Working Of Inductors

I have explained many articles on various electronic circuits, which shows applications of Inductors. But I have not explained the proper working of inductor till now. Inductors are used in many analog circuits and are also used along with capacitors for forming filter circuits and thus signal processing. They are also used in Switched Mode Power Supplies (SMPS), oscillators, transmitters, receivers, voltage regulators and also for over voltage protection.

What is an Inductor?

An Inductor, also known as a reactor is simply a coil of wire, which has many electrical properties when subjected to a magnetic field. When an electric current is passed through it, a magnetic field is created. This magnetic field helps to store the electric current for a short time, even if the supply is removed. When the magnetic field around the coil collapses, the electric current also falls off. Actually, the inductor basics are based on the Faradays Laws of Induction.

The working of an inductor can be further explained with the help of an example.

Inductor Symbol

Simple Inductor Circuit

Consider a basic circuit consisting of a battery and a bulb. For this connection, there are only two outputs.  One is the bulb glow when the battery is connected and the other is the bulb off position when the connection is terminated. The circuit is shown below.

Simple light bulb

Now consider the same circuit with a coil of wire around the iron bar and the ends of the coil given across the bulb. Also connect a switch as shown in the diagram below.

inductor with battery light bulb

When the switch is closed, instead of the bulb to glow as a normal dim light, it makes a transition from bright to dim. As soon as the switch is opened the bulb makes a transition from very bright to off. As you can see, this is very different from the earlier explained connection. This strange behaviour is because of the inductor. When the switch is closed, the current starts flowing from the battery to the coil. Thus the coil starts to make a magnetic field. During this time, the coil inhibits the flow of current. As soon as the magnetic field is built, there is only normal flow of current through the wire. That is why the bulb makes a transition from bright to dim. When the switch is opened, there will be a magnetic field around the coil for a short period, which  keeps the current in the coil steady. As soon as the field dies, the current also stops. That is why there is a sudden transition from bright light to off.

Thus the main two important notes of Inductors can be concluded as

• Inductors are used to store energy in its available magnetic field.

• An inductor resists any change in the amount of current flowing through it.

The value of an Inductor is called Inductance and is measured in Henries. It is actually the SI unit of Inductance.

1 Henry = 1 Weber/ 1 Ampere

Capacity of an Inductor

There are mainly four factors which depends on the capacity of an Inductor. They are

• Inductance increases with the increase in the number of coils and decreases with reduced number of coils.
• Inductance increases with more area in the cross-section of the coil and reduces with lesser area of cross-section.
• Inductance increases with the overlapping or narrowing of coils and decreases vice-versa.
• Inductance depends on the material that the coils are wrapped around (the core).

How to make an Inductor?

To make an inductor we mainly need

A coil of conducting material (mostly copper).

A core (air, ferromagnteic materials, ferrimagnetic materials)

The coil has to be wrapped around the core. The inductance highly depends on the core. When the magnetic field increases, the inductance also increases. For this to happen, the core material must have very high permeability than air. For transformers, low frequency inductors are used. For their construction, the cores are laminated with electrical steel so as to prevent eddy currents. Soft ferrites are widely used for cores above audio frequencies, since they don’t cause the large energy losses at high frequencies that ordinary iron alloys do. Inductances with small inductance can be easily etched on a PCB by laying out the trace in a spiral pattern. They can also be made on IC’s using the same process as that for transistors.

To know more about the making of an Inductor and to find the correct inductance value, please click at the link below.

TAKE A LOOK : HOW TO MAKE AN AIR-CORE INDUCTOR

Inductor Core Coils

There are many types of coils used in an Inductor. Some of them are

Air Core Coil

All coils that are wound in non-magnetic materials like plastic, ceramic and those coils that have air inside their windings are called Air core coils. Though they have very low inductance values they can be used for high frequency applications, because they do not possess any core losses because of the non-existence of ferromagnetic materials. For high frequencies they must be made on a single layer of winding. Air core coils are sometimes subjected to microphony, which causes a variation in the inductance value. This can be reduced if they are firmly supported on a plastic or ceramic base.

Ferromagnetic Core Coil

The core is made of ferromagnetic materials or ferrimagnetic materials. Though this greatly helps in increasing the inductance, there are also some losses that are associated with it. By using materials like iron as core, the magnetic permeability increases to a high extent, thus increasing the magnetic field.

