Experiment 4
AMPLIFIER WITH A BIPOLAR
TRANSISTOR
OBJECTIVES. To bias a bipolar junction transistor (BJT) in order to achieve stability and
linear amplification. To build a single stage amplifier and to measure its basic parameters.
4.1.
DC and small signal models
OBJETIVES. To create subcircuits in Pspice for the large and small signal models of the
BJT. To load the subcircuits in a library.
F1
B
C
Beta
E
VBE
Figure 4.1: Large signal model for the npn transistor operating in the active mode. F1 is a current
controlled current source in Spice where beta = IC /IB is the common-emitter current gain.
1. PSpice work
Draw in PSpice the large signal model of an npn transistor operating in the active
mode (Figure 4.1).
The values of the base-emitter voltage VBE and the DC current gain BETA≡ β
depend on the transistor and its bias point. Consider the BC547B transistor and look
up in its data sheet the typical values for VBE and β for a bias point IC = 2 mA and
VCE = 5 V. Which are these values? Incorporate them into the model of Figure 4.1.
Load the subcircuit in a library or in a page of a different schematic where you keep
other subcircuits. In this experiment, the second option is preferred because it is easy
to copy and paste the circuit and to change its parameters when required.
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Table 4.1: Table to be filled in with the values of the BJT parameters.
IC
VCE
β
VBE
gm
Rpi
α
Re
If the student chooses the first option follow the procedure detailed in Experiment
3. As an example, provide the following names to the parameters: Reference = Q1N,
Implementation name = Bipolar and Part Name = Bipolar. Use three bidirectional
H pins named E, B and C. Load the component in the library COMPONENTES.olb
created in the previous experiment. Edit the symbol and draw the component.
Repeat the same procedure to create the small signal π and T models (Figures 4.2
and 4.3, respectively). The value of the parameters gm, Rpi, α and Re depend on the
bias point. They must be changed in accordance to the value of the collector current
of the transistor, IC (follow the theoretical expressions [1] ). Which are these values
for IC = 2 mA and VCE = 5 V?
F2
B
C
G1
B
C
gain=a
+
Rpi
gm
Re
-
E
E
Figure 4.2: Small-signal π-model for the npn
transistor. G1 is a voltage controlled current
source where gm is the transconductance
4.2.
Figure 4.3: Small-signal T-model for the npn
transistor. F2 is a current controlled current
source in Spice where α is the common-base
current gain.
Biasing the BJT
OBJECTIVES. To analyse the stability of different biasing circuits. To bias a transistor with
a single power supply.
1. Theoretical work
a) Find the values of the resistances of Figure 4.4 so that the bias point of the transistor
BC547B is VCE = 5V and IC = 2mA. Consider VCC = 12V .
In order to find the values of the four resistances, four conditions or equations are
needed. Two of them are the result of applying the Kirchoff laws to the circuit.
The other two are the result of imposing some specifications to the circuit. In
this case, the following conditions are used:
IC RC = VCC /3
IP = 0.1IE
2
VCC=12 V
RC
R1
IP
IB
R2
VCC=12 V
R’C
R’1
IC
IP
IE
IB
RE
IC
IE
R’2
Figure 4.4: Classical biasing for BJTs using a
single power supply and RE 6= 0
Figure 4.5: Simple biasing for BJTs using a
single power supply and RE = 0
These conditions are the result of a compromise among stability, large signal
swing and high input resistance (see p. 316 in [1]).
To make the emitter current IE insensitive to temperature and β variations, we
RB
, where VBB and RB
design the circuit to satisfy VBB ≫ VBE and RE ≫ 1+β
are the parameters that define the Thévenin equivalent of the voltage divider
network: VBB = VCC × R2 /(R1 + R2 ) and RB = R1 k R2 .
There is a limit on how large VBB can be if we also want to provide a large
signal swing (before transistor cut off). Thus, a compromise is needed. As a rule
of thumb, the voltage of the power supply VCC is divided in VBB ≈ VCC /3,
VCB ≈ VCC /3 and IC RC = VCC /3. For this design, choose IC RC = VCC /3.
