MiniProject3_report
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Subject
Electrical Engineering
Date
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docx
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Uploaded by BrigadierBraverySeaLion38
Katie Seifert 68469311
2019/11/06
Elec 301 101: Mini Project 3
Multi-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 3
Page 1
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Katie Seifert 68469311
2019-11-06
The Power of Trust. The Future of Energy.
1
INTRODUCTION
In order to analyse and measure the characteristics of four multi-transistor amplifiers, the cascode
amplifier, an amplifier consisting of a common-base stage followed by a common-collector stage in
cascade, a differential amplifier, and an AM modulator, mini project 3 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 cascode amplifier, an amplifier consisting of a common-base stage followed by a common-collector stage in cascade, a differential amplifier, and an AM modulator (circuits shown in Figure 1, Figure 5, Figure 8 and Figure 13) to develop familiarity and understanding of the characteristics of these multi-transistor amplifiers and circuits.
2.2
Tests Performed
Part 1 – The Cascode Amplifier
a)
D.C. Operating Point
b)
Bode Plot Simulation and Comparison
c)
Mid Band Modelling
d)
Input Impedance
Part 2 – Cascaded Amplifiers – The Common-Base followed by the Common-Collector
e)
Biasing the Circuit
f)
Mid Band Modelling
g)
Bode Plot Simulation and Comparison
Part 3 – The Differential Amplifier
a)
Bode Plot Simulation
b)
Differential Gain and f
H3dB
Modelling and Comparison
c)
Differential Output Voltage Modelling
d)
Common-Mode Signal
i.
Common Mode Gain and Rejection Ratio
ii.
Changing Resistance Common Mode Gain and Rejection Ratio
e)
Differential Signal and Common-Mode Signal Differential Output Voltage Modelling
Part 4 – The AM Modulator
f)
Differential Output Simulation
g)
Variation of Signal Amplitude
h)
Variation of Signal Shape
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3
PART 1 - THE CASCODE AMPLIFIER
3.1
Part A
Simulation:
Using Spice software, the circuit shown in Figure 1 was modelled using the resistor and capacitor values determined using the ¼ rule discussed in lecture, as well as the provided parameters requiring that
R
out
≤ 5 kΩ, 2.5 kΩ ≤ R
in ≤ 10 kΩ, |A
v
| ≥ 50 V/V and ω
L3dB
≤ 500 Hz. From these requirements, the circuit was then simulated and the d.c. operating points were measured and compared to those calculated.
Calculation:
Firstly, β is determined to be 166.67 from simulation. Following this, we are able to determine that R
out
is equivalent to R
C and therefore we are able to determine that R
C
= 5 kΩ. We can then use the ¼ rule to bias the circuit, assuming V
BE
= 0.7V. Following this, we are able to determine the following voltages.
V
C
2
=
3
4
∗
V
CC
=
15
V
V
C
1
=
V
E
2
=
2
4
∗
V
CC
=
10
V
V
E
1
=
1
4
∗
V
CC
=
5
V
V
B
2
=
V
C
1
+
V
BE
=
10.7
V
V
B
1
=
V
E
1
+
V
BE
=
5.7
V
Following this, we can then determine I
C2
and using the relationships between the currents of a transistor, we are able to determine the following currents and resistances.
I
C
2
=
V
CC
−
V
C
2
R
C
2
=
1
mA
I
B
2
=
I
C
2
β
=
6
µA
I
C
1
=
I
E
2
=
I
C
2
+
I
B
2
=
1.006
mA
I
B
1
=
I
C
1
β
=
6.035
µA
I
E
1
=
I
C
1
+
I
B
1
=
1.012
mA
I
RB
1
=
I
E
1
√
β
=
78.38
µA
I
RB
2
=
I
RB
1
−
I
B
2
=
72.38
µA
I
RB
3
=
I
RB
2
−
I
B
1
=
66.35
µA
R
E
=
V
E
1
I
E
1
=
4950.5
Ω
R
B
1
=
V
CC
−
V
B
2
I
RB
1
=
118.64
kΩ
Elec 301 101: Mini Project 3
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The Power of Trust. The Future of Energy.
R
B
2
=
V
B
2
−
V
B
1
I
RB
2
=
69.068
kΩ
R
B
3
=
V
B
1
I
RB
3
=
85.90
kΩ
From this and using the list of common resistors
3
, we can determine the nearest common resistor and input those into our circuit model. The common resistor values used are as follows.
