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University of British Columbia *
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301
Subject
Electrical Engineering
Date
Apr 3, 2024
Type
docx
Pages
26
Uploaded by BrigadierBraverySeaLion38
Katie Seifert 68469311
2019/10/24
Elec 301 101: Mini Project 2
Single Transistor Amplifiers
The Power of Trust. The Future of Energy.
Table of Contents
1
INTRODUCTION
...................................................................................................................................
3
2
GENERAL INFORMATION
...................................................................................................................
3
2.1
Purpose
........................................................................................................................................
3
2.2
.........................................................................................................................................................
3
2.3
Tests Performed
...........................................................................................................................
3
3
PART 1 - COMMON EMITTER MODELLING AND BIASING
...............................................................
4
3.1
Part A
...........................................................................................................................................
4
3.2
Part B
...........................................................................................................................................
4
3.3
Part C
...........................................................................................................................................
5
3.4
Part D
...........................................................................................................................................
7
3.4.1
2N3904
.............................................................................................................................................
7
3.4.2
2N4401
.............................................................................................................................................
8
4
PART 2 – COMMON EMITTER AMPLIFIER SIMULATION
..................................................................
9
4.1
Part A
...........................................................................................................................................
9
4.2
Part B
.........................................................................................................................................
10
4.3
Part C
.........................................................................................................................................
10
4.4
Part D
.........................................................................................................................................
11
4.5
Part E
.........................................................................................................................................
11
4.5.1
2N3904
...........................................................................................................................................
11
4.5.2
2N4401
...........................................................................................................................................
13
4.5.3
Transistor Comparison
...................................................................................................................
14
5
PART 3 – COMMON BASE AMPLIFIER SIMULATION
......................................................................
15
5.1
Part A
.........................................................................................................................................
15
5.2
Part B
.........................................................................................................................................
15
5.3
Part C
.........................................................................................................................................
16
5.4
Part D
.........................................................................................................................................
16
APPENDIX A: COMMON EMITTER MODELLING AND BIASING TEST DATA
.......................................
17
APPENDIX B: COMMON EMITTER AMPLIFIER SIMULATION TEST DATA
...........................................
19
APPENDIX C: COMMON BASE ACOMPLIFIER SIMULATION TEST DATA
...........................................
23
APPENDIX D: REFERENCES
...................................................................................................................
25
Elec 301 101: Mini Project 2
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Katie Seifert 68469311
2019-10-24
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1
INTRODUCTION
In order to analyse and measure the characteristics of two important transistor amplifiers with 3 commonly
available transistors, as well as develop familiarity with the hybrid-π model and the issues surrounding the
biasing of transistors, mini project 2 was conducted. This report summarizes the results of the tests
performed.
2
GENERAL INFORMATION
2.1
Purpose
The purpose of the tests was to model the Common Emitter and Common Base amplifiers using three commonly available transistors (as shown in Figure 8 – Tested circuit and Figure 19), as well as bias the circuits (shown in Figure 7) using simulated and calculated values and compare biasing methods as taught in lecture.
2.2
2.3
Tests Performed
Part 1 – Common Emitter modelling and biasing
a)
Datasheet investigation
b)
Parameter simulation
c)
Bias in the active region
d)
Different transistors
i.
2N3904
ii.
2N4401
Part 2 – Common Emitter amplifier simulation
e)
Bode plot simulation and comparison
f)
Mid band modelling
g)
Input impedance
h)
Output impedance
i)
Different transistors and comparison
i.
2N3904
ii.
2N4401
Part 3 – Common Base amplifier simulation
a)
Bode plot simulation and comparison
b)
Mid band modelling
c)
Input impedance
d)
Output impedance
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3
PART 1 - COMMON EMITTER MODELLING AND BIASING
3.1
Part A
Research:
Using the online datasheet
4
for the 2N2222A, the H-parameters and therefore the hybrid-π model values were determined. This was done by assuming that the transistor was a small signal model and then determining the hybrid-π values by using their corresponding H-parameter values. For the calculations, h
fe
= β, h
ie
= r
π
and h
oe
= 1/r
o
were used to determine the hybrid-π parameters.
Evaluation:
Table 1 – Datasheet
4
Values
Component
Min Value
Max Value
h
fe
50
300
h
ie
2 kΩ
8 kΩ
h
oe
5 μΩ
-1
35 μΩ
-1
β
50
300
r
π
2 kΩ
8 kΩ
r
o
28.57 kΩ
200 kΩ
3.2
Part B
Simulation:
Using SPICE software, the circuit shown in Figure 1 was modelled with the primary varying parameter V
BE
and the secondary varying parameter I
B
and produced the graph seen in Figure 2. Following this, the circuit shown in Figure 3 was modelled with the primary varying parameter V
CE
and the secondary varying
parameter I
B
and produced the graph seen in Figure 4. Finally, the circuit shown in Figure 5 was modelled with the primary varying parameter V
CE
and the secondary varying parameter V
BE
and produced the graph seen in Figure 6. These plots produced were used to graphically determine the β, r
π
, g
m
and r
o using the calculation methods described below.