The loss in this type of a material is

Core Losses

In a ferromagnetic inductor, when current is passed at a time, a time varying magnetic field is produced in its core causing energy loss in the form of heat. This is associated t0 three other parameters. They are eddy current loss, non-linearity and hysteresis loss.

CRO is a very versatile instrument in laboratory for measurement of voltage, current, frequency and phase angle of any electrical quantity. But before we go ahead with dis­cussion on measurement of electrical quantities with CRO, we should understand some basic oscilloscope patterns.

Basic Oscilloscope Patterns

oscilloscope pattern

Assume that a sinusoidal voltage signal is applied to the horizontal deflection plates without applying any voltage signal to the vertical deflec­tion plates, as shown in figure.

At point A in time, the voltage is zero so the spot remains undeflected at centre point of the screen. At point B in time, voltage V_h is maximum positive so the spot is at the extreme right end on the screen. At point C in time, once again the voltage is zero so the spot comes back to the central position on the screen. At point D in time, the voltage is maximum negative and so the spot is at the extreme left end on the screen. At point E in time, the voltage is zero so the spot returns to the central position of the screen. This way for next voltage cycle the spot again moves from point A to point B on the screen. So we get a horizontal line on the screen. One thing is to be kept in mind that this horizontal line is in the central position vertically as no voltage has been applied to vertical defection plates.

If sinusoidal voltage signal is applied to the vertical deflection plates without applying any volt­age signal to horizontal deflection plates then we get a vertical line on the screen of CRO, as shown in figure. This line would be in the central position on the screen horizontally.

By this time we have seen what type of pattern we get when sinusoidal voltage signal is applied to horizontal or vertical deflection plates alone. Now we would discuss what happens when both horizontal and vertical defection plates are supplied with sinusoidal voltage signals simultaneously.

Let us consider a case, when two sinusoidal voltage signals equal in magnitude and frequency and in phase are applied to both of the horizontal and vertical deflection plates, as shown in figure.

At point A in time, voltages at both of the plates are zero so the spot is in the centre of the screen. At point B in time, voltages applied to both of the plates are maximum positive, so the spot appears at the extreme right end in horizontal direction and extreme upward in the vertical direction. At point C in time, again both voltages are zero so the spot moves back to centre of the screen. At point D in time, voltages applied to both of the plates are maximum negative, so the spot appears at the extreme left end in the horizontal direction and extreme downward in the vertical direction. As both of the voltage signals are in phase and equal in amplitude and frequency, so at any time voltage signals applied to horizontal and vertical deflection plates are equal in magnitude as well as in sign. That is why, at any instant movement of the spot is same in horizontal (X-axis) as well as in vertical (Y-axis) directions. Thus a straight line inclined at 45° to the positive X-axis is obtained on the screen, as shown in figure.

Here it is very important to note that at any time the movement of the spot on the screen is the vector sum of the horizontal and vertical deflections and the horizontal and vertical deflections are proportional to the voltages applied to the horizontal and vertical deflection plates re­spectively. So if sinusoidal voltage signals, in phase, and equal in amplitude and frequency are applied to horizontal and vertical deflection plates we get a straight line in­clined at 45° to the positive X-axis, as explained before. If amplitude of sinusoidal voltage signal applied to the verti­cal deflection plates is less than that of the voltage signal applied to horizontal deflection plates, then the deflection

of the spot along Y-axis would be less than that along X-axis direction. So we get a straight line inclined at an angle, less than 45° to the positive X-axis. When voltage applied to the vertical deflection plates is more than that applied to the horizontal deflection plates, we will get a straight line inclined at an angle, more than 45° to positive X-axis.

Now let us consider a case when two sinusoidal voltage signals applied to the horizontal and vertical deflection plates are of equal magnitude but opposite in phase, as shown in figure.

At point A in time, both voltage signals are zero so the spot is at the central position of the screen. At point B in time, voltage applied to horizontal deflection plates is maxi­mum negative while the voltage applied to the vertical deflection plates is maximum positive, so the spot moves a maximum distance to the left and upward, as shown in figure. Similarly at point C in time the spot comes back to the central position of the screen and at point D in time, it goes to maximum right and downward, as shown in the fig. Thus we get a straight line inclined at 135° to the positive X-axis, as shown in figure.

