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Schmitt trigger Comparator and Oscillator | Astable and Bistable Multivibrator | Important analysis

In this article we will study about the Schmitt trigger Comparator and Oscillator circuitry with different related parameters in detail. As we have seen till now that an op-amp is used in various fields of applications and being such a versatile device its importance as a part of analog circuits is immense. One of the most convenient applications of the op-amp is as a multivibrator circuit. We will be studying in detail about types and working of multivibrator circuit constructed using op-amps (op-amp multivibrators) and other passive devices such as capacitors, diodes, resistors etc.


  • Introduction of Multivibrators
  • Positive feedback usage in multivibrator
  • What is Schmitt trigger ?
  • Schmitt trigger comparator closed-loop circuit or bistable multivibrator
  • Voltage transfer characteristics of Bistable multivibrator
  • Astable multivibrator or Schmitt trigger oscillator
  • Oscillator’s duty cycle

Introduction of Multivibrator and Schmitt trigger Circuitry

Multivibrator circuits are sequential logic circuits and are of many types depending on how they are created. Some multivibrators can be made using transistors and logic gates, whereas there are even dedicated chips available as multivibrators such as NE555 timer. The op-amp multivibrator circuit has a few advantages over other multivibrator circuits as they require much fewer components for their working, less biasing, and produces better symmetrical rectangular wave signals using comparatively fewer components.

Types of Multivibrators

There are mainly three types of multivibrator circuits present:

  1. Astable multivibrator,
  2. Monostable multivibrator
  3. Bistable multivibrator.

The monostable multivibrator has single stable state, whereas the number of stable-states a bistable multivibrator has- is 2.

As we have learnt in the previous section about op-amp as a comparator, in the open-loop configuration the comparator can switch in an out of control manner between the positive saturation supply rail voltage and negative saturation supply rail voltage when an input voltage near to that of the reference voltage is applied. Hence, to have control on this uncontrollable switching between the two states, the op-amp is used in a feedback configuration (closed-loop circuit) which is particularly known as closed-loop Schmitt trigger circuit or bistable multivibrator.

Positive feedback usage in multivibrator and hysteresis effect

Till now, we have learnt about the negative feedback configuration in op-amps in the previous sections. There is also another type of feedback configuration known as positive feedback, which is also used for specific applications. In positive feedback configuration, the output voltage is fed back (connected) to the non-inverting (positive) input terminal unlike the negative feedback, where the output voltage was connected to the inverting (negative) input terminal.

An op-amp operated in a positive feedback configuration tends to stay in that particular output state in which it is present, i.e. either the saturated positive or saturated negative state. Technically, this latching behaviour in one of the two states is known as hysteresis.

If the input applied signal in the comparator consists of some additional harmonics or spikes (noise), then the output of the comparator might switch to the two saturated states unexpectedly and uncontrollably. In this case, we won’t get a regular symmetrical square wave output of the applied input sinusoidal waveform.

But if we add some positive feedback to the comparator input signal, i.e. use the comparator in a positive feedback configuration; we will be introducing a latching behaviour in the states, what we technically call as hysteresis into the output. Until and unless there is a major change in the magnitude of the input AC (sinusoidal) voltage signal, the hysteresis effect will continue to make the output of the circuit remain in its current state.

What is Schmitt trigger ?

The Schmitt trigger or bi-stable multi-vibrator operates in positive feedback configuration with a loop-gain greater than unity to perform as a bi-stable mode. Voltage V+ can be.

Schmitt trigger comparator
Schmitt trigger comparator or bistable multivibrator
The Voltage transfer characteristics of Schmitt trigger Comparator

The above figure represents the output voltage versus the input voltage curve (which is also known as the voltage transfer characteristics), particularly showing the hysteresis effect. The transfer characteristic curve has two specific regions, the curve as the input voltage increases and the part of the curve in which the input voltage decreases. The voltage V+ does not have a constant value, but instead, it is a function of the output voltage V0.

Voltage transfer characteristics

In the voltage transfer characteristics, V= VH, or in high state. Then,

Higher Cross-over voltage VTH

If signal is less than that of V+, the output stays at its high state. The cross-over voltage VTH occurs when V= V+ and expressed as follows:

When Vi > VTH, the voltage at the inverting terminal is more than at the non-inverting terminal. Voltage V+ then turn out to be

Lower Cross-over voltage VTL

Since V< VH the input voltage Vi is still more than V+, and the output rests in its low state as Vi carry on to increase; If Vi decreases, as long as the input voltage Vi is larger than V+, the output remains at saturation state. The cross-over voltage here and now occurs when V= V+ and this VTL expressed as

As Vi continues to decrease, it remains less than V+; therefore, V0 remains in its high state. We can observe this transfer characteristic in the above figure. A hysteresis effect is shown in the net transfer characteristic diagram.

What is Schmitt trigger oscillator ?

Astable multivibrator or Schmitt trigger oscillator

Astable multivibrator accomplished by fixing an RC network to the Schmitt trigger circuit in –ve feedback. As we will advance through the section, we will see that the circuit has no stable states and therefore, it also known as the astable multivibrator circuit.

Astable Multivibrator circuit or Schmitt trigger Oscillator

As noticed in the figure, an RC network is set in the negative feedback path, and the inverting input terminal is connected to the ground through the capacitor while the non-inverting terminal is connected to the junction between the resistors R1 and R2 as shown in the figure.

At first, R1 and R2 is to be equal to R, and assume the output switches symmetrically about zero volts, with the high saturated output represented by V= VP and low saturated output indicated by V= -VP. If Vis low, or V= -VP, then V+ = -(1/2)VP.

When Vx drops just slightly below V+, the output switches to high so that V= +VP and V= +(1/2)VP. The equation for the voltage across the capacitor in an RC network can be expressed as:

Where τx is the time constant which can be defined asτx= RxCx. The voltage Vx increases towards a final voltage VP in an exponential manner with respect to time. However, when Vx turn out to be slightly greater than V= +(1/2)VP, the output shifts to its low state of V0 = -VP and Vx = -(1/2)VP. The RxCx network gets triggered by a negative sharp transition of the voltages, and hence, the capacitor Cx start discharging, and the voltage Vx decreasing towards value of –VP. We can therefore express Vas

Where t1 refers to the time instant when the output of the circuit switches to its low state. The capacitor discharge exponentially V+ = -(1/2)VP, the output again shifts to high. The process repeats itself continuously over time, which means a square-wave output signal is produced by the oscillations of this positive feedback circuit. The figure below shows the output voltage V0 and the capacitor voltage Vx with respect to time.

The Schmitt Trigger Oscillator: Plot of Output voltage and Capacitor Voltage with respect to time

Time t1 can be found by substituting t=t1 and Vx = VP/2 in the general equation for the voltage across the capacitor.

From the above equation when we solve for t1, we get

For time t2 (as observed in the above figure), we approach in a similar way, and, from a similar analysis using the above equation, it is evident that the difference between t2 and t1 is also 1.1RxCx. From this, we can infer that the time period of oscillation T can be defined as T = 2.2 RxCx

And the frequency thus can be expressed as  


Duty cycle of Oscillator

The percentage of time the output voltage (V0) of the multi-vibrator is in its high state is particularly termed as the duty cycle of the oscillator.