RB
, the current in the divider must be much larger than the
To satisfy RE ≫ 1+β
base current. If R1 and R2 are made small the input resistance of the circuits is
also small. Again, a compromise is necessary. Typically one selects R1 and R2
such that their current IP is in the range of IE to 0.1IE . For this design, choose
IP = 0.1IE
b) Find the values of the resistances of Figure 4.5 so that the bias point of the transistor
BC547B is VCE = 5V and IC = 2mA. Consider VCC = 12V .
In this design, there are three unknown resistances. The value of IC RC is
determined by the values of IC and VCE and the Kirchoff laws. Thus, we need to
impose only one additional condition. For this circuit, assume
IP = 0.1IE
2. PSpice work
a) Draw the circuits of Figures 4.4 and 4.5 in two different pages of the same schematic
(avoid using similar names in both circuits in order to prevent simulation errors).
Replace the transistor by the large signal model of Figure 4.1. Use the values of the
resistances obtained in the theoretical work. Make a Bias point analysis and determine
the values of IC and VCE in both circuits. Do they coincide with the design values?
If the answer is no, revise the formulas, something is wrong.
b) Once the design has been checked, proceed with a parametric study in both designs
in order to decide which one is the most stable. Firstly, analyse the dependence of the
collector current and VCE with β. Secondly, analyse the dependence of the collector
current and VCE with VBE .
3
Place the component PARAMETRIC, introduce a new variable to be varied by
clicking on New Row... with Name = Beta and Value =(the value you are working
with). In the current controlled current source, write {Beta} as the value of the
parameter GAIN. Following the same procedure, create a second row for the
voltage source VBE : Name = VBE, Value =(the value you are working with) and
in the voltage source write {VBE} .
Study with β. Create a simulation profile DC sweep:
• Options= Primary Sweep:
• Sweep variable = Global parameter
• Parameter Name = Beta
• Start value = your value - 40
• End value = you value + 40
• Increment = 20
Study with V BE. Assuming that V BE decreases by about 2 mV/K with
increasing temperature, consider a variation of ±15K over room temperature.
Which are the maximum V BEmax and minimum V BEmin values of VBE? Create
a simulation profile DC sweep:
• Options= Primary Sweep:
• Sweep variable = Global parameter
• Parameter Name = VBE
• Start value = V BEmin
• End value = V BEmax
• Increment = .01 V
Add current and voltage markers to determine the collector current and VCE . Run
the simulation in both circuits and compare the results. Represent in respective
figures: the collector current IC as a function of β, VCE as a function of β, IC as
a function of V BE and VCE as a function of V BE (see Figure 4.6).
c) Analyse the results. Explain whether something is wrong or strange and propose a
solution. Which is the most stable circuit?
3. Laboratory practice
Consider the most stable circuit and assemble it in the laboratory. Use the closest
commercial values to the ones obtained in the theoretical part (in case you buy the
components) or the closest values you can find in the laboratory (in case you use
these ones). Introduce these values in your PSpice circuit and determine the value of
IC and VCE .
Measure IC and VCE in the laboratory. Which are these values?. What is the relative
difference between the experimental and PSpice results?.
4.3.
Single stage amplifier
OBJECTIVES. To analyse a single-stage amplifier in the common-emitter configuration. To
assemble the amplifier in the laboratory and to measure its voltage gain, input resistance and
output resistance. To study the effect of a bypass capacitor on the voltage gain of the amplifier.
1. Theoretical work
4
Table 4.2: Table to be filled in with the results of the DC analysis.
spice
Circuit A
spice
Circuit B
lab
A or B
R1
R2
RC
RE
IC
VCE
Figure 4.6: Figures to be completed with the DC analysis for the circuits of Figures 4.4 and 4.5.
Consider the amplifier of Figure 4.7 when biased as in Figure 4.4. In particular, refer
to the the bias point used in the previous section. Determine the values of the elements
of the π and T small signal models at this bias point.
Use the following or similar values for the coupling capacitors CC = 10µF and
CB = 10µF and for the bypass capacitor CE = 220µF. The load resistance is RL = 10
KΩ.
The resistance RX = 20 KΩ may be necessary to reduce the amplitude of the input
signal in case the signal generator is at its lower limit.
Draw the equivalent ac circuit of the structure shown in Figure 4.7. Replace the
transistor with its T model and use the values of the parameters obtained above.