R
C
=
4.7
kΩ
R
E
=
4.7
kΩ
R
B
1
=
120
kΩ
R
B
2
=
68
kΩ
R
B
3
=
82
k Ω
The capacitances can then be calculated for the circuit. C
E
is determined to the dominant pole, as it sees a much lower resistance than C
B
, C
C2
or C
C1
, which see in the order of 10
3
Ω, compared to C
E
, which sees in the order of 10
1
Ω. Furthermore, it is provided that C
B
is 500 μF and is therefore is even less dominant due to its large resistance. From this and the provided low cut-in frequency also provided, we can determine C
E
as follows.
500
∗
2
π
=
√
(
1
C
E
∗
[
(
(
1
1
+
β
)
∗
(
(
R
S
∥
R
B
2
∥
R
B
3
)
+
r
π
1
)
)
∥
R
E
]
)
2
−
2
∗
(
1
R
E
∗
C
E
)
2
=
C
E
=
12.799
µF
Due to their minimal impact on the low cut-in frequency, C
C1
and C
C2
can be equal to C
E
. This choice is made to limit cost in designing the circuit, due to their low capacitance values, and the possibility to order in bulk.
Evaluation:
DC operating point
Measured Value
Calculated Value
I
C1
1.037 mA
1.006 mA
I
E1
1.043 mA
1.012 mA
I
B1
6.194 µA
6.035 µA
V
C1
9.875 V
10 V
V
E1
4.895 V
5 V
V
B1
5.497 V
5.7 V
I
C2
1.031 mA
1 mA
I
E2
1.037 mA
1.006 mA
I
B2
6.146 µA
6 µA
V
C2
15.16 V
15 V
V
E2
9.875 V
10 V
V
B2
10.48 V
10.7 V
I
RB1
79.36 µA
78.38 µA
I
RB2
73.23 µA
72.38 µA
I
RB3
67.04 µA
66.35 µA
Elec 301 101: Mini Project 3
Page 4
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Katie Seifert 68469311
2019-11-06
The Power of Trust. The Future of Energy.
The measured d.c. operating points are well within range of the calculated values, which shows that the assumptions made in biasing are valid.
3.2
Part B
Simulation:
Using SPICE software, the circuit shown in Figure 1 was simulated and the Bode plots showing the magnitude and phase were noted in Figure 2 and Figure 3. Using the plots, we can graphically determine
and confirm that the circuit is a band-pass filter and determine the ω
L3dB and ω
H3dB
points
Calculation:
From the earlier biasing and design data, we can determine that ω
L3dB
is equal to 500 Hz. Following this, the high frequency poles can be calculated using C
π
= 18 pF and C
μ
= 5 pF, which can be found on the datasheet
4
. R
L
and R
C
are provided from the circuit design constraints as 50 kΩ and 50 Ω respectively. Using Miller’s theorem, the high poles are then able to be calculated as follows.
ω
HP
1
=
1
(
C
π
+
2
C
µ
)
∗[
R
S
∥
R
B
3
∥
R
B
2
∥
r
π
1
]
=
723.841
M rad
/
s
ω
HP
2
=
1
(
C
π
+
2
C
µ
)
∗
[
r
π
2
1
+
β
]
=
1.437
Grad
/
s
ω
HP
3
=
1
C
µ
∗
R
C
∥
R
❑
L
=
44
M rad
/
s
From this, we can calculate ω
H3dB
as follows.
ω
H
3
dB
=
1
√
(
1
ω
HP
1
)
2
+
(
1
ω
HP
2
)
2
+
(
1
ω
HP
3
)
2
=
43.898
M rad
/
s
From this, we the percent error between the graphically determined and calculated values can be calculated using the following formula.
Error
=
|
Experimental
−
Theoretical
|
¿
Theoretical
∨
¿
∗
100
¿
Evaluation:
3 dB point
Measured Value
Calculated value Percent Error
ω
L3dB
499 Hz
500 Hz
0.2%
ω
H3dB
4.445 MHz
6.987 MHz
36.4%
The error for the low 3 dB point is negligibly small, however the error for the high 3 dB point is relatively high. This can be explained by the error introduced in the high frequency by Miller’s theorem, as well as the inaccuracy of the C
π
and C
μ
values determined graphically from the datasheet
4
.
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3.3
Part C
Simulation:
From the graph shown in Figure 3, the mid band frequency can be determined to be 44 kHz. From this, we can set the source the mid band frequency, then measure the output voltage while incrementally increasing the input voltage. This process gives the graph shown in Figure 4. From this graph, we can determine that the breakdown voltage, V
B
, would be equal to 60 mV.
