Student Name: Peter
Student ID number: ---
Student email: ---
Dates of the experiment: 13 – 9 – 2001, 20 – 9 – 2001
Date of re-submission: 1 – 11 – 2001
After
doing the experiment, I found that the resonance frequency was 8.42 kHz. In the
LC series connection, the root-mean-square voltage observed in the CRO attained
a maximum value at the resonance frequency. When a resistor is added between L
and C, the value of the resonance frequency remains unchanged. This indicates
that resonance frequency is independent to resistance. In the LC parallel
connection, the peak-to-peak voltage value attains a minimum value at the
resonance frequency.
Also,
in the half wave rectification, a diode was used. We could observed that
half-cycle of the input signal is lost which can deduce that only half of the
alternating current signal was used and current pulses are unidirectional. In
the bridge full wave rectification, we could find that current flow through the
load resistor is unidirectional during both half-cycles of the input signal.
By
using different components in half wave CRC filter, the wave produced would be
different. It showed that different electronic components could affect the
output signal. The same result would appear in the full wave CRC filter.
Electrical
oscillators are used in radio and television transmitters and receivers, in
signal generators, oscilloscope and computers to produce alternating current
with waveforms which maybe sinusoials, square, saw-tooth etc. and with
frequencies from a few hertz up to millions of hertz. In addition, the ability
of a resonant circuit to select and amplify a potential difference of one
particular frequency (strictly, a very narrow band of frequencies) applies to
radio and television reception.
In
the second part of the experiment, we will investigate the resonance frequency
of the circuit and how the voltage across the capacitor changes and the storage
of energy in capacitor and inductor at various frequencies. The effect of
resistance to the frequency response curve will also be investigated.
In
a direct current the drift velocity superimposed on the random motion of the
charge carriers (e.g. electrons) is in one direction only while in an
alternating current the direction of the drift velocity reverses, usually many
times a second. The effect of alternating current is essentially the source as
those of direct current. Though alternating current is more easily generated and
distributed than direct current and for this reason the mains supply is
alternating current, processes such as electroplating and battery charging
require direct current rather than alternating current, as does electronic
equipment like radio and television receivers. When necessary, alternating
current can be rectified to give direct current.
In
the third part of the experiment, we will examine how to convert an alternating
current signal into a direct current one. We will also investigate how the
components in the filter work and change the output waveform.
Consider two parallel plates separated by a narrow gap and connected to the terminals of a battery. The charge on each plate is proportional to the given voltage.
Q = C V ------ (1)
where Q, C and V are respectively the
charges on each plate, the capacitance and the potential different between the
two plates.
When
a capacitor is connected across a direct current voltage source, current will
flow and the capacitor will charge up to a value equal to the direct current
source voltage. When the switch is opened then, there is no voltage across the
capacitor at that instant and therefore a potential difference exists between
the battery and the capacitor. This causes the current to flow.
I =δq
/δt
From equation (1),
I = C (δV
/δt)
------ (2)
In particular, if the voltage is sinusoidal, the current in the capacitor,
I = Cδ(Vp sinωt) /δt
=ωC Vp cosωt
=ωC Vp sin (ωt +π/2) ------ (3)
where
ω is
the frequency of the input signal.
In terms of root-mean-square value, equation (3) can be written as
Vc = I [1/(ωC)] ------(4)
where 1/(ωC) is the impedance of the capacitor.
From
equation (3), current leads voltage with the phase angle π/2.
Figure
1 shows the current and voltage relationship in capacitor
In an inductor, the current will produce a magnetic field in a region surrounding the current. Changes of B-field arising from a varying current induce an emf in the current,
V = L (δI /δt) ------ (5)
where L, I and t are respectively the
inductance, the current flow through the coil and the charging time
In particular, if the current is sinusoidal, the voltage in the inductor is
V = Lδ(Ip sinωt)/δt
=ωL Ip cosωt
=ωL Ip sin (ωt +π/2) ------ (6)
where ω is the frequency of the input signal.
In terms of root-ream-square values, equation (6) can be written as
VL =ωL I ------ (7)
WhereωL is the impedance of the inductor.
