bipolar junction transistors...
TRANSCRIPT
EE 230 BJTs – �1
Bipolar junction transistors (BJTs)First transistors – invented at Bell Laboratories in 1947. This is one of the seminal events in the history of technology.
The BJT is essentially two diodes hooked together, creating a sandwich structure.
n np
Because both electrons and holes are involved in the current flow, these are know as bipolar devices.
anodes in common(npn transistor)
cathodes in common(pnp transistor)
p pn
(Note: You cannot make a transistor by hooking together two discrete diodes.)
EE 230 BJTs – �2
Terminology - npn
B
iCC
E iE
iB –
+vCE
–
+
vBC
–
+vBEn
n
p
emitter
base
collector
–
++
– +
–
vBE
vBC
vCE
iE
iC
iB
With two junctions that can be either forward or reverse-biased, there are 4 possible modes of operation. Perhaps the most important is forward active mode. In forward-active operation, the base-emitter junction is forward biased (vBE > 0) and the base-collector is reverse-biased (vBC < 0, vCB > 0). Consequently, the collector-emitter voltage must be positive (vCE = vCB + vCE > 0).
Define voltages in relative manner:
Y%( = Y% � Y(
Y(% = Y( � Y% = �Y%(
and similar for other voltages.
Note that:
KCL: L( = L% + L&
KVL: Y%( � Y%& � Y&( = �
Y&( = Y%( � Y%&
= Y%( + Y&%
EE 230 BJTs – �3
Terminology - pnp
p
p
n
emitter
base
collector
–
++
– +
–
vBE
vBC
vCE
iE
iC
iB B
iCC
E iE
iB –
+vCE
–
+
vBC
–
+vBE
We could change the symbols – describing the relevant voltages as vEB and vEC as variables and also reversing the directions of the current arrows. (Some text books do this.) But our convention will to keep the symbols and definitions the same as used for the npn, and everything will be negative in the pnp case.
The pnp transistor is similar, but everything is reversed. To forward bias the base-emitter, vBE must be negative. To reverse-bias the base-collector, vBC must be positive (vCB is negative.) And the currents will flow in the opposite directions.
EE 230 BJTs – �4
Recall the diode.
ISN and ISP are electron and hole current parameters, and are determined by the doping and physical sizes of the n- and p-type regions.
Since we can design the scaling factors, we can control how much of the total current is carried by electrons or holes.
The terminal current, iD, is just the sum of the two individual currents.
in = ISN�exp
�vBEkT/q
�� 1
�
ip = ISP�exp
�vBEkT/q
�� 1
�
n p
+–
vBE
holes
electrons
emitter base
iB = ip + in
iE = ip + in
npn - forward-active
ISN = ISP → electron and holes are equal, ISN >> ISP → mostly electrons, ISP >> ISN → mostly holes.
EE 230 BJTs – �5
Now add the collector region: Bias it so that the base-collector junction is reverse-biased (collector at higher voltage). Because of the reverse-bias, there are no carriers being injected across the B-C junction.
The presence of the collector has no effect on the original hole current – holes still flow into the base contact, are injected across the B-E junction and exit the emitter contact.
However, the electron story changes. The higher potential of the collector will steer the electrons to across the base and over the B-C junction into the collector region. The electrons leaves through the collector contact.
Electrons are “emitted” on the left and “collected” on the right. The electron current is in the opposite direction – from collector to emitter. The electron current through the base “links” the collector and emitter.
n p
+–
vBE
holes
electrons
emitter base
n
collector+–
vBC
EE 230 BJTs – �6
iC = in
iB = ip
iE = in + ip
iC = ISN�exp
�vBEkT/q
�� 1
�� ISN exp
�vBEkT/q
�
iB = ISP�exp
�vBEkT/q
�� 1
�� ISP exp
�vBEkT/q
�
iE = [ISN + ISP]�
exp
�vBEkT/q
�� 1
�� [ISN + ISP] exp
�vBEkT/q
�
All three currents depend only on vBE. This is especially interesting for iC, which has no physical connection to vBE.
n p
+–
vBE
holes
electrons
emitter base
n
collector
+–
vBC
EE 230 BJTs – �7
iE = [ISN + ISP] exp
�vBEkT/q
�
iC = ISN exp
�vBEkT/q
�
iB = ISP exp
�vBEkT/q
�
We see that ratios of the currents will be constant.
iCiB
=ISNISP
= βFiCiE
=ISN
ISN + ISP= αF αF =
βFβF + 1Note that:
βF is the forward current gain, and is usually the first, most important parameter characterizing the BJT. Generally, we would like it to big(ish) – in the range of 50 - 200.
