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Due Date:2/10/2014 Date submitted: 2/10/2014
Programme Title:
Course No.:
Tutor:
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Course Title:
Student ID: 201000754
Student Name: Mustafa Isa Al-Ansari
Mustafa Isa Al-Ansari 201000754
Assessment Title
Mr. John leek
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This assignment is our own work Any information used has been properly referenced. I understand that a copy of my work may be used for moderation. I have kept a copy of this assignment
Power Electronics
Bachelor of Engineering Technology
ENB6009
operation and investigation of domestic light dimmer
Mustafa Isa Al-Ansari 201000754
Abstract the aim of this assignment is investigate the operation of the light dimmer circuit. This
assignment will include theoretical calculations, experimental results, and simulation result. In
the experimental result three output parameters will be plotted against alpha which is the
firing angle, and a brief description on the method that is used to operate the dimmer will be
provided. There will be a compression between theoretical and experimental results. moreover,
This assignment will consist of simulation results which are RFI components , the frequency
response of the RFI components , and brief description on the reason why the circuit is fitted in
the light dimmer circuit. Finally, the attenuation of the RFI components will be discussed if the
circuit is expected in EN55015 standard which is the RFI specification in Europe.
Objectivesthe objectives of this project are :
to investigate the operation of a domestic light dimmer to connect the light dimmer circuit to mains power , and to the light holder to measure the output power, current , and power factor , experimentally, and plot
them with respect to phase angel. to measure the total harmonics distortion using DSA, to see whether it fits in the RFI
aspect. to draw the dimmer circuit on Altium designer with correct values. to compare the theoretical and experimental result of the output power with respect to
the phase angel. to simulate the RFI components (LC filter) , and determine the frequency response using
Altium.
Mustafa Isa Al-Ansari 201000754
ContentsAbstract.......................................................................................................................................................2
Objectives....................................................................................................................................................2
Technical discussion....................................................................................................................................6
Finding the RMS value of chopped sine wave.........................................................................................6
converting the alpha into angle in degree.............................................................................................7
Finding the cutoff frequency of the low pass filter (LC)...........................................................................8
Find the R load of a second order low pass filter.....................................................................................9
Minimum and maximum Time constant................................................................................................10
simulation results......................................................................................................................................12
Introduction...........................................................................................................................................12
RFI components.....................................................................................................................................12
Discussion and conclusion on the simulation result..............................................................................15
Experimental results..................................................................................................................................16
Introduction...........................................................................................................................................16
Discussion on the output parameter with respect to alpha..................................................................19
Harmonic distortion of the dimmer.......................................................................................................21
Discussion on the harmonics distortion.................................................................................................22
Operation of light dimmer circuit..........................................................................................................23
The circuit's operation...........................................................................................................................24
Comparing the time constant with off time delay of the chopped sine wave.......................................24
Experimental section conclusion...........................................................................................................25
Conclusion section.....................................................................................................................................26
Comparative analysis and discussions...................................................................................................26
References.................................................................................................................................................27
Table of figureFigure 1 The parameters that control the RC time constant.......................................................................9Figure 2 second order low pass filter it known as RFI components...........................................................12Figure 3 cutoff frequency which is 256 KHz...............................................................................................13Figure 4 current agaist alpha.....................................................................................................................17Figure 5 power V Alpha.............................................................................................................................17
Mustafa Isa Al-Ansari 201000754
Figure 6 power factor agaisnt alpha..........................................................................................................18Figure 7 The theoretical and expermental power verses alpha in degree.................................................20Figure 8 Light dimmer circuit with RFI components..................................................................................22
Table of tablesTable 1 output parameters ( experimental values)...................................................................................16Table 2 maximum harmonics....................................................................................................................21Table 3 comparing the time constant with off time delay.........................................................................23
Mustafa Isa Al-Ansari 201000754
Technical discussion
Finding the RMS value of chopped sine wave
The calculations below are related to the RMS value of chopped sine wave. In the light dimmer
the Ac waves are chopped by the triac. In this calculation, half cycle will be used to determine
the area under the curve after chopping the sine, and the time will be between α ( the phase
angle/ firing angle) to π. Then, the area under the curve will multiplied by 1 divided by the time
of half cycle of the real sine wave before chopping it out a which is zero to π.