Calculation:
Using the graph shown in Figure 4 and the provided information that V
CE
= 5 V and I
C
= 1 mA, I
B
can be determined to be 6 μA. This is done by following the current steps of I
C
and determining the value at the operating point provided. From this β can be calculated as follows.
I
C
=
β I
B
=
1
∗
10
−
3
=
β
∗
6
∗
10
−
6
=
β
=
166.7
Following this calculation, g
m
can be calculated following the method below, following the provided information that the transistor is functioning at 25°C, that V
T
= 0.025 V.
g
m
=
I
C
V
T
=
1
∗
10
−
3
0.025
=
0.04
Ω
−
1
Using the calculated g
m
and β, r
π
can be determined using the following calculations.
r
π
=
β
g
m
=
4.1667
kΩ
Elec 301 101: Mini Project 2
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The Power of Trust. The Future of Energy.
To determine the r
o
, the early voltage V
A
must first be determined graphically. V
A
can be found by determining the slope of the linear region of the transistor where I
C
= 1 mA and I
B
= 1 μA and then determining the Y-axis crossing. Using this, the line equation can be found, and V
A
can be determined to be where the line crosses the X-axis using the following calculations.
y
=
0.872
∗
10
−
5
x
+
0.9578
∗
10
−
3
where x = voltage and y = current
Using y = 0, V
A
can be determined as follows.
0
=
0.872
∗
10
−
5
x
+
0.9578
∗
10
−
3
=
x
=
109.84
V
=
V
A
After having determined V
A
, r
o
can be found using the following calculations.
r
o
=
V
A
I
C
=
109.84
1
∗
10
−
3
=
109.8
kΩ
Finally, V
BE
can be found and used in future calculations by using graphical determination and found to be
V
BE
= 0.6 V.
Evaluation:
Table 2 – Measured vs Datasheet
4
Values
Component
Min Value
Max Value
Measured Value
β
50
300
166.7
r
π
2 kΩ
8 kΩ
4.1667 kΩ
r
o
28.57 kΩ
200 kΩ
109.8 kΩ
These values are well within the range provided by the datasheet
4
and are close, however slightly above, the average of each component. Furthermore, although the average can be calculated, the expected value of each component is not provided, therefore there can be no further analysis of the expected vs calculated values past comparing them to the expected range. Comparing to the simulated waveforms, g
m
can be determined to be within expected values and is considered to be within an appropriate range.
3.3
Part C
Calculations:
The circuit used in biasing is shown in Figure 7. We calculate all biases using the provided information that V
cc
= 15 V and I
C
= 1 mA.
First biasing in using the parameters calculated from the curves, using the V
BE
, I
C
and I
B
values calculated in the section 3.2 and the provided knowledge that V
CE ≤ 4 V and that R
E
= 0.5* R
C we are able to calculate
R
C
using the following equations.
4
V
=
15
V
−
(
1
mA
∗
R
C
+
(
1
mA
+
6
µA
)
∗
1
2
R
C
)
=
R
C
=
7.3187
kΩ
Then using the provided relationship between R
E and R
C
,
R
E
=
3.65935
kΩ
We then need to determine R
B1 and R
B2
. To do so, we begin by determining V
E
and V
B
using the following
calculations.
Elec 301 101: Mini Project 2
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I
E
=
(
I
C
+
I
B
)
V
E
=
R
E
∗
(
I
C
+
I
B
)
=
3.68
V
V
B
=
V
BE
+
V
E
=
4.28
V
We can now determine R
B1
and R
B2
. To do so, we begin by finding a ratio between the two resistor values as we are unable to determine exact values. We do so by doing the following calculations.
V
CC
−
V
B
R
B
1
=
I
B
+
V
B
R
B
2
=
R
B
2
=
2140000
∗
R
B
1
5360000
−
3
∗
R
B
1
Using this ratio, we pick a resistors values that are common resistor values or are within error
measurement of a common resistor value. Furthermore, we must pick resistor values that limit power
loss, therefore they should be on the magnitude of 10
5
Ω. By trial of different resistor values from the
common resistor sheet
3
, we are able determine the resistor values as follows.
R
B
1
=
110
kΩ
R
B
2
=
46.799
kΩ
47
kΩ
We then bias using the 1/3
rd
rule. We bias using the V
BE
, I
C
and I
B
values calculated in the section 3.2 as
well as the 1/3
rd
rule equations as shown below.
V
B
=
1
3
∗
V
CC
=
5
V
V
C
=
2
3
∗
V
CC
=
10
V
V
E
=
V
B
−
V
BE
=
4.4
V
Having calculated β in section 3.2 and found it to be 166.7, we are able to calculate I
B1
and I
B2
as follows.
I
B
1
=
I
E
√
B
=
I
C
+
I
B
√
B
=
77.92
µA
I
B
2
=
I
B
1
−
I
B
=
71.92
µA
Having determined the voltage and current values at each node, we are able to determine the resistor values using ohm’s law as follows.
