Introduction
The structure and operation of BJTs
Electronics – Bipolar transistor
Prof. Márta Rencz, Gergely Nagy
BME DED
2013. október 16.
Introduction
The structure and operation of BJTs
Transistors I.
Transistors are the most important semiconductor devices.
They are used in
analog circuit as amplifiers:
the input power of an amplifier is smaller than its output
power,
the energy need for amplification is provided by the supply
voltage,
a transformer is not an amplifier as the power at its terminals
is equal (if the voltage is larger at the output then the current
is smaller),
both analog and digital circuits as switches:
large power can be switched by a small input power,
logic gates can be realized by controlled switches.
Introduction
The structure and operation of BJTs
Transistors II.
The types of transistors:
bipolar transistor:
controlled by current,
its outputs are not interchangeable.
field-effect transistor:
controlled by voltage,
unipolar device.
Introduction
The structure and operation of BJTs
The bipolar transistor I.
The bipolar transistor (BJT) consists of two p-n junctions
placed very close to each other.
There are two types depending on structure: npn, pnp.
Both types are widely used.
The npn transsistors operate faster, so they are more
widespread.
The difference in speed is due to the fact that in npn transistors the current is
made up of electrons, while in pnp it’s made up of holes and electrons move
faster than holes in semiconductors.
Introduction
The structure and operation of BJTs
The bipolar transistor II.
The bipolar transistors have three terminals:
1
2
3
Emitter (E)
Base (B)
Collector (C)
Introduction
The structure and operation of BJTs
The symbol of the bipolar transistor I.
The currents and voltages of the two types are exactly
the opposite.
We’ll discuss the npn transistors – everything is the same in pnp transistors,
only the directions are the opposite.
The arrow in the symbol:
is between the base and the emitter,
shows the forward direction of the p-n junction.
Introduction
The structure and operation of BJTs
The symbol of the bipolar transistor II.
The currents of the bipolar transistor comply to the
KCL:
IE = IC + IB
The direction of the voltages is determined by the p-n
junctions:
the emitter-base junction is assumed to be open,
the collector-base junction is assumed to be closed.
This is the most widely used operating mode of the transistor.
Introduction
The structure and operation of BJTs
The structure of the BJT I.
The BJT consists of two p-n junctions in a proximity of a few
microns (or less).
The figure shows a discrete transistor – there is only one
transistor in a package.
The structure is planar: its width is much bigger than its
depth (just as diodes).
Introduction
The structure and operation of BJTs
The structure of the BJT II.
The collector is lightly doped and is n-type in npn
transistors.
The base is inside the collector, has an average doping
and is p-type in npn transistors.
The emitter is inside the base, it is highly doped and is
n-type in npn transistors.
Introduction
The structure and operation of BJTs
The structure of the BJT III.
In the leftmost figure the size of the chip is 0.5 · 0.5 · 0.3 mm.
The collector terminal is the metal base that the chip is
mounted onto.
Golden wires connect the emitter and base to the leads of the
package.
The wires are connected to the the chip by
thermocompression bonding.
Small power transistors are packaged in plastic, power
transistors are packaged in metal packages.
Introduction
The structure and operation of BJTs
The structure of the BJT IV.
The device is asymmetrical due
to the inhomogeneous doping
densisties.
The densities are determined by
the technology.
The doping of the two p-n
junctions is different.
Introduction
The structure and operation of BJTs
The operating modes of the BJT
There are four operating modes
determined by the direction of the
two junctions’ currents.
The most important is the normal
active mode.
The operating modes
normal active
inverse active
saturation
cut-off
B-E junction
open
closed
open
closed
B-C junction
closed
open
open
closed
Introduction
The structure and operation of BJTs
The normal active operation mode I.
n++
E
iE
iE
iEn
iEp
n+
p
iC
electrons
recombination
holes
iB1
C
iC
iB2
B
vBE
iB
vCB
The B-E junction is open, thus the majority charge
carriers of the two sides are crossing the junction.
The B-C junction is closed, there is a large field in the
space charge region, that forces minority charge carriers
across the junction.
The doping density of the emitter is much higher than that of
the base thus electrons make up most of the B-E current.
