Download Circuit Elements

Dave Shattuck
University of Houston
© Brooks/Cole Publishing Co.
Module 1 – Part 3
Circuit Elements
Filename: DPKC_Mod01_Part03.ppt
Dave Shattuck
University of Houston
© Brooks/Cole Publishing Co.
Overview of this Part
In this part of the module, we will cover the
following topics:
• What a circuit element is
• Independent voltage sources and current sources
• Dependent voltage and current sources
• Resistors and Ohm’s Law
Note: Some of these topics will be review for some students, particularly
those who have had some exposure to circuits before. However, it
would be wise to skim through this material quickly, to make sure that
we are using terms in a way that is familiar to you.
Dave Shattuck
University of Houston
© Brooks/Cole Publishing Co.
Textbook Coverage
This material is covered in your textbook in the following
sections:
• Circuits by Carlson: Sections 1.2, 1.3, 2.3
• Electric Circuits 6th Ed. by Nilsson and Riedel: Sections
2.1, 2.2, 2.3
• Basic Engineering Circuit Analysis 6th Ed. by Irwin and
Wu: Sections 1.3, 2.1
• Fundamentals of Electric Circuits by Alexander and
Sadiku: Section 1.6, 2.2
• Introduction to Electric Circuits 2nd Ed. by Dorf: Sections
2-2, 2-3, 2-4
Dave Shattuck
University of Houston
© Brooks/Cole Publishing Co.
Circuit Elements
• In circuits, we think about basic circuit
elements that are the basic “building
blocks” of our circuits. This is similar to
what we do in Chemistry with chemical
elements like oxygen or nitrogen.
• A circuit element cannot be broken down
or subdivided into other circuit elements.
• A circuit element can be defined in terms
of the behavior of the voltage and current
at its terminals.
Dave Shattuck
University of Houston
© Brooks/Cole Publishing Co.
The 5 Basic Circuit Elements
There are 5 basic circuit elements:
1. Voltage sources
2. Current sources
3. Resistors
4. Inductors
5. Capacitors
We are going to define the first three here in this
module. We will not introduce inductors or
capacitors until later.
Dave Shattuck
University of Houston
© Brooks/Cole Publishing Co.
Voltage Sources
• A voltage source is a two terminal
circuit element that maintains a
voltage across its terminals.
• The value of the voltage is the
defining characteristic of a voltage
source.
• Any current can go through the
voltage source, in any direction. It
can also be zero. The voltage source
does not “care about” current. It
“cares” only about voltage.
Dave Shattuck
University of Houston
Voltage Sources – Ideal and
Practical
© Brooks/Cole Publishing Co.
• A voltage source maintains a voltage across its
terminals no matter what you connect to those
terminals.
• We often think of a battery as being a voltage source.
For many situations, this is fine. Other times it is not a
good model. A real battery will have different
voltages across its terminals in some cases, such as
when it is supplying a large amount of current. As we
have said, a voltage source should not change its
voltage as the current changes.
• We sometimes use the term ideal voltage source for our
circuit elements, and the term practical voltage source
for things like batteries. We will find that a more
accurate model for a battery is an ideal voltage source
in series with a resistor. More on that later.
Dave Shattuck
University of Houston
© Brooks/Cole Publishing Co.
Voltage Sources – 2 kinds
There are 2 kinds of voltage sources:
1. Independent voltage sources
2. Dependent voltage sources, of which there
are 2 forms:
i. Voltage-dependent voltage sources
ii. Current-dependent voltage sources
Dave Shattuck
University of Houston
© Brooks/Cole Publishing Co.
Voltage Sources – Schematic Symbol for
Independent Sources
The schematic symbol that
we use for independent
voltage sources is
shown here.
+
vS=
#[V]
-
Independent
voltage
source
This is intended to indicate that the schematic symbol
can be labeled either with a variable, like vS, or a
value, with some number, and units. An example
might be 1.5[V]. It could also be labeled with both.
Dave Shattuck
University of Houston
Voltage Sources – Schematic Symbols
for Dependent Voltage Sources
© Brooks/Cole Publishing Co.
The schematic symbols that
we use for dependent
voltage sources are
shown here, of which
there are 2 forms:
i. Voltage-dependent
voltage sources
ii. Current-dependent
voltage sources
vS =
m vX
vS =
r iX
+
-
+
-
Voltagedependent
voltage
source
Currentdependent
voltage
source
Dave Shattuck
University of Houston
Notes on Schematic Symbols for
Dependent Voltage Sources
© Brooks/Cole Publishing Co.
The symbol m is the coefficient of the
voltage vX. It is dimensionless. For
example, it might be 4.3 vX. The vX is
a voltage somewhere in the circuit.
vS =
m vX
+
-
The schematic symbols that we use for
dependent voltage sources are shown
here, of which there are 2 forms:
i.