R
C
=
V
CC
−
V
C
I
C
=
5
kΩ
R
E
=
V
E
I
E
=
4.373
kΩ
R
B
1
=
V
CC
−
V
B
I
B
1
=
128.330
kΩ
R
B
2
=
V
B
I
B
2
=
69.518
kΩ
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Finally, we bias using common resistor values found on the resistor reference sheet
3
closest to the resistor values determined above using the 1/3
rd
rule. The resistor values are as follows.
R
C
=
5.1
kΩ
R
E
=
4.3
kΩ
R
B
1
=
130
kΩ
R
B
2
=
68
kΩ
The DC operating points were determined using a simulation of the circuit shown in Figure 7 – Tested circuitand measuring the voltage and current at each node.
Evaluation:
Table 3 – DC Operating Point Values and Comparison
DC operating point
Measured Value
1/3 Bias Value
Common Resistor Value
I
C
1.001 mA
1.003 mA
993.3 µA
I
E
1.007 mA
1.008 mA
999.2 µA
I
B
6.044 µA
5.976 µA
5.923 µA
V
C
7.689 V
9.998 V
9.946 V
V
E
3.678 V
4.401 V
4.287 V
V
B
4.279 V
5.002 V
4.888 V
V
CE
4.011 V
5.597 V
5.597 V
When comparing the values of the measured value bias, 1/3
rd
rule bias and common resistor bias, we can
see that all are within a small margin of error and are all valid biasing methods. Although the measured value bias is the best method for this transistor due to it’s close proximity to the desired bias, the 1/3
rd
method using the common resistor values would be the most economical and most likely to be used in industry, as it is accurate within the percent error of common resistor values (±10%) and saves time and is the easiest to use for any person working within industry as it would be cheaper and easier to acquire.
3.4
Part D
3.4.1
2N3904
Calculations:
Following the parameter measurement methods described in section 3.2, we are able to determine the parameter values of the 2N3904 transistor. The determined values are as follows.
V
BE
=
0.648
V
β
=
114.3
r
π
=
2.8575
kΩ
r
o
=
99.8735
kΩ
I
B
=
8.75
µA
g
m
=
0.04
Ω
−
1
The DC operating points were determined using a simulation of the circuit shown in Figure 7 – Tested circuit and measuring the voltage and current at each node.
Evaluation:
Elec 301 101: Mini Project 2
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Table 4 – DC Operating Point Values and Comparison
DC operating point
Measured Value
1/3 Bias Value
I
C
964.9 µA
965.6 µA
I
E
973.1 µA
973.7 µA
I
B
8.259 µA
8.164 µA
V
C
7.940 V
10.17 V
V
E
3.560 V
4.257 V
V
B
4.206 V
4.902 V
V
CE
4.38 V
5.913 V
When comparing the biasing of the 2N3904 with that of the 2N2222A, it is clear that the measured bias is less accurate for the 2N3904 and varies greatly across transistors. While this method was most accurate for the 2N2222A, it is less versatile and looses accuracy with changing transistors. This demonstrates the
validity of using the 1/3
rd
rule in biasing a variety of transistors, as over a range of multiple transistors, it is most accurate and allows for more versatile usage. Additionally, each transistor will have a range of β values as provided by their data sheet, and the 1/3
rd
rule allows easier accommodation for a range of β values.
3.4.2
2N4401
Simulation:
Following the parameter measurement methods described in section 3.2, we can determine the parameter values of the 2N4401 transistor. The determined values are as follows.
V
BE
=
0.659
V
β
=
142.86
r
π
=
3.5715
kΩ
r
o
=
107.107
kΩ
I
B
=
7
µ A
g
m
=
0.04
Ω
−
1
The DC operating points were determined using a simulation of the circuit shown in Figure 7 – Tested circuit and measuring the voltage and current at each node.
Evaluation:
Table 5 – DC Operating Point Values and Comparison
DC operating point
Measured Value
1/3 Bias Value
I
C
977.8 µA
981.6 µA
I
E
985.5 µA
988.2 µA
I
B
6.732 µA
6.679 µA
V
C
7.851 V
10.10 V
V
E
3.599 V
4.313 V
V
B
4.888 V
4.970 V
V
CE
4.252 V
5.787 V
When comparing the biasing of the 2N4401 with that of the 2N2222A, it is clear that the measured bias is less accurate for the 2N4401 and varies greatly across transistors. While this method was most accurate for the 2N2222A, it is less versatile and looses accuracy when changing transistors. This demonstrates the validity of using the 1/3
rd
rule in biasing a variety of transistors, as over a range of multiple transistors, it is most accurate and allows for more versatile usage. Additionally, each transistor will have a range of Elec 301 101: Mini Project 2
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β values as provided by their data sheet, and the 1/3
rd
rule allows easier accommodation for a range of β values.