3.4
Part D
Simulation: Using the circuit shown in Figure 1 with R
S
removed, with the source set to the mid band frequency with an amplitude of 60 mV, the input resistance was measured to be R
in
= 2.9 kΩ. The mid band gain was measured to be |A
m
| = 78.09 V/V.
Calculation:
Following the process presented in the cascode course notes
1
, R
in
and A
m
can be calculated as follows.
R
¿
=
R
B
3
∥
R
B
2
∥
r
π
1
=
3.747
kΩ
A
m
=−
g
m
2
R
C
∥
R
L
∗
R
B
3
∥
R
B
2
∥
r
π
1
R
B
3
∥
R
B
2
∥
r
π
1
+
R
S
=
93
V
/
V
Evaluation:
These values are within the specifications required and are within a reasonable range of those of the calculated values.
4
PART 2 – CASCADED AMPLIFIERS
4.1
Part A
Calculation:
From the circuit specifications we are provided, we know that our circuit shown in Figure 5 must have the following parameters: R
in
& R
out
= 50 ± 5Ω and f
L3dB
≤ 1000 Hz. From this, we can bias using the 1/3
rd
rule,
assuming β = 114.3, as found via simulation. I
E1
is calculated to begin.
R
¿
=
R
E
∥
r
π
1
1
+
β
=
V
E
1
I
E
1
∥
V
T
I
C
(
β
1
+
β
)
≈
4
I
E
1
∥
25
mV
I
C
≈
25
mV
I
E
1
=
50
Ω
I
E
1
=
0.5
mA
Using I
E1
and the relationships between transistor currents, as well as the 1/3
rd
rule, the voltages and currents and then the resistors can be calculated as follows.
V
E
1
=
4
V
V
B
1
=
V
E
1
+
V
BE
=
4.7
V
V
C
1
=
V
B
2
=
2
3
V
CC
=
8
V
V
E
2
=
V
B
2
−
V
BE
=
7.3
V
I
B
1
=
I
E
1
1
+
β
=
4.3365
µA
Elec 301 101: Mini Project 3
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The Power of Trust. The Future of Energy.
I
RB
1
=
0.1
I
E
1
=
50
µA
I
RB
2
=
I
RB
1
−
I
B
1
=
45.6635
µA
I
C
1
=
βI
B
1
=
0.49566
mA
R
E
1
=
V
E
1
I
E
1
=
8
kΩ
R
B
1
=
V
CC
−
V
B
1
I
RB
1
=
146
kΩ
R
B
2
=
V
B
1
I
RB
2
=
102.927
k Ω
Using substitution, R
E2
can be calculated, and from this, R
C1
and I
E2
can be found as follows.
R
out
=
50
Ω
=
R
C
1
+
r
π
2
1
+
β
∥
R
E
2
=
(
V
CC
−
V
C
1
I
C
1
+
(
V
E
2
(
1
+
β
)
R
E
2
)
1
+
β
+
V
T
∗
R
E
2
V
E
2
)
∥
R
E
2
R
E
2
=
454.223
Ω
Using this value, R
C1
and I
E2
are determined.
I
E
2
=
V
E
2
R
E
2
=
16.07
mA
R
C
1
=
V
CC
−
V
C
1
I
C
1
+
(
I
E
1
1
+
β
)
=
6.299
k Ω
It can be determined that both C
C1 and C
C2
“see” a similar amount of resistance, and therefore it can be assumed that they have the same capacitance and are both dominant poles. C
B
is determined to be at least an order of magnitude smaller then the dominant capacitors to not affect the frequency of the low cut-in point. Using this, C
C1
, C
C2
and C
B
can be determined as follows.
1000
∗
2
π
=
√
(
1
45.04
∗
C
)
2
+
(
1
50
∗
C
)
2
C
C
1
=
C
C
2
=
4.756
µF
1
[
R
B
1
∥
R
B
2
∥
(
r
π
1
+
(
1
+
β
)
R
E
1
)
]
∗
C
B
=
466.8
rad
/
s
C
B
≥
35.37
nF
4.2
Part B
Simulation:
Using the common values table
4
, all calculated values were converted to common values as follows.
C
C
1
=
C
C
2
=
4.7
µF
C
B
=
0.039
µF
Elec 301 101: Mini Project 3
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R
E
1
=
8.2
kΩ
R
E
2
=
470
Ω
R
C
1
=
6.2
k Ω
R
B
1
=
150
k Ω
R
B
2
=
100
k Ω
After testing, R
E1
was changed to 7.5kΩ to meet the input and output resistance parameters.
