What is half wave symmetry?

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A periodic function x(t) which has either odd symmetry or even symmetry along with the half wave symmetry Is said to have quarter wave symmetry. Mathematically, a periodic function x(t) is said to have quarter wave symmetry, if it satisfies the following condition − x(t)=x(−t)orx(t)=−x(−t)andx(t)=−x(t±T2)

A Square Wave Waveform Is symmetrical in shape and has a positive pulse width equal to its negative pulse width resulting in a 50% duty cycle. Square wave waveforms are used in digital systems to represent a logic level “1”, high amplitude and logic level “0”, low amplitude.

A Half-Wave rectifier is an electronic circuit which converts only one-half of the AC cycle into pulsating DC. It utilizes only half of AC cycle for the conversion process. On the other hand, Full wave rectifier is an electronic circuit which converts entire cycle of AC into Pulsating DC.

Half Wave Rectification

The power diode in a half wave rectifier circuit passes just one half of each complete sine wave of the AC supply in order to convert it into a DC supply. Then this type of circuit is called a “half-wave” rectifier Because it passes only half of the incoming AC power supply As shown below.

Half-Wave Symmetry:

The equation represents that a periodic function has a half-wave symmetry if, After it has been shifted by one-half of a period and inverted, it is said to be identical to the original periodic function. The below figure represents the half-wave symmetry.

Answer The square wave in Figure 12 has a graph which is symmetrical about the y-axis and is called an Even function. The saw-tooth wave shown in Figure 13 has no particular symmetry. Examples of odd functions are t, t3,sint,sinnt. A periodic function which is odd is the saw-tooth wave in Figure 15.

The most common periodic waveforms are the Sine, triangle, square, and sawtooth. These waveforms are said to be periodic because the wave they represent can be repeated to produce a constant tone.

Asymmetry. Unlike waveforms that indicate DC Offset, Asymmetric waveform’s mean amplitude will reside on the center axis. However the representations of positive and negative amplitude (energy) will be disproportionate. This can inhibit the amount of gain that can be safely applied to the audio.

AC and the Sine Wave

The sinusoidal waveform is a symmetrical waveform, so the positive peak value is the same as the negative peak value as shown in Figure 2.2. If the positive peak has a value of 10 volts, then the negative peak will also have a value of 10 volts.

Half wave rectifier uses the same principle as PN junction diode and thus Converts AC to DC. In a half-wave rectifier circuit, the load resistance is connected in series with the PN junction diode. Alternating current is the input of the half-wave rectifier.

Advantages of half-wave rectifier:

• Half wave rectifier is a simple circuit.
• It has a low cost.
• We can easy to use it.
• We can easily construct.
• It has a low number of component, therefore it is cheap.

Ripple Factor

Ripple factor is in fact a measure of the remaining alternating components in a filtered rectifier output. It is the ratio of the effective value of the ac components of voltage (or current) present in the output from the rectifier to the dc component in output voltage (or current).

Rectifiers are mainly classified into two types as: Uncontrolled Rectifier. Controlled Rectifier.

The ripple factor is defined as. The ratio of the RMS value of an alternating current component in the rectified output to the average value of rectified output. The ripple factor is denoted as γ. It is a dimensionless quantity and always has a value less than unity.

Symmetry Properties

Represent x(t) as the sum of an even function and an odd function (recall that any function can be represented as the sum of an even part and an odd part). x(t)=xo(t)+xe(t) Express the Fourier Transform of x(t), substitute the above expression and use Euler’s identity for the complex exponential.

In terms of Fourier spectrum, for half wave symmetric signal, Cn = 0 ∀ n even. In other word, the spectrum of a half wave symmetric signal contains only odd harmonics. Half wave symmetry is defined only for periodic signals.

A full wave rectifier is defined as A rectifier that converts the complete cycle of alternating current into pulsating DC. Unlike halfwave rectifiers that utilize only the halfwave of the input AC cycle, full wave rectifiers utilize the full cycle.

A full wave rectifier is defined as A rectifier that converts the complete cycle of alternating current into pulsating DC. Unlike halfwave rectifiers that utilize only the halfwave of the input AC cycle, full wave rectifiers utilize the full cycle.