In third case, if the two sinusoidal voltage signals, 90° out of phase and of equal amplitude and equal frequency, are applied to the horizontal and vertical deflection plates, a circle would appear on the screen, a shown in figure. At point A in time, voltage applied to the horizontal deflection plates is maximum positive and the voltage applied to the vertical deflection plates is zero, so the spot moves extreme right end on the X-axis without any movement along the Y-axis. At point B in time, the voltage applied to horizontal deflection plates is zero but the voltage applied to the vertical deflection plates is maximum positive, so the spot moves maximum in upward direction without any horizon­tal movement. Similarly the spot moves, for points C and D in time, on the screen, as shown in figure. Thus during one cycle of sine wave, the spot traces out a circle on the screen.

MEASUREMENT OF PHASE DIFFERENCE

We have discussed that when two sinusoidal voltage signals of equal frequency having some phase difference are applied to the deflection plates of CRO, a straight line or an ellipse appears on the screen. In the case of straight line appearing on the screen, phase angle difference would be zero or 180° but in case of an ellipse we will have to use a formula for determination of phase difference.

Let there be two sinusoidal voltage signals given by

v_h = V_h Sin ωt

v_v = V_v Sin (ωt+Ф), where Ф is the phase difference.

Since deflection is directly proportional to the amplitude of voltage

So d_h = D_h Sin ωt

d_v = D_v Sin (ωt+Ф)

At time t=0, values of d_h and d_v are d_h0 = 0 and d_v0 = D_v Sin Ф

So Sin Ф = d_v0/D_v

Graphical meaning of d_v0 and D_v are shown in the figure. Thus the phase difference between two sinusoidal voltages of equal frequency can be determined by measuring d_v0 and D_v.

In the given figure V_v is shown by leading V_h by a phase angle Ф. If the situation is reversed and V_h leads V_v by phase angle Ф, then again same ellipse would appear on the screen. Because of this fact we can determine only the phase angle between two sinusoidal voltages. It does not indicate which one is leading and which one is lagging.

MEASUREMENT OF FREQUENCY OF A VOLTAGE SIGNAL

The patterns obtained on CRO screen and discussed in previous sections are called the Lissajous patterns. A Lissajous pattern is a pattern which is stationary on the screen of a CRO. It means that the spot traces out the same pat­tern for every cycle of a voltage signal. As we have already stud­ied that the ratio of frequencies of vertical and horizontal voltage signals should be a rational or fractional number to have steady pattern. So the condition for hav­ing a Lissajous pattern on the CRO screen is

F_y / F_x = A/B
where A and B are integers.

Lissajous patterns are usually of two types. First one is closed Lissajous pattern and has no free end. Second one is open Lissajous pattern and has free ends. Both types of Lissajous patterns are shown in figure.

In a Lissajous pattern ratio of frequency of vertical signal to the frequency of hori­zontal signal is equal to the ratio of positive Y-peaks to positive X-peaks in that pattern.

F_y / F_x = Positive Y – peaks in pattern / Positive X – peaks in pattern

Thus by counting the positive Y-peaks and X-peaks on a Lissajous pattern, ratio of frequencies of two voltage signals can be determined. In case of an open lissajous pattern, free end is treated as half peak. This will be clear from examples.

Voltage signal of unknown frequency is applied to the vertical deflection plates and horizontal deflection plates are supplied by an accurately calibrated variable frequency source. Frequency of the variable frequency source is adjusted until a stationary pattern appears on the screen. Now by reading the value of frequency of horizontal signal, with the help of calibrated scale, frequency of voltage signal applied to vertical deflection plates can be known.

Lissajous Patterns

In case single loop stationary pattern is obtained the frequency of the sinusoidal voltage applied to vertical deflection pates is the same as that of the voltage applied to horizontal deflection plates. In case complex Lissajous figure is obtained, the frequency of alternating voltage may be determined using the relation

Points of tangency to a vertical line / Points of tangency to a horizontal line = ω_x/ω_y = f_x/f_y

One point, very interesting, to know is that sometimes we may have different types of patterns on the CRO screen for the voltage signals of the given frequencies, as shown in figure.

In both of the figures, the ratio of Y-peaks to X-peaks is equal so in both cases, ratios of fre­quencies of vertical and horizontal signals are same. But appearance of Lissajous patterns is different owing to different phase difference of voltage signals applied to vertical arid horizontal deflection plates.

