Apply Mesh Analysis to find i1 and i in the circuit below:
MESH ANALYSIS WITH CURRENT SOURCES
Applying mesh analysis to circuits containing current sources (dependent or independent) may appear
complicated. But it is actually much easier than what we encountered in the previous section, because
the presence of the current sources reduces the number of equations. Consider the following two
possible cases.
Case 1. When a current source exists only in one mesh:
Consider the circuit shown. We set i2 = −5 A and write a
mesh equation for the other mesh in the usual way, that is,
−10 + 4i1 + 6(i1 − i2) = 0
->
i1 = −2 A
Case 2: When a current source exists between two meshes:
Consider the circuit in (a), for example. We create a supermesh by excluding the current source and
any elements connected in series with it,
as shown in (b).
A supermesh results when two meshes have a (dependent or independent)
current source in common.
As shown in (b), we create a supermesh as the periphery of the two meshes and treat it differently.
(If a circuit has two or more supermeshes that intersect, they should be combined to form a larger
supermesh.) Why treat the supermesh differently? Because mesh analysis applies KVL—which
requires that we know the voltage across each branch—and we do not know the voltage across a
current source in advance. However, a supermesh must satisfy KVL like any other mesh.
Therefore, applying KVL to the supermesh in (b) gives
−20 + 6i1 + 10i2 + 4i2 = 0
or
6i1 + 14i2 = 20
We apply KCL to a node in the branch where the two meshes intersect.
Applying KCL to node 0 in (a) gives
i2 = i1 + 6
Solving we get
i1 = −3.2 A,
i2 = 2.8 A (3.20)
Note the following properties of a supermesh:
1. The current source in the supermesh is not completely ignored; it provides the constraint equation
necessary to solve for the mesh currents.
2. A supermesh has no current of its own.
3. A supermesh requires the application of both KVL and KCL.
Use mesh analysis to obtain i0 in the circuit below
1.
2.
3.
4.
5.
Identify the supermesh
write a mesh equation for the super mesh.
Write mesh equations for any addition meshes
Write down any equations from KCL
Solve
NODAL VS MESH ANALYSIS
Both nodal and mesh analyses provide a systematic way of analyzing a complex network. Someone
may ask: Given a network to be analyzed, how do we know which method is better or more efficient?
Mesh analysis:
Networks that contain many series-connected elements, voltage sources, or supermeshes. a circuit
with fewer meshes than nodes is better analyzed using mesh analysis.
Nodal Analysis
Networks with parallel-connected elements, current sources, or supernodes are more suitable for
nodal analysis. A circuit with fewer nodes than meshes is better analyzed using nodal analysis
The key is to select the method that results in the smaller number of equations.
The second factor is the information required. If node voltages are required, it may be expedient to
apply nodal analysis. If branch or mesh currents are required, it may be better to use mesh analysis.
It is helpful to be familiar with both methods of analysis, for at least two reasons. First, one method
can be used to check the results from the other method, if possible. Second, since each method has its
limitations, only one method may be suitable for a particular problem. For example, mesh analysis is
the only method to use in analyzing transistor circuits. Mesh analysis cannot easily be used to solve
an op amp circuit, because there is no direct way to obtain the voltage across the op amp itself.
For nonplanar networks, nodal analysis is the only option, because mesh analysis only applies to
planar networks. Also, nodal analysis is more amenable to solution by computer, as it is easy to
program. This allows one to analyze complicated circuits that defy hand calculation.
A computer software package based on nodal analysis will be introduced next class.
What is a Diode?
When the negative end of the circuit is hooked up to
the N-type layer and the positive end is hooked up to
P-type layer, electrons and holes start moving and the
depletion zone disappears.
When the positive end of the circuit is hooked up to
the N-type layer and the negative end is hooked up to
the P-type layer, free electrons collect on one end of
the diode and holes collect on the other. The
depletion zone gets bigger.
A diode is the simplest sort of semiconductor device.
Broadly speaking, a semiconductor is a material with
a varying ability to conduct electrical current. Most semiconductors are made of a poor conductor that
has had impurities (atoms of another material) added to it. The process of adding impurities is called
doping.