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4
PART 2 – COMMON EMITTER AMPLIFIER SIMULATION
4.1
Part A
Simulation:
Using SPICE software, the circuit shown in Figure 8 – Tested circuit was simulated and the Bode plots showing the magnitude and phase were noted in Figure 9 and Figure 10. Using the plots, we can graphically determine and confirm that the circuit is a band-pass filter.
Calculations:
An example of the graphically determined poles is shown in Figure 11, demonstrating how poles were determined from the Bode plot of a simulated circuit. The graphically determined values are shown in
Table 6 - Pole Locations. The values were determined by estimation, as the frequencies are located after
the steepness of the slope begins to change. This was determined using estimation, as well as measurement and observation.
The pole values were calculated using the Open Circuit and Short Circuit (OC and SC) method. In this method, all capacitors will act as open circuits before their pole frequency is reach, once their pole frequency has been passed, they then begin to act as short circuits. To calculate the frequency ω
p
, we first find the time constant τ
. We do so by opening all capacitors with a lower value than the capacitor of interest and shorting all capacitors of a higher value, as well as the voltage source. From this, the equivalent resistance of the circuit seen by the capacitor of interest may be calculated and therefore we are able to calculate τ
=
RC
. From this we can determine ω
p
=
1
τ
. The zero are calculated similarly, determining at what value the admittance of a branch would be 0.
To begin, the low frequency poles and zeros were calculated using the low frequency small signal model circuit as seen in handout P10 – figure 5a of the course notes
9
. The circuit was modelled using the 1/3
rd
rule bias as shown in section 3.3. C
π
and C
μ
can estimated using the C
IBO
and C
OBO
values found in the datasheet
5
using V
BE
= 0.6 V and V
BC
= 5 V. These were determined to be as follows.
C
π
=
18
pF
C
µ
=
5
pF
Using the OC and SC method discussed above, the low frequency poles and zeroes were calculated as shown below.
ω
LP
1
=
1
C
C
1
∗[
R
¿¿
S
+
[
R
B
2
∥
R
B
1
∥
(
r
π
+
(
1
+
β
)
R
E
)
]
]
¿
ω
LP
2
=
1
C
C
2
∗[
R
L
+
R
C
]
ω
LP
3
=
1
C
E
∗
¿¿
Y
LZ
1
=
sC
C
1
Y
LZ
1
=
sC
C
2
Y
LZ
3
=
0
=
1
R
E
+
sC
E
Elec 301 101: Mini Project 2
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To begin, the high frequency poles and zeros were calculated using the high frequency small signal model circuit as seen in handout P10 – figure 5c of the course notes
3
. Using the OC and SC method discussed above, the high frequency poles and zeroes were calculated as shown below.
ω
HP
4
=
1
[
C
¿
¿
π
+
C
µ
(
1
+
g
m
(
R
L
∥
R
C
)
)]∗[
R
S
∥
R
B
1
∥
R
B
2
∥
r
π
]
¿
ω
HP
5
=
1
C
µ
∗[
R
L
∥
R
C
]
ω
HZ
4
=
g
m
C
µ
Evaluation:
Table 6 - Pole Locations and Comparisons
ω
Graphically determined Value
Calculated Value
Percent Error
P
1L
383.1
mHz
377.98
mHz
1.35%
P
2L
1.551
Hz
1.56
Hz
0.577%
P
3L
627.5
Hz
632.86
Hz
0.847%
P
4H
2.214
MHz
6.107
MHz
63.75%
P
5H
17.78
MHz
15.603
MHz
13.95%
Z
1L
0
Hz
0
Hz
0%
Z
2L
0
Hz
0
Hz
0%
Z
3L
4.516
Hz
3.7
Hz
22.05%
Z
4H
1.212
GHz
1.273
GHz
4.79%
Z
5H
10
GHz
∞
n/a
While most graphically determined pole were within a reasonable margin of error, the transformation performed using the Miller gain created a large margin of error at ω
P4H
and a large margin of error overall for the high poles and zeroes due to its distortion in the high frequency range. This is not seen in the low frequency poles and they are therefore are much closer to the theoretical value.
4.2
Part B
Simulation:
From Figure 10 we can graphically determine the mid band frequency at 39.5 kHz, due to negative gain causing a phase shift from negative to positive at mid band. To determine the plot of the transfer curve, the circuit shown in Figure 8 was used, setting the frequency of the voltage source to the mid band frequency. The voltage amplitude was then varied, and the results of V
o
vs V
s
were plotted in as seen in
Figure 12.
Figure 10 – Phase Bode plot for 2N2222A (in rad/sec)
Evaluation:
Using the transfer curve plotted in Figure 12, we are able to graphically determine the linear break down point as being 60 mV. This is done by using the graph and determining the output voltage when the graph is no longer linear.
4.3
Part C
Simulation:
Using SPICE software, the circuit shown in Figure 8 – Tested circuit was simulated and the V
in
and I
in were measured with the V
s
frequency set to the mid band frequency. From this, the Z
in
was calculated using ohm’s law and omitting the R
s
source resistance. The results are shown in Table 7.