The oscillator’s duty cycle is           

As observed in the figure, depicting output voltage and capacitor voltage versus time, the duty cycle is 50%.

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Op-Amp as Integrator and Differentiators | It’s Working | 5+ Important Facts


  • What is Integrator?
  • Working principle of Integrator
  • Op-amp integrator circuit
  • Output of an integrator
  • Derivation of Op-amp as integrator
  • Practical op-amp integrator
  • Applications of integrator
  • What is Differentiator ?
  • Op-amp as Differentiator
  • Working Principle of Differentiator
  • Output waveform of a differentiator
  • Applications of Differentiator

What is Integrator?

Definition of Integrator

If the feedback path is made through a capacitor instead of a resistance , an RC Network has been established across the operational amplifiers’ negative feedback path. This kind of circuit configuration producing helps in implementing mathematical operation, specifically integration, and this operational amplifier circuit is known as an Operational amplifier Integrator circuit.

The output of the circuit is the integration of the applied input voltage with time.

Integrator circuits are basically inverting operational amplifiers (they work in inverting op-amp configuration, with suitable capacitors and resistors), which generally produce a triangular wave output from a square wave input. Hence, they are also used for creating triangular pulses.

Op-amp as Integrator

Working principle of Integrator

Operational amplifiers can be used for mathematical applications such as Integration and Differentiation by implementing specific op-amp configurations.

When the feedback path is made through a capacitor instead of a resistance , an RC Network has been established across the operational amplifiers’ negative feedback path. This kind of circuit configuration producing helps in implementing mathematical operation, specifically integration, and this operational amplifier circuit is known as an Operational amplifier Integrator circuit. The output of the circuit is the integration of the applied input voltage with time.

Op-amp integrator circuit

Op-amp integrator circuit

Output of an integrator

input and output waveform of an integrator

Integrator circuits are basically inverting operational amplifiers (they work in inverting op-amp configuration, with suitable capacitors and resistors), which generally produce a triangular wave output from a square wave input. Hence, they are also used for creating triangular pulses.

The current in the feedback path is involved in the charging and discharging of the capacitor; therefore, the magnitude of the output signal is dependent on the amount of time a voltage is present (applied) at the input terminal of the circuit.

Derivation of Op-amp as integrator

As we know from the virtual ground concept, the voltage at point 1 is 0V. Hence, the capacitor is present between the terminals, one having zero potential and other at potential V0. When a constant voltage is applied at the input, it outcomes in a linearly increasing voltage (positive or negative as per the sign of the input signal) at the output whose rate of change is proportional to the value of the applied input voltage.

From the above circuitry it is observed, V1 = V2 = 0

The input current as:

Due to the op-amp characteristics (the input impedance of the op-amp is infinite) as the input current to the input of an op-amp is ideally zero. Therefore the current passing from the input resistor by applied input voltage Vi has flown along the feedback path into the capacitor C1.

Therefore the current from the output side can also be expressed as:

Equating the above equations we get,

Therefore the op-amp output of this integrator circuit is:

As a consequence the circuit has a gain constant of -1/RC. The negative sign point toward an 180o phase shift.

Practical op-amp as aintegrator

If we apply a sine wave input signal to the integrator, the integrator allows low-frequency signals to pass while attenuates the high frequencies parts of the signal. Hence, it behaves like a low-pass filter rather than an integrator.

The practical integrator still has other limitations too. Unlike ideal op-amps, practical op-amps have a finite open-loop gain, finite input impedance, an input offset voltage, and an input bias current. This deviation from an ideal op-amp can affect working in several ways. For example, if Vin = 0, current passes through the capacitor due to the presence of both output offset voltage and input bias current. This causes the drifting of the output voltage over time till the op-amp saturates. If the input voltage current is zero in case of the ideal op-amp, then no drift should be present, but it is not true for the practical case.

To nullify the effect caused due to the input bias current, we have to modify the circuit such that Rom = R1||RF||RL

In this case, the error voltage will be 

Therefore the same voltage drop appears at both the positive and negative terminals because of the input bias current.

For an ideal op-amp operating in the dc state, the capacitor performs as an open circuit, and hence, the gain of the circuit is infinite. To overcome this, a high resistance value resistor RF is connected in parallel with the capacitor in the feedback path. Because of this, the gain of the circuit is limited to a finite value (effectively small) and hence gets a small voltage error.

practical op-amp integrator
  • VIOS refers to the input offset voltage
  • IBI refers to the input bias current

What is Differentiator ?

Definition of Differentiator

If the input resistance in the inverting terminal is replaced by a capacitor, an RC Network has been established across the operational amplifiers’ negative feedback path. This kind of circuit configuration helps in implementing differentiation of the input voltage, and this operational amplifier circuit configuration is known as an Operational amplifier differentiator circuit.

An operational amplifier differentiator basically works as a high pass filter and, the amplitude of the output voltage produced by the differentiator is proportionate to the change of the applied input voltage.

Op-amp as a Differentiator

As we have studied earlier in the integrator circuit, op-amps can be used for implementing different mathematical applications. Here we will be studying the differential op-amp configuration in detail. The differentiator amplifier is also used for creating wave shapes and also in frequency modulators.

An operational amplifier differentiator basically works as a high pass filter and, the amplitude of the output voltage produced by the differentiator is proportionate to the change of the applied input voltage.

Working Principle of Differentiator

When the input resistance in the inverting terminal is replaced by a capacitor, an RC Network has been established across the operational amplifiers’ negative feedback path. This kind of circuit configuration helps in implementing differentiation of the input voltage, and this operational amplifier circuit configuration is known as an Operational amplifier differentiator circuit.

In a differentiating op-amp circuit, the output of the circuit is the differentiation of the input voltage applied to the op-amp with respect to time. Therefore the op-amp differentiator works in an inverting amplifier configuration, which causes the output to be 180 degrees out of phase with the input. Differentiating op-amp configuration generally responds to triangular or rectangular input waveforms.

A Differentiator Circuit

Op-amp differentiator circuit

As shown in the figure, a connection of capacitor in series with the input voltage source has been made. The input capacitor C1 is initially uncharged and hence operate as an open-circuit. The non-inverting terminal of the amplifier is connected to the ground, whereas the inverting input terminal is through the negative feedback resistor Rf and connected to output terminal.

Due to the ideal op-amp characteristics (the input impedance of the op-amp is infinite) as the input current, I to the input of an op-amp is ideally zero. Therefore the current flowing through the capacitor (in this configuration, the input resistance is replaced by a capacitor) due to the applied input voltage Vin flows along the feedback path through the feedback resistor Rf.

As observed from the figure, point X is virtually grounded (according to the virtual ground concept) because the non-inverting input terminal is grounded (point Y is at ground potential i.e., 0V).

Consequently, Vx = Vy = 0

With respect to the input side capacitor, the current carrying through the capacitor can be written as:

With respect to the output side feedback resistor, the current flowing through it can be represented as:

From the above equations when we equate the currents in both the results we get,

The differentiating amplifier circuit requires a very small time constant for its application (differentiation), and hence it is one of its main advantages.

