first understand working principle of operational amplifier.

Operational amplifier working principle:

Let us see the symbol of operational amplifier and its terminals before going to see working of op-amp.

It has two input terminals one is marked negative and other as positive and one output terminal. The input terminal which is marked negative is called inverting input because when we apply an input signal to this inverting input we get a phase shift of 180° in the amplified output signal with respect to the applied input signal. The input terminal which is marked positive is called Non-inverting input because when we apply an input signal to this Non-inverting input there is no phase shift between input signal and amplified output signal.

                             It has two input power supply terminals +Vs and -Vs. +Vs is connected to positive terminal of battery and -Vs is connected to negative terminal of other battery. If we require a ground we need to provide ground separately as there is no common ground provided in op-amp.

Open loop operation of op-amp:

In this open loop operation we apply two input signals one at inverting input and other at Non-inverting input as shown in the figure.

 So it has differential input(since one is + and other is -) which means difference of two applied input signals and one output is obtained. The gain of open loop operation of op-amp is given by

Gain = output / input

Aol = Vo / V1 - V2

so output voltage is

Vo is output voltage

V1 is voltage at non-inverting terminal 

V2 is voltage at inverting terminal 

V1 - V2 is differential input voltage

Aol is open loop gain

Open loop gain is very high even a small signal given at input amplifies to large amount but its value will not exceed the supply voltage of op-amp as it obeys law of conservation of energy.

Closed loop operation of op-amp:

If we introduce a feed back in the circuit it is called closed loop operation. Here a part of output signal is fed back to one of the input terminals. The terminal where feed back is given two signals are present simultaneously one is feed back signal and the other is original applied signal it can be seen in the following diagram.

If we apply feed back signal from output to non-inverting terminal it is called positive feed back which is used in oscillator circuits. And if we apply feed back signal from output to inverting terminal it is called negative feedback here phase shift is present between applied signal and feed back signal. This negative feed back is used for amplifier circuits. Closed loop gain of op-amp is given by

Acl = Vo / V1 - V2

 Now output voltage will be

where Vd = V1 - V2.

Acl = closed loop gain.

As we have learnt operation of op-amp now we can clearly understand the application of op-amp as differentiator and integrator.

Op-amp as integrator:

When an operational amplifier work as integrator we get output as integration of voltage with respect to time. Here we use capacitors at a right place in the circuit which helps to perform integration of applied input voltage. The arrangement can be seen from the following diagram.

                           

The above circuit is called an ideal op-amp integrator circuit.

Here the negative feed back is taken and a capacitor is connected between output terminal and inverting input terminal. Because of negative feedback node X is at virtual ground and if the input voltage is 0 V then no current flows through input resistance Rin then the capacitor will remain uncharged. So we get output as 0 V.

                          Now if we apply a constant positive DC voltage at the input then  we get a linearly falling voltage at output. If we apply a constant negative DC voltage at input then we get a linearly raising voltage at output. And this rate of change of output voltage will be directly proportional to input voltage. 

Output voltage calculation:

Now we calculate the output voltage of this circuit.

According to virtual ground concept as non-inverting terminal is grounded then node X will also be at ground potential

                                                            VX = VY = 0

For an ideal op-amp input impedance is high so input current is very less and the current flowing through resistor R1 also flows through capacitor C.

Input current equation is given by,

I = (Vin – VX) / R1 

I = Vin / R1.

output current equation is given by

I = C [d(VX – Vout)/dt] = -Cf[d(Vout)/dt]

Now we equate both current equations as current flowing through resistance R1 (input) and capacitor C (output) are same(since op-amp has high input impedance all current flows through capacitor). We get,

                                         [Vin / R1] = – C [d(Vout)/dt]

Apply integration on both sides, now we get,

The above equation clearly says that output voltage is - 1 / R1 . C times the integration of input voltage. This shows that op-amp acts as an integrator by this circuit arrangement. Here R1.C is called integrator time constant and negative sign shows that there is a phase shift of 180° between input and output voltage. The phase shift is because we have applied signal to inverting terminal.

                        We use integrator circuit to convert a square wave input to triangular wave output as shown in the following circuit.

As discussed when we apply constant positive dc voltage we get a falling output voltage at linear rate and if we apply constant negative dc voltage we get a rising output voltage at linear rate(if a step signal is integrated we get ramp signal).

An integrator op-amp circuit acts as low pass filter it attenuates high frequency signals.

OP-amp as differentiator:

A differential op-amp has output voltage which is proportional to rate of change of input voltage. This op-amp can act as differentiator by keeping a capacitor in series with the input voltage source. This can be seen from the diagram given below 

The capacitor acts as open circuit for dc input. Here we ground the non-inverting terminal of op-amp and the inverting input terminal is connected to output through a feed back resistor Rf. This makes the circuit to behave as voltage follower. The input current to op-amp is very less due to high input impedance of op-amp we have same current through capacitor and resistor Rf.

Output voltage calculation:

Now we calculate the output voltage of this circuit.

According to virtual ground concept as non-inverting terminal is grounded then node X will also be at ground potential

                                                            VX = VY = 0

Input current is given by,

                            I = C [d(Vin-Vx)/dt] = C [d(Vin)/dt]

output current is given by,

                            I = -{(Vout-Vx)/Rf} = -{Vout/Rf}

 Now we equate both equations as current through capacitor and resistor are same.