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Calculations:
The input impedance was calculated using the mid band circuit as shown in P10 – figure 5b of the course notes
9
. The calculation is shown below, and result is shown in Table 7.
Z
¿
=
R
BB
||
r
π
Evaluation:
Table 7 – Input Impedance Comparison
Impedance
Simulated Value
Calculated Value
Percent Error
Z
in
3.802
k Ω
3.811
k Ω
0.236%
The percent error is such a small value that it can be considered negligible, therefore the theoretical value
and the calculated value can be considered equal, therefore the mid band circuit model can be considered to be a highly accurate representation of the circuits mid band behaviour.
4.4
Part D
Simulation:
Using SPICE software, the circuit shown in Figure 8 – Tested circuit was simulated and the V
out
and I
out were measured with the V
s
frequency set to the mid band frequency. From this, the Z
out
was calculated using ohm’s law and omitting the R
L
source resistance. The results are shown in Table 8.
Calculations:
The output impedance was calculated using the mid band circuit as shown in P10 – figure 5b of the course notes
9
. The calculation is shown below, and result is shown in Table 8.
Z
out
=
R
C
Evaluation:
Table 8 – Output Impedance Comparison
Impedance
Simulated Value
Calculated Value
Percent Error
Z
out
5.0998
k Ω
5.1
k Ω
0.00392%
The percent error is such a small value that it can be considered negligible, therefore the theoretical value
and the calculated value can be considered equal, therefore the mid band circuit model can be considered to be a highly accurate representation of the circuits mid band behaviour.
4.5
Part E
4.5.1
2N3904
Simulation:
Using SPICE software, the circuit shown in Figure 8 – Tested circuit was simulated and the Bode plots showing the magnitude and phase were noted in Figure 13 and Figure 14. Using the plots, we can graphically determine and confirm that the circuit is a band-pass filter.
Following this, from Figure 14 we are able to graphically determine the mid band frequency at 80 kHz, due to negative gain causing a phase shift from negative to positive at mid band. To determine the plot of
the transfer curve, the circuit shown in Figure 8 was used, setting the frequency of the voltage source to Elec 301 101: Mini Project 2
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the mid band frequency. The voltage amplitude was then varied, and the results of V
o
vs V
s
were plotted in as seen in Figure 15. Calculations:
An example of the graphically determined poles is shown in Figure 11, demonstrating how poles were determined from the Bode plot of a simulated circuit. The graphically determined values are shown in
Table 6 - Pole Locations. The values were determined by estimation, as the frequencies are located after
the steepness of the slope begins to change. This was determined using estimation, as well as measurement and observation.
The pole values were calculated using the Open Circuit and Short Circuit (OC and SC) method. In this method, all capacitors will act as open circuits before their pole frequency is reach, once their pole frequency has been passed, they then begin to act as short circuits. To calculate the frequency ω
p
, we first find the time constant τ
. We do so by opening all capacitors with a lower value than the capacitor of interest and shorting all capacitors of a higher value, as well as the voltage source. From this, the equivalent resistance of the circuit seen by the capacitor of interest may be calculated and therefore we are able to calculate τ
=
RC
. From this we can determine ω
p
=
1
τ
. The zero are calculated similarly, determining at what value the admittance of a branch would be 0.
To begin, the low frequency poles and zeros were calculated using the low frequency small signal model circuit as seen in handout P10 – figure 5a of the course notes
9
. The circuit was modelled using the 1/3
rd
rule bias as shown in section 3.3. C
π
and C
μ
can estimated using the C
IBO
and C
OBO
values found in the datasheet
6
using V
BE
= 0.648 V and V
BC
= 5 V. These were determined to be as follows.
C
π
=
3.6
pF
C
µ
=
3
pF
Using the OC and SC method discussed above, the low frequency poles and zeroes were calculated as shown below.
Evaluation:
Table 9 - Pole Locations and Comparisons
ω
Graphically determined Value
Calculated Value
Percent Error
P
1L
403
mHz
387.92
mHz
3.89%
P
2L
1.575
Hz
1.56
Hz
0.962%
P
3L
634.8
Hz
634.859
Hz
0.00929 %
P
4H
12.74
MHz
10.372
MHz
22.83%
P
5H
19.47
MHz
20.8046
MHz
6.42%
Z
1L
0
Hz
0
Hz
0%
Z
2L
0
Hz
0
Hz
0%
Z
3L
3.909
Hz
3.7
Hz
5.65%
Z
4H
1.889
GHz
2.12207
MHz
10.98%
Z
5H
∞
∞
n/a
While most graphically determined pole were within a reasonable margin of error, with some within a negligible amount due to the large resolution used in the simulation, the transformation performed using the Miller gain created a larger margin of error at ω
P4H
and a larger margin of error overall for the high poles and zeroes due to its distortion in the high frequency range. This is not seen in the low frequency poles and they are therefore are much closer to the theoretical value.
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Following this, using the transfer curve plotted in Figure 15 we are able to graphically determine the linear
break down point as being 50 mV. This is done by using the graph and determining the output voltage when the graph is no longer linear.
