Download P10 and P11 Walkthrough P10 Electrical and Electronic Principles

P10 and P11 Walkthrough
P10 Electrical and Electronic Principles
Use single phase ac circuit theory to determine the characteristics of a sinusoidal AC waveform
P11 Electrical and Electronic Principles
Use an oscilloscope to measure and determine the inputs and outputs of a single phase AC circuit
Introduction
A perfect sine wave has no harmonics, this means that all the available energy is contained by the sine wave, a sine wave is easy
to generate (relatively) and is perfect for power transmission since being an alternating voltage it is easy to step up and step
down thus avoiding (as much as possible) power loss in transmission lines due to the I2R effect.
In principles you are required to know the fundamentals of a sine wave, to be able to carry out simple calculations that predict
voltage against time and lastly to be able to measure the inputs and outputs of a circuit that has a sine wave applied to it.
We will start with the fundamental characteristics of a sine wave. As always Google images provides some excellent resources
to show the basics.
Both images convey almost all the information you need for P10.
The amplitude is the maximum or peak value of the sine wave
The peak to peak value (positive peak + negative peak)
The RMS value is the average value in terms of DC power represented by the sine wave
The centre line or neutral line is the point where a sine waves polarity changes from positive to negative or vice versa
The frequency is the amount of times the waveform repeats in one second
The periodic time (T) is the amount of time taken for the waveform to complete one whole cycle
If you want to see how a sine wave is generated then you can follow this link.
http://www.kwantlen.bc.ca/science/physics/faculty/mcoombes/P2421_Notes/Phasors/Phasors.html
Suffice to say that the main thing to recognize is that a sine wave is generated by a rotating phasor and that one full waveform
is completed once the phasor has travelled 360®.
The basic mathematical form of a sine wave is represented by the equation:
Vinst = Vpeak x sin(ωt +/- φ)
Where Vinst is the instantaneous voltage, which means it is the value you are attempting to find at a given point in time
Vpeak is the maximum value of the sine wave
sin is of course sin on your calculator
ω (omega) represents 2π x the frequency of the sine wave
t represents the time elapsed
φ represents phase (up to 90® before or after t = 0)
So a quick word about phase. As long as a sine wave is applied to a circuit that contains only resistive elements then the voltage
and current will rise and fall at the same time.
However most (well actually all to some degree) contain elements of inductance and capacitance. Both properties cause
something known as reactance which you can think of as a sort of frequency dependant resistance.
They also cause the voltage to lead the current in the case of inductance and to lag the current in the case of capacitance. This
means that a voltage measured on the output of a circuit that has reactance will not be in phase with the input voltage as
shown on the diagram below.
To demonstrate the basic equation we are going to do a simple simulation and then show it practically.
Let Vinst = 1.5 x sin(1000 x 2π x 0.00025)
The circuit is shown in Multisim. Let’s do the math first.
Vinst =1.5 x sin(6280 x 0.00025)
= 1.5 x sin(1.57)
It is crucial to note at this point that the 1.57 is in radians
Before you can use the sin on your calculator the 1.57 must be converted to degrees. It’s really easy
1 radian = 57.3 degrees
Therefore 1.57 radians = 90 degrees (give or take a very small amount)
sin 90 = 1
Therefore the voltage after 0.00025 seconds have elapsed is
1.5 volts
You can check this with the grapher on Multisim:
Adjust the blue and red cursors so that one is positioned just as the voltage crosses the neutral line and the other is positioned
at the next peak voltage. The legend dx will give you the amount of time eplased (in my example .246 micro seconds) and dy
will give you the amplitude which in this case is 1.4914 volts. In practice you might find it difficult to get the cursors in the exact
positions. Don’t sweat it just get close enough to prove the general rules.
Because there is no phase shift associated with this circuit t= 0 can be taken from any time that the waveform crosses the
neutral line in an ascending direction.
P11
For the pass you are required to be able to measure the inputs and outputs of an ac circuit. We will do this in 2 different ways.
Firstly using Multisim and secondly using a computer based oscilloscope.
Here is the circuit in Multisim.
Now the presence of a capacitor will change the waveform shown by channel B of the oscilloscope. Theory tells us the
following:
At a certain frequency known as the cutoff frequency the voltage across the output (in this case the capacitor) will be 0.707
times in input voltage. Furthermore the voltage across the capacitor will lead the input voltage by 45®. The capacitor will cause
this phase change.
This frequency is often called the -3 dB cutoff point, the point where a signal has diminished so that it is no longer considered as
viable by the rest of the system. It has great importance in many electronic applications e.g. in audio filters.
The frequency is calculated thus:
FCUTOFF = 1/2π x R x C
Doing the math for the circuit above then
FCUTOFF = approx 159 Hz
We can check this in Multisim again, but this time I will use an ac analysis which will be explained in the video. Here I will just
show the readouts and explain them.
Note how in the first readout, the smaller voltage leads and is smaller than the input voltage. Now you could mess around with
the cursor for ages, get your calculator out and end up with a headache trying to work out the phase shift. Fortunately ac
analysis gives us a much easier way.
Here is the readout.
The bottom graph shows the input phase related to the output. The cursor you are reading is y1 which shows the phase at very
near to -3 dB to be -44.2296. Don’t spend half your life trying to get it spot on, near enough is just fine.