Fundamentals of Microelectronics
CH1 Why Microelectronics? CH2 Basic Physics of Semiconductors CH3 Diode Circuits CH4 Physics of Bipolar Transistors CH5 Bipolar Amplifiers CH6 Physics of MOS Transistors CH7 CMOS Amplifiers CH8 Operational Amplifier As A Black Box CH16 Digital CMOS Circuits
1 Chapter 5 Bipolar Amplifiers
5.1 General Considerations
5.2 Operating Point Analysis and Design
5.3 Bipolar Amplifier Topologies
5.4 Summary and Additional Examples
2 Bipolar Amplifiers
CH5 Bipolar Amplifiers 3 Voltage Amplifier
In an ideal voltage amplifier, the input impedance is infinite and the output impedance zero. But in reality, input or output impedances depart from their ideal values. CH5 Bipolar Amplifiers 4 Input/Output Impedances
Vx Rx ix
The figure above shows the techniques of measuring input and output impedances.
CH5 Bipolar Amplifiers 5 Input Impedance Example I
vx r ix
When calculating input/output impedance, small-signal analysis is assumed.
CH5 Bipolar Amplifiers 6 Impedance at a Node
When calculating I/O impedances at a port, we usually ground one terminal while applying the test source to the other terminal of interest.
CH5 Bipolar Amplifiers 7 Impedance at Collector
Rout ro
With Early effect, the impedance seen at the collector is equal to the intrinsic output impedance of the transistor (if emitter is grounded). CH5 Bipolar Amplifiers 8 Impedance at Emitter
v 1 x 1 ix g m r 1 Rout g m
(VA )
The impedance seen at the emitter of a transistor is approximately equal to one over its transconductance (if the base is grounded).
CH5 Bipolar Amplifiers 9 Three Master Rules of Transistor Impedances
Rule # 1: looking into the base, the impedance is r if emitter is (ac) grounded.
Rule # 2: looking into the collector, the impedance is ro if emitter is (ac) grounded.
Rule # 3: looking into the emitter, the impedance is 1/gm if base is (ac) grounded and Early effect is neglected.
CH5 Bipolar Amplifiers 10 Biasing of BJT
Transistors and circuits must be biased because (1) transistors must operate in the active region, (2) their small- signal parameters depend on the bias conditions. CH5 Bipolar Amplifiers 11 DC Analysis vs. Small-Signal Analysis
First, DC analysis is performed to determine operating point and obtain small-signal parameters. Second, sources are set to zero and small-signal model is used.
CH5 Bipolar Amplifiers 12 Notation Simplification
Hereafter, the battery that supplies power to the circuit is replaced by a horizontal bar labeled Vcc, and input signal is simplified as one node called Vin.
CH5 Bipolar Amplifiers 13 Example of Bad Biasing
The microphone is connected to the amplifier in an attempt to amplify the small output signal of the microphone. Unfortunately, there’s no DC bias current running thru the transistor to set the transconductance. CH5 Bipolar Amplifiers 14 Another Example of Bad Biasing
The base of the amplifier is connected to Vcc, trying to establish a DC bias. Unfortunately, the output signal produced by the microphone is shorted to the power supply.
CH5 Bipolar Amplifiers 15 Biasing with Base Resistor
VCC VBE VCC VBE I B , I C RB RB
Assuming a constant value for VBE, one can solve for both IB and IC and determine the terminal voltages of the transistor. However, bias point is sensitive to variations.
CH5 Bipolar Amplifiers 16 Improved Biasing: Resistive Divider
R2 VX VCC R1 R2
R2 VCC IC I S exp( ) R1 R2 VT
Using resistor divider to set VBE, it is possible to produce an IC that is relatively independent of if base current is small.
CH5 Bipolar Amplifiers 17 Accounting for Base Current
VThev I B RThev IC I S exp VT
With proper ratio of R1 and R2, IC can be insensitive to ; however, its exponential dependence on resistor deviations makes it less useful.