From
equation (6), current lags behind voltage with the phase angle π/2.
Figure
2 shows the current and voltage relationship in inductor.
Figure 3 shows the phase
relationship among the inductive reactance, the capacitive reactance and the
resistance
By the phase relationship in equations (3) and (6),
Z = R + [ω L – 1 / (ωC)] ------ (8)
By ohm law, I = V/Z = V / { R + [ω L – 1 / (ωC)] } ------ (9)
and the phase difference between source voltage and circuit current
ψ=
arctan {[ω
L – 1 / (ωC)]
/ R}
The current flowing through the circuit is at maximum when the inductive reactance is equal to the capacitive reactance. Hence,
ωL = 1/ωC
ω = 2πf = 1/(LC) ------ (10)
At this frequency the circuit is in resonance, and the current I = V / R.
Figure 4 shows the reactance curve – resonance frequency when Xc and X curves cross.
Q factor is defined as Q = X / R ------ (11)
where X and R are respectively the impedance of inductor and resistance of resistor
And the bandwidth is defined as B = f / Q ------ (12)
Where
f
is the resonant frequency.
The diode used in this experiment is a
junction diode. Figure 5 shows a conductor function diode. A junction diode is
with an abrupt transmission from p-type to n-type semiconductor material. The
p-type material is the result of a doping with acceptor atoms, whereas the
n-type material is doped with donor atoms. As for this diode, a positive value
of an external potential results in a movement of the holes of the left hand
region to the right and free electrons of the right-hand region to the left. As
electrons have a negative charge the crossing of the junction by both types of
carriers results in a positive diode current. On the other hand, there are few
carriers that contribute to a current in the opposite direction. As a result,
the diode current for a negative external potential tends to be very small.
Hence, with different connection of diode, they will have different function.
[1]
There
will be voltage drop after passing the diode since there is a barrier voltage in
the diode. Also the diode cannot block the current absolutely due to reverse
bias, There will be some leakage, therefore the voltage will not be absolutely
zero.
Rectification
is the conversion of an alternating current signal into a direct current one by
a rectifier. There are two methods of rectification, half-wave and full-wave
rectification.
In
the half-wave rectification, the rectifying circuit in Figure 6(a) consists of a
rectifier in series with the alternating current input to be rectified and the
‘load’ requiring the direct current output. In Figure 6(b) the alternating
input potential difference applied to the rectifier and load is shown. If the
first half-cycle acts in the forward direction of the rectifier, a pulse of
current flows round the circuit, creating a potential difference across R which
will have almost the same value as the applied potential difference if the
forward resistance of the rectifier is small compared with R. The second
half-cycle reverse biases the rectifier, little or no current flows and the
potential difference across R is zero. This is repeated for each cycle of
alternating current input. The current pulses are unidirectional and so the
potential difference across R is direct, for although it fluctuates it never
change direction.
In
the bridge full-wave rectification, four rectifiers are arranged in a bridge
network as in Figure 7(a). If A is positive during the first half-cycle,
rectifiers 1 and 2 conduct and current takes the path ABC, R, DEF. On the next
half-cycle when F is positive, rectifiers 3 and 4 are forward biased and current
follows the path FEC, R DBA. Once again current flowing through R is
unidirectional during both half-cycles of the input potential difference and a
direct current output is obtained as in Figure 7(b).
To produce a steady direct current from the varying but unidirectional output from a half- or full-wave rectifier, smoothing and filtering effect is necessary. A reservoir capacitor C1 has a useful smoothing effect but it is usually supplemented by a filter circuit consists of a choke L and a large capacitor C2 arranged as in Figure 8(a). The smoothing action of C1 arises from its large capacitance making the time constant C1R large so that the potential difference across it cannot follow the variations of the input potential difference. The action of filter circuit of L-C2 can be understood if V1 is resolved into steady direct potential difference and alternating potential difference, which is illustrated in Figure 8(b).
(2a)
Series connection
The experiment setup was shown in
Figure 9. The signal frequency was varied from signal generator until the
voltage reading from the CRO was at maximum. The frequency was taken as the
resonance frequency of the circuit. The signal frequency was then changed by
–3000Hz and +3000Hz about the resonance frequency in steps of 500Hz. The
root-mean-square voltage across the capacitor was taken at each frequency and a
frequency response curve was sketched with the data. The experimental value was
determined from the frequency response curve and the Q factor was also deduced.