In the case of LEDs, the conductor material is typically aluminum-gallium-arsenide (AlGaAs). In
pure aluminum-gallium-arsenide, all of the atoms bond perfectly to their neighbors, leaving no free
electrons (negatively charged particles) to conduct electric current. In doped material, additional
atoms change the balance, either adding free electrons or creating holes where electrons can go.
Either of these alterations make the material more conductive.
A semiconductor with extra electrons is called N-type material, since it has extra negatively charged
particles. In N-type material, free electrons move from a negatively charged area to a positively
charged area.
A semiconductor with extra holes is called P-type
material, since it effectively has extra positively charged
particles. Electrons can jump from hole to hole, moving
from a negatively charged area to a positively charged
area. As a result, the holes themselves appear to move
from a positively charged area to a negatively charged
area.
A diode consists of a section of N-type material bonded
to a section of P-type material, with electrodes on each
end. This arrangement conducts electricity in only one
direction. When no voltage is applied to the diode,
electrons from the N-type material fill holes from the Ptype material along the junction between the layers,
forming a depletion zone. In a depletion zone, the
semiconductor material is returned to its original
insulating state -- all of the holes are filled, so there
are no free electrons or empty spaces for electrons,
and charge can't flow.
To get rid of the depletion zone, you have to get
electrons moving from the N-type area to the P-type
area and holes moving in the reverse direction. To do
this, you connect the N-type side of the diode to the
negative end of a circuit and the P-type side to the
positive end. The free electrons in the N-type material
are repelled by the negative electrode and drawn to the
positive electrode. The holes in the P-type material
move the other way. When the voltage difference
between the electrodes is high enough, the electrons in
the depletion zone are boosted out of their holes and
begin moving freely again. The depletion zone disappears, and charge moves across the diode.
If you try to run current the other way, with the P-type side connected to the negative end of the
circuit and the N-type side connected to the positive end, current will not flow. The negative electrons
in the N-type material are attracted to the positive electrode. The positive holes in the P-type material
are attracted to the negative electrode. No current flows across the junction because the holes and the
electrons are each moving in the wrong direction. The depletion zone increases.
DC TRANSISTOR CIRCUITS
Most of us deal with electronic products on a routine
basis and have some experience with personal
computers. A basic component for the integrated
circuits found in these electronics and computers is the
active, three-terminal device known as the transistor.
Understanding the transistor is essential before an
engineer can start an electronic circuit design.
All about NPN and PNP transistors
TO3, TO46,
TO92, TO220
Packages
A transistor is a semiconductor, meaning that sometimes it conducts electricity,
and sometimes it doesn’t. Its internal resistance varies, depending on the
power that you apply to its base. NPN and PNP transistors are bipolar semiconductors. They contain
two slightly different variants of silicon, and conduct using both polarities of carriers—holes and
electrons.
The NPN type is a sandwich with P-type silicon in the middle, and the PNP type is a sandwich with
N-type silicon in the middle. If you want to know more about this terminology, and the behavior of
electrons when they try to cross an NP junction or a PN junction, you’ll have to read a separate
source on this subject.(Or take ELEC 60 or PHY 4C) It’s too technical for this course. All you need
to remember is:
 All bipolar transistors have three connections: Collector, Base, and Emitter, abbreviated as C,
B, and E on the manufacturer’s data sheet, which will identify the pins for you.
 NPN transistors are activated by positive voltage on the base relative to the emitter.
 PNP transistors are activated by negative voltage on the base relative to the emitter.
In their passive state, both types block the flow of electricity between the collector and emitter, just
like an SPST relay in which the contacts are normally open. (Actually a transistor allows a tiny bit of
current known as “leakage.”)
NPN
You can think of a bipolar transistor as if it
contains a button that can connect the collector
and the emitter. In an NPN transistor, a small
positive potential presses the button.
PNP
In a PNP transistor, a small negative potential has
the same effect of connecting the emitter and
collector. The arrows point in the direction of
“positive current flow.”