RMS value=√ 1(b−a)∫a
b
f 2 ( t )dt
RMS value=√ 1(π−0)∫α
π
Vp2∗sin2(t)dt
sin2 (t )=1−cos (2 t)2
RMS value=√Vp2(π)∫απ 1−cos (2 t)
2dt
RMS value= Vp√2 π √∫
α
π
1−cos (2 t)dt
RMS value= Vp√2 π √[ t−sin (2 t)2 ]
RMS value= Vp√2∗√2π √[ t−sin (2t )] πα
Mustafa Isa Al-Ansari 201000754
RMS value= Vp2∗√ π
∗√ [ (π−sin (2∗π ) )−(α−sin (2α ) ) ]
RMS value= Vp2∗√ π
∗√ [ (π−0 )−(α−sin (2α ) ) ]
RMS value= Vp2∗√ π
∗√ [π−(α−sin (2α ) ) ]
RMS value=Vp2 ∗√[1−απ +(sin (2α ) )
π ]The importance of this equation is that it is going to be used to find out the power which is proportional to Vrms squared. note- the value of alpha must be in radian ( not degree).
converting the alpha into angle in degreethe phase angle was not calculated directly, but it was converted from seconds to degrees. This
was done by measuring the off time of the chopped sine wave by using the scope cursors and
the off time is changes depending on the value of the variable resistor. the following equation
was used to convert the delta time ( off time ) into angle in degree which is the phase angle.
phaseangle (degree )=offTime∗36020ms
phaseangle (degree )=offTime∗18010ms
Off time degree6.3ms 113.46ms 1085.6ms 100.84.9ms 88.24.2ms 75.63.48 ms 62.642.2ms 39.60 0
Mustafa Isa Al-Ansari 201000754
Finding the cutoff frequency of the low pass filter (LC).
The light dimmer circuit produces harmonics distortion ( radio frequency interference) which affects the
circuits nearby such as radio and mobile phone. So low pass filter consists of inductor , and Capacitor is
used to minimize the harmonics distortion. The value of L=36.4 uH c= 10 nF were measured using Multi
meter on Elvis board. the cutoff frequency is determined by the following equation.
Cutoff frequency= 12π √LC
Cutoff frequency= 12π √36.4uH∗10nf
Cutoff frequency=263.8KHz
Mustafa Isa Al-Ansari 201000754
Find the R load of a second order low pass filter
The Rload of the filter can be calculated using the equation of the quality factor of an RLC circuit
where R parallel with C and L is in series with C. the value of Q was chosen so it give a normal
frequency response so the cutoff frequency can be determined at - 3DB
Q=Rload √CL0.707=Rload √ 10n
36.4uH
0.707=Rload √ 10n36.4uH
0.707
√ 10n36.4uH
=Rload
Rload=42.65 ohms
Mustafa Isa Al-Ansari 201000754
Minimum and maximum Time constantCalculating the maximum and minimum time constant from the value of the Capacitor and the variable resistor:
basically the value maximum value of the variable resistor is 470 Kohms, and minimum value is 0 ohms. The value of the capacitor is fixed which is 100 nF. the RC time constant is determined as the following formula time constant= R*C
.
Figure 1 The parameters that control the RC time constant
When the time constant is describe as minimum time constant, this mean that the potentiometer has a
very small value, and can be determined as few hundred of ohms. so this value will be assumed as 100
ohms
when the time constant is minimum the components in the circuit above can be describe as the
following
R2=100
R1=3.3K ohms
R3=660K ohms
C2=100nF
Mustafa Isa Al-Ansari 201000754
1Rt
= 1R2+R1
+ 1R3
1Rt
= 13300+100
+ 1660000
RT=3.4kohms=Rminimum
minimum time constant
Timeconstant (minumum )=R (minimum )∗¿C2
Timeconstant (minumum )=R (minimum )∗C 2
Timeconstant (minumum )=3400∗100∗10−9
Timeconstant (minumum )=340us
when the time constant is maximum the components in the circuit above can be describe as the
following
R2maximum=470Kohms
R1=3.3K ohms
R3=660Kohms
C2=100nF
1Rt
= 1R2+R1
+ 1R3
1Rt
= 1470000+3300
+ 1660000
RT=275.64 kohms=R maximum
maximum time constant
Timeconstant (maximum )=R (maximum )∗¿C2
Timeconstant (maximum )=275.64∗100∗10−9
Mustafa Isa Al-Ansari 201000754
Timeconstant (maximum )=27.6ms
simulation results
Introduction
the aims of this sections are to draw the RFI components(second order low pass filter) on
Altium designer , and simulate the circuit to observe the cutoff frequency of the filter. This
section is also required to see whether the attenuation of the RFI components can fit in the
curve of the RFI spec EN55015 or not. This section will include a schematic circuit of the light
dimmer with brief explanation on how it works. Finally the simulation result of the RFI
components ( frequency response) will be represented .