The resistance of the inductor was measured by using multi-meter.
(2b)
Parallel connection
The experimental setup was shown in
Figure 10. The experimental procedure was the same as in series connection. But
the resonance frequency was determined by varying the signal frequency until the
reading was minimized.
(3a)
Half-wave rectification
The
circuit was connected as shown in Figure 11. The waveform observed was drawn and
the frequency was recorded. Another CRO probe across the signal source was then
connected to check if the observed waveform and that from the signal source are
in phase. The above steps were then repeated after reversing the diode.
(3b) Full-wave rectification
The
circuit was connected was shown in Figure 12. The observed waveform and the
frequency were recorded.
(3c) Have-wave rectification with CRC filter
The
circuit was connected as shown in Figure 13. The waveform was observed and the
ripple voltage across the load resistor was measured. The circuit was then
modified separately with changing the capacitors to 1μF
from the original circuit, replacing the resistor with a choke and replacing the
load resistor with a 100Ω
resistor, and each time, the observed new waveform and new ripple voltage across
the load resistor was recorded.
(3d)
Full-wave rectification with CRC filter
The circuit was connected as shown in Figure 14. The waveform was observed and the ripple voltage across the load resistor was measured. The circuit was then modified by changing the capacitors to 1μF from the original circuit, and the observed new waveform and new ripple voltage across the load resistor was recorded.
(2a)
Series connection
Without
470Ω
resistor:
Acceptable range for the experimental resonance
= (1 / [2π ] ) [( ) + ( )]
= (1 / [2π ] ) ( + )
=
+ 0.8377 kHz
Root-mean-square Voltage = 52.40 + 0.005V
Resistance of the Coil = 51.8Ω
Resonance
Frequency = 8.42 + 0.005 kHz
The
raw data is shown in Table 1 in the Appendix. A graph of Frequency
response curve is plotted and shown in Figure 15.
Error in the 0.01μF capacitor = 0.01 x 10%
= 0.001μF
Hence
capacitance of 0.01μF
capacitor is 0.010 + 0.001μF.
Error in the 33.3 mH inductor = 33.3 x 10%
= 3.33 mH
Hence
inductance of the 33.3 mH inductor is 33.30 + 3.33 mH.
Calculated resonance frequency, fo = 1 / [2π ]
= 1 / [2π ]
= 8.721 kHz
By equation (11), calculated Q factor = =
=
= 35.23
By equation (12), calculated bandwidth = fo / Q
= 8721 / 35.23
= 247.54 Hz
In the experiment, the resonant frequency is 8.42kHz.
Experimental
Q factor = 34.01
From the graph, maximum voltage is 54.42V.
V = 0.7071 Vo = 0.7071 (52.42) = 37.07V.
In the graph, we draw a line for V = 37.07V to cut the curve in two points, which are 8700Hz and 8125Hz.
Hence
the experimental bandwidth = (8700 – 8125) Hz = 575 Hz.
With
470Ω
resistor:
Root-mean-square Voltage = 11.64 + 0.005 V
Resistance of the Coil = 51.8Ω
Resonance
Frequency = 8.33 + 0.005 kHz
The
raw data is shown in Table 2 in the Appendix. A graph of Frequency
response curve is plotted and shown in Figure 16.
Comparing
Figure 12 and 13, the curve without the 470Ω
resistor is less sharper than that with the resistor. The bandwidth without the
470Ω
resistor is higher than that with the resistor.
Calculated resonance frequency, fo = 1 / [2π ]
= 1 / [2π ]
= 8.721 kHz
By
equation (11), Q factor = 3.497
By equation (12), calculated bandwidth = fo / Q
= 8721 / 3.497
= 2493.85 Hz
In the experiment, the resonant frequency is 8.33kHz.
Experimental
Q factor =
= 3.34
From the graph, maximum voltage is 54.42V.