The product value C1Rf is known as differentiator’s time constant, and output of the differentiator is C1Rf times the differentiation of Vin signal. The -ve sign in the equation refers that the output is 180o difference in phase with reference to the input.

When we apply a constant voltage with one step change at t=0 like a step signal in the input terminal of the differentiator, the output should be ideally zero as the differentiation of constant is zero. But in practice, the output is not exactly zero because the constant input wave takes some amount of time to step from 0 volts to some Vmax volts. Therefore the output waveform appears to have a spike at time t=0.

Output waveform Containing spike

Therefore for a square wave input, we get something like shown in the below figure,

Output waveform of a differentiator for a square wave input

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What is Log and antilog amplifier ? | It’s Working; Circuits; Important Uses

The operational amplifier circuit configurations which can perform mathematical operations such as log and antilog (exponential), including an amplification of the input signal provided to the circuit, are known as Logarithmic amplifier and Antilogarithmic amplifier respectively. In this section, we are going to learn about the Logarithmic amplifier and Antilog in detail.


  • Introduction
  • Logarithmic (Log) Amplifier
  • Log amplifier configuration
  • Diode based Log amplifier configuration
  • Transistor based Log amplifier configuration
  • Output and Working Principle of Log Amplifier
  • Applications of the log amplifier
  • What is Antilog?
  • Antilog Amplifier
  • Log amplifier configuration
  • Diode based antilog amplifier configuration
  • Transistor based antilog amplifier configuration
  • Output and Working Principle of Log Amplifier
  • Applications of the antilog amplifier

Logarithm (Log) Amplifier

An operational amplifier in which the output voltage of the amplifier (V0) is directly proportional to the natural logarithm of the input voltage (Vi) is known as a logarithmic amplifier. Basically, the natural logarithm of the input voltage is multiplied by a constant value and produced as output.

Log Amplifier Circuit

Log Amplifier Using Transistor

Log amplifier
Log amplifier using Transistor

Log Amplifier using Diode

Log amplifier
Log amplifier using Diode

Output and Working Principle of Log Amplifier

This can be expressed as follows:

Where K is the constant term, and Vref refers to a normalization constant, which we get to know in this section.

Generally, logarithm amplifiers may require more than one op-amp, in which case they are known as compensated logarithm amplifiers. They even require high performing op-amps for their proper functioning, such as LM1458, LM771, and LM714, are being some of the widely used logarithm amplifier.

The diode is connected in forward biasing. So, the diode current can be represented as:

Where Is is the saturation current, VD is the voltage drop for the diode. The  VT is the thermal voltage. The diode current can be rewritten with high biasing condition,

The i1 expressed by,

Since the voltage at inverting terminal of the op-amp is at virtual ground, hence, the output voltage is given by V= -VD

Noting that i= iD, we can write

But, as noted earlier, VD = -V0 and so,

Taking natural logarithm on both sides of this equation, we found



The equation of the output voltage (V0) of the logarithm amplifier contains a negative sign, which indicates that there is a phase difference of 180 o. Or, 


A more advanced one utilize bipolar transistors to remove Is in the logarithmic term. In this type of logarithm amplifier configuration, the output voltage is given as:

Applications of the logarithmic amplifier

Log amplifier is used for mathematical applications and also in different devices as per their need. Some of the applications of the log amplifier are as follows:

  • Log amplifiers are used for mathematical applications, mainly in multiplication. It is also used in the division and other exponential operations too. As it can perform multiplication operation, hence it is used in analog computers, in synthesizing audio effects, measuring instruments that require multiplication operation such as in calculating power (multiplication of current and voltage).
  • As we know that when we need to calculate the decibel equivalent of a given quantity, we require the use of a logarithmic operator, and hence, log amplifiers are used to calculate decibel (dB) value of a quantity.
  • Monolithic logarithmic amplifiers are used in certain situations, like in Radio Frequency domain, for efficient spacing (reducing components and space needed by them), and also to improve bandwidth and noise rejection.
  • It is also used in different ranges of applications such as rot mean square converter, an analog-to-digital converter, etc.

What is Antilog?

Antilog Amplifier

An Op-amp in which the output voltage of the amplifier (V0) is directly proportionate to the anti-log of the input voltage (Vi) is known as an anti-logarithmic amplifier or anti-log amplifier. Here, we are going to discuss the operational amplifier configuration that forms the anti-logarithmic amplifier in detail.

Antilog Amplifier Circuit

Antilog Amplifier Using Transistor

Antilog Amplifier using Transistor

Antilog Amplifier using Diode

In the antilog amplifier, the input signal is at the inverting pin of the operational amplifier, which passes through a diode.

Antilog Amplifier using Diode

Output and Working Principle of Antilog Amplifier

As observed in the circuit shown above, the negative feedback is achieved by connecting the output to the inverting input terminal. According to the concept of the virtual ground between the input terminals of an amplifier, the voltage V1 at the inverting terminal will be zero. Because of ideally infinite input impedance, the current flowing through the diode due to the applied input voltage in the inverting terminal will not enter the op-amp; instead, it will flow along the feedback path through the resistor R as shown in the figure.

The compliment or inverse function of the logarithmic amplifier is ‘exponential’,  anti-logarithmic or simply known as ‘antilog’. Consider the circuit given in the figure. The diode current is

Where, VD is the diode voltage. According to the concept of virtual ground, V1=0 as the non-inverting terminal is grounded as shown in the figure. Therefore the voltage across the diode can be expressed as V= V– V1 or VD = Vi Hence, the current through the diode is

Due to the ideal characteristics of an op-amp (infinite input impedance), the current flowing through the diode ( iD) flows along the feedback path through the resistor R, as we can observe in the figure.

Therefore i= i2

And, V0 = -i2R = -iDR

Replacing iD in the above equation we get 

The parameters n, VT and Iare constants (they are only depend on the diode characteristics which are always constant for a particular diode). Therefore if the value of the feedback resistor R is fixed, then the output voltage V0 is directly proportional to the natural anti-logarithm (exponential) of the applied input voltage Vi. The above equation then can be simply represented as


Where K = – ISR and a =

Therefore we can notice that the anti-logarithmic op-amp produces its output signal as the exponential value of the input voltage signal applied.

The gain of the anti-log amplifier is given by the value of K that is equal to -ISR.

The –ve sign point out that there is a phase difference of 180degrees between the applied input s and the output of the anti-log amplifier.

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Inverting Amplifier | It’s Circuit and application as Transresistance amplifier

As we have seen in the earlier discussions, the open-loop gain of an operational amplifier (Op-amp) can be extremely high, about 1,000,000 or more. This very high gain makes the operational amplifier very unstable, and a very small input signal, even if they are in μV, is enough to cause the output voltage to rise to uncontrollable extents where they saturate, and we completely lose control over the output. Therefore we are going to study about feed-backs and inverting amplifier as a solution to the above related problems.


