Download 07-Transistors[1].

Transistors
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Fundamentals
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What transistors do
How to analyse transistor circuits
Small and large signals
Common-Emitter Amplifier
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Review of analysis and design
The Bipolar Junction Transistor
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BJT is a current amplifier
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The collector current is controlled by a much smaller base
current
The sum of the collector and base currents flow into or out
of the emitter
Base-emitter junction looks a lot like a PN junction
diode
Operating Regions - Cut Off
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IC  0
IB  0
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If the base current is zero, the
collector current is also zero
It doesn’t matter how big the collectoremitter voltage, VCE, is
i.e. collector-emitter junction looks like
an open circuit
In this state, the transistor is in the
cut-off region
Operating Regions - Active
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IB
VBE
IC
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Base current flows and controls the
larger collector current
Collector current is proportional to the
base current
Transistor is in the active region
Operation can be summarised by two
equations:
VBE 
I C  I S exp  
 VT 
I C  I B
VT  kT / q  25 mV 
Operating Regions - Saturation
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VS
IC 
R
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1 VS
IB 
 R
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Collector current rises in proportion to
the base current
As collector current rises, resistor
voltage rises and collector-emitter
voltage falls
When VCE  0, it can’t go any lower
and the collector current cannot get
any higher
The transistor is saturated
Collector-emitter junction looks like a
short circuit
Amplification
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BJT amplifiers work by controlling the
collector current by the base-emitter voltage
This is only possible in the active region
Cut-off and saturation regions correspond to
the transistor turning fully ‘off’ or ‘on’ like a
switch
In the active region, the transistor is only
partly ‘on’ and the current can be controlled
Small Signals
Current
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iv
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DI = i
I
DV = v
V
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Voltage
We want circuits with a linear
response but real transistors
aren’t linear
If the range of voltages/currents
is kept small, response is
approximately linear
Average (or quiescent) levels
are denoted by capital letters
Small variations (i.e. signals!)
are denoted by lower case
Small Signal Collector Current
VBE 
I C  I S exp  
 VT 
iC  vBE
Mutual Conductance
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iC  g m vBE
IC and VBE are exponentially
related
iC and vBE, on the other hand,
are approximately linearly
related
The constant of
proportionality, gm, is known
as the mutual conductance
It isn’t a real conductance,
but it is the ratio between a
current and a voltage
Estimating gm
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The small signal behaviour is
estimated by a tangent to the
exponential IC-VBE curve
gm is, therefore, simply the
gradient of the curve
VBE 
dI C
d
gm 

I S exp  
dVBE dVBE
 VT 
iC  g m vBE
VBE 
IS
 exp  
VT
 VT 
IC

VT
Amplification
Assume that the transistor is biased in the
active region somehow…
iC  g m vBE
RC
VBE
IC
VC
Collector voltage, VC, is related to IC by Ohm’s
law
VC  VS  I C RC
Small signal ratio between collector voltage
and collector current is:
vC dVC

  RC
i C dI C
So:
vC vC iC

  RC g m
vBE iC vBE
Simple Common-Emitter Amplifier
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IB provides a d.c. base current to
bias the transistor in the active
region
CIN couples the input voltage,
removing the d.c. base bias voltage
CIN is a short circuit to a.c. signals…
…but an open circuit to the d.c.
bias current
vBE is, therefore, equal to vIN
Analysis
vBE  vIN
iC  g m vBE  g m vIN
VOUT  VS  I C RC
vOUT dVOUT

  RC
iC
dI C
vOUT vOUT iC


  RC g m
vIN
iC
vIN
Biasing
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Gain is proportional to gm which is,
in turn, proportional to IC
In this circuit,
I C  I B
Unfortunately,  has a very wide
tolerance
The gain is, therefore, not
predictable
Reliable Biasing
I E  I B  IC
I C  I B
 IC  I E
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Collector current is set
accurately regardless of 
CE ensures that the whole of
the a.c. input voltage is still
dropped across VBE
RB provides the d.c. base
bias current
Usually, the current source is
approximated by a resistor
Practical Amplifier
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To analyse the circuit:
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Determine quiescent
conditions
Calculate mutual
conductance
Calculate small signal
performance
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Voltage Gain
Input Impedance
Output Impedance
Cut-off frequency
The Story so Far
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Small signal analysis is used to simplify calculations
by ‘linearising’ the non-linear response of the
transistor
Using mutual conductance, gain calculations are now
only a couple of lines of equations
Careful choice of the biasing network leads to reliable
performance
Next time – practical amplifier calculations, input &
output impedances and capacitor calculations