4.5.2
2N4401
Simulation:
Using SPICE software, the circuit shown in Figure 8 – Tested circuit was simulated and the Bode plots showing the magnitude and phase were noted in Figure 16 and Figure 17. Using the plots, we can graphically determine and confirm that the circuit is a band-pass filter.
Following this, from Figure 17 we are able to graphically determine the mid band frequency at 48 kHz, due to negative gain causing a phase shift from negative to positive at mid band. To determine the plot of
the transfer curve, the circuit shown in Figure 8 was used, setting the frequency of the voltage source to the mid band frequency. The voltage amplitude was then varied, and the results of V
o
vs V
s
were plotted in as seen in Figure 18. Calculations:
An example of the graphically determined poles is shown in Figure 11, demonstrating how poles were determined from the Bode plot of a simulated circuit. The graphically determined values are shown in
Table 10 - Pole Locations and Comparisons. The values were determined by estimation, as the frequencies are located after the steepness of the slope begins to change. This was determined using estimation, as well as measurement and observation.
The pole values were calculated using the Open Circuit and Short Circuit (OC and SC) method. In this method, all capacitors will act as open circuits before their pole frequency is reach, once their pole frequency has been passed, they then begin to act as short circuits. To calculate the frequency ω
p
, we first find the time constant τ
. We do so by opening all capacitors with a lower value than the capacitor of interest and shorting all capacitors of a higher value, as well as the voltage source. From this, the equivalent resistance of the circuit seen by the capacitor of interest may be calculated and therefore we are able to calculate τ
=
RC
. From this we can determine ω
p
=
1
τ
. The zero are calculated similarly, determining at what value the admittance of a branch would be 0.
To begin, the low frequency poles and zeros were calculated using the low frequency small signal model circuit as seen in handout P10 – figure 5a of the course notes
9
. The circuit was modelled using the 1/3
rd
rule bias as shown in section 3.3. C
π
and C
μ
can estimated using the C
IBO
and C
OBO
values found in the datasheet
7
using V
BE
= 0.659 V and V
BC
= 5 V. These were determined to be as follows.
C
π
=
19.5
pF
C
µ
=
7.9
pF
Using the OC and SC method discussed above, the low frequency poles and zeroes were calculated as shown below.
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Evaluation:
Table 10 - Pole Locations and Comparisons
ω
Graphically determined Value
Calculated Value
Percent Error
P
1L
379.3
mHz
381.6
mHz
0.602%
P
2L
1.547
Hz
1.56
Hz
0.833%
P
3L
631.0
Hz
635.936
Hz
0.776%
P
4H
4.079
MHz
4.061128
MHz
0.44%
P
5H
7.122
MHz
7.9005
MHz
9.85%
Z
1L
0
Hz
0
Hz
0%
Z
2L
0
Hz
0
Hz
0%
Z
3L
3.793
Hz
3.7
Hz
2.51%
Z
4H
0.804
GHz
0.80585
GHz
0.229%
Z
5H
32.01
GHz
∞
n/a
While most graphically determined pole were within a reasonable margin of error, with some within a negligible amount due to the large resolution used in the simulation, the transformation performed using the Miller gain created a larger margin of error at ω
P5H
and a larger margin of error overall for the high poles and zeroes due to its distortion in the high frequency range. This is not seen in the low frequency poles and they are therefore are much closer to the theoretical value.
Following this, using the transfer curve plotted in Figure 18, we are able to graphically determine the linear break down point as being 50 mV. This is done by using the graph and determining the output voltage when the graph is no longer linear.
4.5.3
Transistor Comparison
Each transistor would offer different benefits depending on it’s use case. For example, the 2N2222A has the smallest pass band, meaning that the transistor would give the best performance if the use case required a very limited amount of frequencies to pass through. Similarly, the 2N4401 has the largest pass band, allowing for the largest range of frequencies to pass through. Therefore, there is not one transistor that gives the best performance, as it depends on what it will be required to perform within the circuit or amplifier it is placed in.
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5
PART 3 – COMMON BASE AMPLIFIER SIMULATION
5.1
Part A
Simulation:
Using SPICE software, the circuit shown in Figure 19 was simulated and the Bode plots showing the magnitude and phase were noted in Figure 20 and Figure 21. Using the plots, we can graphically determine and confirm that the circuit is a band-pass filter.
Calculations:
An example of the graphically determined poles is shown in Figure 11, demonstrating how poles were determined from the Bode plot of a simulated circuit. The graphically determined values are shown in
Table 11 - Pole Locations and Comparisons. The values were determined by estimation, as the frequencies are located after the steepness of the slope begins to change. This was determined using estimation, as well as measurement and observation.
The pole values were calculated using the Open Circuit and Short Circuit (OC and SC) method. In this method, all capacitors will act as open circuits before their pole frequency is reach, once their pole frequency has been passed, they then begin to act as short circuits. To calculate the frequency ω
p
, we first find the time constant τ
. We do so by opening all capacitors with a lower value than the capacitor of interest and shorting all capacitors of a higher value, as well as the voltage source. From this, the equivalent resistance of the circuit seen by the capacitor of interest may be calculated and therefore we are able to calculate τ
=
RC
. From this we can determine ω
p
=
1
τ
. The zero are calculated similarly, determining at what value the admittance of a branch would be 0.
