Part B-3AMPLIFIERS: Small signal low
frequency transistor amplifier circuits: h-parameter representation of a transistor,
Analysis of single stage transistor amplifier using h-parameters: voltage
gain, current gain, Input impedance and output impedance. Comparison of
transistor configurations in terms of Ai , Ri, Av, Ro.
Introduction to Amplifiers
• The BJT is an an excellent amplifier when biased in the forward-active region.
• The FET can be used as an amplifier if operated in the saturation region.
• In these regions, the transistors can provide high voltage, current and power gains.
• DC bias is provided to stabilize the operating point in the desired operation region.
• The DC Q-point also determines– The small-signal parameters of the transistor– The voltage gain, input resistance, and output resistance– The maximum input and output signal amplitudes– The overall power consumption of the amplifier
A Simple BJT Amplifier
The BJT is biased in the forward active region by dc voltage sources VBE and VCC = 10 V. The DC Q-point is set at, (VCE, IC) = (5 V, 1.5 mA) with IB
= 15 A.
Total base-emitter voltage is: bevBEVBEv
Collector-emitter voltage is: This produces a load line.
CR
Ci
CEv 10
BJT Amplifier (continued)
An 8 mV peak change in vBE gives a 5 A change in iB and a 0.5 mA change in iC.
The 0.5 mA change in iC gives a 1.65 V change in vCE .
If changes in operating currents and voltages are small enough, then IC and VCE waveforms are undistorted replicas of the input signal.
A small voltage change at the base causes a large voltage change at the collector. The voltage gain is given by:
The minus sign indicates a 1800 phase shift between input and output signals.
˜ A v˜ v ce˜ v be
1.651800.0080
206180 206
A Simple MOSFET Amplifier
The MOSFET is biased in the saturation region by dc voltage sources VGS and VDS = 10 V. The DC Q-point is set at (VDS, IDS) = (4.8 V, 1.56 mA) with VGS = 3.5 V.
Total gate-source voltage is: gsvGS
VGS
v
A 1 V p-p change in vGS gives a 1.25 mA p-p change in iDS and a 4 V p-p changein vDS. Notice the characteristic non-linear I/O relationship compared to the BJT.
A Practical BJT Amplifier using Coupling and Bypass Capacitors
• AC coupling through capacitors is used to inject an ac input signal and extract the ac output signal without disturbing the DC Q-point
• Capacitors provide negligible impedance at frequencies of interest and provide open circuits at dc.
In a practical amplifier design, C1 and C3 are large coupling capacitors or dc blocking capacitors, their reactance (XC
= |ZC| = 1/C) at signal frequency is negligible. They are effective open circuits for the circuit when DC bias is considered.
C2 is a bypass capacitor. It provides a low impedance path for ac current from emitter to ground. It effectively removes RE (required for good Q-point stability) from the circuit when ac signals are considered.
DC and AC Analysis -- Application of Superposition
• DC analysis:– Find the DC equivalent circuit by replacing all capacitors by open
circuits and inductors (if any) by short circuits.– Find the DC Q-point from the equivalent circuit by using the
appropriate large-signal transistor model.• AC analysis:
– Find the AC equivalent circuit by replacing all capacitors by short circuits, inductors (if any) by open circuits, dc voltage sources by ground connections and dc current sources by open circuits.
– Replace the transistor by its small-signal model (to be developed).– Use this equivalent circuit to analyze the AC characteristics of the
amplifier.– Combine the results of dc and ac analysis (superposition) to yield the
total voltages and currents in the circuit.
DC Equivalent for the BJT Amplifier
• All capacitors in the original amplifier circuit are replaced by open circuits, disconnecting vI, RI, and R3 from the circuit and leaving RE intact. The the transistor Q will be replaced by its DC model.
DC Equivalent Circuit
AC Equivalent for the BJT Amplifier
• The coupling and bypass capacitors are replaced by short circuits. The DC voltage supplies are replaced with short circuits, which in this case connect to ground.
AC Equivalent for the BJT Amplifier (continued)
RBR
1R
210k 30k
RRC
R34.3k100k
• By combining parallel resistors into equivalent RB and R, the equivalent AC circuit above is constructed. Here, the transistor will be replaced by its equivalent small-signal AC model (to be developed).
