PowerPoint PresentationInput Signal Source
BJT Amplifier (continued)
An 8 mV peak change in vBE gives a 5 mA 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.
Dr. D G Borse
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/wC) 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.
Dr. D G Borse
D C Equivalent for the BJT Amplifier (Step1)
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
A C Equivalent for the BJT Amplifier (Step 2)
Coupling capacitor CC and Emitter bypass capacitor CE are replaced by short circuits.
DC voltage supply is replaced with short circuits, which in this case is connected to ground.
R1IIR2=RB
A C Equivalent for the BJT Amplifier (continued)
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).
All externally connected capacitors are assumed as short circuited elements for ac signal
Dr. D G Borse
calculate small signal parameters
• DC Voltage sources are shorted to ground
• DC Current sources are open circuited
• Large capacitors are short circuits
• Large inductors are open circuits
3) Use a Thevenin circuit (sometimes a
Norton) where necessary. Ideally the
base should be a single resistor + a single
source. Do not confuse this with the DC
Thevenin you did in step 1.
4) Replace transistor with small signal model
5) Simplify the circuit as much as necessary.
Steps to Analyze a Transistor Amplifier
6) Calculate the small signal parameters and gain etc.
Step 1
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:
(VA=100V for npn)
Dr. D G Borse
h22 = ho = Output Admittance
Dr. D G Borse
The Mid-frequency small-signal models
67.unknown
68.unknown
69.unknown
A common emitter (CE) amplifier
The mid-frequency circuit is drawn as follows:
the coupling capacitors (Ci and Co) and the
bypass capacitor (CE) are short circuits
short the DC supply voltage (superposition)
replace the BJT with the hybrid-p model
The resulting mid-frequency circuit is shown below.
An a c Equivalent Circuit
ro
73.unknown
74.unknown
Rs
Rs
Dr. D G Borse
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.
Dr. D G Borse
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.
But vbe=0.
Dr. D G Borse
High-Frequency Response – BJT Amplifiers
• Cbe, Cbc, Cce – internal capacitances
• Cwi, Cwo – wiring capacitances
• CS, CC – coupling capacitors
Dr. D G Borse
Frequency Response of Amplifiers
The voltage gain of an amplifier is typically flat over the mid-frequency range, but drops drastically for low or high frequencies. A typical frequency response is shown below.
For a CE BJT: (shown on lower right)
low-frequency drop-off is due to CE, Ci and Co
high-frequency drop-off is due to device capacitances Cp and Cm (combined to form Ctotal)
Each capacitor forms a break point (simple pole or zero) with a break frequency of the form f=1/(2pREqC), where REq is the resistance seen by the capacitor
CE usually yields the highest low-frequency break
which establishes fLow.
Amplifier Power Dissipation
Static power dissipation in amplifiers is determined from their DC equivalent circuits.
Total power dissipated in C-B and E-B junctions is:
where
The difference is the power dissipated by the bias resistors.
Dr. D G Borse
Dr. D G Borse
Figure 4.36a Emitter follower.
Dr. D G Borse
Unity Voltage gain with no phase shift
High current gain
Can be used for impedance matching or a circuit for providing electrical isolation
An Emitter Follower (CC Amplifier) Amplifier
Dr. D G Borse
Figure 4.36b Emitter follower.
Dr. D G Borse
Figure 4.36c Emitter follower.
Dr. D G Borse
Capacitor Selection for the CE Amplifier
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.
Dr. D G Borse
CE/CS, CB/CG, CC/CD
= h11
Small-signal Current Gain and Amplification Factor of the BJT
bo > bF for iC < IM, and bo < bF for iC > IM, however, bo and bF are usually assumed to be about equal.
The amplification factor is given by:
For VCE << VA,
mF represents the maximum voltage gain an individual BJT can provide, independent of the operating point.
Dr. D G Borse
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:
A 1 V p-p change in vGS gives a 1.25 mA p-p change in iDS and a 4 V p-p change
in vDS. Notice the characteristic non-linear I/O relationship compared to the BJT.
Dr. D G Borse
Eber-Moll BJT Model
The Eber-Moll Model for BJTs is fairly complex, but it is valid in all regions of BJT operation. The circuit diagram below shows all the components of the Eber-Moll Model:
E
C
B
IR
IF
IE
IC
IB
RIE
RIC
IES = Reverse-Saturation Current of B-E Junction
ICS = Reverse-Saturation Current of B-C Junction
IC = FIF – IR IB = IE - IC
IE = IF - RIR
IF = IES [exp(qVBE/kT) – 1] IR = IC [exp (qVBC/kT) – 1]
If IES & ICS are not given, they can be determined using various
BJT parameters.
Small Signal BJT Equivalent Circuit
The small-signal model can be used when the BJT is in the active region. The small-signal active-region model for a CB circuit is shown below:
iB
r
iE
iC
iB
B
C
E
r = ( + 1) * 0.026
VCE
IC
Early Effect Example
Given: The common-emitter circuit below with IB = 25A, VCC = 15V, = 100 and VA = 80.
Find: a) The ideal collector current
b) The actual collector current
Circuit Diagram
IC = 2.5 mA
b) IC’ = IC VCE + 1 = 2.5x10-3 15 + 1 = 2.96 mA
VA 80
The maximum voltage that the BJT can withstand.
BVCEO = The breakdown voltage for a common-emitter biased circuit. This breakdown voltage usually ranges from ~20-1000 Volts.
BVCBO = The breakdown voltage for a common-base biased circuit. This breakdown voltage is usually much higher than BVCEO and has a minimum value of ~60 Volts.
Breakdown Voltage is Determined By:
The Base Width
Material Being Used
Most popular biasing circuit.
Problem: bdc can vary over a wide range for BJT’s (even with the same part number)
Solution: Adding the feedback resistor RE. How large should RE be? Let’s see.
Substituting the active region model into the circuit to the left and analyzing the circuit yields the following well known equation:
ICEO has little effect and is often neglected yielding the simpler relationship:
Test for stability: For a stable Q-point w.r.t. variations in bdc choose:
Why? Because then
Replacing the input circuit by a Thevenin equivalent circuit yields:
102.unknown
103.unknown
Example :
The BJT has the following specifications:
bdc = 100, rsat = 100 W (Vo not specified, so assume Vo = 0.7 V)
Example :
Repeat Example 3 if RC is changed from 1k to 2.2k.
109.unknown
Example
The BJT has the following specifications:
bdc varies from 50 to 400, Vo = 0.7 V, ICBO = 10 nA
Solution:
Case 1: bdc = 50
Case 2: bdc = 400 Similar to Case 1 above. Results are: IC = 0.659 mA, VCE = 6.14 V Summary:
110.unknown
dc
IC
VCE
50
400
BJT Amplifier Configurations and Relationships:
Using the hybrid-p model.
Note: The biasing circuit is the same for each amplifier.
v
s
112.unknown
114.unknown
Dr. D G Borse
Dr. D G Borse
Dr. D G Borse
Figure 4.19a BJT large-signal models. (Note: Values shown are appropriate for typical small-signal silicon devices at
a temperature of 300K.
Dr. D G Borse
Figure 4.19b BJT large-signal models. (Note: Values shown are appropriate for typical small-signal silicon devices at
a temperature of 300K.
Dr. D G Borse
Figure 4.19c BJT large-signal models. (Note: Values shown are appropriate for typical small-signal silicon devices at
a temperature of 300K.
Dr. D G Borse
n
1
I
= h
h
b
b
b
e
r
d
g
m
v
v
i
i
i
i
o
v
o
c
e
 
R + R
I = (independent of )
R + + 1R + 1RR