Introduction
The structure and operation of BJTs
The normal active operation mode II.
n++
E
iE
iE
iEn
iEp
n+
p
iC
electrons
recombination
holes
iB1
C
iC
iB2
B
vBE
iB
vCB
The electrons arriving in the base are forced away from
the B-E junction by diffusion.
When they reach the proximity of the collector, they are
drifted across the junction by the field as they are
minority carriers in the base.
Although the B-C junction is closed, its current is large due to
the large number of electrons that enter the base from the
emitter, diffuse towards the B-C junction and then drift over
the reverse biased junction.
Introduction
The structure and operation of BJTs
The normal active operation mode III.
n++
E
iE
iE
iEn
iEp
n+
p
iC
electrons
recombination
holes
iB1
C
iC
iB2
B
vBE
iB
vCB
The emitter emits charge carriers to the base, hence its name.
The charge carriers in the base are collected by the collector.
The narrower the base, the bigger the chances that
electrons get through to the collector without
recombining with holes.
The collector current is almost equal to the emitter current:
the difference is the amount of electrons lost to recombination
during their way across the base.
Introduction
The structure and operation of BJTs
The normal active operation mode IV.
n++
E
iE
iE
iEn
iEp
n+
p
iC
electrons
recombination
holes
iB1
C
iC
iB2
B
vBE
iB
vCB
The relationship between the emitter current and the collector
current:
IC = AN · IE
where AN is common base, normal active, DC current
gain of the transistor (AN = 0.98 − 0.995).
This operating mode is used for amplification.
Introduction
The structure and operation of BJTs
The common-emitter configuration I.
The collector current is
proportional to the emitter current
but the current gain is smaller than
1.
The difference between IE and IC
is the small IB .
By controlling IB , a large
current gain can be obtained.
In the common-emitter configuration the base current is the
input and the collector current is the output.
Introduction
The structure and operation of BJTs
The common-emitter configuration II.
According to the KCL:
IC = AN · IE = AN (IC + IB )
AN
IB = BN · IB
1 − AN
BN is the common emitter, normal active, DC current
gain, and BN = 50 − 200.
IC =
BN is larger than 1, thus this configuration amplifies current.
The N in the index is usually omitted: IC = B · IB .
In some textbooks A is denoted with α and B with β.
Introduction
The structure and operation of BJTs
The other operating modes
Inverse active mode: the role of the emitter and collector
are swapped.
Due to the inhomogeneous structure, the transistor effect is,
although present, much smaller.
This mode is very scarcely used (it was used in traditional TTL
gates).
Saturation: both p-n junctions are open.
Large current flows through the device while the
collector-emitter voltage is small.
The transistor is in this mode when it’s operated as a switch
that is turned on.
Cut-off region: both junctions are closed.
Only the saturation currents flow in the device.
These can be neglected as they are in the range of nA.
This is the operating mode of a switch that is turned off.
When the transistor is operated as a switch, it switches
between saturation and the cut-off region.
Introduction
The structure and operation of BJTs
Characteristic curves of the BJT
The currents of the transistor are depicted as a function
of the voltages.
As the device has three terminals, at least two current-voltage
pairs are needed to describe the operating point.
The most widely used characteristic curves are the
common-emitter curves:
IB = f (VBE )
IC = g(VCE , IB )
Introduction
The structure and operation of BJTs
Common-emitter characteristic curves I.
Input characteristic curve
Output characteristic curve
The input characteristic curve: depicts the relationship
between the input quantities.
It resembles the diode’s characteristic curve – IB is an exponential function of
VBE . This is due to the fact the there is a diode operating in the forward
direction between the B and E terminals.
Output characteristic curves: depict the collector current as
a function of the collector-emitter voltage and the base
current (IB4 > IB3 > IB2 > IB1 ).
Introduction
The structure and operation of BJTs
Common-emitter characteristic curves II.
The output characteristic curves:
They are a set of VCE − IC curves for increasing IB values.
The area where the curves are close to being horizontal is the
normal active region.
The steep part of the curves constitute the saturation region.
In saturation the collector and emitter forward currents flow in
opposite directions, thus their difference appears as a
macroscopic current.
Introduction
Voltage amplification using a transistor
The transistor is in a common-emitter
configuration.
The base voltage is sinusoidal with an
offset.
The collector is connected to the
supply voltage through a resistor.
The output is the collector.
The structure and operation of BJTs
Introduction
The structure and operation of BJTs
The operating point of the circuit I.