Find the values of 1
a)
b)
c)
d)
e)
The voltage gain Av = vo /v1
The input resistance Ri
The output resistance Ro
The overall voltage gain Gv = vo /v2
If small signal operation is desired (for linearity), then the sine-wave vπ = vbe is
to be limited to 5 mV peak. What is the maximum allowed peak amplitude of v2
(v2max ) and the corresponding peak amplitude of vo (vomax )?
Remove the capacitor CE and find the new values of, Av = vo /v1 , Ri , Ro and
Gv = vo /v2 .
Compare both sets of results in a table and extract the conclusions.
2. PSpice work
1
Consider a frequency such that the capacitors can be considered as short circuits.
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Figure 4.7: Common-emitter amplifier
Draw in PSpice the equivalent ac circuit of the structure shown in Figure 4.7. Replace
the transistor with its π model created in the Section 4.1, and use the values of the
parameters obtained in the theoretical part. Use a voltage source VSIN. Its amplitude
VAMPL must be lower than the maximum allowed peak amplitude of v2 found above,
and FREQ = 5kHz.
Define a Transient type simulation profile with Run to Time = 1ms. Introduce voltage
markers at vo , v1 and v2 and run the simulation.
Find the voltage gain Av = vo /v1 and the overall voltage gain Gv = vo /v2 . To do
this click on Trace → Evaluate measurement → ConversionGain(1,2) and select the
voltages to evaluate the gains.
Consider the circuit of Figure 4.8 where the AC equivalent circuit model of a voltage
amplifier is represented. Find a formula to evaluate the input resistance Ri if v1 , v2
and Rx are known. Using this formula, find the input resistance of the ac circuit
drawn in PSpice. Replace v1 and v2 by their maximum values M ax(v1 ) and M ax(v2 )
that can be found with the option Evaluate measurement.
Consider the circuits of Figures 4.9a and b, where the resistance RL has been replaced
by an open circuit (Figure 4.9a) and a resistance RP (Figure 4.9b). If RP , vo1 and
vo2 are known, find a formula to determine Ro. Repeat this procedure to determine
the output resistance in your PSpice ac circuit. Use a resistance RP close to the value
you expect to find for Ro .
Rx
+
+
v2
v1
Ro
+
Ri
AvoVi
RL
-
-
Figure 4.8: AC equivalent circuit model of a voltage amplifier.
3. Laboratory practice
Assemble the circuit of figure 4.7. Use commercial values for the elements close to the
theoretical ones. The transistor is the BC547B.
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Rx
Rx
+
+
v2
v1
-
-
+
+
+
vo1
v2
v1
-
-
-
Ro
+
Ri
AvoVi
Ro
+
Ri
RP vo2
AvoVi
-
+
-
(a)
-
(b)
Figure 4.9: AC equivalent circuit model of a voltage amplifier.
Table 4.3: Table to be filled in with the results of the AC analysis.
Theory
without CE
Theory
with CE
PSpice
with CE
Laboratory
with CE
Laboratory
without CE
—
—
—
—
—
—
Av
Ri
Ro
Gv
vomax
v2max
—
—
At 5 KHz, determine the experimental value of:
a) The voltage gain Av and the overall voltage gain Gv (measure the amplitude of
the input and output signals)
b) The input resistance Ri . Use the method explained in section 4.3.2.
c) The output resistance Ro . Use the method explained in section 4.3.2.
Remove the capacitor CE and determine again the voltage gain Av , the overall voltage
gain Gv , the input resistance Ri and the output resistance Ro .
Compare both sets of results. What are the conclusions?.
Complete the table 4.3 with all the results of this experience.
References
[1] A. S. Sedra and K.C. Smith, ”Microelectronic circuits”, 6th Ed., New York, Oxford University
Press 2011
[2] López Villanueva, J.A., Jiménez Tejada, J.A., ”Fundamentos de Teorı́a de Circuitos para
Electrónica”, http://hdl.handle.net/10481/14700.
[3] Jiménez Tejada, J.A., López Villanueva, J.A., ”Problemas de Electrónica Básica”
[4] F. M. Gómez Campos, J. E. Carceller, A. Godoy, J. A. López Villanueva, J. A. Jiménez
Tejada, P. Lara Bullejos, S. Rodrı́guez Bolı́var, A. Luque Rodrı́guez, F. Mier Mota ”Video
sobre manejo del osciloscopio”, htpp//www.ugr.es/∼tejada
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