Before learning about the inverting amplifier we need to know about feed-backs and what is meant by saturation. The output voltage of an op-amp is limited to a minimum and maximum value, which is Almost equal to the supplied power voltage.

inverting amplifier
Op-amp input terminals: inverting amplifier input & non-inverting amplifier input

The connection from the output to the input via external wiring is known as feedback connection. There are generally two types of feedback: positive feedback and negative feedback.

feedback configuration

Negative feedback and inverting operational amplifier configuration

Negative feedback configuration

If the feedback is connected to the inverting amplifier input terminal (negative) of the op-amp, using a suitable resistor called feedback resistor, then the feedback is known as negative feedback. And, if the feedback connection is made between the output and the non-inverting (positive) terminal of the op-amp through a suitable feedback resistor, then it is known as positive feedback. In most applications of the op-amp the negative feedback is most widely used.

The negative feedback results in a different value of voltage in the inverting input (-ve), resulting in a new signal rather than the actual input signal as the inverting terminal voltage will be the summation of the voltages and the negative feedback voltage coming from the output terminal. Therefore to separate the actual input signal from the inverting terminal input signal an Input Resistor, R1 is being used.

If we contemplate an ideal equivalent circuit, the closed-loop voltage gain is

Specifically, if output voltage is VO, at that moment

The gain A will be infinity; the voltage V1 idyllically turn out to be equal to V2. This is signified as a virtual short circuit condition. A virtually short circuit shows that whether the voltage is at one and only of the input terminals will automatically act at the other input terminal due to infinite or practically very high gain. The non-inverting terminal 2 is grounded, thus V2= 0 and V1 = 0. Hence, terminal 1 is being virtually ground, that means it actually representing zero volt even without being grounded.

Inverting Amplifier Configuration and Working

inverting amplifier
Inverting op-amp configuration

Current i1 through R1 can be given as:

This current i1 cannot go into op-amp, since an ideal inverting amplifier has infinite input resistance and hence draws zero current. Therefore, I! will pass through the R2 resistor and will go towards the terminal no. 3.

Applying ohm’s law, we can determine Vas:

Vo = V1 – i1R2

     = 0 –

Therefore, the closed-loop voltage gain is:

As we observed that the –ve is accompanying with the closed-loop gain term, hence this configuration of the op-amp is recognized as the inverting configuration.

Due to the virtual ground concept, the input resistance is defined as R= Vi/i= R1

The equation for the output voltage (Vo) implies that the circuit works in a linear way for a constant amplifier gain Av as Vo = Vi x Av. This property is very useful for converting a small magnitude signal to a much larger voltage signal. And as there are no capacitors in the inverting operational amplifier circuit, hence, the input and the output voltages, as well as the currents in the resistors, can be DC signals, and therefore the op-amp will be able to amplify DC signals too.

Application of inverting amplifier

What is Transresistance amplifier ?

Transresistance amplifier or current-to-voltage converter

A very useful application of an inverting operational amplifier is that of a Trans-impedance amplifier or current to voltage converter. A Trans-resistance or a trans-impedance op-amp is employed as a current-to-voltage converter circuitry. These are comprehensively utilized in circuit designing as it’s good to convert a very small current generated by a circuitry or sensor to sufficiently high proportionate output voltage.

Transresistance amplifier
Transresistance amplifier or current-to-voltage converter

Consider the circuit in the figure. The input resistance Ri at virtual node is R= V1/i1 = 0 as studied before.

The current i1 is essentially equal to Is and so,

i= i= Is

And, V= -i2Rf = -IsRf

The o/p voltage is directly proportionate to signal current, and the feedback resistance Rf is equivalent to the ratio of the output voltage to current in input terminal.

We will be learning about the non-inverting amplifier in the upcoming section.

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Differential amplifier | It’s Working | 4 Important factors and Applications


A differential Amplifiers are most extensively used building blocks in the analog integrated circuit design. A differential amplifier is basically an electronic circuit which consists of two inputs, inverting and non-inverting input operated in a negative feedback configuration. The differential amplifier basically amplifies the difference between the applied input voltages in these two input terminals and rejects any common signal to these two input terminals

Basically, all operational amplifiers are Differential Amplifiers because all of them have the same input configuration. If an input voltage signal is applied on one of the input pin and one more voltage signal is applied to the other pin rather than being grounded, the resultant output voltage proportionate to the variance between the two input voltages connected in the two respective input terminals.

 Differential amplifier
 Differential amplifier with non-ideal op-amp, Image Credit – Arthur Ogawa, Op-Amp Differential Amplifier input impedence and common biasCC BY-SA 1.0

Construction and working

Consider the circuit, which is shown in fig (a), with inputs Vi1 and Vi2. To analyze the circuit, we will use the concept of superposition and virtual short. Fig (b) demonstrate the circuitry with Vi2 = 0. No current will flow in R3 and R4; therefore, V2a = 0. The resulting circuit will behave as an inverting amplifier so,

 Differential amplifier
Differential Amplifier Circuit

  The difference amplifier in the above circuit consists of both inverting and non-inverting amplifier configuration.

Whereas, if the inverting pin is grounded, the circuit acts as a non-inverting amplifier, as shown in the respective circuit diagrams. When the inverting input terminals are grounded, R2, and R1 functions as the feedback components connecting the output terminal and the inverting terminal and a suitable feedback condition is achieved for the non-inverting amplifier.

 Differential amplifier
 Differential amplifier

Fig (c) shows the circuit with Vi1 = 0. Now, the current of the op-amp is 0. So, R3 and R4 form a voltage divider. Therefore,

From the concept of virtual short we get, V1b = V2b and the circuit becomes a non-inverting amplifier, for which

Substituting in the above equations, we obtain


Since the net output voltage is the sum of individual terms, we have

                                                                              V0 = V01 + V02


A property of an ideal differential amplifier is that the output voltage is zero when Vi1 = Vi2. On analysis of the last equation, this condition is met if

The output voltage is then,

We can appropriately add supplementary resistors in parallel connection with the input resistors as per our necessity, and the differential amplifier circuit can be configured to either add or subtract it as per our need.

Some important terms related to differential amplifier

Differential input resistance:

In the figure, we have set the condition that   and have set R= R3 and R= R4. The input resistance is then defined as,

 Differential amplifier

Taking into account the concept of virtual short, we can write the following loop equation,

V= iR+ iR1 = i(2R1)

Therefore, the input resistance is R= 2R1

Common-mode input signal:

: In the ideal difference amplifier, a common mode input Vcm would make the inputs (Vi1 + Vcm) and (Vi2 + Vcm), i.e., gets added to each of the input applied voltages and hence, it will get cancelled out when the difference of the two input voltages are being taken and amplified.

The output Vis zero when Vi1 = Vi2. However, if these resistor ratios are not precisely equal i.e.

 , then, as a result, the common-mode voltage Vcm will not cancel out completely.

As practically it is impossible to have resistor ratios of perfectly exact values, it is likely that some common-mode output voltage will be present.

When Vi1 = Vi2, the input is called a common-mode input signal. The common-mode input voltage can be expressed as

the common mode gain can then be expressed as,

Common Mode Rejection Ratio (CMRR):

The CMRR can be explained as the modulus value of the ratio of differential gain to common-mode gain. Basically, it is the capability of a differential amplifier to reject input signals which are in common mode.