RFI components
the main aim of light dimmer circuit is to control the brightness of the light by chopping up the
current that is drawn on the load. Therefore, a harmonic distortion(RFI) will be produced
because the wave is not sine wave anymore. So The light dimmer circuit produces radio
frequency interference. this type of frequency affects some electric circuits nearby such as
radio and mobile phones. As a result, low pass filter is used in the dimmer to attenuate the
harmonic distortion that is produced by the dimmer. The filter consists of an inductor and a
capacitor. the figures below represents the schematic circuit of the low pass filter, and the bode
plot of the amplitude (db) against the frequency to observe the cutoff frequency of the filter.
Mustafa Isa Al-Ansari 201000754
Note that R2 was calculated in the technical discussion. the following steps are repeated.
Q=Rload √CL0.707=Rload √ 10n
36.4uH
0.707=Rload √ 10n36.4uH
0.707
√ 10n36.4uH
=Rload
Rload=42.65 ohms
Figure 2 second order low pass filter it known as RFI components
Mustafa Isa Al-Ansari 201000754
Figure 3 cutoff frequency which is 256 KHz
Mustafa Isa Al-Ansari 201000754
Discussion and conclusion on the simulation result
The circuit of RFI components was simulated using Altium designer, the circuit is shown in
figure 2, and the simulation is represented in figure 3. In figure 3, the cutoff frequency is 265
KHz which is very close to the theoretical cutoff frequency (263 KHZ). this means that the
simulation , and the theoretical cutoff frequency match each other. The cutoff frequency above
is 265 KHz when means the noise that are produces by the bulb will be attenuated when the
frequency reaches the 256KHz. Finally, the objective of this section was to indentify the RFI
components which are presented in figure 2, simulate the RFI circuit to determine the cutoff
frequency. The value of the cutoff frequency was very similar to the theoretical cutoff
frequency, which means that the theoretical calculation matches the simulation result.
Mustafa Isa Al-Ansari 201000754
Experimental results
IntroductionThe aims of this section are to include the experiment methods on testing a light dimmer, and
record the output parameters such as current, power , power factor, and plot them against the
phase angle. this section will also include a compression graph between the theoretical and
experimental output power against alpha( phase angle). also, a table will be created to record
the maximum harmonic distortion that are produced by the light bulb.
A light dimmer circuit, bulb, bulb holder and amp plug were given to the students by the tutor
in order to wire them up and construct a light dimmer. The light dimmer circuit was connected
in series with the amp mains plug and the holder of the bulb. After that, the circuit was checked
by the tutor, and the wirings in the holder were covered with an isolation materiel to prevent
injuries. Then the amp plug was connected to the main socket , and the bulb was operated
which the student could control the brightness of the light by varying the knob of the light
dimmer circuit. This was followed by connecting the variac to the connection box, and it was
connected to the wattmeter to measure the power, current, supply voltage , and power factor.
finally the main power was switched on , the variac was set so it produces 240 volt. A current
prob was connected to the connection between the wattmeter ( current) and the connection
box, and the other end was connected to the Elvis Board scope channel. to see how the shape
of the current wave is look like when it is drawn on the load
Mustafa Isa Al-Ansari 201000754
After checking all the wirings, and making sure that the supply voltage (output of the VARIAC)
is 240 volt, then the scope (from LabView launcher) was opened to observe the currents
behavior. the shape of the current( current drawn on the load) looked like chopped sine
waves. the size of the chopped sine wave is controlled by the knob of the circuit which is a
potentiometer resistor, and its function is to change the phase angle. This is accomplish by the
time it takes to change up the capacitor , and it is known as RC time constant. By changing the
phase angle then the power and the current that are delivered to the bulb changes. The table
below includes the relationship between the power, current , and power factor with respect to
alpha( phase angle). Moreover, the total harmonics distortion was recorded using DSA in
LabView launcher. the reason why these parameters are recorded is because the current,
power , power factor have a relationship with the phase angle.