EE 230 BJTs – �8
To make βF large, the transistor is built so that ISN >> ISP. This means that most of the current crossing the B-E junction is in the form of electrons. Of course, those electrons will end up in the collector, and our goal is to maximize that. (The holes injected from base to emitter are not really interesting to forward active operation and re essentially an unavoidable nuisance. If we could, we would dispense with them altogether.) If ISN >> ISP, then βF is large and the hole current (i.e. base current) will be relatively small. (As a first approximation, we could even call it zero.) Also, αF ≈ 1, meaning that the collector current is almost the same as the emitter current.
Because all the currents are inter-related, we have more parameters than needed to specify the BJT. Usually, we use just ISN and βF. (These are usually in the data sheet.) Then the set of currents can be written as
iC = ISN exp
�vBEkT/q
�
iB =ISNβF
exp
�vBEkT/q
�
iE = iC + iB =βF
βF + 1 ISN exp
�vBEkT/q
�
We will see shortly that we don’t even need to know ISN in many cases – βF is often sufficient.
EE 230 BJTs – �9
When analyzing a circuit containing a BJT, it would seem essential to find vBE, since all currents depend on it. However, the exponential relationships make finding vBE tricky, in the same way that calculating the exact voltage a diode across is tricky.
However, since the base-emitter is simply a p-n diode, we might expect that the voltage across it when forward-biased will probably be on the order of 0.7 V, just like we saw when handling diode circuits. Our past experience with diodes suggests that perhaps we can assume that the base-emitter voltage will be about 0.7 V, and then use the rest of the base-emitter circuit loop to solve for the base and/or emitter current.
In that case, the key step is find the base current, iB. If the BJT is in forward-active operation, then iC = βFiB and iE = (βF +1)iB.
Alternatively, in some circuits, it might be easier to first find iE, and then
iC =βF�
βF + 1� iE iB =
iE�βF + 1
�and
But generally we will not be able to find iC without finding one of the other currents first. The following examples illustrate the approach with forward-active BJTs.
EE 230 BJTs – �10
vCE in forward active
B
iCC
E iE
iB –
+vCE
–
+
vBC
–
+vBE
The forward-active mode of operation means that the base-emitter junction is forward biased and the base emitter is reverse-biased. As usual for a forward-biased silicon p-n junction, vBE ≈ 0.7 V. For the base-collector to be reversed-biased, vBC < 0. (Or so. We could probably extend vBC to about +0.5 V before the BC junction begins to turn on.
So every time we solve a circuit we should check these voltages to make certain that they are appropriate for forward active operation.
However, as we will soon see, we are often interested in the voltage between the collector and emitter, vCE. Using KVL, we see that
vCE = vBE – vBC.
With vBE ≈ 0.7 V and vBC < +0.5, then vCE must be greater than about 0.2 V for the BJT to be in forward-active. This will become a very convenient check for forward-active operation.
EE 230 BJTs – �11
Forward active - example 1For the circuit shown, use the exact BJT equations to find iC, iB, and vCE.
For the BJT, ISN = 10–14 A and βF = 100.
L% =L&շ)
=�.���P$
��� = $ܟ��.�
At room temperature, kT/q = 0.0258 V.
Assume forward active operation. vBE = VBB
It is in forward-active. Of course, this is a dangerous circuit, because we are applying a voltage directly to a p-n junction. If we increase vBE to 0.75 V, then iC = 42 mA and vCE = –76 V. Oops.
VBB
VCC
iB
iC
–
+vCE
–+vBE
RC
0.625 V
2 k!
8 V
L& =������$
�exp
��.���9�.����9
�= �.���P$
Y&( = 9&& � L&5& = �9� (�.���P$) (�Nۙ) = �.��9
EE 230 BJTs – �12
VBB
VCC = 8 V
iB
iC
–
+vCE
–+vBE
RC
3 V
2 k!
+–
RB
100 k!
This circuit is safer.
For the BJT, ISN = 10–14 A and βF = 100.
At room temperature, kT/q = 0.0258 V.
Assume forward active operation.
Write an equation around the base-emitter loop.