                                                    CMRR =

Generally, the CMRR is expressed in dB,

CMRR(dB) =

In an ideal world, the common-mode rejection ratio is infinite. In the actual differential amplifier case, we desire CMRR to be as large as possible.

Applications of Differential Amplifier

Wheatstone Bridge Differential Amplifier

Wheatstone Bridge Differential Amplifier

In this case, the resistors are arranged in a Wheatstone (resistive) bridge such a manner, can works as a differential voltage comparator by comparing the input voltages.

When a fixed reference input voltage is applied on one end of the Wheatstone bridge network and a thermistor or a light-dependent resistor (LDR) on the other end of the network, then the circuit can be used to detect different levels of temperature or light intensity. The output voltage of this differential operational amplifier circuit is a linear function of the differences in the active end of the circuit in which is the thermistor or LDR.

 A Wheatstone bridge differential circuitry utilized to calculate the value of the unknown resistance by pro tem as a comparator between the input voltages across the individual resistances.


Light dependent differential amplifier

The light-dependent differential circuit works as a light-dependent switch, which will either gives the output as “on” or “off” with the help of a relay. The applied voltage at V1 sets the amplifier’s trip point (provides the threshold value), and a variable resistance acting as a potential meter VR2 is used for hysteresis switching.

 On the inverting terminal of the differential amplifier, a standard light dependant resistor is connected, which changes its value of resistance value depending on the amount of light on its incident on it. The photodiode resistance present in the LDR is proportional to the light level and decreases with increasing intensity of light, and hence, the voltage level at point V2 will also vary and depending on whether it is above or below the threshold point, the variable resistor VR1 will indicate its value.

Now, as the light incidents on the light-dependent resistor (LDR), on the basis of its intensity, whether it exceeds or remains below the set threshold value at the non-inverting input terminal V1, the output shows ON or OFF.

The light level trip or threshold value position can be adjusted with the help of the potentiometer VR1 and the switching hysteresis potentiometer VR2. Therefore in this way, a light-sensitive switch can be made using a differential amplifier.

The circuit can be configured to detect changes in temperature, by replacing the VR1 and the LDR, with a thermistor and a suitable variable resistor to detect heat or cold. The disadvantage of a differential amplifier is that the input impedance’s are much lower as compared to that of the other operational amplifier circuit configurations. A differential amplifier circuit works well for low impedance sources but not for high impedance sources. By using a Unity Gain Buffer Amplifier, this problem can be overcome.

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Faraday’s Law of Induction

Michel Faraday has elaborated

How a changing magnetic field generates an electric current in a conductor?

Faraday’s Law of Induction

He has stated that the induced voltage in a circuit is proportionate to the rate of change the magnetic flux per time or if the magnetic field changes, induced e.m.f. or voltage will be more and the direction of the change in the magnetic field regulates current’s direction. This is known as Faraday’s law.

Michael Faraday
Michael Faraday, Image By – Thomas PhillipsM Faraday Th Phillips oil 1842, marked as public domain, more details on Wikimedia Commons

Magnetic Flux

Magnetic Flux can be stated mathematically as ΦB = BA cos

A is the surface in which B uniform magnetic field is acting on.
ΦB is the magnetic flux. is the angle between and B and A.

Ways to change the magnetic flux:-

  • From the above equation, it is understandable that the flux could be varied if we change the magnitude magnetic field.
  • The angle in-between magnetic field B and the plane of coil could be changed too, surface area A is also a changeable parameter.

Some important facts about magnetic flux:

  • Magnetic flux is a scalar quantity.
  • S.I unit of Magnetic flux is denoted as weber(Wb)
  • 1 Wb = 1 Tesla.
  • C.G.S unit of magnetic flux is Maxwell.
  • 1Wb = Maxwell.

Now, according to Faraday’s Law of induction, e(t)= ΦB.

In case of a coil of N turns, change of flux with each turn is the same and hence the total induced emf becomes, e(t)= ΦB.

The negative sign specifies the direction of induced emf, which is in accordance with the Lenz’s Law which is stated as follows:

The direction of the emf induced and hence the direction of the induced current in a circuit is to oppose the cause due to which they were produced, i.e. if the flux is increasing, then the induced emf will be produced in such a direction that will try to decrease the flux and vice-versa.

In reality, Lenz’s law is a coincidence of the conservation of energy. As the emf is induced in such a way that it opposes the change in flux, hence work has to be done against this opposition given by the induced emf to ensure that the flux change continues in the same way. This work done appears as electrical energy in the circuit.

From the equations above we can state that the induced emf or the electric current in the circuit can be increased in the following ways:-

  • Changing the flux very rapidly can increase the induced emf.
  • Using a rod of soft iron core inside the coil.
  • Increasing N, i.e., increasing the number of turns of the coil.

As seen in the figure, we can generate an emf when the magnet is placing near to a circuit or when a circuit is placed nearer to a magnet. In these cases, the direction of the induced current is shown.

direction of induced electric field according to Lenz's Law
Direction of induced electric field according to Lenz’s Law

Another way in which emf can be induced is the working principle of AC, where the circuit is a coil of conducting wire circulating in a magnetic field and hence flux ΦB changes in a sinusoidal way in time.

Motional Electromotive Force (an implication of Faraday’s Law of induction)

Faraday's law
Electromotive force induced due to change in area of magnetic flux due to relative motion

The above figure shows a rectangular conductor ABCD upon which a conducting rod EF moves with constant velocity. The magnetic field is perpendicular, i.e., inwards to the plane of the closed conducting loop ABFE. 

The magnetic flux enclosed by the loop at time t = t s is,

ΦB(t)= = BA=Blx(t),

The time rate of change of this flux, induces an emf given by e= ΦB = (-Blx(t))= Bl.x(t) = Blv.                                                                                                                          

This electromotive force obtained due to the motion of the conductor EF instead of changing the magnetic field is known as a motional electromotive force.

Electromagnetic induction explains the induction of currents and voltages as a coincidence of changing magnetic fields. But the more modern view states that the induction occurs even in the absence of a conducting wire or any material medium.

Transformer: an overview|| 4 important conditions for good efficiency


A transformer is a simple electrical device, which uses the property of mutual induction to transform an alternating voltage from one to another of greater or smaller value.

The first constant-potential one was invented in 1885, and since then, it has become a necessity as an essential device for the transmission, distribution, and utilization of alternating current (AC).

shell form DBZ design transformer at 1885
Shell form DBZ design transformer at 1885, Image Credit – Zátonyi Sándor, (ifj.), DBZ trafoCC BY-SA 3.0

There are different types of transformers having different designs suitable for different electronic and electric power applications. Their sizes range from Radio Frequency application having a volume less than a cubic centimeter, to huge units weighing hundreds of tons used in power grids.

transformers in an electric substation, Image Credit – Allalone89Melbourne Terminal Station, marked as public domain, more details on Wikimedia Commons

They are most widely used in transmission and distribution of energy over long distance by stepping up the voltage output from the transformer so that the current is reduced and subsequently, the resistive core loss is less significant, so signal can be transferred over the distances to the substation contiguous to the consumers where the voltage is again stepped down for further use.

