A sinusoidal function or sinusoidal signal is a function that describes a smooth periodic oscillation.Continuous-Time Sinusoidal SignalA sinusoidal signal which is defined for every instant of time is called continuous-time sinusoidal signal. The continuous time sinusoidal signal is given as follows −𝑥(𝑡) = 𝐴 sin(𝜔𝑡 + 𝜑) = 𝐴 sin(2𝜋𝑓𝑡 + 𝜑)Where, A is the amplitude of the signal. That is the peak deviation of the signal from zero.ω=2πf is the angular frequency in radians per seconds.f is the frequency of the signal in Hz.φ is the phase angle in radians.All the continuous-time sinusoidal signals are periodic signal. The time ... Read More

What is Time Shifting?Time shifting or Shifting of a signal in time means that the signal may be either delayed in the time axis or advanced in the time axis.Time Shifting of Continuous-Time SignalThe time shifting of a continuous time signal x(t) is represented as, 𝑦(𝑡) = 𝑥(𝑡 − 𝑡0)The time-shifting of a signal results in the time delay or time advancement. The above expression shows that the signal y(t) can be obtained by time shifting the signal x(t) by t0 units. If t0 is positive in the above expression, then the shift of the signal is to the right ... Read More

What is Time Reversal of a Signal?The time reversal of a signal is folding of the signal about the time origin (or t = 0). The time reversal or folding of a signal is also called as the reflection of the signal about the time origin (or t = 0). Time reversal of a signal is a useful operation on signals in convolution.Time Reversal of a Continuous-Time SignalThe time reversal of a continuous time signal x(t) is the rotation of the signal by 180° about the vertical axis. Mathematically, for the continuous time signal x(t), the time reversal is given ... Read More

Discrete Time SignalsThe signals which are defined only at discrete instants of time are known as discrete time signals. The discrete time signals are represented by x(n) where n is the independent variable in time domain.Representation of Discrete Time SignalsA discrete time signal may be represented by any one of the following four ways −Graphical RepresentationFunctional RepresentationTabular RepresentationSequence RepresentationGraphical Representation of Discrete Time SignalsConsider a discrete time signal x(n) with the values, x(−3) = −2, x(−2) = 3, x(−1) = 0, x(0) = −1, x(1) = 2, x(2) = 3, x(3) = 1This discrete time signal can be represented graphically ... Read More

Even SignalA signal is said to be an even signal if it is symmetrical about the vertical axis or time origin, i.e., 𝑥(𝑡) = 𝑥(−𝑡); for all 𝑡 … continuous time signal𝑥(𝑛) = 𝑥(−𝑛); for all 𝑛 … discrete time signalOdd SignalA signal is said to be an odd signal if it is anti-symmetrical about the vertical axis, i.e., 𝑥(−𝑡) = −𝑥(𝑡); for all 𝑡 … continuous time signal𝑥(−𝑛) = −𝑥(𝑛); for all 𝑛 … discrete time signalProperties of Even and Odd SignalsAddition and Subtraction Properties of Even and Odd SignalsThe addition or subtraction of two odd signals is also ... Read More

A synchronous motor is not inherently self-starting. Therefore, it requires some auxiliary means of starting. In order to start a synchronous motor, there are following two methods −Starting with an external prime moverStarting with damper windingsSynchronous Motor Starting with an External Prime MoverIn this method of starting a synchronous motor, an external motor is used to drive the synchronous motor as shown in Figure-1.The external motor brings the synchronous motor to synchronous speed and then the synchronous motor is synchronised with the AC supply as a synchronous generator. Then the prime mover (i.e., the external motor) is disconnected. Once synchronised, ... Read More

A motor in general is an electrical machine that converts electrical energy into mechanical energy. Electric motors can either be DC Motors or AC Motors, depending on the type of power supply that is supplied as its input.AC motors are further classified into two types−Asynchronous or Induction MotorSynchronous MotorA synchronous motor always runs at synchronous speed, while an induction motor runs at a speed less than the synchronous speed.Read through this article to find out more about synchronous motors and induction motors and how they are different from each other.What is a Synchronous Motor?A synchronous motor is a type of ... Read More

Units of Synchronizing Power Coefficient (𝑷𝐬𝐲𝐧)Generally, the synchronizing power coefficient is expressed in Watts per electrical radian, i.e., $$\mathrm{𝑃_{syn} =\frac{𝑉 𝐸_{𝑓}}{𝑋_{𝑠}}cos\:𝛿 \:\:Watts/electrical\:radian …(1)}$$$$\mathrm{∵ \:𝜋\:radians = 180\:degrees}$$$$\mathrm{\Rightarrow\:1\:radian =\frac{180}{𝜋}\:degrees}$$$$\mathrm{∵ \:𝑃_{syn}=\frac{𝑑𝑃}{𝑑𝛿}\:\:Watts/ \left(\frac{180}{𝜋}\:degrees \right)}$$$$\mathrm{\Rightarrow\:𝑃_{syn}=\left( \frac{𝑑𝑃}{𝑑𝛿}\right)\left(\frac{𝜋}{180}\right)\:\:Watt/electrical\:degree …(2)}$$If p is the total number of pole pairs in the machine, then$$\mathrm{𝜃_{electrical} = 𝑝 \cdot 𝜃_{mechanical}}$$Therefore, the synchronizing power coefficient per mechanical radian is given by, $$\mathrm{𝑃_{syn} = 𝑝 \cdot\left( \frac{𝑑𝑃}{𝑑𝛿}\right)\:\:Watts/mech. radian …(3)}$$And, the synchronizing power coefficient per mechanical degree is given by, $$\mathrm{𝑃_{syn} =\left( \frac{𝑑𝑃}{𝑑𝛿}\right)\left(\frac{𝑝\:𝜋}{180}\right)\:Watts/mech.degree …(4)}$$Significance of Synchronizing Power CoefficientThe synchronizing power coefficient ($𝑃_{syn}$) is the measure of the stiffness of the electromagnetic coupling between the stator ... Read More

When the flux density distribution in the alternator is non-sinusoidal, the induced voltage in the winding will also be non-sinusoidal. Thus, the pitch factor or coil span factor, distribution factor and winding factor will be different for each harmonic voltage.Pitch Factor for nth HarmonicAs the electrical angle is directly proportional to the number of poles and the angle between the adjacent slots, i.e., $$\mathrm{𝜃_{𝑒} =\frac{𝑃}{2}𝜃_{𝑚} … (1)}$$The chording angle increases with an increase in the order of the harmonics (n). In a short pitch coil, the chording angle is α° (electrical) for the fundamental flux wave. For the nth harmonic, ... Read More

A 1-phase supply produces a pulsating magnetic field which does not rotate in the space. Therefore, a 1-phase supply cannot produce rotation in a stationary rotor. Although, like a 3-phase supply, the 2-phase supply can also produce a rotating magnetic field of constant magnitude. Therefore, all the single-phase induction motors, except shaded pole induction motor, are started as 2-phase motor. Once so started, the motor will continue to run on the 1-phase supply.How does a 2-Phase Supply Produce Rotating Magnetic Field of Constant Magnitude?Consider a 2-phase, 2 pole motor, where the phases A and B are fed by a balanced ... Read More