Unformatted text preview: position along the path. A wire has a finite thickness, and interesting
electrical behavior occurs across the wire. We ignore such field effects.
Lumped parameter means that the effects of the various electrical compo-
nents may be considered to be concentrated at one point. The converse of a
lumped-parameter circuit is a distributed-parameter circuit. The analysis of
distributed-parameter circuits often involves partial differential equations,
which we discuss briefly near the end of this text. Antennas are an example of
At each point in the circuit there are two quantities of interest: voltage
(or potential) and current (or flow of charge). Current is, by convention, the
net flow of positive charge. A branch is part of a circuit with two terminals to
which connections can be made, a node is a point where two or more
branches come together (a node is denoted in our sketches -. ), and a loop
is a closed path formed by connecting branches, Our basic modeling laws are
Kirchhoff's circuit laws, the current and voltage laws:
Current law: The algebraic sum of the currents entering a
node at any instant is zero.
Voltage law: The algebraic sum of the voltage drops
around a loop at any instant is zero.
The voltage law is equivalent to saying that the voltage drop from one point
to another is the same in any direction. We will discuss these laws shortly.
To set up the circuit equations, a current variable is assigned to each
branch. One can talk either of the potentials (voltages) at the nodes or of the
potential drops across the branches. Kirchhoff's current law may then be
applied to each node, and the voltage law to each loop. This procedure
exhibits a certain amount of arbitrariness. There is usually some redundancy
among the equations, and the determination of a minimal number of equa-
tions is generally computationally nontrivial.
In this section we discuss only single- or double-loop circuits. Let us
consider the branch containing a two-terminal device shown in Figure 1.10.1.
The current is denoted by i. The voltages at the two nodes are denoted vo
and v. The voltage drop is defined to be the difference, U = Vo - Up. For our
purposes, the behavior of the device is completely determined if we know u
and i at any time . The relationship between v and i is called the v-i
characteristic of the particular device.
device. The nodal
We shall consider only the following five basic types of devices.
denoted by Vo and
Resistor If the voltage drop v (measured in volts) is uniquely determined by
Up, the voltage drop
the current i (measured in amperes) and the time,
U = Uo - Up, and the
current is denoted by i.
U = f(i, 1),...
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- Fall '10