Evaluation:
Table 11 - Pole Locations and Comparisons
ω
Graphically determined Value
Calculated Value
Percent Error
P
1L
1.547
Hz
1.56
Hz
0.833%
P
2L
1.624
Hz
1.634
Hz
0.612%
P
3L
63.1
Hz
63.363
Hz
0.415%
P
4H
12.44
MHz
12.483
MHz
0.345%
P
5H
532.5
MHz
534.7
MHz
0.411%
Z
1L
0
Hz
0
Hz
0%
Z
2L
0
Hz
0
Hz
0%
Z
3L
361.3
m Hz
356.5
m Hz
1.35%
Z
4H
∞
∞
n/a
Z
5H
∞
∞
n/a
While most graphically determined pole were within a reasonable margin of error, with some within a negligible amount due to the large resolution used in the simulation, the ω
z3L
had a comparably large margin of error, due to its location within the plot and the relative difficulty graphically determining it’s value.
5.2
Part B
Simulation:
From Figure 22 we can graphically determine the mid band frequency at 67.9 kHz, due to negative gain causing a phase shift from negative to positive at mid band. To determine the plot of the transfer curve, Elec 301 101: Mini Project 2
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the circuit shown in Figure 19 was used, setting the frequency of the voltage source to the mid band frequency. The voltage amplitude was then varied, and the results of V
o
vs V
s
were plotted in as seen in
Figure 22. Evaluation:
Using the transfer curve plotted in Figure 22, we can graphically determine the linear break down point as
being 110 mV. This is done by using the graph and determining the output voltage when the graph is no longer linear.
5.3
Part C
Simulation:
Using SPICE software, the circuit shown in Figure 19 was simulated and the V
in
and I
in were measured with the V
s
frequency set to the mid band frequency. From this, the Z
in
was calculated using ohm’s law and omitting the R
s
source resistance. The results are shown in Table 12 – Input Impedance Comparison.
Calculations:
The input impedance was calculated using the mid band circuit. The calculation is shown below, and result is shown in Table 12.
Z
¿
=
¿¿
Evaluation:
Table 12 – Input Impedance Comparison
Impedance
Simulated Value
Calculated Value
Percent Error
Z
in
28.2889
Ω
24.708
Ω
14.5%
The percent error is within a reasonable limit, as most common
resistors are made to be within a ±10% error margin. It is therefore reasonable to conclude that the mid band circuit model to be considered to be an accurate representation of the circuits mid band behaviour.
5.4
Part D
Simulation:
Using SPICE software, the circuit shown in Figure 19 was simulated and the V
out
and I
out were measured with the V
s
frequency set to the mid band frequency. From this, the Z
out
was calculated using ohm’s law and omitting the R
L
source resistance. The results are shown in Table 13.
Calculations:
The output impedance was calculated using the mid band circuit. The calculation is shown below, and result is shown in Table 13.
Z
out
=
R
C
Evaluation:
Table 13 – Output Impedance Comparison
Impedance
Simulated Value
Calculated Value
Percent Error
Z
out
5.0996
k Ω
5.1
k Ω
0.00784%
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The percent error is such a small value that it can be considered negligible, therefore the theoretical value
and the calculated value can be considered equal, therefore the mid band circuit model can be considered to be a highly accurate representation of the circuits mid band behaviour.