CH5 Bipolar Amplifiers 18 Emitter Degeneration Biasing
The presence of RE helps to absorb the error in VX so VBE stays relatively constant.
This bias technique is less sensitive to (I1 >> IB) and VBE variations.
CH5 Bipolar Amplifiers 19 Design Procedure
Choose an IC to provide the necessary small signal parameters, gm, r, etc.
Considering the variations of R1, R2, and VBE, choose a value for VRE.
With VRE chosen, and VBE calculated, Vx can be determined.
Select R1 and R2 to provide Vx.
20 Self-Biasing Technique
This bias technique utilizes the collector voltage to provide the necessary Vx and IB. One important characteristic of this technique is that collector has a higher potential than the base, thus guaranteeing active operation of the transistor. CH5 Bipolar Amplifiers 21 Example 5.13
22 Example 5.15
23 Example 5.15
24 Self-Biasing Design Guidelines
R R B (1) C
(2) VBE VCC VBE
(1) provides insensitivity to .
(2) provides insensitivity to variation in VBE .
CH5 Bipolar Amplifiers 25 Summary of Biasing Techniques
CH5 Bipolar Amplifiers 26 PNP Biasing Techniques
Same principles that apply to NPN biasing also apply to PNP biasing with only polarity modifications.
CH5 Bipolar Amplifiers 27 Example 5.18
28 Possible Bipolar Amplifier Topologies
Three possible ways to apply an input to an amplifier and three possible ways to sense its output. However, in reality only three of six input/output combinations are useful. CH5 Bipolar Amplifiers 29 Study of Common-Emitter Topology
Analysis of CE Core Inclusion of Early Effect Emitter Degeneration Inclusion of Early Effect CE Stage with Biasing
30 Common-Emitter Topology
CH5 Bipolar Amplifiers 31 Small Signal of CE Amplifier
vout Av vin
vout gmv gmvin RC
Av gm RC CH5 Bipolar Amplifiers 32 Limitation on CE Voltage Gain
IC RC VRC VCC VBE Av Av Av VT VT VT
Since gm can be written as IC/VT, the CE voltage gain can be written as the ratio of VRC and VT. VRC is the potential difference between VCC and VCE, and VCE cannot go below VBE in order for the transistor to be in active region.
CH5 Bipolar Amplifiers 33 Tradeoff between Voltage Gain and Headroom
CH5 Bipolar Amplifiers 34 I/O Impedances of CE Stage
v v X X Rout RC Rin r iX iX
When measuring output impedance, the input port has to
be grounded so that Vin = 0.
CH5 Bipolar Amplifiers 35 CE Stage Trade-offs
CH5 Bipolar Amplifiers 36 Example 5.21
37 Inclusion of Early Effect
Av gm (RC || rO )
Rout RC || rO
Early effect will lower the gain of the CE amplifier, as it
appears in parallel with RC.
CH5 Bipolar Amplifiers 38 Intrinsic Gain
Av gmrO
VA Av VT
As RC goes to infinity, the voltage gain reaches the product of gm and rO, which represents the maximum voltage gain the amplifier can have. The intrinsic gain is independent of the bias current.
CH5 Bipolar Amplifiers 39 Current Gain
iout AI iin
AI CE
Another parameter of the amplifier is the current gain, which is defined as the ratio of current delivered to the load to the current flowing into the input. For a CE stage, it is equal to .
CH5 Bipolar Amplifiers 40 Emitter Degeneration
By inserting a resistor in series with the emitter, we “degenerate” the CE stage. This topology will decrease the gain of the amplifier but improve other aspects, such as linearity, and input impedance.
CH5 Bipolar Amplifiers 41 Small-Signal Model*
g R A m C v 1 1 gm RE r g R m C 1 1 gm 1 RE g R R m C C 1 1 gm RE RE gm
Interestingly, this gain is equal to the total load resistance
to ground divided by 1/gm plus the total resistance placed in series with the emitter.