Voltage-dependent voltage sources
ii. Current-dependent voltage sources
The symbol r is the coefficient of the current iX.
It has dimensions of [voltage/current]. For
example, it might be 4.3[V/A] iX. The iX is a
current somewhere in the circuit.
vS =
r iX
+
-
Voltagedependent
voltage
source
Currentdependent
voltage
source
Dave Shattuck
University of Houston
© Brooks/Cole Publishing Co.
Current Sources
• A current source is a two terminal
circuit element that maintains a
current through its terminals.
• The value of the current is the
defining characteristic of the current
source.
• Any voltage can be across the
current source, in either polarity. It
can also be zero. The current source
does not “care about” voltage. It
“cares” only about current.
Dave Shattuck
University of Houston
© Brooks/Cole Publishing Co.
Current Sources - Ideal
• A current source maintains a current
through its terminals no matter what you
connect to those terminals.
• While there will be devices that reasonably
model current sources, these devices are
not as familiar as batteries.
• We sometimes use the term ideal current
source for our circuit elements, and the
term practical current source for actual
devices. We will find that a good model
for these devices is an ideal current source
in parallel with a resistor. More on that
later.
Dave Shattuck
University of Houston
© Brooks/Cole Publishing Co.
Current Sources – 2 kinds
There are 2 kinds of current sources:
1. Independent current sources
2. Dependent current sources, of which there
are 2 forms:
i. Voltage-dependent current sources
ii. Current-dependent current sources
Dave Shattuck
University of Houston
© Brooks/Cole Publishing Co.
Current Sources – Schematic Symbol for
Independent Sources
The schematic symbols that
we use for current
sources are shown here.
1. Independent current
sources
iS=
#[A]
Independent
current
source
This is intended to indicate that the schematic symbol
can be labeled either with a variable, like iS, or a
value, with some number, and units. An example
might be 0.2[A]. It could also be labeled with both.
Dave Shattuck
University of Houston
Current Sources – Schematic Symbols
for Dependent Current Sources
© Brooks/Cole Publishing Co.
The schematic symbols that
we use for dependent
current sources are
shown here, of which
there are 2 forms:
i. Voltage-dependent
current sources
ii. Current-dependent
current sources
iS=
g vX
Voltagedependent
current
source
iS=
b iX
Currentdependent
current
source
Dave Shattuck
University of Houston
© Brooks/Cole Publishing Co.
Notes on Schematic Symbols for
Dependent Current Sources
The symbol g is the coefficient of the
voltage vX. It has dimensions of
[current/voltage]. For example, it
might be 16[A/V] vX. The vX is a
voltage somewhere in the circuit.
iS=
g vX
Voltagedependent
current
source
iS=
b iX
Currentdependent
current
source
The schematic symbols that we use for
dependent current sources are shown
here, of which there are 2 forms:
i.
Voltage-dependent current sources
ii. Current-dependent current sources
The symbol b is the coefficient of the
current iX. It is dimensionless. For
example, it might be 53.7 iX. The iX
is a current somewhere in the circuit.
Dave Shattuck
University of Houston
© Brooks/Cole Publishing Co.
Voltage and Current Polarities
•
•
•
Previously, we have
emphasized the important of
reference polarities of currents
and voltages.
Notice that the schematic
symbols for the voltage sources
and current sources indicate
these polarities.
The voltage sources have a “+”
and a “–” to show the voltage
reference polarity. The current
sources have an arrow to show
the current reference polarity.
Dave Shattuck
University of Houston
Dependent Voltage and Current Sources –
Units of Coefficients
© Brooks/Cole Publishing Co.
•
•
Some textbooks use symbols other than the ones we have used here (m,
b, r, and g). There are no firm standards. We hope this is not
confusing.
Perhaps more important is that the different textbooks take different
approaches to the use of units with the coefficients r and g. There
seems to be two approaches:
1.
2.
Assume that r always has units of [V/A], which is the same thing as Ohms
[W]. Assume that g always has units of [A/V], which is the same thing as
Siemens [S]. The values for these coefficients are always shown without
units.
Always show units for the coefficients r and g, somewhere in a given
problem.
Most textbooks follow Approach 1. However, for these modules, we will
follow Approach 2, and always show units. This seems to be the
clearest thing to do when the students may or may not have already
made an assumption about the units that will be used.
As always, when in doubt, show units.
Dave Shattuck
University of Houston
© Brooks/Cole Publishing Co.
Showing Units of Coefficients
In these modules, we will always show units for the values of
the coefficients r and g, somewhere in a given problem.