Basic Structure and Working of Transformer

The basic structure of a transformer generally consists of two coils wound around a soft iron core, namely primary and secondary coils. The ac input voltage is applied to primary coil and the ac output voltage is observed in the secondary side. 

As we know that an induced emf or voltage is only generated when the magnetic field flux is changing relative to the coil or circuit, hence, mutual inductance between two coils is only possible with an alternating, i.e. changing/AC voltage, and not with direct, i.e. steady/DC voltage.

working of transformer and leakage flux
Working of transformer and leakage flux
Image Credit :My self, Transformer fluxCC BY-SA 3.0

The transformers are used to transmute voltage and current levels as per the ratio of input to output coil turns. The turns in the primary and secondary coil are Np and Ns, respectively. Let Φ be the flux linked through both primary and secondary coils. Then,

Induced emf across the primary coil,   =

Induced emf across the secondary coil,  = 

From these equations, we can relate that  

Where the symbols have the following meanings:


Power, P = IpVp = IsVs

Relating to the previous equations,

Thus we have Vs = ()Vand Is = IP

For step up: Vs > Vp so Ns>Np and Is<Ip

For step down: Vs <Vp so Ns < Np and Is > Ip

Primary and Secondary coil in a transformer

Primary and secondary winding
Image Credit: anonymous, Transformer3d colCC BY-SA 3.0

The above relation is based on some assumptions, which are as follows:

  • The same flux links both primary and secondary without any flux leakage.
  • The secondary current is small.
  • Primary resistance and current are negligible.

Hence, transformer efficiency cannot be 100%. Although a well-designed one can have an efficiency of up to 95%. For having higher efficiency the main four reasons of energy loss in it should be kept in mind.

Cause of Transformer energy loss:

  • Flux leakage: There is always some flux leakage as its almost impossible for all the flux from primary to pass to the secondary without any leak.
  • Eddy currents: The varying magnetic flux will induce eddy currents in the iron core, which may causes heating and hence energy loss. These could be minimized by using a laminated iron core.
  • Resistance in the winding: Energy is lost in the form of heat dissipation through the wires but can be minimized by the use of comparatively thick wires.
  • Hysteresis: When the magnetization of the core is repeatedly reversed by an alternating magnetic field, it results in expenditure or loss of energy by the generation of heat inside the core. This can be reduced by using materials having lower magnetic hysteresis loss.

We will be studying about Eddy currents and Magnetic Hysteresis in details in the further sections.

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Hall Effect Sensors | It’s types | 5 important applications


  • Introduction
  • Magnetic Sensors
  • Hall Effect Sensors
  • What is Hall voltage (VH)?
  • Hall Coefficient (RH)
  • Construction of Hall Effect Sensors
  • Symbol of Hall Effect Sensor
  • Working Principle of Hall Effect sensors
  • Hall Effect experiment
  • Analog and Digital Hall Effect Sensor
  • Type of Hall Effect Sensors
  • Applications of Hall Effect Sensors

What is magnetic sensor?

Magnetic Sensors

Magnetic sensors are devices which are able to detect and analyze magnetic fields generated by magnet or current. They can be used for different kinds of applications such as to sense the change in the position and angle of a magnetic field, to sense the change in strength or the direction of the applied magnetic field, etc.

There are various types of magnetic sensors like Hall Effect sensor (Hall switches, linear Hall sensors, etc.) used for detecting a change in the strength of the magnetic field, Magneto Resistive sensor used for detecting a change in the direction of the magnetic field, angle sensors used for detecting a change in the angle of a magnetic field, 3D Hall sensors and as well as magnetic speed sensors. Hall Effect sensors are employed in an extensive range of applications such as proximity sensor, position and speed measurement etc. They are even used in computer printer, pneumatic cylinder, computer keyboards etc.

Magnetic sensors are generally a solid-state device which is in high demand now a day due to its high precision and accuracy, contact less operation, comparatively low maintenance cost, compact design, etc. Now a day coreless magnetic sensors dedicated for different kinds of industrial applications are available for example, sealed Hall Effect devices are water-proof and are made in such a way to resist any vibration too.

Magnetic sensors are extensively used in automotive systems especially for analysing the position of the car seats, seat belts and for controlling air-bag system and also for detection of wheel rotation speed for the anti-lock braking system (ABS).

Hall Effect Sensors

Hall Effect sensors are magnetic sensors whose output is dependent on the magnetic field or magnetic flux density around the magnetic sensor.

  • The word “Hall” came from Dr Edwin Hall, who discovered this Hall Effect for the first time.
  • If there is an external magnetic field vertical to the object through which current is passing, an electromotive force will generates in the direction perpendicular to the magnetic field and to the current.
Hall Effect sensor
Hall Effect sensor device 1880

What is Hall voltage (VH)?

If an external magnetic field is applied in the magnetic sensor, it gets activated. Hall Effect sensor’s output voltage is proportionate to the strength of the applied magnetic field passing by. After a particular threshold of magnetic flux density is exceeded by the external field, an output voltage is generated, which is commonly known as Hall voltage (VH).

Hall Coefficient (RH)

The quantity of the potential difference per unit thickness of metal stripe in the Hall Effect distributed by the product of the magnetic intensity and the longitudinal current density.

The units of Hall coefficient RH are in general conveyed as m3/C, or Ω·cm/G.

Construction of Hall Effect Sensors:

Hall Sensor Design

Hall Effect sensors generally consist of a rectangular piece of semiconductor such as indium antimonite (InSb) or gallium arsenide (GaAs) known as a Hall probe mounted on an aluminum plate and covered altogether inside the probe head. A probe handle made up of a non-magnetic material is connected with the probe head such that the plane of the rectangular plate of semiconductor is perpendicular to the probe handle.

When the device is activated, a continuous flow of current occurs through the semiconductor. If the external magnetic field lines are at right angles to the probe head such that the filed lines are passing through the right angles through the sensor of the probe, a voltage originates which known as the “Hall effect” voltage and the device provides a reading of magnetic flux density (B) of the external field.

Symbol of Hall Effect Sensor:

Hall Effect sensor symbol, Image Credit – Grahamatwp at English WikipediaCommon Hall Sensor SymbolCC BY-SA 3.0

What is Hall Effect Transducer ?