CH5 Bipolar Amplifiers 42 Emitter Degeneration Example I
R A C v 1 RE || r 2 gm1
The input impedance of Q2 can be combined in parallel with RE to yield an equivalent impedance that degenerates Q1.
CH5 Bipolar Amplifiers 43 Emitter Degeneration Example II
R || r A C 2 v 1 RE gm1
In this example, the input impedance of Q2 can be combined in parallel with RC to yield an equivalent collector impedance to ground.
CH5 Bipolar Amplifiers 44 Input Impedance of Degenerated CE Stage
VA
vX r iX RE (1 )iX
vX Rin r ( 1)RE iX With emitter degeneration, the input impedance is
increased from r to r + (+1)RE; a desirable effect.
CH5 Bipolar Amplifiers 45 Output Impedance of Degenerated CE Stage
VA v vin 0 v g mv RE v 0 r
vX Rout RC iX
Emitter degeneration does not alter the output impedance in this case. (More on this later.)
CH5 Bipolar Amplifiers 46 Capacitor at Emitter
At DC the capacitor is open and the current source biases the amplifier. For ac signals, the capacitor is short and the amplifier is
degenerated by RE.
CH5 Bipolar Amplifiers 47 Example: Design CE Stage with Degeneration as a Black Box
VA
vin iout g m 1 1 (r g m )RE
iout g m Gm vin 1 g m RE
If gmRE is much greater than unity, Gm is more linear.
CH5 Bipolar Amplifiers 48 Degenerated CE Stage with Base Resistance
VA v v v out A . out vin vin v A v R out C vin r ( 1)RE RB
RC Av 1 RB RE CH5 Bipolar Amplifiers g m 1 49 Input/Output Impedances
VA
Rin1 r ( 1)RE
Rin2 RB r 2 ( 1)RE
Rout RC
Rin1 is more important in practice as RB is often the output impedance of the previous stage.
CH5 Bipolar Amplifiers 50 Emitter Degeneration Example III
(RC || R1) Av 1 RB R2 gm 1
Rin r ( 1)R2
Rout RC || R1
CH5 Bipolar Amplifiers 51 Output Impedance of Degenerated Stage with VA<
Rout 1 gm (RE || r )rO RE || r
Rout rO (gmrO 1)(RE || r )
Rout rO 1 gm (RE || r ) Emitter degeneration boosts the output impedance by a factor of 1+gm(RE||r). This improves the gain of the amplifier and makes the circuit a better current source.
CH5 Bipolar Amplifiers 52 Two Special Cases
1) RE r
Rout rO (1 g m r ) rO
2) RE r
Rout (1 g m RE )rO
CH5 Bipolar Amplifiers 53 Analysis by Inspection
R R || R out 1 out1 Rout1 1 gm (R2 || r )rO Rout 1 gm (R2 || r )rO || R1
This seemingly complicated circuit can be greatly simplified by first recognizing that the capacitor creates an AC short to ground, and gradually transforming the circuit to a known topology.
CH5 Bipolar Amplifiers 54 Example: Degeneration by Another Transistor
Rout 1 gm1(rO2 || r1)rO1 rO2 || r1
1 gm1(rO2 || r1)rO1
Called a “cascode”, the circuit offers many advantages that are described later in the book.
CH5 Bipolar Amplifiers 55 Study of Common-Emitter Topology
Analysis of CE Core Inclusion of Early Effect Emitter Degeneration Inclusion of Early Effect CE Stage with Biasing
56 Bad Input Connection
Since the microphone has a very low resistance that
connects from the base of Q1 to ground, it attenuates the base voltage and renders Q1 without a bias current.
CH5 Bipolar Amplifiers 57 Use of Coupling Capacitor
Capacitor isolates the bias network from the microphone at DC but shorts the microphone to the amplifier at higher frequencies.
CH5 Bipolar Amplifiers 58 DC and AC Analysis
Av gm (RC || rO )
Rin r || RB
Rout RC || rO
Coupling capacitor is open for DC calculations and shorted for AC calculations.