CRO is not a precision instrument for measuring frequency of an alternating voltage because the accuracy depends directly on the accuracy of calibrated scale of variable frequency source, which is usually a few percent. It is used for rough estimate of fre­quency or when voltage waveform is so complex that a frequency counter would not operate reliably.

Measurement of Voltage and Current

Cathode Ray Oscilloscope can be used for the measurement of voltage of any electrical specification as the deflection of the electrostatic beam is directly proportional to the deflection plate voltage.

For measurement of the direct voltage, firstly the spot is centered on the screen without applying any voltage signal to the deflection plates. Then direct voltage to be measured is applied between a pair of deflection plates and the deflection of the spot is observed on the screen. The magnitude of the deflection multiplied by the deflection factor gives the value of the direct voltage applied. Usually the screen is calibrated for fixed operating condition, so by reading the scale, voltage can be measured directly by the CRO.

In case of measurement of alternating voltage of sinusoidal wave-form, it is applied between a pair of deflection plates and the length of the straight line is measured. Knowing the deflection sensitivity, the peak to peak value of applied ac voltage can be determined. The rms value of ac voltage applied will be equal to this peak value divided by 2√2 for sinusoidal wave-form.

For measurement of current, the current under measurement is passed through a known non-inductive resistance and the voltage drop across it is measured by CRO, as mentioned above. The current can be determined simply by dividing the voltage drop measured by the value of non-inductive resistance. When the current to be measured is of very small magnitude, the voltage drop across non-inductive resistance (small value) is usually amplified by a calibrated amplifier.

The current and voltage can be measured simultaneously by using double beam cathode ray oscilloscope.

Voltage-controlled-oscillator-Block-Diagram

In most cases, the frequency of an oscillator is determined by the time constant RC. However, in cases or applications such as FM, tone generators, and frequency-shift keying (FSK), the frequency is to be controlled by means of an input voltage, called the control voltage. This can be achieved in a voltage-controlled oscillator (VCO). A VCO is a circuit that provides an oscillating output signal (typically of square-wave or triangular waveform) whose frequency can be adjusted over a range by a dc voltage. An example of a VCO is the 566 IC unit, that provides simultaneously the square-wave and triangular-wave outputs as a function of input voltage. The frequency of oscillation is set by an external resistor R₁ and a capacitor C₁ and the voltage V_c applied to the control terminals. Figure shows that the 566 IC unit contains current sources to charge and discharge an external capacitor C_v at a rate set by an external resistor R₁ and the modulating dc input voltage. A Schmitt trigger circuit is employed to switch the current sources between charging and discharging the capacitor, and the triangular voltage produced across the capacitor and square-wave from the Schmitt trigger are provided as outputs through buffer amplifiers. Both the output waveforms are buffered so that the output impedance of each is 50 f2. The typical magnitude of the triangular wave and the square wave are 2.4 V_peak._to-peak and 5.4V_peak._to._peak.

The frequency of the output waveforms is approximated by

f_out = 2(V⁺ - V_c)/R₁C₁V⁺

Voltage-controlled-oscillator-Circuit-Diagram

Figure shows the pin connection of the 566 unit. The VCO can be programmed over a 10-to-l frequency range by proper selection of an external resistor and capacitor, and then modulated over a 10-to-l frequency range by a control voltage, V_{c The voltage controlled oscillators (VCOs) are commonly used in converting low-frequency signals such as EEG (electro-encephalograms) or ECG (electro-cardiograms) into an audio­frequency (AF range).}

A function generator is a signal source that has the capability of producing different types of waveforms as its output signal. The most common output waveforms are sine-waves, triangular waves, square waves, and sawtooth waves. The frequencies of such waveforms may be adjusted from a fraction of a hertz to several hundred kHz.

Actually the function generators are very versatile instruments as they are capable of producing a wide  variety of waveforms and frequencies. In fact, each of the waveform they generate are particularly suitable for a different group of applications. The uses of sinusoidal outputs and square-wave outputs have already been described in the earlier Arts. The triangular-wave and sawtooth wave outputs of function generators are commonly used for those applications which need a signal that increases (or reduces) at a specific linear rate. They are also used in driving sweep oscillators in oscilloscopes and the X-axis of X-Y recorders.

