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Electronic
Engineering
The following presentation is a part of the level 5 module -- Electronic Engineering. This resources is a part of the
2009/2010 Engineering (foundation degree, BEng and HN) courses from University of Wales Newport (course codes
H101, H691, H620, HH37 and 001H). This resource is a part of the core modules for the full time 1 st year
undergraduate programme.
The BEng & Foundation Degrees and HNC/D in Engineering are designed to meet the needs of employers by placing
the emphasis on the theoretical, practical and vocational aspects of engineering within the workplace and beyond.
Engineering is becoming more high profile, and therefore more in demand as a skill set, in today’s high-tech world. This
course has been designed to provide you with knowledge, skills and practical experience encountered in everyday
engineering environments.
Contents
 Circuit calculations using active non-linear devices.
 Equivalent Circuits
 Bipolar Transistor.
 The Hybrid Parameter Network.
 The Hybrid
Model
 The electronic equivalent circuit is drawn in the followi...
 Model at High Frequencies
 The Miller Effect
 Field Effect Transistor FET
 Credits
In addition to the resource below, there are supporting documents which should be used in combination with this
resource. Please see:
Clayton G, 2000, Operational Amplifiers 4th Ed, Newnes
James M, 2004, Higher Electronics, Newnes
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Circuit calculations using active
non-linear devices.
Circuit theorems such as:



Kirchhoff’s Laws
Thévenin’s Theorem
Superposition
work only if the circuit components are linear i.e. if you
double the voltage, you double the current.
Components such as resistors, capacitors and
inductors are, on the whole linear in nature. When we
come to analysing circuits with non-linear components
such as diodes, bipolar transistors and field effect
transistors we must adopt one of two techniques:
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1.
2.
Graphical
Equivalent Circuits
The graphical method uses plots of the input and output
characteristics to determine the characteristics of
the created amplifier or circuit. This requires a
large amount of graphical information to be
available especially if a design is being formulated
with a wide range of possible devices to be
considered.
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Electronic Engineering
IB
X
Vs/Rc
iB
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Vsupply (Vs)
Equivalent Circuits
The other approach is to use a circuit comprising linear
components, which responds in the same way as the nonlinear active device. The equivalent circuit may not be
perfect but will often give us a starting point when
designing. Note that electronics on the whole is far from
exact as we are working with components with relatively
high tolerance:
Resistors typically 5% and Capacitors typically 10% as well
as active devices which can vary dramatically in terms of
their characteristics from one device to another.
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Diode
Anode
Cathode
R
E
D
The diode can be modelled using a resistor R, a voltage
source E and an ideal diode
The diode D only conducts when the anode is positive
with respect to the cathode. The supply E ensures
that the anode of D only goes positive when the
applied voltage reaches a certain positive level. The
resistor R controls the current once the diode is
conducting.
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The result is a characteristic that looks like:
Current
flow
This approximates
the characteristic
for a simple diode
where E for Silicon
Slope = 1/R
is about 0.6v. Of
course this is not
exact but is fairly
good over the
Applied
E
limited range
voltage V
where the diode is
conducting.
This type of model is called a small signal model as it has
good approximation for a small range of inputs.
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3
2.5
2
1.5
1A
1
0.5
0.05V
R = 0.05
0
0.4
0.45
0.5
0.55
0.53V
0.6
0.65
Bipolar Transistor.
The models for both NPN and PNP are the same. The
models vary subtly for different configurations. We
will examine the most common configuration – that of
the common emitter.
Input
Output
The input on the left is
between the base and
the emitter and the
output on the right is
between the collector
and the emitter.
The emitter is therefore common to input and output
which gives the configuration the name.
There are a number of models that exist for this device.
We will look in detail at two of these.
The Hybrid Parameter Network.
This replaces the input and the output sides by
conventional circuit theory equivalent circuits.
The input is replaced by a
Thévenin equivalent i.e. a
resistor in series with a
voltage source.