9%% � L%5% � Y%( = � L% =L&շ)
=,61շ)
exp
�Y%(N7/T
�
Again, use the exact BJT equations to find iC, iB, and vCE.
9%% � ,615%
շ)exp
�Y%(N7/T
�� Y%( = �
Bah! It’s a transcendental equation.
Example 2
EE 230 BJTs – �13
9%% � ,615%
շ)exp
�Y%(N7/T
�� Y%( = �
Plug in the numbers.
� 9�������9
�exp
� Y%(�.����9
�� Y%( = �
vBE (V) LHS (V)0.7 –3.770.6 +2.2740.65 +1.4760.675 +0.02170.676 –0.07030.6755 –0.0240.67525 –0.0010
Start guessing.
Close enough.
vBE = 0.67525 V
L& =������$
�exp
��.�����9�.����9
�= �.��P$
L% =L&շ)
=�.��P$��� = $ܟ�.��
Y&( = 9&& � L&5& = �9� (�.��P$) (�Nۙ) = �.��9
It is in forward-active. But that calculation was no fun at all.
Answer, after iterating:
EE 230 BJTs – �14
VBB
VCC = 8 V
iB
iC
–
+vCE
–+vBE
RC
3 V
2 k!
+–
RB
100 k!
Try again, but this time start by assuming that vBE ≈ 0.7 V.
Assume forward active operation, again.
Write the same equation around the base-emitter loop.
9%% � L%5% � Y%( = �
L% =9%% � Y%(
5%=�9� �.�9���Nۙ = $ܟ��
L& = շ)L% = ��� ($ܟ��) = �.�P$
Y&( = 9&& � L&5& = �9� (�.�P$) (�Nۙ) = �.�9
Confirmed: forward-active. Nearly the same answers, but with only 10% of the work.
Example 3
EE 230 BJTs – �15
VCC = 8 V
iB
iC
–
+vCE
–+vBE
RC
2 k!267 k!R1
160 k!R2
Here’s another one. This is a common method to set up the DC voltages currents in BJT with only one power supply. It looks tricky, though!
It’s the same BJT, ISN = 10–14 A and βF = 100. Find the base and collector currents and vCE.
Write a node equation at the base.
9&& � Y%(5�
= L% +Y%(5�
Assuming vBE ≈ 0.7 V,
Use the vBE approximation, so we don’t care about ISN. Assume forward active, again.
L% =9&& � Y%(
5�� Y%(
5�=
�9� �.�9���Nۙ � �.�9
���Nۙ = $ܟ��
Hey! Same base current as example 3, so we know iC = 2.3 mA and vCE = 3.4 V.
Example 4
EE 230 BJTs – �16
Alternative approach: Find the Thevenin equivalent seen by base.
VTh3 V
+–
RTh
100 k!267 k!R1
160 k!
R2
VCC = 8 V
Thevenin
We saw this one about a thousand times in EE 201.
Here are the numbers for the Thevenin.
VTh
VCC = 8 V
iB
iC
–
+vCE
–+vBE
RC
3 V
2 k!
+–
RTh
100 k!
It’s the exact same circuit as Example 3! So it has the exact same currents and voltages.
(Apparently, someone is trying to be clever.)
iB = 23 µA, iC = 2.3 mA, vCE = 3.4 V.
EE 230 BJTs – �17
VBB + vA sin (ωt) � iBRB � VBE = 0<latexit sha1_base64="zNi3HhxbuJQ06xBpooqV+LtLmH0=">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</latexit><latexit sha1_base64="zNi3HhxbuJQ06xBpooqV+LtLmH0=">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</latexit><latexit sha1_base64="zNi3HhxbuJQ06xBpooqV+LtLmH0=">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</latexit><latexit sha1_base64="zNi3HhxbuJQ06xBpooqV+LtLmH0=">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</latexit>
iB =VBB + vA sin (ωt) � VBE
RB= 0
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iC = βFiB =BFRB
[VBB � VBE + vA sin (ωt)]<latexit sha1_base64="QHc3VbNat5PjNFuDjOJCP9xLZxM=">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</latexit><latexit sha1_base64="QHc3VbNat5PjNFuDjOJCP9xLZxM=">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</latexit><latexit sha1_base64="QHc3VbNat5PjNFuDjOJCP9xLZxM=">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</latexit><latexit sha1_base64="QHc3VbNat5PjNFuDjOJCP9xLZxM=">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</latexit>
Example 5
A DC voltage and an AC voltage applied to the base. It is the same basic approach.