APPENDIX A: COMMON EMITTER MODELLING AND BIASING TEST DATA
Figure 1 - I
b
vs V
be
with I
b
as variable parameter tested circuit
Figure 2 – I
B
vs V
BE
with I
B
as variable parameter waveform
Figure 3 – I
C
vs V
CE
with I
B
as variable parameter tested circuit
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Figure 4 – I
C
vs V
CE
with I
B
as variable parameter waveform
Figure 5 – I
C
vs V
CE
with V
BE
as variable parameter tested circuit
Figure 6 – I
C
vs V
CE
with V
BE
as variable parameter waveform
Figure 7 – Tested circuit
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APPENDIX B: COMMON EMITTER AMPLIFIER SIMULATION TEST DATA
Figure 8 – Tested circuit
Figure 9 – Magnitude Bode plot for 2N2222A (in DB)
Figure 10 – Phase Bode plot for 2N2222A (in rad/sec)
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Figure 11 – Example of graphical pole determination
0.03
0.05
0.08
0.1
0.13
0.15
0.18
0.2
0.25
0.5
0.75
1
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
Transfer Curve (Vo/Vs) @ 39.5 kHz
Vs (in V)
Vo (in V)
Figure 12 – Transfer curve (V
o
/V
s
) for 2N2222A graph
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Figure 13 – Magnitude Bode plot for 2N3904 (in DB)
Figure 14 – Phase Bode plot for 2N3904 (in rad/sec)
0.03
0.05
0.1
0.13
0.15
0.18
0.2
0.25
0.5
1
0
0.5
1
1.5
2
2.5
3
3.5
Transfer Curve (Vo/Vs) @ 80 kHz
Vs (in V)
Vo (in V)
Figure 15 – Transfer curve (V
o
/V
s
) for 2N3904 graph
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Figure 16 – Magnitude Bode plot for 2N4401 (in DB)
Figure 17 – Phase Bode plot for 2N4401 (in rad/sec)
0.03
0.05
0.08
0.1
0.13
0.15
0.18
0.2
0.25
0.5
0.75
1
0
0.5
1
1.5
2
2.5
3
3.5
4
Transfer Curve (Vo/Vs) @ 48 kHz
Vs (in V)
Vo (in V)
Figure 18 – Transfer curve (V
o
/V
s
) for 2N4401 graph
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APPENDIX C: COMMON BASE ACOMPLIFIER SIMULATION TEST DATA
Figure 19 – Tested circuit
Figure 20 – Magnitude Bode plot for 2N2222A (in DB)
Figure 21 – Phase Bode plot for 2N2222A (in rad/sec)
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0
0.2
0.4
0.6
0.8
1
1.2
0
0.5
1
1.5
2
2.5
Transfer Curve (Vo/Vs) @ 67.9 kHz
Vs (in V)
Vo (in V)
Figure 22 – Transfer curve (V
o
/V
s
) for 2N2222A graph
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APPENDIX D: REFERENCES
1.
ELEC 301 Course Notes
2.
A. Sedra and K. Smith, "Microelectronic Circuits," 5
th
(or higher) Ed., Oxford University Press, New York
3.
Standard Values List http://ecee.colorado.edu/~mcclurel/resistorsandcaps.pdf
4.
2N2222A ON Semiconductor datasheet http://web.mit.edu/6.101/www/reference/2N2222A.pdf?
fbclid=IwAR0O8VHMSLVdlZ_bdDbGrQ60LX412Vmv173vXmDQZ8fgfcfGL6pO4TA5868
5.
2N2222A ST microelectronics https://www.st.com/resource/en/datasheet/cd00003223.pdf
6.
2N3904 ON Semiconductor datasheet https://www.onsemi.com/pub/Collateral/2N3903-D.PDF
7.
2N4401 ON Semiconductor datasheet https://www.onsemi.com/pub/Collateral/2N4401-D.PDF
8.
CircuitMaker™ (or other circuit simulator) User’s Manual
9.
Notes on CANVAS
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- Please answer with reasons why its true or false. Thank youarrow_forwardPlease answer the questions 1 c, and d with details on why it is true or false. Please make handwriting legible. Thank you.arrow_forwardHow does the construction of a transistor differ from the construction of a PN junction diode? What are the two types of transistors? What are the three parts of a transistor called? Draw and label the schematic symbols for an NPN and a PNP transistor. What are transistors used for? How are transistors classified? What symbols are used to identify transistors? What purposes does the packaging of a transistor serve? How are transistor packages labeled? What are the basic functions of a transistor? What is the proper method for biasing a transistor? What is the difference between biasing an NPN and a PNP transistor? What is the barrier voltage for a germanium and a silicon transistor? What is the difference between the collector-base junction and the emitter- base junction bias voltages? What may cause a transistor to fail? What are two methods of testing a transistor? When using an ohmmeter, what should the results be for an NPN transistor? What are the two…arrow_forward
- Please answer in typing format please ASAP for the like please clear the solution of above question is given to Please answer in typing format please ASAP for the like pleasearrow_forwardDetermine VB, VE, VC, VCE, IB, IE, and IC in Figure. The 2N3904 is a general purpose transistor with a typical BDC 200 Vcc +30 V WWII VCE VB R₁ • 22 ΚΩ IC(mA) Chọn... * Chọn... * IB(UA) Chọn... * IE(MA) Chọn... ◆ Chọn... * Chọn... * Chọn... * VE VC R₂ ´ 10 ΚΩ www Rc 1.0 ΚΩ 2N3904 PDC=200 RE 1.0 ΚΩarrow_forwardTHE PAIR of transistors Q1 and Q2 in the figure have gains β1 = 200 and β2 = 75 respectively. Determine the value of the equivalent gain βeq for the equivalent transistor Qeq. ( NEED ONLY HANDWRITTEN SOLUTION PLEASE OTHERWISE DOWNVOTE).arrow_forward
- The breakdown voltage of a lot of transistors is assumed to follow a normal distribution.Ten samples are tested from this lot, getting the following measurements for breakdownvoltage.- Customer specifications are.-Upper limit: 52.8Lower limit: 47.2What is the Cpk for this lot ?.If this lot has a million transistors, how many would be found below the lower limit and how many above the upper limit ?arrow_forwardExercise 1:-arrow_forwardHow much is the voltage across the base-collector junction (VBC) of the transistor?How is the base-collector junction of the transistor biased?arrow_forward
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