The output part of the
transistor is replaced by a
Norton equivalent circuit
comprising a current source
in parallel with a resistor, as
shown
The reason for the choice of equivalent circuits is that
the input is voltage driven whilst the output is
associated with current flow.
If we now combine these we have the Hybrid Parameter
Network.
IB
hie
IC
hfe x IB
VBE
hoe
hre x VCE
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VCE
There are 4 parameters associated with this model,
these being:
hie – hybrid input common emitter
This is a measure of the input resistance of the transistor
and is measured in ohms. It is given by:
VBE
I B
hre – hybrid reverse gain common emitter
This is a measure of the effect of the output voltage on the
input and is effectively a reverse voltage gain. It has no
units. It is given by:
V BE
VCE
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hfe – hybrid forward gain common emitter
This is a measure of the effect of the input current on the
output and is effectively a forward current gain. It has no
units. It is given by:
I C
I B
hoe – hybrid output common emitter
This is a measure of the output conductance of the
transistor and is measured in Siemens. It is given by:
I C
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VCE
The reason for the resistor on the output being
expressed as a conductor will become apparent when
we start to generate equations.
By looking at the input side and the output side we can
generate two equations, these are
Input side:
VBE
=
hie x IB
+
hre x VCE
Output side
IC
=
hfe x IB
+
hoe x VCE
The symmetry between the equations can be seen – this
would not be true if hoe were quoted as a resistor.
If we wish to measure the four parameters then we can
see how this can be done using the equations:
VBE
=
hie x IB
+
hre x VCE
IC
=
hfe x IB
+
hoe x VCE
hie = VBE/IB as long as VCE is zero
this is written as:
hie = VBE/IB |VCE = 0
What are the equations for the other three?
In any circuit containing a common emitter transistor,
the transistor can now be replaced by the four
interconnected components.
NOTES.
1.
2.
3.
4.
5.
This is a small signal model and only works effectively
over a limited range of input conditions.
This is an a.c. model and cannot be used to set up the
initial d.c. conditions around the transistor (i.e.
biasing)
This model does not take into account variations in
frequency and can only be used within the normal
operating frequencies of the amplifier.
All capacitors in the transistor circuit are considered
to be short circuits when constructing the equivalent
circuit.
All d.c. power supplies act as large capacitors and can
therefore also be thought of as short circuits.
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We are now ready to start analysing transistor circuits
but before we do here are some typical values for the
parameters:
Parameter
Value
hie
1 k
hre
3 x 10-4
hfe
250
hoe
300 S
This is for a BC107 –
other transistor values
can be found in
manufacturer’s
literature.
NOTE – The values are typical values for that device
and will vary considerably.
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Example
Rb1 = 68k
Vs
Rb1
Rc
Rb2 = 27k
Vout
Vin
Rc = 1.8k
Re = 1k
Ce = 100F
Rb2
Re
Ce
Ground
Other caps = 0.1F
Vs = 9v
Input is a voltage source with an internal resistance of 50
Output is a 120 loudspeaker
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The Hybrid  Model
This is model based on the physical construction of the
transistor. A typical transistor has the following
construction:
rce
rb’e
rb’c
b’
Emitter
Cb’e
rbb’
Base
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Collector
Cb’c
From the diagram:
rbb’ this is the resistance from the base connection to
the centre of the base region.
rb’e this is the resistance from the centre of the
base to the emitter connection.
rb’c this is the resistance from the centre of the
base to the collector connection.
rce this is the resistance from the collector
connection to the emitter connection.
Cb’e this is the junction capacitance of the base
emitter junction.
Cb’c this is the junction capacitance of the base
collector junction.
The current generator has a value given by gM x Vb’e.
gM is called the transistors transconductance.