vCE = VCC � iCRC = VCC � BFRCRB
[VBB � VBE + vA sin (ωt)]<latexit sha1_base64="/+BBdcifUOQdUj7uIWypOCFs3Ls=">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</latexit><latexit sha1_base64="/+BBdcifUOQdUj7uIWypOCFs3Ls=">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</latexit><latexit sha1_base64="/+BBdcifUOQdUj7uIWypOCFs3Ls=">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</latexit><latexit sha1_base64="/+BBdcifUOQdUj7uIWypOCFs3Ls=">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</latexit>
=
�VCC � BFRC
RB(VBB � VBE)
��
�BFRCRB
vA�
sin (ωt)<latexit sha1_base64="mmEOVx9S0Ou0wl0vVqTPUOfOioY=">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</latexit><latexit sha1_base64="mmEOVx9S0Ou0wl0vVqTPUOfOioY=">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</latexit><latexit sha1_base64="mmEOVx9S0Ou0wl0vVqTPUOfOioY=">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</latexit><latexit sha1_base64="mmEOVx9S0Ou0wl0vVqTPUOfOioY=">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</latexit>
= 7.5 V� (2.5 V) sin (ωt)<latexit sha1_base64="c4xKUAqzUOWXmTCOTl8xuJ8nIp4=">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</latexit><latexit sha1_base64="c4xKUAqzUOWXmTCOTl8xuJ8nIp4=">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</latexit><latexit sha1_base64="c4xKUAqzUOWXmTCOTl8xuJ8nIp4=">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</latexit><latexit sha1_base64="XrksgbkpHa/EE0ylR/hU6eC2dbM=">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</latexit><latexit sha1_base64="kL5b0Sy87535iRTCINnpyNFA2iM=">AAACp3icbZFNixNBEIY749caV8169dK4CFlYw8zCsnoQBBf04CGC2SxkQqjp1Eya9MfQXSMJQ/6Qv8br+mvsSSIkWQsaXp63u6qrKiuV9BTHd63owcNHj58cPW0/O37+4mXn5PjG28oJHAirrLvNwKOSBgckSeFt6RB0pnCYzT83/vAnOi+t+UHLEscaCiNzKYACmnSuP171LnlKuKCa36z4O54qzKl7sUtTJ4sZnaVemo2bWo0FcNoak85p3IvXwe+LZCtO2Tb6k5PWMJ1aUWk0JBR4P0riksY1OJJC4aqdVh5LEHMocBSkAY1+XK/bXfG3gUx5bl04hvia7r6oQXu/1Fm4qYFm/tBr4P+8UUX5+3EtTVkRGrEplFeKk+XN7PhUOhSklkGAcDL8lYsZOBAUJrxXZZ27RLHXSb2ojBR2igdU0YIcBOiRNEjTdFX3QYUVGfsPh3wN717LQpI//9aY518c4vxs5247rCI5HPx9Mbjofegl32N2xF6zN6zLEnbFPrGvrM8GTLBf7De7Y3+iy2gUwWZnUWu7vFdsLyLxFyFN1s4=</latexit><latexit sha1_base64="kL5b0Sy87535iRTCINnpyNFA2iM=">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</latexit><latexit sha1_base64="nBvC2m1uQUSyrnY0SnLoOiO58fk=">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</latexit><latexit sha1_base64="c4xKUAqzUOWXmTCOTl8xuJ8nIp4=">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</latexit><latexit sha1_base64="c4xKUAqzUOWXmTCOTl8xuJ8nIp4=">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</latexit><latexit sha1_base64="c4xKUAqzUOWXmTCOTl8xuJ8nIp4=">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</latexit><latexit sha1_base64="c4xKUAqzUOWXmTCOTl8xuJ8nIp4=">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</latexit><latexit sha1_base64="c4xKUAqzUOWXmTCOTl8xuJ8nIp4=">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</latexit><latexit sha1_base64="c4xKUAqzUOWXmTCOTl8xuJ8nIp4=">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</latexit>
RB
VBB
VCC = 15 V
RC
iB
iC
–
+vCE
–+VBE
5 k!
100 k!+–
+–2.2 V
vAsin(ωt)vA = 0.5 V