Many function generators are also capable of generating two different waveforms simultaneously (from different output terminals, of course). This can be a useful feature when two generated signals are required for particular application. For instance, by provid­ing a square wave for linearity measurements in an audio-system, a simultaneous sawtooth output may be used to drive the horizontal deflection amplifier of an oscilloscope, providing a visual display of the measurement result. For another example, a triangular-wave and a sine-wave of equal frequencies can be produced simultaneously. If the zero crossings of both the waves are made to occur at the same time, a linearly varying waveform is available which can be started at the point of zero phase of a sine-wave.

Another important feature of some function generators is their capability of phase-locking to an external signal source. One function generator may be used to phase lock a second function generator, and the two output signals can be displaced in phase by an adjustable amount. In addition, one function generator may be phase locked to a harmonic of the sine-wave of another function generator. By adjustment of the phase and the amplitude of the

harmonics, almost any waveform may be produced by the summation of the fundamental frequency generated by one function generator and the harmonic generated by the other function generator. The function generator can also be phase locked to an accurate fre­quency standard, and all its output waveforms will have the same frequency, stability, and accuracy as the standard.

Function Generator Block Diagram

The block diagram of a function generator is given in figure. In this instrument the frequency is controlled by varying the magnitude of current that drives the integrator. This instrument provides different types of waveforms (such as sinusoidal, triangular and square waves) as its output signal with a frequency range of 0.01 Hz to 100 kHz.

The frequency controlled voltage regulates two current supply sources. Current supply source 1 supplies constant current to the integrator whose output voltage rises linearly with time. An increase or decrease in the current increases or reduces the slope of the output voltage and thus controls the frequency.

The voltage comparator multivibrator changes state at a predetermined maximum level, of the integrator output voltage. This change cuts-off the current supply from supply source 1 and switches to the supply source 2. The current supply source 2 supplies a reverse current to the integrator so that its output drops linearly with time. When the output attains a pre­determined level, the voltage comparator again changes state and switches on to the current supply source. The output of the integrator is a triangular wave whose frequency depends on the current supplied by the constant current supply sources. The comparator output provides a square wave of the same frequency as output. The resistance diode network changes the slope of the triangular wave as its amplitude changes and produces a sinusoidal wave with less than 1% distortion.

PUT CONTROLLED SAWTOOTH WAVE GENERATOR

A PUT controlled sawtooth generator circuit is shown in figure. When power is first applied, the programmable unijunction transistor (PUT) is off. The capacitor C begins to charge up and the output voltage rises. This continues until the output voltage (which is also the PUT anode voltage) is about 0.7 V above the control input (the gate voltage). The PUT gets switched on. The capacitor C is shorted out through PUT and, therefore, capacitor gets immediately dis­charged through the PUT. The output voltage, which is equal to the voltage across the capacitor, falls. When the current through the PUT falls below its holding current I_H, it goes off and the cycle repeats. When the PUT turns off, approximately 1 V is usually left on the capacitor. The output waveform is shown in figure.

PUT CONTROLLED SAWTOOTH WAVE FORM

The time period of the PUT controlled sawtooth generator depends on the charge rate (V/RC) and the control voltage V_control. This is obvious from figure.

Time period, T = Distance / Rate = (V_control + 0.7 V) – 1V / (І-V І/RC)

= V_control RC / І-V І………………. {І-V І = magnitude of –V}

and frequency, f = 1/T = І-V І/V_control RC

The PUT controlled sawtooth generator can be used as a voltage-to-frequency converter.

Precautions

• The cathode of the PUT must be tied to ground or virtual ground and current flows only from anode to cathode. So PUT cannot be used to control a negative ramp generator.
• To turn-off the current through the PUT must drop below its holding current I_H (specified by the manufacturer). When the PUT is on, a current equal to that used to charge the capacitor, in addition to capacitor discharge current, flows through the PUT. This current flows through R to V^- must be below I_H.

That is, I = V/R < I_H

Failing which, once the PUT goes on, it will be held on by this charge current, even when the capacitor has fully discharged. This charge current can be lowered by increasing R or reducing negative voltage V^-.. However, both of these factors affect the change rate and. Therefore, the frequency. For keeping frequency unaffected the changes in either R or V^- will have to be balanced with appropriate changes in C.