Working Principle of Hall Effect sensors

  • The Hall Effect sensor primarily works due to the effect of Lorentz Force (it is the force experienced by a charged particle due to an electric field or a magnetic field, i.e. simply an electromagnetic field).
  • In the presence of an existing external magnetic field of sufficient magnitude, the electrons in the semiconductor slab are deflected toward one edge of the slab, i.e. the holes and the electrons shift towards either side of the slab due to the Lorentz force acting on them.
  • For this, one side of the semiconductor is negative charged, and the opposite side turn out to be positive charged. This produces a voltage gradient across the two opposite sides of the rectangular slab due to the accumulation of opposite charges at these two sides. This voltage is known as Hall voltage (VH), and the effect of generating this measurable Hall voltage by using an external magnetic field is known as the Hall Effect.
  • To generate a potential difference such that a measurable voltage is produced, the external magnetic field lines must be at a right angle to the plane where the current flows through the slab. Also, a correct polarity should be provided for the Hall Effect sensors to work.
Hall effect transducer Working
  • As the electrons and holes shift apart from each other, a potential gradient is generated, and the separation increases until the force due to the electric field balances the force produced by the magnetic field. When both the forces balance each other, the current is not changing, and the Hall voltage that is detected at this point and from this magnetic flux density (B) has been calculated.                       
  • If the output voltage depends linearly on magnetic flux density, then we call it as linear Hall Effect sensors, and if there is a sharp decrease of the output voltage at different magnetic flux density, then it is called as threshold Hall Effect sensor.
  • We have heard about Inductive sensors which respond to a changing magnetic field as it induces a current in a coil of wire and hence generates a voltage in its output. Therefore inductive sensors can detect only static (non-changing) magnetic fields whereas the Hall Effect sensors can detect both changing and non-changing magnetic field.
  • The Hall Effect sensor can give information regarding the type of magnetic pole used to generate the voltage and also the magnitude of the external magnetic flux density (B). Using a group of sensors, we can find the relative position of the external magnet used.
  • The output voltage of the Hall Effect sensor is generally of a quite small magnitude, like a few micro-volts even when a strong external magnetic field is applied across the sensor. Hence, most commercially available Hall Effect sensors are constructed with a built-in DC amplifier and voltage regulators to improve the sensor’s sensitivity and magnitude of the output voltage.

Hall Effect Experiment

Close loop Hall effect current sensor
Image credit: DracheschreckClosed loop hall effect current sensorCC BY-SA 3.0

Analog and Digital Hall Effect Sensor

Hall Effect Sensor’s output can either be linear (analog) or digital. The output of the linear Hall Effect sensor is directly proportionate to the external magnetic field, i.e. magnetic flux density passing through the sensor and the output is taken from the output of the differential OP-AMP. Hall Effect Linear (analog) sensors have a continuous voltage output that changes as per the strength of the external magnetic field changes.

Formula of Hall effects Sensor:

The output of the linear Hall Effect sensor can be expressed as:


  • VH is the Hall Voltage
  • RH is the Hall Effect co-efficient
  • I is the current flowing through the sensor (semiconductor slab)
  • t is the thickness of the sensor
  • B is the external magnetic flux density

In the case of the Hall Effect digital sensor’s output is taken from the output of the OPAMP, which in turn is connected with a Schmitt-trigger with built-in hysteresis which reduces oscillations in the output voltage. In this case, only when the external field strength is higher than a specific value in the device, the device switches to the ON condition from OFF condition.

Type of Hall Effect Sensors:

Depending on the type of the external magnetic pole required for them to operate, Hall Effect sensors are of two types.

  1. Bipolar
  2. Unipolar

The two of the most common sensing configurations in a Hall Effect sensor using a single magnet are Head-on Detection and Sideways Detection. In sideways detection, it is required to move the magnet in a sideways motion in front of the face of the Hall Effect element. While in head-on detection the magnet moves towards and away from the hall element in a way perpendicular to the plane of the element.

Hall effect sensor used in engine fan
Image CreditФигушкиClutch with Hall Effect sensorCC BY 2.0

Applications of Hall Effect Sensors:

  • Position sensor: When operating in the on/off mode, i.e. having a digital output, detecting the occurrence of magnetic materials is one of the important industrial applications of Hall Effect sensors.
  • DC transformers: The Hall Effect sensor is used to measure the DC magnetic flux, and as a result, the DC current can be calculated.
  • Keyboard switch: For some computer keyboards Hall Effect switches are being used. But due to its comparatively high cost, it is limited to the field of aerospace and military for their high reliability.
  • Fuel level indicator: The Hall Effect sensor senses the position of a floating element using position sensing and employed as automotive fuel level indicator.
  • Electric treadmill: Hall sensors are used here for speed sensors and also for emergency stop due to any accidental fall. The waistband of the user in the treadmill is attached to a pull cord which is in turn attached to a magnet. If accidentally the user falls, the magnet gets detached, and there is an interruption to the power supply which stops the machine.

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An Overview of Eddy Currents | 5+ Important Applications

Here we will be studying about eddy currents and what is meant by electromagnetic damping. But changing magnetic flux also induces currents in bulk pieces of conductors, and their flow pattern resembles that of swirling eddies in the water.

François Arago, a mathematician and even the 25th prime minister of France, first observed the eddy currents in 1824. Later a physicist named Foucault discovered these currents, which are termed explicitly as eddy currents.

Eddy Current
Eddy Current, Image By – ChetvornoEddy currents due to magnetCC0 1.0

A Simple Demonstration of Eddy Current

The cause and effect of eddy currents can be understood by a simple experiment, as mentioned. A copper’s plate is swinging like pendulums.

These produce hindrances in the swinging motion of the plate, and hence, the swinging motion is damped. In some time, the plate comes to rest in the magnetic field. 

This electromagnetic damping effect can be reduced by cutting down the available area for the flow of eddy currents. Hence, if we can introduce rectangular slots and holes in the plate, and because of the fact that the magnetic moments of the induced currents depend on the area enclosed by it, we can reduce the electromagnetic damping and the plate swings more freely.


The dissipation power of eddy currents can be expressed as:


P refers to the power lost per unit mass.

Bp refers to the maximum magnetic fields.

d refers to the thickness.

f refers to the frequency.

k refers to a constant .

ρ refers to the resistivity.

D refers to the density.

Eddy current is decreased by using laminations in the metal core. Because of this, the magnitude is substantially reduced.

As the dissipation of energy in the form of heat is depended on squares of the magnitude of the eddy currents, the heat loss and subsequently, the energy loss is decreased. Energy losses can further be reduced by using thinner lamination with very low-carbon content iron or soft iron and wires with larger cross-sections.

eddy currents in a slab with and with-out laminations
eddy currents in a slab with and with-out lamination, Image Credit – ChetvornoLaminated core eddy currents 2CC0 1.0

Here’s a straightforward experiment where we can notice electromagnetic damping.

Two hollow thin cylindrical pipes of same geometrical orientations but one made up of aluminum and the other a PVC pipe is being clamped vertically. A cylindrical magnet having a diameter a little less than that of the cylinder’s diameters is dropped through both the pipes in such a way that they don’t get to touch the inner walls of the cylindrical pipes. The magnet dropped through the PVC pipe takes the same time to come out of the pipe as it would take if dropped from the same height without any pipe. The magnet in the aluminum pipe comparatively takes a longer time to come out of the pipe.

This is due to the eddy currents which are produced in the aluminum pipe that opposes the changing magnetic flux when the magnet moves through the aluminum pipe. As PVC is an insulator, no eddy currents are formed in it. This phenomenon where a retarding force due to the eddy currents restricts the motion of an object is known as electromagnetic damping.


