Bredhurst Receiving and Transmitting Society

Syllabus Sections:-

A.C. circuits

3g.1 1 Understand that the root mean square (RMS) value of a sinusoidal current has the same heating effect as a direct current of the same value and is 0·707 of its peak value.

Let's take a look at the sine wave that you were first introduced to in the Foundation Licence course, but several new items are added in this course.

Up to now you have only been considering that part of the sine wave marked 0 to 360 but you have learned that the sign wave in fact does continue on indefinitely until the equipment if turned off.

Looking at the diagram you can see Peak Value. This is the maximum voltage of the sine wave. Knowledge of this is needed to understand RMS.

Looking at the diagram you can see RMS Value. This stands for Root Mean Square value. The RMS has the same heating effect as a direct current of the same numeric value. The RMS is numerically equal to 0.707 of its peak value which is the equation given below as the 1/ square root of 2  is 0.707.

which is the same as V_rms = V_peak x 0.707

Thus if the peak value was 240V AC the RMS would be 240 x 0.707 = 169. So if you had a DC you would only need to have a voltage of 169 volts to given the same heating as 240V AC.

Also the average value of the AC sine wave is numerically equal to 0.636 of its peak value.

Also observe that the measurement between one peak and the next is called the Peak to Peak value.

Finally the horizontal axis through the centre is the time axis and is measured in seconds. The vertical axis is the + and - volts.

There is more about the sine wave that you need to know.

1. One complete cycle as is shown above is completed in a time period of T in seconds

2. The number of cycles completed in one second is the frequency f and the unit is Hz (Hertz)

3. Thus T = 1 / f or time to do one complete cycle is one divided by the frequency in Hz

4. And f = 1 / T or the frequency in Hz is given by one divided by the time T to do one cycle.

Example

If a RF signal has a frequency of 3MHz what is its periodic time ?

a 2ms b 500us c 2 us d 300 ns

Answer 3MHz is 3,000,000 cycles in one second, so to find the period it is simply one second divided by the number of cycles.  (from T = 1/f )

1 / 3000000 = 0.0000003 or 300ns

so correct answer is d

You can see that there are marking at the bottom of 0 - 180 - 360 which are measurements in degrees. There are 360 degrees in a circle (see diagram above) just as there are in one cycle of the sine wave.

Phase

The word phase is used in the context of the waveform to mean an amount of time. The amount of time to do one complete cycle is 360 degree and half a cycle 180 and so on.

Phase angle

Thus if two sine waves are on the same diagram but start and finish at different places the time difference between them can be expressed conveniently as a phase angle.

Out of phase

The amount that a curve lags of leads is given in degrees according to where the same point on the first curve the second one is. In the diagram above you can see that the angle = 90^o so by using the circle you could assess the amount of lead or lag in degrees.

From the point of view of the sine wave "A" at point 0, the wave form "C" is leading wave "A" by 90 degrees. If you look at the diagram above "C" as it was at the same point on the time line 90 degree earlier than "A".

Where as wave "B" lags wave "A" by 90 degrees as it has not yet reached the point on the time line where "A" is at 0.

All the waves "A", "B" and "C" are said to be out of phase.

In phase

If two curves start and finish at the same time even though they have different magnitudes they are said to be in phase.