V
= 0.7071 Vo = 0.7071 (11.63) = 8.22V. In the graph, we draw a line for V = 8.22V
to cut the curve in two points, which are 9600Hz and 6800Hz. Hence the
experimental bandwidth = (9600 – 6800) Hz = 2800 Hz.
(2b)
Parallel Connection
Root-mean-square Voltage = 1.186 + 0.005V
Experimental
Resonance Frequency = 8.64 + 0.005 kHz
The raw data is shown in Table 2 in the Appendix. A graph of Frequency response curve is plotted and shown in Figure 17. From the graph, we obtain a minima at resonance frequency in parallel connection.
Calculated resonance frequency, fo = 1 / [2π ]
= 1 / [2π ]
= 8.721 kHz
By
equation (11), Q factor = 35.23
By equation (12), calculated bandwidth = fo / Q
= 8721 / 34.908
= 247.54 Hz
In the experiment, the resonant frequency is 8.64kHz.
Experimental
Q factor = 34.9
From the graph, the voltage range = (5.48 – 1.17)V = 4.31.
V = 0.7071 Vo = 0.7071 (4.31) = 3.048V.
In
the graph, we draw a line for V = 3.048V to cut the curve in two points, which
are 9200Hz and 8000Hz. Therefore the experimental bandwidth = (9200 – 8000) Hz
= 1200 Hz.
(3a)
Half-wave rectification
The
observed waveform for the input and output signal is shown in Figure 18. The
frequency is 57.310+0.005Hz. Also, we can find that the two waveforms are
in phase.
When
the direction of the diode is reversed, the observed waveform is shown in Figure
19. The frequency is also 57.310+0.005Hz. The waveforms for input and
output signal are in phase. But the output signal (wave 2) in Figure 19 is up
side down to the wave 1 in Figure 18.
(3b)
Full-wave rectification
The
observed waveform for the output signal is shown in Figure 20. The frequency is
119.000 + 0.005 Hz.
We
can see that the frequency of the waveform in wave 3 is twice the frequency of
the input waveform in half-wave rectification.
(3c)
Half-wave with CRC filter
(1) By using 10μF capacitor, the observed waveform is shown in Figure 21.
Ripple Voltage = 5.254 + 0.005V
Frequency = 513.8 + 0.005 Hz
(2) By using 1μF capacitor, the observed waveform is shown in Figure 22.
Ripple Voltage = 14.56 + 0.005V
The ripple voltage in wave 5 is higher than
that in wave 4 when a smaller capacitor is used.
(3) By replacing R1 with choke, the observed waveform is shown in Figure 23.
Ripple Voltage = 1.639 + 0.005V
The ripple voltage in wave 6 is lower than
that in wave 4 when replacing R1 with choke.
(4) By replacing RL with a 100Ω resistor, the observed waveform is shown in Figure 24.
Ripple Voltage = 12.14 + 0.005V
The ripple voltage in wave 7 is higher than
that in wave 4 in Figure 21 when replacing RL
with a 100Ω
resistor.
(3d)
Full-wave with CRC filter
(1) By using 10μF capacitor, the observed waveform is shown in Figure 25.
Ripple Voltage = 5.425 + 0.005V
Frequency = 1.088 + 0.005 kHz
The frequency in wave 8 is twice that in wave 4
(2) By using 1μF capacitor, the observed waveform is shown in Figure 26.
Ripple Voltage = 8.126 + 0.005V
The ripple voltage in wave 9 in Figure 26 is
higher than that in wave 8 in Figure 25 when a smaller capacitor is used.
(2a)
Series Connection
Without
470Ω
resistor:
The
experimental and theoretical bandwidth is respectively 575Hz and 249.83 Hz. One
reason for the large discrepancy is that the experimental bandwidth is found by
drawing a line across the curve, which is highly inaccurate.
In
the series connection, the source of energy is the alternating current
generator. Some of the energy produced is stored in the electric field in the
capacitor and some is stored in the magnetic field in the inductor, and some is
dissipated as thermal energy in the resistor.
In
the capacitor, during the first quarter cycle of the current input, energy taken
from the source is stored in the electric field due to the potential difference
between the plates of the charged capacitor. During the next quarter-cycle the
capacitor discharges and the energy flows to the inductor. While in the
inductor, during the first quarter cycle of the current input, energy is taken
from the capacitor and energy is stored in the magnetic field of the inductor.