                            C{d(Vin)/dt} = -Vout/Rf

                            Vout = -C.Rf {d(Vin)/dt 

The above equation clearly says that output voltage is - C.Rf  times the differentiation of input voltage. This shows that op-amp acts as adifferentiator by this circuit arrangement.     Here    Rf.C is called differentiator time constant and negative sign shows that there is a phase shift of 180° between input and output voltage. The phase shift is because we have applied signal to inverting terminal.

                Here if we give a square wave input to differentiator the output has to be zero( since differentiation of constant is zero) but we get negative and positive spikes because input signal takes time to change from 0 to Vm. At constant positive DC input we get negative spike at output and at constant negative DC input we get positive spike at output. This can be seen from the following diagram.

 If we give a sin wave as input to differentiator we get cos wave as output.

                              Vout = -C.Rf {d(Vm sin ωt)/dt}

                               Vout = – Vm. ω. cos ωt consider(C.Rf = 1)

This can be seen in the following diagram

A differential op-amp circuit acts as high pass filter it attenuates low frequency signals.

In this post we have learnt op- amp as integrator and op-amp as differentiator.

To download this post on operational amplifier as integrator and differentiator as PDF clik here

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January 12, 2017 at 08:05PM by EEE, ADBU

Conversion from binary code to gray code and gray code to binary code

Conversion from binary code to gray code and gray code to binary code

 In this post let us see conversion from binary code to gray code and gray code to binary code.

Purpose for converting binary code to gray code?

Gray code has occupied a prominent role now-a-days because of its special characteristics. It is, there is change in only one bit for two successive values. This gray code is widely used for error correction in digital communications.

Steps to convert from binary code to gray code:

Let us consider an example to clearly understand the conversion from binary code to gray code

Consider binary code = 1110

Now represent this binary code as b3 b2 b1 b0 = 1 1 1 0

Let the representation of this binary code in gray code be g3 g2 g1 g0

Here b3, g3 are called most significant bits(MSB) and b0,g0 are called least significant bits(LSB).

Step 1: The most significant bit(MSB) of gray code is equal to most significant(MSB) bit of binary code.

In this example g3 = b3 = 1.

Step 2: Now the second most significant bit i.e,which is adjacent to most significant bit(MSB) in the gray code is equal to the sum of most significant bit(MSB) and second most significant bit of binary code. If addition produces any carry ignore the carry.

Note:

Carry is produced when we add two 1's i.e, 1 + 1 = 0, 1 is carry( from Boolean algebra) 

In the following example

g2 = b3 + b2

g2 = 1 + 1 = 0, carry 1 is neglected.

Step 3: The third most significant bit of gray code i.e, which is adjacent to the second most significant bit in the gray code is equal to the sum of second most significant bit and third most significant bit of binary code. If any carry is generated ignore it.

In the considered example:

g1 = b2 +b1

g1 = 1 + 1 = 0, carry 1 is neglected.

Step 4: The above process is continued until the least significant bit(LSB) of gray code is obtained. This least significant bit (LSB) of gray code is obtained by adding last most significant bit and the least significant bit of binary code.If any carry is produced that has to be neglected.

In the following example we have,

g0 = b1 + b0.

g0 = 1 + 0 = 1.

So finally we get the gray code as g3 g2 g1 g0 = 1 0 0 1

Diagrammatically conversion from binary code to gray code  can be represented as follows,

Example can be represented diagrammatically as follows,

 Hence by following above steps conversion from binary code to gray code is done.

Steps to convert from binary code to gray code:

Let us consider an example to clearly understand the conversion from gray code to binary code. 

Consider gray code = 1001.

Now represent this gray code as g3 g2 g1 g0 = 1 0 0 1.

Let the representation of this gray code in binary code be b3 b2 b1 b0.

Here b3, g3 are called most significant bits(MSB) and b0,g0 are called least significant bits(LSB).

Step 1: The most significant bit(MSB) of binary code is equal to most significant(MSB) bit of gray code.

In the example,

b3 = g3 = 1.

Step 2: Now the second most significant bit i.e,which is adjacent to most significant bit(MSB) in the binary code is equal to the sum of most significant bit(MSB) of binary code( It is obtained from step 1) and second most significant bit of gray code. If addition produces any carry ignore the carry.

In this example,

b2 = b3 + g2.

b2 = 1 + 0 = 1.

Step 3: The third most significant bit of binary code i.e, which is adjacent to the second most significant bit in the binary code is equal to the sum of second most significant bit of binary code(It is obtained from step 2)and third most significant bit of gray code. If any carry is generated ignore it.

In the considered example,

b1 = b2 + g1.

b1 = 1 + 0 = 1.

Step 4: The above process is continued until the least significant bit(LSB) of binary code is obtained. This least significant bit (LSB) of binary code is obtained by adding last most significant bit of binary code and the least significant bit of gray code. If any carry is produced that has to be neglected.

In this example,

b0 = b1 + g0.

b0 = 1 + 1 = 0, 1 is carry it is neglected.

So finally we get the binary code as b3 b2 b1 b0 = 1 1 1 0.

Diagrammatically conversion from gray code to binary code can be represented as follows,

Example can be represented diagrammatically as follows,

Hence by following above steps conversion from  gray code to binary code is done.

Today in this post we have learnt conversion from binary code to gray code and gray code to binary code.

This post on conversion from binary code to gray code and gray code to binary code can be downloaded as PDF here.

January 11, 2017 at 06:36PM by EEE, ADBU