Given this, as shown in Figure 6 55kHz is found to be within the mid band region. Using this, the input and output resistances can be measured and found to be:
R
¿
=
53.33
Ω,
R
out
=
52.47
Ω
The mid band gain is measured to be as follows.
|
A
m
|
=
146.2
V
V
These measured resistance values, once the resistors are adjusted to meet the design parameters, are within the required limits of being 50 ± 5Ω.
4.3
Part C
Simulation:
Using SPICE simulation, the circuit shown in Figure 5 with the adjusted resistor values was simulated, producing the graphs shown in Figure 6 and Figure 7. From the plots, the 3 dB points can be graphically determined to be as follows.
ω
L
3
dB
=
803.1
∗
2
π rad
/
s ,
ω
H
3
dB
=
4.558
∗
2
π Mrad
/
s
These values are within the required parameters and meet the design requirements without further alternation of the calculated values. The low frequency 3 dB point is well within the required range of below 1000 Hz, thus confirming our calculations and assumptions.
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The Power of Trust. The Future of Energy.
5
PART 3 – THE DIFFERENTIAL AMPLIFIER
5.1
Part A
Simulation:
Before the circuit was modelled, the current mirror circuit needed to be designed. The begin I
ref
was computed, and then using this result, R
ref (displayed in the circuit as R3) was calculated as follows.
I
ref
=
I
o
(
1
+
2
β
)
=
2.024
mA
R
ref
=
12
V
−
0.7
V
2.024
mA
=
5.583
k Ω
Using SPICE simulation, the circuit shown in Figure 8 was then simulated, producing the graphs shown in
Figure 9 and Figure 10.
5.2
Part B
Simulation:
Using the graphs shown in Figure 9 and Figure 10, the f
H3dB
and differential gain (A
D
) were graphically determined to be as follows.
ω
H
3
dB
=
2.415
∗
2
π Mrad
/
s
|
A
D
|
=
289.6
V
V
Calculation:
Using C
π
= 18 pF, C
μ
= 5 pF and r
π
= 4.167kΩ, the theoretical values of ω
H3dB
and A
D can be calculated as follows.
K
=−
g
m
R
c
=−
40
m Ω
−
1
⋅
8
k
=−
320
g
m
=
α I
E
2
V
T
=
0.994
⋅
1
mA
25
mV
=
40
mΩ
−
1
ω
H P
1
=
1
[
Cπ
2
+
C
u
2
⋅
(
1
+
320
)
]
∗
2
r
π
¿
∨
R
s
=
24.794
Mrad
/
s
ω
HP
2
=
1
[
C
μ
2
(
1
+
1
320
)
]
∗
2
R
c
=
24.922
Mrad
/
s
ω
H
3
dB
1
√
(
1
ω
HP
1
)
2
+
(
1
ω
HP
2
)
2
=
17.577
Mrad
/
s
A
m
=
v
o
v
s
=−
g
m
R
c
=−
318.09
V
V
A
d
=
v
0
v
d
=−
g
m
R
C
=−
318.09
V
V
Elec 301 101: Mini Project 3
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The Power of Trust. The Future of Energy.
Evaluation:
Comparison Point
Measured Value
Calculated value
Percent Error
ω
H3dB
2.415 MHz
2.797 MHz
13.7%
|A
D
|
289.6 V/V
318.09
8.96%
The percent error confirms that the calculated vs measured values are within a reasonable tolerance considering the common percent accuracy of components such as resistors and capacitors.
5.3
Part C
Simulation:
Using the graphs shown in Figure 9 and Figure 10, the mid band frequency was determined to be 1 kHz. Using this, the circuit shown in Figure 8 was modelled with a differential signal of 0.5mV
p
and the output voltage was measured. The output voltage vs the input voltage was graphed in Figure 11, producing a transfer curve. From this curve, the breakdown voltage (V
B
) was determined to be 30mV.
5.4
Part D
5.4.1
Common Resistors
Simulation:
The circuit shown in Figure 8 was modelled with a common-mode signal of less then 0.5V
p
, with the base of each transistor receiving the same signal with the signal shorted between them. Theoretically, this should produce an output of 0 due to the common connection between the two transistors collectors that should then see a difference of 0 V between them. In simulation using transient analysis, the transient response is seen to be zero, therefore confirming the model.
Calculation:
The common mode gain can be calculated as follows.
¿
A
CM
∨
¿
∆ R
C
2
∗
R
ref
Since both transistors have the same R
c
, ΔR
C
= 0, therefore A
cm
is equal to 0. Due to this, the common mode rejection ration is also 0.