In the second quarter, the current and the magnetic field decrease and the e.m.f.
induced in the inductor enables it to act as generator, returning the stored
energy in the magnetic field to the capacitor again.
Figure
27 (a) and (b) show the curve for the power in a pure inductive and in a pure
capacitive circuit respectively. In the capacitor and the inductor, by equations
(3) and (6), power = 1/2 Io Vo sin 2ωt
= Irms
Vrms
sin 2ωt.
From the graphs in Figure 27, we can see how voltage varies with the frequency,
so the power at the resonant frequency will be maximized. The above equation
represents a sinusoidal variation with mean value power is zero. It follows that
the power absorbed by the capacitor and the inductor in a cycle is zero. Since
the energy is proportional to the power, so the energy of the capacitor and the
inductor is similar to the power.
The difference between the experimental and calculated resonant frequency
= (8.721 – 8.42) kHz
= 0.301 kHz
The experimental value of the resonant frequency is acceptable compared with the calculated resonant frequency, since the error in resonant frequency is + 0.84 kHz which is within the range.
The
percentage discrepancy = 3.45%
With
470Ω
resistor:
The difference between the experimental and calculated resonant frequency
= (8.721 – 8.33) kHz
= 0.391 kHz
The experimental value of the resonant frequency is acceptable compared with the calculated resonant frequency, since the error in resonant frequency is + 0.84 kHz which is within the range.
The percentage discrepancy = x 100%
= 4.48%
Overall in (2a) experiment:
In
the graph in Figure 12, the voltage drops except in resonance. The voltage
across resistor is VR = IR. From equation (4),
voltage across the resistor is Vc = I [1/(ωC)].
From equation (7), voltage across the inductor is VL
=ωL I.
When the circuit is in resonance, Vc = VL
and since they are 180°out
of phase, they cancel each other. Therefore, the resistor receives the whole
voltage from the input signal, and so the current is maximized. When the current
in the circuit is at maximum, by equation (4) voltage across the capacitor is
also at maximum. But when the circuit is not in resonance, although Vc and VL are still 180°out
of phase, they do not cancel each other completely. By equation (9), the current
in the circuit will be lower than that in resonance, and hence by equation (4)
the voltage across the capacitor will drop.
By comparing the two curves in Figure 12, the curve without the resistor is sharper than that with the resistor. From the calculation of the bandwidth and the Q factor, the curve without the resistor has lower bandwidth but higher Q factor than that with the resistor. This is because Qα1/R and Bwα1/Q, so Bw is proportional to R. Therefore, when using larger resistor, the bandwidth is larger and the curve is less sharp. Quantitatively, by equations (4) and (9),
Vc = V / { R + [ω L – 1 / (ωC)] } * [1/(ωC)] ------ (13)
Differentiating equation (13) with respect to ω,
δVc/δω= (V/C){1/[ R + [ω L – 1 / (ωC)] ] } – {1/{2ω[ R + [ω L – 1 / (ωC)] ] }}
Hence
for small value of R, δVc/δω
is large, which means that the change of voltage is large with respect to the
frequency, and therefore the curve is sharp. For large value of R, δVc/δω
is small and thus the curve is less sharp.
Also,
the voltage across the capacitor for the circuit without 470Ω
resistor is higher than that with the resistor for all frequencies. This is
because when increasing the resistance in the series connection of the RLC
circuit, by equation (9), the current in the circuit is lower. Hence by equation
(4) the voltage across the capacitor for all frequencies is lower than that with
470Ω
resistor.
(2b)
Parallel Connection
The difference between the experimental and calculated resonant frequency
= (8.721 – 8.64) kHz
= 0.081 kHz
The experimental value of the resonant frequency is acceptable compared with the calculated resonant frequency, since the error in resonant frequency is + 0.84 kHz which is within the range.
The percentage discrepancy = x 100%
= 0.93%
In the parallel connection, the resonant frequency was taken when the minimum voltage reading was observed in CRO. The circuit in Figure 28 is considered.