You can think of a bipolar transistor as if it contains a little button inside. When the button is pressed, it allows a large
current to flow. To press the button, you inject a much smaller current into the base by applying a small voltage to the base.
In an NPN transistor,
the control voltage is positive. In a PNP transistor, the control voltage is negative.
NPN transistor basics
• To start the flow of current from collector to emitter, apply a relatively positive voltage to the base.
• In the schematic symbol, the arrow points from base to emitter and shows the direction of positive current.
• The base must be at least 0.6 volts “more positive” than the emitter, to start the flow.
• The collector must be “more positive” than the emitter.
PNP transistor basics
• To start the flow of current from emitter to collector, apply a relatively negative voltage to the base.
• In the schematic symbol, the arrow points from emitter to base and shows the direction of positive current.
• The base must be at least 0.6 volts “more negative” than the emitter, to start the flow.
• The emitter must be “more positive” than the collector.
All-transistor basics








Never apply a power supply directly across a transistor. You WILL BURN IT OUT with too much current.
Protect a transistor with a resistor, in the same way you would protect an LED.
Avoid reversing the connection of a transistor between positive and negative voltages.
Sometimes an NPN transistor is more convenient in a circuit; sometimes a PNP happens to fit more easily.
They both function as switches and amplifiers, the only difference being that you apply a relatively positive voltage
to the base of an NPN transistor, and a relatively negative voltage to the base of a PNP transistor.
PNP transistors are used relatively seldom, mainly because they were more difficult to manufacture in the early
days of semiconductors. People got into the habit of designing circuits around NPN transistors.
Remember that bipolar transistors amplify current, not voltage. A small fluctuation of current through the base
enables a large change in current between emitter and collector.
Schematics sometimes show transistors with circles around them, and sometimes don’t. I’ll generally use circles
to draw attention to them unless I forget.
NPN
PNP
The symbol for an NPN transistor always has an
arrow pointing from its base to its emitter. Some
people include a circle around the transistor;
others don’t bother. The style of the arrow may
vary, but the meaning is always the same.



The symbol for a PNP transistor always has an
arrow pointing from its emitter to its base. Some
people include a circle around the transistor;
others don’t bother. The style of the arrow may
vary, but the meaning is always the same.
Schematics may show the emitter at the top and the collector at the bottom, or vice versa. The base may be on
the left, or on the right, depending on what was most convenient for the person drawing the schematic. Be careful
to look carefully at the arrow in the transistor to see which way up it is, and whether it is NPN or PNP. You can
damage a transistor by connecting it incorrectly.
Transistors come in various different sizes and configurations. In many of them, there is no way to tell which wires
connect to the emitter, the collector, or the base, and some transistors have no part numbers on them. Before you
throw away the packaging that came with a transistor, check to see whether it identifies the terminals.
If you forget which wire is which, some multimeters have a function that will identify emitter, collector, and base for
you.
Transistors and relays
One limitation of NPN and PNP transistors is that they are naturally “off” until you turn them “on.” They behave like a
normally open pushbutton, which conducts electricity only for as long as you hold it down. They don’t normally behave like
a normal on switch, which stays on until you apply a signal to turn it off.
A relay offers more switching options. It can be normally open, normally closed, or it can contain a double-throw switch,
which gives you a choice of two “on” positions. It can also contain a double-pole switch, which makes (or breaks) two
entirely separate connections when you energize it. Single-transistor devices cannot provide the double-throw or doublepole features, although you can design more complex circuits that emulate this behavior.
Here is a table that compares Transistor and Relay characteristics:
There are two basic types of transistors: bipolar junction transistors (BJTs) and field-effect transistors
(FETs). Here, we consider only the BJTs, which were the first of the two and are still used today.
Our objective is to present enough detail about the BJT to enable us to apply the techniques
developed in this chapter to analyze dc transistor circuits.
There are two types of BJTs: npn and pnp, with their circuit symbols as shown in Fig. Each type has
three terminals, designated as emitter (E), base (B), and collector (C).
