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# AC Waveforms and Theory

Alternating current is that which changes its direction periodically. As we discuses earlier AC current is bi directional in nature. The AC waveform is that which represents / describes all the characters of the alternating current.

Generally we will represent AC waveform by Sinusoidal waveform and its mathematical formulae is

A (t) = A sin (2πƒt)

Where ,

A is Amplitude of signal

t is the time period

f is the frequency of signal

In the process of generation of AC current , a wire or coil is rotated in a magnetic field produced by 2 magnets. If we plot the instances of the moving coil / wire with respect to time, it will form a graph of alternating current which is called “AC waveform”. Alternating current waveforms vary with time so they are also known as time dependent signals or Periodic signals.

Based on the generation methods of AC current, we will get different types of waveforms. But sine waveform is the most commonly used waveform for describing the AC current.

Outline

## AC Waveform Representation

With the help of a sine waveform, we can understand all the features and evolution of AC current. We represent the sine wave with its amplitude with respect to its time period. The amplitude (or sometimes called as voltage) is represented in vertical axis and the horizontal axis represents the time period.

In the AC waveform expression, A (t) = A sin (2πƒt), A (t) is the function which varies with respect to the time. In general the AC waveform will be as shown below.

The AC waveform has the same amplitude in both positive half cycle and negative half cycle. The amplitude of the waveform will be measured with respect to time. That is why the AC waveform is time-dependent.

### Types  of Periodic Waveform

There are many types of wave forms with which we can explain the alternating current. As the AC current is time dependent i.e. periodic, all the wave forms which are use to describe the AC current are also periodic. The other types of wave forms that are commonly used to represent the AC current are stated below.

• Sine wave
• Square wave
• Saw – tooth wave
• Triangular wave

As we are already familiar with sine wave, let’s start from Square wave form.

#### 1. Square Waveform

The square wave forms are mostly used for representing the electrical signals like voltage circuit outputs and for clock signal representation also. These are symmetrical in nature that means they represent equal duration in both positive and negative wave forms.

These wave forms are not rounded. Rather than being at peak amplitudes, they have vertical up and downs with flat top at the peak voltage level. Because of the flat top, they look like square shaped. That’s why they are called “Square wave forms”. The example of square wave is shown in below figure

We already learn that the square wave forms are symmetrical in nature. In this, the time taken to complete the positive half cycle must be equal to the time taken to complete the negative half cycle. So that we can calculate the duty cycle of the square wave by calculating the rise time and fall times. The Duty cycle means “The time taken for the positive half cycle by the to the wave form”.

If we say the time taken for the + ve half cycle is “On time” and the time taken for the – ve half cycle is “Off time”. The frequency of the square wave form can be found by the given formula.

Frequency=1/ (“ON” time+ “OFF” time)

Most of the digital electronic circuit wave forms are represented in square wave forms only.

#### 2. SAW – TOOTH Waveform

This is another type of periodic wave form. In this wave form the peaks of the wave-form at extreme times (low or high) are like teeth of Hack-saw blade. That’s why we call this as Saw-tooth wave form. Saw tooth wave forms are of two types. One is positive ramp saw-tooth wave and other is negative ramp saw-tooth wave form.
In the positive ramp saw tooth wave, it has slow rising time and high steep decay.

In the negative ramp saw tooth wave, it has fast rising time and slow steep decay.

The most used saw tooth wave form is positive ramp wave. It has the frequency in the ratio of even harmonics like 1/2, 1/4, 1/6 1/8 … 1/n etc.

The saw tooth wave form is used by musicians to produce the high clarity sound in audio devices, because of its high harmonic capacity.

#### 3. Triangular Wave

Triangular waves are those which will oscillate between positive and negative values. These are also bi directional in nature. Its shape is similar to that of linear positive ramp saw tooth wave form. The triangular waves have slow rising time and sloe decaying times.

The rate of change of voltages in the triangular wave forms, in their positive and negative half cycles is equal.

The triangular wave forms have their duty cycle as 50%, since it takes equal time to rise and fall down. The frequency of the triangular wave is the average of its voltage level.

### AC Waveform Characteristics

The AC wave form can be explained by its basic key characters like amplitude, frequency, time period.

#### 1. Amplitude

The maximum value of current or voltage is known as “Amplitude”. This is represented by either the positive peak or negative peak value of the sine wave. This maximum voltage level is also said to be the peak voltage. It may be either positive or negative. The negative sign in the value indicates the direction of current flow.

#### 2. Time Period

The time taken to complete one full cycle is known as “Time period”. It is denoted as ‘T’. The time period can be calculated, starting from any point on the AC sine wave. No matter where we start measuring the time period, it is the matter of completing one full cycle.

#### 3. Frequency

The frequency of a wave form is the reciprocal of its time period. It can also be explained as “The number of times that sine wave cycle occurs in a second”. Frequency is measured in HERTZ, by the name of a German scientist Henrich Hertz, who proved the existence of electromagnetic waves.

It is represented by the letter ‘f’

Frequency can be measured by the below given formula.

Frequency = 1 / Time Period.

### Summary

• The current which changes its direction periodically is called as “Alternating current” or “AC current”.
• The wave form which represents the characteristics of AC wave form is known as “AC wave forms”.
• Generally we use sine wave to explain the AC current characteristics.
• There are many other types of wave forms with which we can explain about AC current. They are
• Square wave form
• Triangular wave form
• Saw – tooth wave form
• The basic characteristics of AC wave form are amplitude, time period and frequency.