From equation (4), Ic = V / Xc = VωC
From equation (7), IL = V / XL = V /ωL
When
the circuit is in resonance, IL
and Ic are 180°out
of phase and so cancel out. Also oscillation occurs. In the oscillation, current
only flows back and forth between the inductor and capacitor, and no current
flows from the source. Hence the LC circuit appears to be with infinite or very
high impedance. [2]
Hence
in the parallel connection circuit of the experiment, at the resonant frequency
the LC circuit has very high impedance and gets most of the voltage. Then the
resistance gets little. So the resonant frequency was taken when minimum voltage
reading was observed in CRO. When frequency is not at resonant, the impedance
across LC circuit is lower and the resistor gets higher voltage.
Overall in (2a) and (2b) experiment:
Both
the circuits in (2a) and (2b) experiment are band stop filter for the load. The
band stop filter can block or attenuates a band of frequencies centered on the
resonant frequency of the LC circuit. The two circuits have the same frequency
response curve as shown in Figure 29.
In
the series resonant circuit, the CL impedance is very low at and around
resonance, so these frequencies are rejected or shunted away from the output.
Above and below resonance, the series have very high impedance, which result in
no shunting of the signal away from the output. In the parallel resonant
circuit, the LC circuit is in series with the load. At resonance, the impedance
of a parallel resonance circuit will be very high, and the band of frequency
centered around the resonance will be blocked. Above and below resonance,
impedance of a parallel resonant circuit will be low, output signal will not be
blocked. [3]
(3a)
Half-wave rectification
The
waveform is observed, since the diode can only allow the current to flow in one
direction only. Hence if a sinusoidal wave is input, at the positive half of the
wave, the current can pass through but in the negative half one, the current
cannot pass through. Therefore the output will only have positive half wave
while the negative half will become 0V. If the diode is reversed, the negative
half of input wave can pass through the diode. Therefore the current will only
have negative half wave while the positive half will become 0V.
Actually
there will be a small voltage drop after passing through the diode since there
is a barrier voltage in the diode. Also, the diode cannot absolutely block the
current due to reverse bias. There will be some leakage, so the voltage will not
absolutely be zero.
(3b)
Full-wave rectification
The
observed waveform is shown in wave 3 in Figure 20. With the bridge rectifier,
the operation of this circuit may be described by tracing the current on the
alternate half-cycle of the input voltage. The frequency of the output signal
will be twice because the signal is repeated for each half wave while the input
signal is a full wave. This frequency doubling makes it easier for the pulsating
direct-current voltage to be converted into a constant direct-current voltage
level. The waveform is not sharp at voltage equal zero since the diode cannot
absolutely block the current due to reverse bias. There will be some leakage, so
the voltage will not absolutely be zero.
The
half-wave rectifier circuit produces a waveform that uses only half of the
alternating current signal. The full-wave circuit uses the entire alternating
current signal. The full-wave is more efficient. Also, the full-wave
output is closer to pure direct current than the half-wave output. It requires
less filtering to create pure direct current.
(3c)
Half-wave with CRC filter
(1)
By using 10μF
capacitor, the waveform is shown in wave 4 in Figure 21. At the first quarter of
input wave, the output will get the signal, at the same time it will charge up
the capacitor. At the rest of the input wave, the capacitor starts to discharge
so the output signal starts to decay. When the second input wave is inserted,
the capacitor starts to charge up again.
(2)
By using 1μF
capacitor, while charging the two 10μF capacitor instead of the 1μF
capacitor, the peak-to-peak voltage will become higher. This is because the time
constant, t = RC where R and C are respectively the resistance and the
capacitance. As for lowing the capacitance, the time constant will be lower.
Therefore the time required to charge and discharge is short. Since the 1μF
capacitor can discharge quickly in a period, so the ripple voltage is high. But
the frequency will remain the same as using 10μF
capacitor.
(3)
By replacing R1 with a choke, the
waveform becomes smooth and the peak-to-peak voltage will decrease. The choke
contributes to the filtering action by offering a much greater impedance to the
alternating current component and most of the unwanted ripple potential
difference appears across the choke. For the direct current component, the
capacitor C2 has infinite resistance and the whole of this component
is developed across C2 except for the small drop due to the
resistance of the choke.