Voltage supply = 240 V
Table 1 output parameters ( experimental values)
Phase angle Power(watt) Current(amp) Power Factor THD (%)
113.4 36.3 0.31 0.48 92.6
108 41 0.33 0.53 82
100.8 53 0.36 0.63 71
88.2 65 0.38 0.71 61
75.6 80 0.41 0.81 49
62.4 93 0.43 0.89 37
39.6 106 0.45 0.97 20
0 110 0.46 1 3
the table above demonstrate that the current, power, phase angel changes with respect to alpha. These changes are represented in the figures below.
Mustafa Isa Al-Ansari 201000754
Figure 4 current agaist alpha
Figure 5 power V Alpha
Mustafa Isa Al-Ansari 201000754
Figure 6 power factor agaisnt alpha
Discussion on the output parameter with respect to alphaThe output power and alpha have relationship and it can be explained in the figure5. the
power decreases when alpha increases. this happen because alpha affects the brightness by
chopping the AC sine waves by an RC time constant which is the time it take to charge a
capacitor through a resistor. In this case R is a potentiometer, therefore alpha is changing and
causing the power to change. and this mean that alpha controls the power that is consuming by
the light bulb. another explanation, when alpha increasing this mean that the off time delay
will increase causing the size (size of the wave) of the rms voltage to reduce, and it is known
that the power is proportional to RMS voltage square , so power is decreasing because the RMS
voltage is decreasing and vice versa. Another graph is represented which is figure 4. this graph
shows the relationship between current and alpha. when a current sine wave is chopped the
current decreases depending on how much the waves is chopped. figure 4 prove the argument,
when alpha is decreasing the current increasing. exactly at zero degrees. the current is not
Mustafa Isa Al-Ansari 201000754
chopped any more. so the power factor can be described as unity. figure 6 shows that at 0
degrees the power factor is 1 which is unity because the current is exact replica of the voltage
supply , and they are in phase. The light bulb is basically a resistive load, and it is known that a
resistive load have unity power factor. However, the table1 above shows something completely
different. The power factor changes with respect to alpha. the reason why the power factor
does not stay unity is because the current that is drawn on the load is chopped out which
causing the power factor to change. Figure 6 shows that the more the wave is chopped out the
lower the power factor is observed which means when alpha is increased the power factor
decrease and vice versa.
The output power was compared to the theoretical power. the theoretical power was calculated using the formula of Vrms which is :
RMS value=Vp2 ∗√[1−απ +(sin (2α ) )
π ]the relationship between power and Vrms is that p is proportional to Vrms square. the
following formula was used and alpha was converted to radian, and then the answer of the
divided by a number to make the two lines appears to each other in order to compare them.
this number was considered as the resistance of the light. because vrms square will be a huge
number comparing the experimental power. after doing the calculations in Matlab, the graph
was looked like the following:
Mustafa Isa Al-Ansari 201000754
Figure 7 The theoretical and expermental power verses alpha in degree
The figure above represents the theoretical and experimental power against alpha. It is shown
that both graph matches each other . However, there is a little bit of a gap because of the schematic
error which is because of the bulb which is a changeable resistive load. it change its resistance with
respect to temperature. the theoretical power was divided by the resistance at only one state which is
when the light is in full brightness the resistance was 500 ohms this value was assumed as the resistance
of the light.
Harmonic distortion of the dimmerduring the practical part the amplitude of the maximum harmonics were recorded. this was done by reducing the output power to half exactly at 55 watt, the maximum harmonics were appeared in labview DSA.
Mustafa Isa Al-Ansari 201000754
Table 2 maximum harmonics
Discussion on the harmonics distortion
The table above represents the maximum harmonics the bulb is producing. the amplitude
reduces as the number of odd harmonics increases, that happening because the harmonics get
attenuated by the RFI components as the number of odd harmonics increases ,the graph will look like a
decay. table one demonstrate the argument. it can be seen that as the number frequency get multiplied
by the number of harmonics the amplitude of the harmonics gets smaller and smaller.
Frequency Harmonics order DB/Vrms
50 first -32.5
150 third -35
250 fifth -43
350 seventh -45
450 ninth -47.5
550 Eleventh -49
650 thirteenth -51
750 fifteenth -52.5
Mustafa Isa Al-Ansari 201000754
Operation of light dimmer circuit
The Light dimmer circuit was drawn using Altium designer software. The circuit was given to the student,
and the student measured the values according the circuit.
