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ELEC 351L
Electronics II Laboratory
Spring 2004
Lab #9: Frequency Response of BJT Amplifiers
Introduction
Capacitors are used in many amplifier circuits for DC blocking and for AC bypassing. The usual
assumption in the initial stages of the design process is that the capacitors are large enough so
that they can be regarded as short circuits at AC. However, this assumption is not valid at low
frequencies, where the capacitive reactances can be substantially large. Also, there are “stray,”
or unintended, capacitances inherent in the physical structures that make up the circuit and in the
semiconductor devices themselves. For example, in the 2N2222 transistor there is a junction
capacitance of 5-10 pF between the collector and the base. There are also stray inductances. In
this lab experiment you will investigate the effects of capacitors and capacitances on the
performance of a common-emitter amplifier.
Theoretical Background
Figure 1 shows a common-emitter amplifier with emitter degeneration. Capacitors Ci and Co
provide DC isolation for the bias levels, capacitor CE bypasses the emitter resistor, and capacitor
CCC bypasses the power supply. In addition to these four physical capacitors, there is stray
capacitance between the component leads and across the pn-junctions inside the transistor. The
VCC = +12 V
CCC +
22 F
Rs
50 
vs
+
−
vin
R1
30 k
RC
3.9 k
Co
10 F
+
+
vout
Ci
10 F
RL
R2
9.1 k
+
RE
2 k
CE
22 F
Figure 1. Common emitter amplifier with emitter degeneration bypass capacitor
and DC blocking capacitors. The operating point of the BJT is IC = 1 mA and
VCE = 6.1 V.
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former type of capacitance (stray capacitance between leads) is usually negligible, at least at
frequencies below a few MHz, but the latter (junction capacitance) typically sets the upper useful
frequency limit of the amplifier.
The junction capacitances are incorporated into the small-signal model as shown in Figure 2.
The collector-base capacitance C is on the order of 8 pF for a 2N2222 npn BJT. The baseemitter capacitance varies with the bias level according to the equation
C 
gm
o
 C 
 C
2f T
2f T r
where fT is a parameter called the unity-gain frequency, which is the frequency at which the
effective small-signal current gain () of the amplifier falls to unity (a value of one). The value
of () changes with frequency due to the effects of C and C. For a bias collector current (IC)
level of 1 mA and an fT of 250 MHz (typical for the 2N2222), the value of C is around 17 pF.
The parameter rx represents the small resistance (around 10 ) of the ohmic contact used to
connect the base wire lead to the region of silicon that makes up the base. In many cases rx can
be ignored. These small resistances exist at the other two connection points (at the collector and
at the emitter), but it is seldom necessary to model their effects. There is also a tiny amount of
capacitance between the collector and the emitter, but its effect is also usually negligible.
rx
C
B
C
+
ib
C
r
rce
v
gmv
−
E
Figure 2. Small-signal model of BJT that includes junction capacitances.
Capacitance C is the base-emitter capacitance, and C is the collector-base
capacitance.
The reactances of C and C are given by
X 
1
1