Hybrid-Pi Small-signal AC Model for the BJT
• The hybrid-pi small-signal model is the intrinsic low-frequency representation of the BJT.
• The small-signal parameters are controlled by the Q-point and are independent of the geometry of the BJT.
Transconductance:
gmIC
VT
40IC
Input resistance:
r oV
TIC
ogm
Output resistance:
roV
AV
CEIC
Small-signal Current Gain and Amplification Factor of the BJT
int
11
poQCiF
FC
I
Frmgo
o > F for iC < IM, and o < F for iC > IM, however, o and F are usually assumed to be about
equal.
The amplification factor is given by:
For VCE << VA,
F represents the maximum voltage gain an individual BJT can provide, independent of the operating point.
F
V
AV
T
40VA
F vce
vbe
,vce rogmvbe
F
gmroIC
VT
VAV
CEIC
V
AV
CEV
T
Example o Calculation for 2N2222A
Choose the Q-point at about (5 V, 5 mA) for this analysis. Notice the slope of the DC current gain characteristic in this region. Ideally, the slope would be zero.
ogmr
F
1 IC
1
F
F
iC
Q po int
o
F
1 IC
1
F
F
IC
Q po int
F
IC
200 100
10 2 10 35.6x103 at about IC = 5 mA and 25 °C
o 180
1 5x10 3 5.6x103
180
1801 0.15
212 for F = 180
Given the tolerances usually encountered in forward current gain, the assumption of F = o seems reasonable for preliminary analysis and initial designs.
From Figure 3 for the 2N2222A BJT at the chosen Q-point…
Equivalent Forms of the Small-signal Model for the BJT
• The voltage-controlled current source gmvbe can be transformed into a current-controlled current source,
• The basic relationship ic=ib is useful in both dc and ac analysis when the BJT is biased in the forward-active region.
vbe
ib
r ibogm
gmvbe
gmib
r oib
icgmvbe
vcero
gmvbe
oib
Small Signal Operation of BJT
...3
61
2
211
expexp
TVbe
v
TVbe
v
TVbe
vC
I
TVbe
v
TVBEV
SIciC
ICi
TVBE
v
SI
Ci exp
...3
61
2
21
TVbe
v
TVbe
v
TVbe
vC
IC
ICici
For linearity, ic should be directly proportional to vbe.
vbe
2VT
50 mV
icIC
vbe
VT
IC
VT
vbe
gmvbe
If we limit vbe to 5 mV, the relative change in ic compared to IC that
corresponds to small-signal operation is:
icIC
gmv
beIC
vbe
VT
0.0050.025
0.200
for
Small-Signal Analysis of the Complete C-E Amplifier: AC Equivalent
• The AC equivalent circuit is constructed by assuming that all capacitances have zero impedance at signal frequency and the AC voltage source is at ground.
• Assume that the DC Q-point has already been calculated.
Small-Signal Analysis of Complete C-E Amplifier: Small-Signal Equivalent
RLro R
CR
3
Overall voltage gain from source vi to output voltage vo across R3 is:
Avvovi
vovbe
vbevi
Av gmRL
RB
rR
I R
Br
vo gmvbe
RL
and
vbe
vi
RB
r
RI R
Br
Capacitor Selection for the CE Amplifier
Zc 1jC
Capacitive Reactance XcZc 1C
where 2f
Xc1
RB
r Make Xc1
0.01 RB
r
for < 1% gain error.
Xc2
0 Make Xc2
1 for <1% gain error.
Xc3
R3 Make X
c30.01 R
3
for <1% gain error.
The key objective in design is to make the capacitive reactance much smaller at the operating frequency f than the associated resistance that must be coupled or bypassed.
C-E Amplifier Input Resistance
• The input resistance, the total resistance looking into the amplifier at coupling capacitor C1, represents the total resistance presented to the AC source.
rRRrBRR
rBR
21xixv
in
)(xixv
C-E Amplifier Output Resistance
• The output resistance is the total equivalent resistance looking into the output of the amplifier at coupling capacitor C3. The input source is set to 0 and a test source is applied at the output.
CRorC
RR
mgorC
R
xixv
out
bevxvxv
xi But vBE=0.
since ro is usually >> RC.