The DC input voltage (VIN ) determines a base current (IB ) –
it can be found using the input characteristic curve.
With the help of IB , the curve that holds the operating point
can be chosen from the set of output characteristic curves.
The exact OP is defined by the supply voltage and the resistor
as VCE also affects IC , though only slightly.
Introduction
The structure and operation of BJTs
The operating point of the circuit II.
The linear elements surrounding the transistor determine the
load line.
The intersection of the load line and the characteristic curve is
the operating point.
According to the KCL the load line is:
VCC = RC IC + VCE
→
IC =
VCC − VCE
RC
Introduction
The structure and operation of BJTs
The operating point of the circuit III.
The load line can be found in an easier way:
When IC = 0 the collector’s potential has to be equal to the
supply voltage (Ohm’s law for RC ).
If VCE = 0, the entire supply voltage is dropped on RC , thus
IC = VCC /RC
By connecting these two points, we get the load line. This is
due to the fact that the two points were determined according
to the characteristic equation of the linear elements (RC ), thus
they have to be on the load line.
Introduction
The structure and operation of BJTs
The gain of the circuit I.
The base current has an ib amplitude around Ib0 (as
the input is a sinusoid with an offset):
IB (t) = IB0 + ib · sin(ωt)
In the operating point the characteristic equation is
substituted with its tangent:
ib =
∂IB
∂IB ∂IE
vin =
·
vin
∂VBE
∂IE ∂VBE
using the chain rule.
As IE = IC + IB = (B + 1)IB and assuming that the
B-E junction is ideal (IE = IE0 (exp (VBE /VT ) − 1)):
ib =
IE
1
·
· vin
B + 1 VT
Introduction
The structure and operation of BJTs
The gain of the circuit II.
A change in the base current
results in a change in the collector
current:
IC = IC0 + ic · sin(ωt)
The change approximated with a
linear equation:
ic =
∂IC
∂IB
· ib = B · ib
The output voltage:
VC (t) = VCC − IC (t) · RC
By substituting the equation of IC into the one describing the
output voltage:
VC (t) = VCC − IC0 · RC − ic · RC · sin(ωt) = VCE0 − B · ib · RC · sin(ωt) =
B
B
IE
IE
VCE0 −
·
· RC ·vin · sin(ωt) = VCE0 −
·
·RC · vin · sin(ωt)
B + 1 VT
B + 1 VT
| {z } |{z}
|
{z
}
AC gain
≈1
≈ r1
e
Introduction
Overview of the gain calculation
The structure and operation of BJTs
Introduction
The structure and operation of BJTs
Simplified calculation
Small-signal analysis is performed at the operating point.
The characteristic equation is substituted with its tangent
– a linear equation.
A small-signal model of the circuit is created which consists
of linear elements only. Such a circuit describes the AC
behavior only.
The value of the elements in the circuit is determined by
the operating point currents and voltages.
The small-signal model is easy to calculate.
It neglects the non-linearity of the characteristic equation,
thus the results are not exactly accurate.
Introduction
The structure and operation of BJTs
Common-emitter, small-signal equivalent circuits
The collector current is proportional to the base current: this
can be modelled with a current controlled current source:
β=
∂IC
∂IB
≈B
IC = B · IB
as
The B-E diode can be substituted with its differential
resistance: re = ∂VBE /∂IE = VT /IE , but in this case the input
resistance is re · (β + 1).
The input resistance can be calculated as follows:
∂VBE
∂IB
=
∂VBE
∂IE
|
·
∂IE
∂IB
{z
}
chain rule
=
VT
IE
(β + 1) = (β + 1) · re
Introduction
The structure and operation of BJTs
Calculation of the gain using the small-signal equivalent I.
The AC equivalent circuit:
the transistor is substituted with its small-signal
equivalent,
the DC supply voltage sources are substituted with short
circuits (as the changes pass through them).
Introduction
The structure and operation of BJTs
Calculation of the gain using the small-signal equivalent II.
The calculation:
The base current as a function of the input current:
ib =
vin
(β + 1) · re
The collector current: ic = β · ib
The output voltage:
vout = −ic · Rc = −β · ib · RC = −
β
RC
RC
·
vin ≈ −
vin
β + 1 re
re
The negative sign shows that changes at the output occur in
the opposite direction as at the input.