Basic Electronics leeson 10 Power

 Power Electronics

1.3 AC signals

Voltages and currents that vary in time are called AC quantities.

Common AC signals.

1.     Sinusoidal signals.

Sinusoidal voltages can be written

V = A sin(2πft + φ) = A sin(ωt + φ) (1.43)

where A is the amplitude, f is the frequency in cycles/second or hertz (abbreviated

Hz), φ is the phase, and ω is the angular frequency (in radians/second). The

repetition time trep is also called the period T of the signal, and this is related to

the frequency of the signal by T = 1/f

AC Waveform Characteristics

Frequency (f)

One of the most important properties of any regular waveform identifies the number of complete cycles it goes through a fixed period of time. Frequency refers to the number of times the waveform repeats itself within one second time period. It is commonly measured in cycles per second (cycles/sec) and is expressed in units of Hertz (Hz) with a mathematical equation representation by the letter ‘f’.

Period (T)

Period refers to the time in seconds that the waveform takes to repeat itself from start to finish. It is the time duration of one cycle of the waveform and the time interval required between successive repetitions of the periodic waveform. The best approach in measuring the period is to use successive crossings of the zero axis with a positive slope.

1. What is the periodic time, (T) of a 50Hz sinusoidal waveform. 2. what will be the oscillating frequency of a waveform that has a periodic time of 10mS.

1. Periodic Time

2. Frequency

Amplitude (A)

Amplitude refers to the magnitude or intensity of the signal waveform measured in volts or amps. It is the maximum value, positive or negative, that the waveform can attain.

(a) The peak amplitude A or Ap.

(b) The peak-to-peak amplitude App = 2A.

(c) The rms amplitude Arms = A/√2

Wavelength (lambda)

Wavelength refers to the distance of the cycle of the wave to complete one cycle. Lambda is a Greek letter that is used to represent the wavelength in mathematical expression. It is similar to Period except that wavelength is measured in distance per cycle whereas Period is measured in time per cycle. For a continuous DC voltage, the average or mean value will always be equal to its maximum peak value as a DC voltage is constant. The average value would be equal to zero as the positive and negative halves will cancel each other out if the average value is calculated over the full cycle in a pure sine wave. In the image below, the average or mean value of an AC waveform is calculated or measured over a half cycle.

Other Forms of Alternating Waves

While electromechanical alternators and many other physical phenomena naturally produce sine waves, this is not the only kind of alternating wave in existence. Other “waveforms” of AC are commonly produced within electronic circuitry. Here are but a few sample waveforms and their common designations in the figure below.

Some common waveshapes (waveforms).

Why Is AC Important?

There are several reasons why sinusoidal waveforms are important in electronics. The first obviousreason has to do with the ease of converting circular mechanical motion into induced current via an ac generator. However, another very important reason for using sinusoidal waveforms is that if you differentiate or integrate a sinusoid, you get a sinusoid. Applying sinusoidal voltage to capacitors and inductors leads to sinusoidal current. It also avoids problems on systems. But one of the most important benefits of ac involves the ability to increase voltage or decrease voltage (at the expense of current) by using a transformer. In dc, a transformer is useless, and increasing or decreasing a voltage is a bit tricky, usually involving some resistive power losses.

Transformers are very efficient, on the other hand, and little power is lost in the voltage conversion.