5.4.2
1/2% Difference
Simulation:
The circuit shown in Figure 8 was modelled with a common-mode signal of less then 0.5V
p
, with the base of each transistor receiving the same signal with the signal shorted between them. Due to the difference in R
C
, the output voltage will not be zero to the lack of balance between the two sides of the circuit, despite the common voltage source.
Calculation:
The difference between the two R
C
values is equal to 80 Ω, with one side having a resistance of 8.04kΩ and the other having a resistance of 7.96kΩ. Using this, the common mode gain and common mode rejection ratio are then calculated as follows.
|
A
CM
|
=
80
Ω
2
∗
5583
Ω
=
7.1646
∗
10
−
3
CMMR
=
20log
10
¿¿
This is as expected due to the lack of symmetry in the circuit due to the change in resistor value from each side.
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5.5
Part E
Simulation:
The circuit mentioned above then has both a 0.5 V
p
common-mode signal, as well as a 0.5mV
p
differential
signal applied, with the common-mode signal at 1/10
th
of the frequency of the differential signal. This causes the higher frequency to envelope the lower frequency and create modulation of the lower frequency. This is then seen within the simulation in Figure 12 and is therefore confirmed as the signal is viewed within an envelope of the other, creating modulation. Elec 301 101: Mini Project 3
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6
PART 4 - THE AM MODULATOR
6.1
Part A
Simulation:
The circuit shown in Figure 13 was modelled with an input of 50 mV
p
with a frequency of 1 kHz using SPICE simulation. The differential output is shown in Figure 14. In this figure you can see the modulation
of the input frequency with the carrier frequency, where the amplitude varies with the amplitude of the carrier.
6.2
Part B
Simulation:
The circuit was then modelled with an input varying from 10 mV
p
to 100 mV
p
. The results are shown in
Figure 15 and Figure 16. In these graphs, we can observe that as stated above, the modulation of the input frequency in terms of the carrier frequency, with smaller V
p
having less modulation in the amplitude. Although 10 mV
p
demonstrates the least amount of distortion, due to the difference in frequency and the circuits design, there is always a slight amount of distortion of the input signal.
6.3
Part C
Simulation:
The circuit was finally modelled with an input varying from 10 mV
p
to 100 mV
p
using a square wave. The results are shown in Figure 17. In this graph, we see the same trend as previously observed, the amplitude of the input modulates with the frequency of the carrier voltage, therefore, when the square wave is high, we see a much larger amplitude in the input voltage, and when it drops back down, the amplitude of the input voltage drops as well. This circuit allows for input waves to be “carried” by carrier waves, where the amplitude modulates with the frequency of the carrier, creating a group frequency that carries the input.
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APPENDIX A: THE CASCODE AMPLIFIER TEST DATA
Figure 1 - Tested Circuit
Figure 2 - Magnitude Bode Plot (in dB)
Figure 3 - Phase Bode Plot (in rad)
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0.03
0.05
0.08
0.1
0.13
0.15
0.18
0.2
0.25
0.5
0.75
1
0
1
2
3
4
5
6
7
8
Transfer Curve (Vo/Vs) @ 44 kHz
Vs (in V)
Vo (in V)
Figure 4 - Transfer curve (V
o
/V
s
)
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APPENDIX B: CASCADED AMPLIFIERS TEST DATA
Figure 5 – Tested circuit (initial)
Figure 6 – Magnitude Bode plot (in DB)
Figure 7 – Phase Bode plot (in rad)
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APPENDIX C: THE DIFFERENTIAL AMPLIFIER TEST DATA
Figure 8 - Tested circuit
Figure 9 - Magnitude Bode plot (in dB)
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Figure 10 - Phase Bode (in rad)
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0
1
2
3
4
5
6
7
8
9
10
Transfer Curve (Vo/Vs) @ 1 kHz
Vs (in V)
Vo (in V)
Figure 11 - Transfer curve (V
o
/V
s
)
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Figure 12 – Common-mode and differential input transient
APPENDIX D: THE AM MODULATOR
Figure 13 - Tested circuit
Figure 14 – 50 mV
p
input differential output
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Figure 15 - 10 mV
p
input differential output
Figure 16 - 100 mVp input differential output
Figure 17 - 50 mVp square wave input differential output
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APPENDIX E: REFERENCES
1.
ELEC 301 Course Notes
2.
A. Sedra and K. Smith, "Microelectronic Circuits," 5th , 6th , or 7th 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.
CircuitMaker™ (or other circuit simulator) User’s Manual
8.
Notes on CANVAS
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