CH5 Bipolar Amplifiers 59 Bad Output Connection
Since the speaker has an inductor, connecting it directly to the amplifier would short the collector at DC and therefore push the transistor into deep saturation.
CH5 Bipolar Amplifiers 60 Still No Gain!!!
In this example, the AC coupling indeed allows correct biasing. However, due to the speaker’s small input impedance, the overall gain drops considerably.
CH5 Bipolar Amplifiers 61 CE Stage with Biasing
Av gm (RC || rO )
Rin r || R1 || R2
Rout RC || rO
CH5 Bipolar Amplifiers 62 CE Stage with Robust Biasing
VA
R A C v 1 RE gm
Rin r ( 1)RE || R1 || R2
Rout RC
CH5 Bipolar Amplifiers 63 Removal of Degeneration for Signals at AC
Av gm RC
Rin r || R1 || R2
Rout RC
Capacitor shorts out RE at higher frequencies and removes degeneration.
CH5 Bipolar Amplifiers 64 Complete CE Stage*
R || R R || R R || R V V C L , A 1 2 C L out Thev 1 R v 1 R || R || R Thev Rs R1 || R2 s 1 2 RE RE gm 1 gm 1
CH5 Bipolar Amplifiers 65 Summary of CE Concepts
CH5 Bipolar Amplifiers 66 Common Base (CB) Amplifier
In common base topology, where the base terminal is biased with a fixed voltage, emitter is fed with a signal, and collector is the output.
CH5 Bipolar Amplifiers 67 CB Core
Av gm RC
The voltage gain of CB stage is gmRC, which is identical to that of CE stage in magnitude and opposite in phase.
CH5 Bipolar Amplifiers 68 Tradeoff between Gain and Headroom
IC Av .RC VT V V CC BE VT
To maintain the transistor out of saturation, the maximum
voltage drop across RC cannot exceed VCC-VBE.
CH5 Bipolar Amplifiers 69 Simple CB Example
VCC 1.8 V
IC 0.2 mA 17 I S 510 A 100
VBE 0.754 V
Vb 0.6 V 0.754 V 1.354 V Av gm RC 17.2 RC (1.8 1.354) V / 0.2 mA 2.23 kΩ
I B IC / 2 μA R1 22.3 kΩ
I1 10I B 20 μA R2 67.7 kΩ R1 R2 1.8 V / 20A 90 k CH5 Bipolar Amplifiers 70 Input Impedance of CB
1 Rin gm 1/ r 1 1 gm 11/ gm
The input impedance of CB stage is much smaller than that of the CE stage.
CH5 Bipolar Amplifiers 71 Practical Application of CB Stage
To avoid “reflections”, need impedance matching. CB stage’s low input impedance can be used to create a match with 50 . CH5 Bipolar Amplifiers 72 Output Impedance of CB Stage
Rout rO || RC
The output impedance of CB stage is similar to that of CE stage.
CH5 Bipolar Amplifiers 73 CB Stage with Source Resistance
1 g 1/ r A m g R v 1 m C RS gm 1/ r g R m C RS gm 1/ r 1 R C RS 11/ 1/ gm R C RS 1/ gm
With an inclusion of a source resistor, the input signal is attenuated before it reaches the emitter of the amplifier; therefore, we see a lower voltage gain. This is similar to CE stage emitter degeneration; only the phase is reversed.
CH5 Bipolar Amplifiers 74 Practical Example of CB Stage
An antenna usually has low output impedance; therefore, a correspondingly low input impedance is required for the following stage. CH5 Bipolar Amplifiers 75 Realistic Output Impedance of CB Stage
Effect of RB ignored
Rout1 1 gm (RE || r )rO RE || r
Rout RC || Rout1
The output impedance of CB stage is equal to RC in parallel with the impedance looking down into the collector.