How a BJT (Bipolar Junction
Transistor) Works: Its all in the
doping
The way a transistor works can be described
based on the figure which shows the basic doping
of a junction transistor and figure below which
shows the method of operation of the device.
The operation of the transistor is very dependent
on the degree of doping of the various parts of the
semiconductor crystal. The N type emitter is very
heavily doped to provide many free electrons as
majority charge carriers. The lightly doped P type
base region is extremely thin, and
the N type collector is very
heavily doped to give it a low
resistivity apart from a layer of
less heavily doped material near
to the base region. This change in
the resistivity of the collector
close to the base, ensures that a
large potential is present within
the collector material close to the
base. The importance of this will
become apparent from the
following description.
During normal operation, a
potential is applied across the
base/emitter junction so that the
base is approximately 0.6v more
positive than the emitter, this
makes the base/emitter junction
forward biased.
A much higher potential is
applied across the base/collector
junction with a relatively high positive voltage applied to the collector, so that the base/collector
junction is heavily reverse biased. This makes the depletion layer between base and collector quite
thick once power is applied.
As mentioned above, the collector is made up of mainly low resistivity material with a layer of high
resistivity material next to the base/collector junction. This means that most of the voltage between
collector and base is developed across this high resistivity layer, giving a high voltage gradient near
the collector base junction.
When the base emitter junction is forward biased, a small current will flow into the base. Therefore
holes are injected into the P type material. These holes attract electrons across the forward biased
base/emitter junction to combine with the holes. However, because the emitter region is very heavily
doped, many more electrons cross into the base region than are able to combine with holes. This
means there is a large concentration of electrons in the base region and most of these electrons are
swept straight through the very thin base, and into the base/collector depletion layer. Once here, they
come under the influence of the strong electric field across the base/collector junction. This field is so
strong due to the potential gradient in the collector material mentioned earlier, that the electrons are
swept across the depletion layer and into the collector material, and so towards the collector terminal.
Varying the current flowing into the base, affects the number of electrons attracted from the emitter.
In this way very small changes in base current cause very large changes in the current flowing from
emitter to collector, so current amplification is taking place.
Circuit Analysis of Transistors
For the npn transistor, the currents and voltages of the transistor are
specified as shown at right.
Applying KCL gives
IE = IB + IC
where IE, IC , and IB are emitter, collector, and base currents,
respectively.
Similarly, applying KVL to (b) gives
VCE + VEB + VBC = 0
where VCE, VEB , and VBC are collector-emitter, emitter-base, and base
collector voltages. The BJT can operate in one of three modes: active,
cutoff, and saturation. When transistors operate in the active mode,
typically VBE ~ 0.7 V,
IC = αIE
where α is called the common-base current gain. α denotes the fraction
electrons injected by the emitter that are collected by the collector. Also,
of
IC = βIB
where β is known as the common-emitter current gain. The α and β are characteristic properties of a
given transistor and assume constant values for that transistor. Typically, α takes values in the range
of 0.98 to 0.999, while β takes values in the range 50 to 1000.
It is evident that
IE = (1 + β)IB
and


1
These equations show that, in the active mode, the BJT
can be modeled as a dependent current-controlled
current source. Thus, in circuit analysis, the dc
equivalent model in (b) may be used to replace the npn
transistor in (a). Since β is large, a small base current
controls large currents in the output circuit.
Consequently, the bipolar transistor can serve as an
amplifier, producing both current gain and voltage gain.
Such amplifiers can be used to furnish a considerable
amount of power to transducers such as loudspeakers or control motors.
Find IB , IC , and vo in the transistor circuit. Assume that the transistor operates in the active mode and
that β = 50. Hint: recall that Vbe = 0.7 V in active mode.
First find IB
Next find IC
IC = βIB = 50 × 165 µA = 8.25 mA
Now use KVL to find v0.
−vo − 100IC + 6 = 0
or
vo = 6 − 100IC = 6 − 0.825 = 5.175 V
Note that vo = VCE in this case.
Do Transistor Lab
INSTALL PSPICE FOR NEXT TIME