We first define what an ac signal is. There are many ac signals, but we usually refer to a sinusoidal signal as the ac signal. The terms, the ac signal and the sinusoidal signal, are used as if they are synonymous terms.
Next we outline the importance of ac signal. The significance of ac signal, or sinusoidal signal, stems from the fact that it is the most commonly used signal. The mains utility is a sinusoidal voltage source. All the power appliances, such as the refrigerator, washing machine, fan and, air-conditioner, are excited by a sinusoidal signal. Hence a technique has been developed to analyze circuits excited by sinusoidal signals.
We define next the properties of ac signal. In this case, we refer to the sinusoidal signal. The signal is repetitive. It means that the signal has a frequency, it is sinusoidal in shape and it has an amplitude. The precise definition is presented later. Another property is that when a linear network is excited by a sinusoidal signal, all the responses of the network are sinusoidal after the network has reached the steady-state, and hence there is a necessity for a technique for sinusoidal analysis of circuits.
We take up next the mathematical equation that defines and describes an ac signal. The sinusoidal signal is a deterministic signal, meaning that its value is known at any given instant and it can be defined by an equation, as we will see.
Even though the mathematical equation, defining the sinusoidal signal, does not call for complex number, it is necessary to know about complex numbers, and how to manipulate them, in order to analyze ac circuits.
After learning about complex numbers, we take up the topic of phasors. Phasors are similar to complex numbers in some respect, and yet they are different. Sinusoidal voltages and currents are expressed as phasors. The basic aspects of phasors are explained next.
As stated earlier, there are similarities between phasors and complex numbers. For algebraic operations, such as addition, subtraction, multiplication and division, the same technique is used for both complex numbers and phasors. The difference is in what they represent. A complex number is used to represent a point on a plane. A planar surface has two axes, which are perpendicular to each other, and hence complex number representation of a point contains information about the two co-ordinates. On the other hand, a phasor is used to represent a sinusoidal signal varying as a function of time. We shall see more explanation of these aspects a little later.
In this chapter, it will be shown how the time domain expression and its phasor are related. It is necessary to understand to make transition from time domain to phasor domain and vice versa.
For a complex number, the imaginary operator is used to identify the imaginary part, whereas it has a different significance in relation to phasors. It refers to the phase relationship. We shall see more about it later on.
When an ac signal is applied to a circuit, inductors and capacitors have reactances. We will find out how we can calculate the reactance of a capacitor, and the reactance of an inductor.
In the case of dc circuits, Ohm's law defines the ratio of voltage to current of a resistor, as the resistance. In the case of ac circuits, we need to introduce additional terms, which are impedance and reactance. We know that conductance is the reciprocal of resistance. Similarly, admittance is the reciprocal of impedance, and susceptance is the reciprocal of reactance. We will explain these terms later. We will also be introducing phasor diagrams, to explain the phase relationship between voltage and current of a component.
Next we study how simple ac circuits can be analyzed. The phasor diagrams are used to explain the behaviour of ac circuits.
We know how to calculate the power absorbed by a resistor. We will find how the power absorbed by an ac circuit can be calculated. We will come across new terms and concepts. We talk about real or active power, reactive power, apparent power, and complex power. We will define the root mean square value of voltage or current, and then introduce what power factor of an ac circuit is.
The term, immittance, is used to refer to either impedance or admittance. We will see how the immittance of commonly used circuit combinations can be obtained. As can be seen, a lot of terminology and concepts are introduced in this chapter.