CH5 Bipolar Amplifiers 76 Output Impedance of CE and CB Stages
The output impedances of CE, CB stages are the same if both circuits are under the same condition. This is because when calculating output impedance, the input port is grounded, which renders the same circuit for both CE and CB stages.
CH5 Bipolar Amplifiers 77 Fallacy of the “Old Wisdom”
The statement “CB output impedance is higher than CE output impedance” is flawed.
CH5 Bipolar Amplifiers 78 CB with Base Resistance
vout RL 1 R B v RB 1 Rin in RE gm 1/ r 1 1 gm 1 R B gm 1
With an addition of base resistance, the voltage gain degrades.
CH5 Bipolar Amplifiers 79 Comparison of CE and CB Stages with Base Resistance
The voltage gain of CB amplifier with base resistance is exactly the same as that of CE stage with base resistance and emitter degeneration, except for a negative sign.
CH5 Bipolar Amplifiers 80 Input Impedance of CB Stage with Base Resistance
v r R 1 R X B B iX 1 gm 1
The input impedance of CB with base resistance is equal to 1/gm plus RB divided by (+1). This is in contrast to degenerated CE stage, in which the resistance in series with the emitter is multiplied by (+1) when seen from the base. CH5 Bipolar Amplifiers 81 Input Impedance Seen at Emitter and Base
CH5 Bipolar Amplifiers 82 Input Impedance Example
1 1 1 R B RX gm2 1 gm1 1
To find the RX, we have to first find Req, treat it as the base resistance of Q2 and divide it by (+1).
CH5 Bipolar Amplifiers 83 Bad Bias Technique for CB Stage
Unfortunately, no emitter current can flow.
CH5 Bipolar Amplifiers 84 Still No Good
In haste, the student connects the emitter to ground, thinking it will provide a DC current path to bias the amplifier. Little did he/she know that the input signal has been shorted to ground as well. The circuit still does not amplify.
CH5 Bipolar Amplifiers 85 Proper Biasing for CB Stage
1 RRin || E gm
vout RE gRmC vin R E1 g m R E R S CH5 Bipolar Amplifiers 86 Reduction of Input Impedance Due to RE
The reduction of input impedance due to RE is bad because it shunts part of the input current to ground instead of to Q1 (and Rc) .
CH5 Bipolar Amplifiers 87 Creation of Vb
Resistive divider lowers the gain. To remedy this problem, a capacitor is inserted from base to ground to short out the resistor divider at the frequency of interest. CH5 Bipolar Amplifiers 88 Example of CB Stage with Bias
For the circuit shown above, RE >> 1/gm. R1 and R2 are chosen so that Vb is at the appropriate value and the current that flows thru the divider is much larger than the base current.
Capacitors are chosen to be small compared to 1/gm at the required frequency.
CH5 Bipolar Amplifiers 89 Emitter Follower (Common Collector Amplifier)
CH5 Bipolar Amplifiers 90 Emitter Follower Core
When the input is increased by V, output is also increased by an amount that is less than V due to the increase in collector current and hence the increase in potential drop across RE. However the absolute values of input and output differ by a VBE. CH5 Bipolar Amplifiers 91 Small-Signal Model of Emitter Follower
VA v 1 R out E r 1 1 vin 1 RE 1 RE gm
As shown above, the voltage gain is less than unity and positive.
CH5 Bipolar Amplifiers 92 Unity-Gain Emitter Follower
VA
Av 1
The voltage gain is unity because a constant collector current (= I1) results in a constant VBE, and hence Vout follows Vin exactly.
CH5 Bipolar Amplifiers 93 Analysis of Emitter Follower as a Voltage Divider
VA CH5 Bipolar Amplifiers 94 Emitter Follower with Source Resistance
VA v R out E R 1 vin S RE 1 gm
CH5 Bipolar Amplifiers 95 Input Impedance of Emitter Follower
VA vX r (1 )RE iX
The input impedance of emitter follower is exactly the same as that of CE stage with emitter degeneration. This is not surprising because the input impedance of CE with emitter degeneration does not depend on the collector resistance. CH5 Bipolar Amplifiers 96 Emitter Follower as Buffer
Since the emitter follower increases the load resistance to a much higher value, it is suited as a buffer between a CE stage and a heavy load resistance to alleviate the problem of gain degradation.