C 2fC
and X  
1
1
,

C  2fC
so as the frequency rises, their reactance values drop. This has a profound effect on the gain at
high frequencies. If the reactance of C is much less than the resistance of r, for example, then
the value of v is much smaller than it is at lower frequencies. The implication of this is that the
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small-signal collector current ic (which is equal to gmv or, equivalently, ()ib) falls at high
frequencies. If the frequency is high enough so that C acts essentially as a short, then the
transistor will draw no small-signal collector current whatsoever. Capacitance C affects the
operation of the transistor at high frequencies as well. If its reactance is low, then current will be
drawn away from r, also reducing the value of v, which in turn reduces the available gain.
In earlier experiments we have usually designed amplifiers to work at only a single frequency,
and we have chosen values for the DC blocking and emitter bypass capacitors such that we could
regard them as short circuits at the design frequency. More typically, amplifiers are designed to
be used over a range of frequencies. For example, a stereo amplifier must faithfully amplify
sound over the range of 20-20,000 Hz or so. At the upper and lower ends of the frequency range
the physical capacitors and the junction capacitances affect the gain. The behavior of an
amplifier, that is, its gain, input resistance, and output resistance, over a given range of
frequencies is called its frequency response.
The analysis of frequency response is an important aspect of amplifier design. Fortunately, the
effects due to the physical capacitors in the circuit and those due to the junction capacitances can
be treated separately. It is therefore possible to draw a low-frequency small-signal model of the
circuit and a high-frequency model and avoid an analysis that incorporates all of the capacitances
at once, which would be a tedious task. We will concentrate in this experiment on only the lowfrequency model, which is shown in Figure 3. This model includes only those capacitors that
cause the gain to drop off at frequencies below the midband range, where the amplifier’s
characteristics remain essentially constant with respect to frequency. Figure 3 does not include
C and C because the reactances of those capacitors are too large to affect the low-frequency
performance of the amplifier significantly. Consequently, those two capacitors can be treated as
open circuits at low frequencies.
Rs
Ci
Co
vout
vin
vs
+
−
+
R1||R2
r
RC
v
−
RL
gmv
CE
RE
Figure 3. Low-frequency small-signal model of the common emitter amplifier.
Even with C and C missing from the circuit, a full analysis of the voltage gain with the three
remaining capacitors is a daunting task. However, a simple procedure can be employed with this
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type of amplifier to determine its behavior at low frequencies. First, we recognize that the
presence of all three capacitors Ci, Co, and CE leads to a reduction in gain at frequencies low
enough for their reactances to become an important factor. As the frequency drops and reactance
rises, capacitor CE no longer serves as a low-impedance bypass; input capacitor Ci reduces the
amount of signal current flowing into the base of the BJT; and output capacitor Co limits the
current flowing through RL, which in turn reduces the value of vout. All of these effects cause a
reduction in the small-signal voltage gain. The particular frequency below which each capacitor
affects the gain varies with the capacitor’s value and with the equivalent resistance “seen” by the
capacitor. To obtain a rough estimate of the dominant “breakpoint” frequency, which separates
the midband (constant-gain) region from the low-frequency roll-off region, the following
procedure can be applied separately to each “low-frequency” capacitor in the circuit:
1. Identify one capacitor, and short-circuit all of the others (because, in the midband
frequency range, “low-frequency” capacitors act as shorts).
2. Find the small-signal Thévenin resistance rth “seen” by the capacitor under consideration.
(All of the independent voltage and current sources must be turned off.)
3. Calculate the breakpoint radian frequency  (the Bode plot pole) associated with that
capacitor using 1/Crth, where C is the value of the capacitor.
4. Repeat steps 1-3 for each capacitor, calculating the breakpoint frequency for each one.
5. The overall breakpoint frequency is approximately the sum of all the individual
breakpoint frequencies.
Applying this procedure to the low-frequency small-signal model shown in Figure 3 leads to
 pi 
 po 
 pe 
1
,
Ci Rs  R1 R2 r


1
C o RL  RC 
1
, and
 r  R1 R2 Rs 

C E RE 



o


,
where each pole frequency is associated with one of the three capacitors. If the source resistance
Rs is very small compared to the parallel combination of R1, R2, and r, then Rs can be neglected
in the first equation. The breakpoint frequency given by the third equation is usually the
dominant one because the quantity in parentheses in that equation is typically only a few tens of
Ohms, and the value of CE is usually within an order of magnitude of the values of Ci and Co.
A similar procedure to that described above can be applied to the “high-frequency” capacitors C
and C. Each capacitor is treated separately in turn, but they are replaced with open circuits
instead of short circuits. This is because “high-frequency” capacitors act as open circuits in the
midband frequency range. The overall breakpoint frequency is the reciprocal of the sum of the
reciprocals of the individual breakpoint frequencies (in a manner analogous to the parallelresistor formula).
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Experimental Procedure

Assemble the common emitter amplifier circuit shown in Figure 1 around a 2N2222 or
2N3904 npn BJT. Use the resistor values shown in the figure to establish the bias collector
current at 1 mA . Remember that electrolytic capacitors are polarized.

Verify that the BJT is operating at the proper Q-point. Of course, these measurements must
be taken with no source voltage vs applied to the amplifier.

Estimate the low-frequency breakpoints of the amplifier. Note that you will have to find the
value of r in order to obtain two of them. You may assume that the ambient temperature is
290 K. The source resistance Rs of the function generator is around 50 .

Measure the small-signal voltage transfer function of the amplifier as a function of
frequency. This will require you to record |vout| vs. |vs| and the phase shift at each frequency.
Remember to keep the input voltage down to only a few tens of mV to ensure that the
amplifier operates in its linear region. This may require you to use a voltage divider at the
output of the function generator. If you must use a voltage divider, make the Thévenin
equivalent resistance of the generator/voltage divider combination close to 50 . Also,
remember that you cannot trust the numerical voltage value displayed by the oscilloscope if
the waveform on the screen is fuzzy. Take data at a wide enough range of frequencies that
the magnitude of the gain at the upper and lower limits of the range is less than one-tenth the
value measured in the midband range. (In the midband range, neither the physical capacitors
nor the junction capacitances significantly affect the gain. The gain should be “flat,” or
relatively unchanging, in this range.)

Plot the magnitude of the gain of the amplifier in dB vs. frequency (f). Use a logarithmic
scale for the frequency. Recall that the gain expressed is dB is calculated using
gain in dB  20 log
vout
,
vs
in which the common logarithm (base 10) is used. Also, plot the phase shift in degrees vs.
frequency, again using a logarithmic scale for the frequency. Is the lower breakpoint
frequency (the dominant one) where you expected it to be? Discuss any discrepancies
(significant or insignificant), and explain what the implications of those results might be.
Reference
M. Wasserman, Laboratory Manual for Microelectronic Circuits and Devices, 2nd ed., PrenticeHall, Inc., Upper Saddle River, NJ, 1996
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