General practice in electrical engineering is that variables
should not have units. Rather, when we substitute in a
value for a variable, the units must be given with that value.
•For example, all of these
expressions are fine:
vX = 120[V]
iQ = 35[A]
pabs = 24.5[kW]
pdel = vQ(13[A])
pabs = vXiX
•For example, there are
missing units in the
following expressions:
vX = 1.5
pdel = 25iQ
iX = 15
Dave Shattuck
University of Houston
© Brooks/Cole Publishing Co.
Why do we have these dependent
sources?
• Students who are new to circuits often question why
dependent sources are included. Some students find these
to be confusing, and they do add to the complexity of our
solution techniques.
• However, there is no way around them. We need
dependent sources to be able to model amplifiers, and
amplifier-like device. Amplifiers are crucial in electronics.
Therefore, we simply need to understand and be able to
work with dependent sources.
Go back to
Overview
slide.
Dave Shattuck
University of Houston
© Brooks/Cole Publishing Co.
Resistors
• A resistor is a two terminal
circuit element that has a
constant ratio of the voltage
across its terminals to the
current through its terminals.
• The value of the ratio of
voltage to current is the
defining characteristic of the
resistor.
In many cases a
light bulb can be
modeled with a
resistor.
Dave Shattuck
University of Houston
Resistors – Definition and Units
© Brooks/Cole Publishing Co.
• A resistor obeys the expression
vR
R
iR
where vR is the voltage across the resistor, and
iR is the current through the resistor, and R is
called the resistance.
• In addition, it works both ways. If something
obeys this expression, we can think of it, and
model it, as a resistor.
• This expression is called Ohm’s
Law. The unit ([Ohm] or [W]) is
named for Ohm, and is equal to
a [Volt/Ampere].
• It is very important to use Ohm’s Law only on
resistors. It does not hold for sources.
To a first-order approximation,
the body can modeled as a
resistor. Our goal will be to
avoid applying large voltages
across our bodies, because it
results in large currents through
our body. This is not good.
Dave Shattuck
University of Houston
© Brooks/Cole Publishing Co.
Schematic Symbol for Resistors
The schematic symbols that we use for resistors
are shown here.
This is intended to indicate that the schematic symbol
can be labeled either with a variable, like RX, or a
value, with some number, and units. An example
might be 390[W]. It could also be labeled with both.
RX=
#[W]
+
vX
iX
-
vX
RX 
iX
Dave Shattuck
University of Houston
© Brooks/Cole Publishing Co.
Resistor Polarities
•
•
Previously, we have
emphasized the important of
reference polarities of current
sources and voltages sources.
There is no corresponding
polarity to a resistor. You can
flip it end-for-end, and it will
behave the same way.
However, even in a resistor,
direction matters in one sense;
we need to have defined the
voltage and current in the
passive sign convention to use
the Ohm’s Law equation the
way we have it listed here.
Dave Shattuck
University of Houston
© Brooks/Cole Publishing Co.
Getting the Sign Right with Ohm’s Law
If we use the Passive Sign Convention
to write our reference polarities
for the voltage and current, then
we have
If we use the Active Sign Convention
to write our reference polarities
for the voltage and current, then
we have
vX
RX 
iX
vX
RX  
iX
RX=
#[W]
+
vX
RX=
#[W]
iX
-
+
vX
iX
-
Dave Shattuck
University of Houston
© Brooks/Cole Publishing Co.
Why do we have to worry about the sign
in Ohm’s Law?
• It is reasonable to ask why the sign in Ohm’s Law matters.
We may be used to thinking that resistance is always
positive.
• Unfortunately, this is not true. The resistors we use,
particularly the electronic components we call resistors,
will always have positive resistances. However, we will
have cases where a device will have a constant ratio of
voltage to current, but the value of the ratio is negative
when the passive sign convention is used. These devices
have negative resistance. They provide positive power.
This can be done using dependent sources.
Go back to
Overview
slide.
Dave Shattuck
University of Houston
© Brooks/Cole Publishing Co.
Why do we have to worry about the sign
in Everything?
• This is one of the central themes in circuit analysis. The polarity, and
the sign that goes with that polarity, matters. The key is to find a way to
get the sign correct every time.
• This is why we need to define reference polarities for every voltage and
current.
• This is why we need to take care about what relationship we have used
to assign reference polarities (passive sign convention and active sign
convention).
An analogy: Suppose I was going to give you $10,000. This
would probably be fine with you. However, it will matter a
great deal which direction the money flows. You will care a
great deal about the sign of the $10,000 in this transaction.
If I give you -$10,000, it means that you are giving $10,000 to
me. This would probably not be fine with you!
Go back to
Overview
slide.