Figure 8 Light dimmer circuit with RFI components
Mustafa Isa Al-Ansari 201000754
The circuit's operation
Generally, a light dimmer circuit is used to control the power this consumed by the light bulb by
allowing a portion of an AC signal to pass through the load which is a light bulb. the circuit
above is one type of dimmer circuits. The operation of this circuit can be explained as during
the positive cycle the capacitor charge through a resistor, and it will charge up until the diac
start conducting at 32 volt which is the breakdown voltage of the DIAC, this will cause the
capacitor to discharge thought the gate of the TRIAC. one the TRIAC is triggered the current will
pass through the bulb and will cause the circuit to be a close circuit. During the negative cycle
the same process happen. the capacitor charge in reverse polarity, and the DIAC is bidirectional
component , so it will conduct at negative voltage. When the capacitor reaches the breakdown
voltage of the DIAC, then the DIAC will start conducting and will let the capacitor to discharge ,
and triggering the gate of the TRIAC. After that, the current passes through the light bulb , and
will close the circuit. The brightness of the light is controlled by changing the phase angle. this
happens by an RC time constant which is controlled by potentiometer R2. this value is added to
R1 because they are in series and then added in parallel with r3 then the value is multiplied by
C2. the value of this equation is called the time constant. In this case, the time constant will be
defined as be how fast the capacitor reaches the break down voltage of the DIAC. Moreover, a
second order low pass filter is added to the circuit to reduce the RFI ( radio wave interference).
R4 is placed in the circuit to limit the current through the TRIAC.
Comparing the time constant with off time delay of the chopped sine wave
The minimum and maximum time constant were calculated in the technical discussion section. The delta time which is the off time delay was observed on LabView scope. the table below include the differences between the theoretical value and the experimental values.
Table 3 comparing the time constant with off time delay
Time constant ( theory) Off time ( expermental)Minimum value 340 us 0Maximum value 27 ms 6.3 ms
Mustafa Isa Al-Ansari 201000754
As it is shown in the table above there is differences between the experimental and theoretical values. the time constant by itself does not give the correct value of the phase angle. there are some issues such as the tolerance of the resistors and capacitor can affect the value of delta time ( off time).
Experimental section conclusionThe objectives of this section were to plot the output parameters(current power and power
factor) against alpha, and discuss the relationship between each parameter with respect to
alpha, compare the output power with the theoretical power, and discussing the differences.
also the section discussed the relationship between the amplitude of harmonics when the
number of odd harmonics increase. As they get reduced by the RFI components. finally the time
constant was not the correct value that gives the exact phase angle.
Mustafa Isa Al-Ansari 201000754
Conclusion sectionIn conclusion, the operation of the light dimmer circuit were discussed, the RFI components
were defined, and simulated, the effect of harmonics distortion were indentified , and the
method of reducing the harmonic distortion was provided which by adding second order low
pass filter. furthermore, the output parameters were recorded using Labview DSA, scope , and
using Wattmeter. the parameter such as current , power, power factor were plotted against
alpha to see the relationship, as it was explained.
Comparative analysis and discussionsFirst of all, the experimental power was compared with the theoretical power, there was a little
gap between the two lines, but they were so close. the differences between the two graphs
happened because the resistance of the bulb change at certain amount of temperature. which
effects the power because power is V square divided by R which is the resistance o the bulb.
Also, the devices that were used are not so accurate. The cutoff frequency was calculated
theoretically(263KHz) and observed in Altium(265KHz). The two value match each other, the
differences that is occurred because the device that measure the rfi components is not so
accurate, add to that the tolerances of the components. Furthermore, the minimum time
constant was compared with the minimum off time of the copped sine waves, as well as the
maximum time constant was compared with the maximum off time delay, they minimum time
can agree with each other because 340 us is very close to zero, but the maximum time has big
error the time constant is 27ms , and the off time delay is only 6.3ms. so they do not agree with
each other, to conclude the time constant by itself does not give the correct the phase angle
according to the calculations.
Mustafa Isa Al-Ansari 201000754
References
http://www.electronics-tutorials.ws/filter/second-order-filters.html
http://www.lvcem.com/sf/studies/pwrelectronics/TRIAC%20Circuit%20analysis.pdf