CH5 Bipolar Amplifiers 97 Output Impedance of Emitter Follower
Rs 1 Rout || RE 1 gm
Emitter follower lowers the source impedance by a factor of +1 improved driving capability.
CH5 Bipolar Amplifiers 98 Example 5.46
99 Emitter Follower with Early Effect
RE || rO Av RS 1 RE || rO 1 gm
Rin r 1RE || rO
Rs 1 Rout || RE || rO 1 gm
Since rO is in parallel with RE, its effect can be easily incorporated into voltage gain and input and output impedance equations. CH5 Bipolar Amplifiers 100 Current Gain
There is a current gain of (+1) from base to emitter. Effectively speaking, the load resistance is multiplied by (+1) as seen from the base.
CH5 Bipolar Amplifiers 101 Emitter Follower with Biasing
A biasing technique similar to that of CE stage can be used for the emitter follower.
Also, Vb can be close to Vcc because the collector is also at Vcc.
CH5 Bipolar Amplifiers 102 Supply-Independent Biasing
By putting a constant current source at the emitter, the bias
current, VBE, and IBRB are fixed regardless of the supply value. CH5 Bipolar Amplifiers 103 Summary of Amplifier Topologies
The three amplifier topologies studied so far have different properties and are used on different occasions. CE and CB have voltage gain with magnitude greater than one, while follower’s voltage gain is at most one.
CH5 Bipolar Amplifiers 104 Amplifier Example I
v R || R R out 2 C 1 R || R 1 vin 1 S R1 RS RE 1 gm
The keys in solving this problem are recognizing the AC
ground between R1 and R2, and Thevenin transformation of the input network.
CH5 Bipolar Amplifiers 105 Amplifier Example II
v R R out C 1 R || R 1 vin S 1 R1 RS R2 1 gm
Again, AC ground/short and Thevenin transformation are needed to transform the complex circuit into a simple stage with emitter degeneration.
CH5 Bipolar Amplifiers 106 Amplifier Example III
Rin r1 R1 r 2 R A C v 1 R 1 1 g m1 1 gm2
The key for solving this problem is first identifying Req, which is the impedance seen at the emitter of Q2 in parallel with the infinite output impedance of an ideal current source. Second, use the equations for degenerated CE stage with RE replaced by Req. CH5 Bipolar Amplifiers 107 Amplifier Example IV
R || R A C 1 v 1 RS gm
The key for solving this problem is recognizing that CB at frequency of interest shorts out R2 and provide a ground for R1. R1 appears in parallel with RC and the circuit simplifies to a simple CB stage. CH5 Bipolar Amplifiers 108 Amplifier Example V
1RS 1 1 RRin || E 11ggmm21
The key for solving this problem is recognizing the equivalent base resistance of Q1 is the parallel connection of RE and the impedance seen at the emitter of Q2.
CH5 Bipolar Amplifiers 109 Amplifier Example VI
v R || R || r R out E 2 O 1 1 R ||R vin S 1 R1 RS RE || R2 || rO gm 1
RS || R1 1 Rout || RE || R2 || rO 1 gm The key in solving this problem is recognizing a DC supply is actually an AC ground and using Thevenin transformation to simplify the circuit into an emitter follower.
CH5 Bipolar Amplifiers 110 Amplifier Example VII
RB1 1 Rin r 3 1 R E 1 gm2
RB2 1 RRout C 1 gm1
RB2 1 RC 1 gm1 Av RB1 11 RE 1 ggmm23
Impedances seen at the emitter of Q1 and Q2 can be lumped with RC and RE, respectively, to form the equivalent emitter and collector impedances.
CH5 Bipolar Amplifiers 111