# Transistors by nyut545e2

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```									Transistors
   Fundamentals
   What transistors do
   How to analyse transistor circuits
   Small and large signals
   Common-Emitter Amplifier
   Review of analysis and design
The Bipolar Junction Transistor

   BJT is a current amplifier
   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
   If the base current is zero, the
collector current is also zero
   It doesn’t matter how big the collector-
emitter voltage, VCE, is
   i.e. collector-emitter junction looks like
IC  0       an open circuit
   In this state, the transistor is in the
IB  0                    cut-off region
Operating Regions - Active
   Base current flows and controls the
larger collector current
   Collector current is proportional to the
base current
   Transistor is in the active region
IC
IB           Operation can be summarised by two
equations:
VBE
VBE 
I C  I S exp        I C  I B
 VT 

VT  kT / q  25 mV 
Operating Regions - Saturation
   Collector current rises in proportion to
the base current
   As collector current rises, resistor
voltage rises and collector-emitter
VS       voltage falls
IC            When VCE  0, it can’t go any lower
R
and the collector current cannot get
any higher
   The transistor is saturated
1 VS                  Collector-emitter junction looks like a
IB                         short circuit
 R
Amplification
   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
   We want circuits with a linear
response but real transistors
aren’t linear
Current

iv                  If the range of voltages/currents
is kept small, response is
DI = i
I                                approximately linear
DV = v
   Average (or quiescent) levels
are denoted by capital letters
V                  Small variations (i.e. signals!)
Voltage       are denoted by lower case
Small Signal Collector Current

VBE 
I C  I S exp        iC  vBE
 VT 
Mutual Conductance
   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
iC  g mvBE       current and a voltage
Estimating gm
    The small signal behaviour is
estimated by a tangent to the
exponential IC-VBE curve
    gm is, therefore, simply the
dI C   d         VBE 
gm           I S exp  
dVBE dVBE          VT 
IS   VBE 
 exp  
VT    VT 
iC  g mvBE           I
 C
VT
Amplification
Assume that the transistor is biased in the
active region somehow…
iC  g mvBE
Collector voltage, VC, is related to IC by Ohm’s
RC         law
IC     VC  VS  I C RC

VC
Small signal ratio between collector voltage
VBE
and collector current is:
vC dVC
       RC
i C dI C
vC vC iC
So:               RC g m
vBE iC vBE
Simple Common-Emitter Amplifier
   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 mvBE  g mvIN
VOUT  VS  I C RC
vOUT dVOUT
        RC
iC   dI C
vOUT vOUT iC
           RC g m
vIN   iC   vIN
Biasing
   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
   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
    To analyse the circuit:
   Determine quiescent
conditions
   Calculate mutual
conductance
   Calculate small signal
performance
   Voltage Gain
   Input Impedance
   Output Impedance
   Cut-off frequency
The Story so Far
   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

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