Harmonics

In acoustics and telecommunication, a harmonic of a wave is a component frequency of the signal that is an integer multiple of the fundamental frequency. For example, if the fundamental frequency is f, the harmonics have frequencies f, 2f, 3f, 4f, etc. The harmonics have the property that they are all periodic at the fundamental frequency, therefore the sum of harmonics is also periodic at that frequency. Harmonic frequencies are equally spaced by the width of the fundamental frequency and can be found by repeatedly adding that frequency. For example, if the fundamental frequency is 25 Hz, the frequencies of the harmonics are: 25 Hz, 50 Hz, 75 Hz, 100 Hz, etc.

Behaviour of Purely Inductive Circuit

When two things (Waves) are in step, going through a cycle together, falling together and rising together, they are in phase. When they are out of phase, the angle of lead or lag-the number of electrical degrees by which one of the values leads or lags the other-is a measure of the amount they are out of step. The time it takes the current in an inductor to build up to maximum and to fall to zero is important for another reason. It helps illustrate a very useful characteristic of inductive circuits-the current through the inductor always lags the voltage across the inductor.

In the case of a circuit having inductance, the opposing force of the counter emf would be enough to keep the current from remaining in phase with the applied voltage. You learned that in a dc circuit containing pure inductance the current took time to rise to maximum even though the full applied voltage was immediately at maximum. Figure1shows the wave forms for a purely inductive ac circuit in steps of quarter-cycles.

Figure1. - Voltage and current waveforms in an inductive circuit.

With an ac voltage, in the first quarter-cycle (0° to 90°) the applied ac voltage is continually increasing. If there was no inductance in the circuit, the current would also increase during this first quarter-cycle. You know this circuit does have inductance. Since inductance opposes any change in current flow, no current flows during the first quarter-cycle. In the next quarter-cycle (90° to 180°) the voltage decreases back to zero; current begins to flow in the circuit and reaches a maximum value at the same instant the voltage reaches zero. The applied voltage now begins to build up to maximum in the other direction, to be followed by the resulting current. When the voltage again reaches its maximum at the end of the third quarter-cycle (270°) all values are exactly opposite to what they were during the first half-cycle. The applied voltage leads the resulting current by one quarter-cycle or 90 degrees. To complete the full 360° cycle of the voltage, the voltage again decreases to zero and the current builds to a maximum value.

You must not get the idea that any of these values stops cold at a particular instant. Until the applied voltage is removed, both current and voltage are always changing in amplitude and direction.

As you know the sine wave can be compared to a circle. Just as you mark off a circle into 360 degrees, you can mark off the time of one cycle of a sine wave into 360 electrical degrees. This relationship is shown in figure2. By referring to this figure you can see why the current is said to lag the voltage, in a purely inductive circuit, by 90 degrees. Furthermore, by referring to figures2 and 4-1(A) you can see why the current and voltage are said to be in phase in a purely resistive circuit. In a circuit having both resistance and inductance then, as you would expect, the current lags the voltage by an amount somewhere between 0 and 90 degrees.

Figure2. - Comparison of sine wave and circle in an inductive circuit.

Behaviour of Purely Resistive Circuit

Pure resistive AC circuit: resistor voltage and current are in phase.
If we were to plot the current and voltage for a very simple AC circuit consisting of a source and a resistor (Figure above), it would look something like this: (Figure below)

Voltage and current “in phase” for resistive circuit.
Because the resistor simply and directly resists the flow of electrons at all periods of time, the waveform for the voltage drop across the resistor is exactly in phase with the waveform for the current through it. We can look at any point in time along the horizontal axis of the plot and compare those values of current and voltage with each other (any “snapshot” look at the values of a wave are referred to as instantaneous values, meaning the values at that instant in time). When the instantaneous value for current is zero, the instantaneous voltage across the resistor is also zero. Likewise, at the moment in time where the current through the resistor is at its positive peak, the voltage across the resistor is also at its positive peak, and so on. At any given point in time along the waves, Ohm's Law holds true for the instantaneous values of voltage and current.
We can also calculate the power dissipated by this resistor, and plot those values on the same graph: (Figure below)

Instantaneous AC power in a pure resistive circuit is always positive.
Note that the power is never a negative value. When the current is positive (above the line), the voltage is also positive, resulting in a power (p=ie) of a positive value. Conversely, when the current is negative (below the line), the voltage is also negative, which results in a positive value for power (a negative number multiplied by a negative number equals a positive number). This consistent “polarity” of power tells us that the resistor is always dissipating power, taking it from the source and releasing it in the form of heat energy. Whether the current is positive or negative, a resistor still dissipates energy.

Behaviour of AC Circuits

In dc circuits, voltage and current are constant w.r.t time. The solution of the circuit may be attemted simply by applying ohm's law i.e. I=V/R. In ac circuits, voltage applied to the circuit (V) and current flowing through it (I) change from instant to instant. Thus, the above simple relation will not hold good in these circuits. The Variation of current w.r.t time set up magnetic effects and variation in emf set up electrostatic effects. Both these effects, must be taken into account while dealing with ac circuits. Magnetic effects will be appreciably large with low voltage, heavy current circuits. Electrostatic effects are usually appreciable with high voltage circuits.

Electric Drives

Electric Drives is very common in industries. In the industries the device/mechanism use to control the speed of a motor is known as electric drives. Infact Drive is an integrated system consists of Supply, the Power Modulator (Converter), Motor, Load, Sensors and control logic.

The eletric motor in any drive is choosen as per the load-torque characteistics required by the motor. In any drive we select a motor which best suits the speed trorque characterics required by the load. It should be clearly unterstood that the motor is not selected as per the supply available or any other factor. The selection criteria solely depends upon the requirement of the load.