Typical values for the device are:
Parameter
rbb’
rb’e
rb’c
Value
300 
2000 
1.5 M
rce
Cb’e
Cb’c
25 k
8 pF
4 pF
gM
0.125 S
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The electronic equivalent circuit is drawn in the
following way:
b
Cb’c
b’
c
rbb’
VBE
Vb’e rb’e
IC
rb’c
rce
Cb’e
e
It is possible to draw some
comparisons between the
two models and in doing so
we can equate certain
components:
VCE
gM x Vb’e
Hybrid
Hybrid - 
hie
rbb’ + rb’e
hre
rb’e/rb’c
hfe
gM x rb’e
hoe
1/rce
When we are working at low to medium frequencies, the
capacitors will have relatively high values:
Cb’e = 8 pF will have a reactance at 20 kHz of
1/2fC = 995 k
This is so large compared to the other resistors both of
the capacitors and rb’c are removed giving us:
b
b’
gM x Vb’e
rbb’
VBE
Vb’e rb’e
c
IC
rce
VCE
e
This model is now very similar to the original H parameter
model.
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Model at High Frequencies
At higher frequencies the reactance of the capacitors
begins to drop and their effect increases. What they
effectively do is reduce the current flow through
Rb’e by allowing it to flow via other paths as shown.
Cb’c
b
b’
c
rbb’
VBE
Vb’e rb’e
IC
rb’c
rce
Cb’e
e
gM x Vb’e
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VCE
We need to determine the flow through Cb’c
Note. The transistor amplifier inverts the signal as it
amplifies which means that as the input goes positive
the output goes negative. The upshot of this is that
the voltage across Cb’c is given by:
Vb’e + Vce
but Vce = gain x Vb’e so this gives us
Vb’e + Vb’e x gain = Vb’e (1 + gain)
an approximation for the gain is gM x RL so
Voltage across Cb’c = Vb’e (1 + gM x RL)
Which means the current is Vb’e (1 + gM x RL) j Cb’c
This has the same effect as a capacitor from b’ to e
whose value is:
Cb’c x (1 + gM x RL)
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The input part of the circuit can therefore be redrawn
as:
b
b’
rbb’
VBE
Vb’e rb’e
Cb’c x (1 + gM x RL)
Cb’e
The two capacitors in parallel can now be combined to
given a single capacitor CIN given by
Cb’e + Cb’c x (1 + gM x RL)
What has effectively happened is that the value of the
feedback capacitor has been amplified and applied across
the input. This is called the Miller Effect.
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The Miller Effect
If we have an inverting amplifier with a capacitor
connected between it’s input and output then this is
equivalent to the amplifier with one capacitor
connected from its input to ground and another
between its output and ground.
The value of the input capacitor is C (A + 1) and the
output capacitor is given by C (A + 1)/A
C
A
A
~AC
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~C
Going back to our amplifier;
it is important to know the frequency at which the
amplifiers gain begins to reduce due to the effect of
the capacitors. The point at which we define the
amplifier to be beyond it’s working limit, i.e. outside
its bandwidth, is when the resistance of rb’e equals
the reactance of CIN. (This is the amplifiers -3dB
point)
rb’e = 1/(2fCIN) from which we can say that the
break frequency for the amplifier is:
f = 1/(2CIN rb’e)
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Field Effect Transistor FET
The equivalent circuit of an FET is relatively simple
compared to the bipolar transistor. The circuit below
shows the complete model.
Gate
VGS
Cgd
ID
rds
Cgs
Drain
Typical Values for the
parameters are:
VDS
gM x VGS
Source
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rds
Cgs
Cgd
gM
100K
4 pF
1 pF
5mS
At low frequencies the model simplifies to become:
Gate
ID
VGS
rds
Drain
VDS
gM x VGS
Source
If we have load RL and RL << rds then:
VDS =
gM VGS RL
Giving Gain = VDS/VGS
=
gM RL
At high frequencies the Miller effect can once again be
used to give us an equivalent input capacitance of:
Cin = Cgs + Cgd (1 + gM RL)
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If we have a Voltage Source connected to the input
then the input circuit becomes:
RS
VS
~
VGS
Cin
Reactance of the capacitor is
1
jCin
therefore
1
jCin
Vgs  Vs 
Rs  1
jCin
1
Vgs  Vs 
1  jCinRs
this gives us a gain of:
gm  Rl
Gain 
1  jCinRs
This produces a gain that rolls
off above a certain frequency.