(4)
By replacing RL with a 100Ω
resistor, the peak-to-peak voltage is lower when a resistor with 100Ω
resistance is used instead of RL
with 1000Ω
resistor. As the time constant, t = RC where R and C are respectively the
resistance and the capacitance, lower resistance means lower time constant.
Therefore the time required to charge and discharge is short. Since the 10μF
capacitor can discharge quickly in a period, so the ripple voltage is high. [5]
(3d)
Full-wave with CRC filter
(1)
By using 10μF
capacitor, the frequency of the output signal is twice. This is because the
signal is repeated for each half wave, while the input signal is in full wave.
(2)
By using a 1μF
capacitor, while charging the two 10μF capacitor instead of the 1μF
capacitor, the peak-to-peak voltage becomes higher. It is because the time
constant is defined as the product of resistance and capacitance, therefore
lowering capacitance will lower time constant. Hence the time required to charge
and discharge is short. Since the 1μF
capacitor can discharge well in a period, so the ripple voltage is high.
Source of error:
(1) Internal resistance of the wire reduce the accuracy of the reading of the (2a) and (2b) experiment.
(2) The background E-field and B-field may affect the energy stored in the capacitor and the inductor.
(3) The change in temperature can affect the barrier voltage in the diode, reducing the accuracy of the peak-to-peak voltage taken in Part 3.
(4)
Poor contact between the wire of the components and the breadboard.
Improvement:
(1) Use thicker and short connecting wire.
(2) Make sure the apparatus is far away from the wall and things that can produce E-field and B-field.
(3) Keep the room temperature constant.
(4)
Make sure the components contact well and remove any grease or rust on
the connecting wire.
From
the experiment, it is found that the resonant frequency of the series and
parallel connection are more or less the same. The voltage across the capacitor
and inductor when in resonance is at maximum, while the voltage across the load
resistor is at minimum. Since the load impedance is minimized at resonance, both
connections are used as band stop filter. Also the resistance can affect the
sharpness of the frequency response curve. The higher the resistance is, the
less sharp the curve will be.
In
the series connection, at resonance the maximum root-mean-square voltage was
51.400 + 0.005V and the corresponding resonant frequency was 8.420 +
0.005 kHz. The experimental Q factor and the bandwidth were respectively 34.01
and 575Hz. When the 470Ω
resistor was added between L and C, the maximum root-mean-square voltage was
11.640 + 0.005V and the corresponding resonant frequency was 8.330 +
0.005 kHz. The experimental Q factor and the bandwidth were then respectively
3.34 and 2800Hz.
In
the parallel connection, at resonance the minimum root-mean-square voltage was
1.186 + 0.005V and the corresponding resonant frequency was 8.640 +
0.005 kHz. The experimental Q factor and the bandwidth were respectively 34.9
and 1200Hz.
Also,
the diode can be used as the rectifier, so that an alternating current signal
can be rectified to become a direct current signal. When using one diode,
one-half of the input signals are lost. While using a bridge rectifier, a
repeated set of half wave signal would be obtained. So the frequency of the wave
in full wave rectification is twice that in half wave rectification. Also, a
capacitor and a resistor can affect the speed of charging and discharging.
Smaller capacitance and smaller resistance allow the capacitor to charge and
discharge quicker, thus having larger ripple voltage. Moreover, the use of choke
can lower the ripple voltage, thus showing the filtering effect. Therefore, we
can see that the results are consistent with the theory.
Reference
[1] Electronic Concepts – An Introduction, first edition, by Jerrold Krenz, P.370-385
[2] Analog Electronics, second edition, by T.E. Price, P. 28-31
[3] Analog Electronics, second edition, by T.E. Price, P. 54-63
[4] Basic Electronics For Scientists, fifth edition, by James Brophy, P.137-145
[5] Basic Electronics For Scientists, fifth edition, by James Brophy, P.75-86
[6] Fundamentals of Electronic Devices, fourth edition, By Ronald Tocci, P.62
[7] Handouts of Experiment 2A of PHYS211