Although eddy currents are undesirable in some applications, there are many applications in which eddy currents are a necessity for their working. Some of them are magnetic braking in trains, electromagnetic damping, induction furnace, electrical power meters, levitation, identification of metals, Vibration and position sensing, structural testing, etc. Some of them have been explained in details as follows:

  • Magnetic braking in trains: As we know that the trains are quite heavy and can move at great speeds, hence, the braking system of trains should be very powerful and smooth. Eddy currents make this possible. Strong electromagnets can induces eddy currents in the rails. As there is no friction involved as there are no mechanical linkages; hence, the braking system becomes very smooth. But this application is used in some electrically powered trains only.
  • Induction furnace: They are used to melt iron, steel, copper, aluminum, and other precious metals for welding purposes, reshaping purposes, or for making alloys. In an induction furnace, the eddy current produces very high temperatures suitable enough to melt the metals.
  • Electromagnetic damping: Few measuring instruments like galvanometers make use of the effect of eddy currents in opposing the motion. They have a fixed core made up of a non-magnetic but metallic material in which the eddy currents are generated when the coil oscillates, which in turn opposes the motion of the coil and brings it to rest position quickly.
  • Repulsive effects and levitation: when a changing magnetic field is applied, it induces eddy currents that exhibit the behaviour of diamagnetic-like repulsion due to which a metal or any conductive material will experience a repulsion force.

For more about eddy current application, may read article on eddy current testing, eddy current sensor and eddy current brake.

Overview on magnets | It’s 2 important types | Permanent and Electromagnet


  • History of Magnets
  • Types of Magnetic materials
  • Diamagnetic materials
  • Paramagnetic materials
  • Ferromagnetic materials
  • Types of Magnet
  • Hard magnets and Soft magnets
  • Permanent magnet and electromagnet
  • Applications of electromagnets

History of Magnets

From lodestones (or magnetite) first, people got an idea about the working of magnets, which are magnetized pieces of iron ore found in nature. The word magnet came from Greek, from the land named “Magnesia”, a part of ancient Greece where lodestones were found. By the end of the 12th century AD,magnets were used and magnetic compasses were built and used in navigation in different parts of the world like China, Europe, etc.

A naturally occurring permanent magnet: lodestone (black)
Image Credit : Teravolt (talk), Lodestone (black)CC BY 3.0

Basically, magnets are material that produces magnetic fields. Physicists Curie and Faraday observed that almost all materials have certain magnetic properties and according to their magnetic behavior divided them into three categories:

  • Diamagnetic materials
  • Paramagnetic materials
  • Ferromagnetic materials

Types of Magnet:

Hard Magnetic Materials: 

Hard magnets are generally ferromagnetic materials which have the ability to retain the magnetization for a quite a long period of time, i.e. the material should have high retentivity.

Hard magnets should also have a high degree of coercivity, i.e. only a large magnitude of the external magnetic field should be able to eliminate the residual magnetism retained by the material.

Some examples of hard magnetic materials are Alnico (an alloy formed by the combination of iron, cobalt, aluminum, nickel and copper) and lodestone (a naturally occurring metal).

Hysteresis loop for Hard Magnets

Soft magnetic Materials: 

Soft magnets are also ferromagnetic materials which can retain their magnetization as long as the external magnetic field exits, i.e. they have low retentivity. They also have a low degree of coercivity, i.e. their retained magnetization (although being very less) can be eliminated very easily.

Hence, they can be easily magnetized and demagnetized.

These kinds of materials (soft magnets) are being used to make electromagnet as an electromagnetic material should have a low retentivity and also a low coercivity. Soft iron is a suitable material as a soft ferromagnet.


Hysteresis Loop for Soft Magnet

The two types of magnets: Permanent magnet and electromagnet

Permanent magnets:

Permanent magnets

The materials that can retain their ferromagnetic properties for long periods of time at normal room temperature can be classified as permanent magnets.

A high degree of retentivity (the magnet can retain its magnetism in the absence of external magnetic field) and also a high degree of coercivity (the magnetic property is not wiped out by external magnetic fields) is necessary to be a permanent magnet.

Permanent magnets should also be resistant to mechanical stress and temperature change. 

As stated before, a magnetic field is produced by a changing electric field. Hence it is theorized that the magnetic field of a permanent magnet is a consequence of the uniform spin of the electrons in a particular direction within the atoms of the material as the electric charge in motion produces a changing electric field. This kind of uniform spinning of the electrons in a material’s atoms is basically due to the atomic structure and electronic orientation of the material. Therefore, only a few types of substances have the ability to permanently sustain or retain a magnetic field.

Lodestone, Alnico, as mentioned in the hard magnets, can be an example of permanent magnet. From the discussions we had it can be inferred that steel is more suitable for the manufacture of permanent magnet than iron as steel has a much higher value of coercivity than iron although iron has a little higher retentivity than steel. A number of alloys with quite large values of retentivity and coercivity have been developed for the manufacturing of permanent magnet. Such an alloy with a very high coercivity value is named as vocally (an alloy made up of vanadium, iron and cobalt).


Electromagnets are generally constructed by winding a material (usually ferromagnetic materials) by a wire in a coil and connecting the wires to a variable power supply (such that the current in the wires can be varied).

An Electromagnet

How does an electromagnet work?

When a current flows through the wires, the magnetic field produced by each of the individual coil loops is summed up with the magnetic field of the neighbouring loops, and altogether it works as a strong bar magnet with the distinct North Pole and the South Pole.

This resultant bar magnet with its distinct North and South Pole is much stronger than any permanent bar magnet which can be magnetized and demagnetized at will, i.e. it can behave as a magnet only when it is needed.

The material used as core should have high permeability, low retentivity and also low coercivity. In an electromagnet, the magnetic field and flux density can easily be varied according to the current in the windings. This property of an electromagnet is widely used in different applications, but unlike permanent magnet this one requires a power supply for it to work and also for electromagnet, there is some energy loss in magnetization and demagnetization of the core as studied previously in the form of the hysteresis loop.

The North Pole and South Pole formation when current flows through the windings depends on the direction of current flow in the loops. Where the North and the South Pole will be formed can be predicted by the diagram shown below.

North-South Pole according to the direction of current in the coil

Factors on which the strength of the electromagnet depends

The magnetic field strength or the magnetic flux density depends on the amount of current flowing through the windings and also to the number of turns in the coil. More specifically, the magnetic field strength is directly proportional to both of them, which is relevant from the expression of the magnetomotive force, which is as follows:

Magneto-motive force (MMF) = I X N 

where  is the current flowing through the winding and N is the number of turns.

Another condition on which the magnetic strength of an electromagnet depends is the material used as the core. Generally, the core is made up of ferromagnetic material with a high degree of permeability (the measure of the ease by which a magnetizing field can penetrate or permeate a given material). If we use any non-magnetic material like wood, plastic, etc., it can be assumed as if the core is made up of free space as the permeability of such material is very low and hence, the magnetic flux density will be negligible.

Application of Electromagnet
Image Credit: AntennamaxAGEM5520CC BY-SA 3.0

Applications of electromagnets

  • Electromagnets are extensively used in electrical devices such as electric bells, induction heaters, electric fans, telegraph, electric trains, electric motor-generator etc.
  • They are used for magnetic levitation as in maglev trains.
  • They are used in headphones, speakers, tape recorders and even in hard disks of our computers.
  • They are used as relays and in equipment such as mass spectrometers and even in particle accelerators.
  • They are even used in medical purposes such as for removing pieces of iron from wounds and also in MRI (magnetic resonance imaging) machines. 

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