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BASIC TERMS AND CONCEPTS
Admittance: ratio of the phasor current into a two-terminal device to the phasor voltage across the
device; mathematically Yin(jϖ)=1/[ Yin(jϖ)]= Iin/ Vin.
Alternating current: a sinusoidally time-varying current signal having the form Asin(ϖt + φ).
Audio frequencies: frequencies below 20 kHz.
Band-pass circuit: circuit that passes frequencies within a specified band, while attenuating
frequencies outside the band.
Band-reject circuit: circuit in which a central band of frequencies are significantly attenuated
while passing those frequencies outside the band with little to no attenuation.
Battery: a device that converts chemical energy into electrical energy and maintains approximately
a constant voltage between its terminals.
Branch: a two-terminal circuit element, denoted by a line segment.
Charge: an electric property of matter, measured in coulombs. Like charges repel and unlike
charges attract each other. Each electron carries an amount of charge equal to —1.6xl0-19 C.
Circuit: energy or signal processor consisting of interconnections of “simple’ elements or devices.
An element, called a source, will generate a voltage or a current representing some type of
information. An interconnection of circuit elements will process this signal into a new voltage or
current.
Circuit model: an approximation to a real circuit that is amenable to mathematical analysis. One
can think of a circuit model as an interconnection of ideal circuit elements (circuit diagram) or as
some mathematical equation.
Closed node sequence: a finite sequence of nodes that begins and ends with the same node.
Closed path: a connection of devices or branches through a sequence of nodes that ends on the
node where it began and that traverses each node only once.
Complex exponential forcing function: a function of the form v(t) = Vest, where V= = Vejφ, and s
= σ + jω are complex numbers. A special case (σ = 0) resulting in v(t) = Ve j(ω t+φ) is used
throughout this chapter as a shortcut in sinusoidal steady-state analysis.
Conductance: reciprocal of resistance, with mhos (or Siemens) as its unit, the real part of a
possibly complex admittance.
Conductor: a material, usually a metal, in which electrons can move to neighboring atoms with
relative ease.
Conservation of power (energy): the sum of the powers (energies) generated by a group of circuit
elements is equal to the sum of the powers (energies) absorbed by the remaining circuit elements.
Common mode rejection ratio, CMRR: for a difference amplifier, the ratio of difference mode
gain to common mode gain; i.e., CMRR = Ai/Ac.
Common mode voltage gain, Ac: for a difference amplifier, Ac = Vo/Vс when both inputs V1 and V2
have the same value Vo.
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Connected circuit: a circuit for which any node can-be reached from any other node by some path
through the circuit elements or in which every pair of nodes is joined by some set of branches.
Bounded voltage or current: voltage or current signal whose absolute value remains below some
fixed finite constant for all time.
Capacitance of a pair of conductors: a property of conductors separated by a dielectric that
permits the storage of electrically separated charge when a potential difference exists between the
conductors. Capacitance is measured in stored charge per unit of potential difference between the
conductors.
Capacitor (linear): a two-terminal device whose current is proportional to the time derivative of
the voltage across it.
Coil: another name for an inductor.
Conservation-of-charge principle: principle that the total charge transferred into a junction (or out
of a junction) is zero.
Continuity property of the capacitor: property such that if the current iC(t) through a capacitor is
bounded over the time interval t1 < t < t2, then the voltage across the capacitor is continuous for t1 <
t < t2. In particular, if t1 < t0 < t2, then vc(tQ) = vc(t^), even when vC(t0)= vC(t0), even iC(t0)=/ iC(t0).
Continuity property of the inductor: property such that if the voltage vL(t) across an inductor is
bounded over the time interval t1 < t < t2, then the current through the inductor is continuous for t1 <
t < t2. In particular, if t1 < t0 < t2, then iL(t0)=/ iL(t0)., even when vL(t0)= vL(t0).
Coulomb: quantity of charge that, in 1 sec, passes through any cross section of a conductor
maintaining a constant one-amp current flow.
Cramer's rule: a method for solving a linear matrix equation for its unknowns, one by one,
through the use of determinants.
Current: movement of charges. Current is measured in amperes. One ampere is the movement of
charges through a surface at the rate of 1 C/sec.
Current division: property wherein, in a parallel connection of admittances driven by a current
source, the current through a particular branch is proportional to the ratio of the admittance of the
branch to the total parallel admittance.
Current division: formula showing that the distribution of current in a branch of a parallel resistive
circuit is proportional to the conductance of the particular resistor, Gj, divided by the total parallel
conductance of the circuit, Geq = G1+ G2-+ G3.
Dependent (controlled) current source: a current source whose strength depends on the voltage or
current of some other element in the circuit.
Dependent (controlled) voltage source: a voltage source whose strength depends on the voltage or
current of some other element in the circuit.
Deactivating (killing) an independent current source: replacing the said source by an open
circuit.
Deactivating (killing) an independent voltage source: replacing the said source by a short circuit.
Dielectric: an insulating material often used between two conducting surfaces to form a capacitor.
Difference amplifier (differential amplifier): an amplifier with two inputs V1 and V2 and a single
output V0 that, for the ideal case, depend only on the difference of the two inputs;
i.e.,Vα(V1-V2).
Difference mode voltage gain, Ad: for a difference amplifier, Ad = Vo/Vd when both inputs have
equal magnitudes of O.5Vd, but opposite polarities, i.e., when V1= —V2 = 0.5Vd.
Direct current: a current that remains constant with time.
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Dual circuits: two planar circuits N and N* are dual circuits if, with proper labeling of the
branches, KCL, KVL, and branch v-i equations in TV become, respectively, KCL, KVL, and
branch i-v equations in YV* upon the interchange of voltage and current variables.
Efficiency of a device: the ratio of the output power to the input power times 100%.
Electric field: property such that if a charge is placed at a point in space, then the charge
experiences a force. If this is true, we say that an electric field exists at that point.
Equivalent n-terminal networks: two n -terminal networks having the same terminal voltagecurrent relationship. As an alternative definition, two n -terminal networks are said to be equivalent
when, after substituting one for the other in every possible network N, the voltages and currents in
N are unaffected.
Euler identity: ejθ = cos(θ) + j sin(θ).
Gaussian surface: a closed curve or closed surface surrounding two or more nodes or a closed
curve in the plane or a closed surface in three dimensions with a well-defined inside and outside..
Graph of a circuit: diagram in which each branch (element) of a network is replaced by a line
segment; thus, a graph represents information about the connections between the circuit elements.
Ideal conductor: material that offers zero resistance to the movement of electrons.
Ideal insulator: material that offers infinite opposition to the movement of electrons.
Imaginary part: the variable b in a complex number z = a + jb for real numbers a and b; denoted
Im[z].
Impedance: an ordinarily complex, frequency-dependent quantity defined as Z(jϖ)= V/I, where V
is the phasor voltage across a two-terminal device and I is the phasor current through the device.
For the resistor, ZR(jϖ)= R Ω; for the capacitor, ZC(jϖ)= 1/(jϖC) Ω; and for the inductor, ZL(jϖ)=
jϖL Ω.
Independent (ideal) current source: an ideal device that delivers current as a prescribed function
of time (e.g., {Acos(ϖt+φ)} A), no matter what circuit element is connected across its terminals.
Independent (ideal) voltage source: an ideal device whose terminal voltage is a prescribed
function of time (e.g., {Acos(ϖt+φ)} V), no matter what current goes through the device.
Inductor (linear): a two-terminal device whose voltage is proportional to the time derivative of the
current through it.
Instantaneous power: the value of p(t) = v(t)i(t) at a particular instant of time, in watts when v(t) is
in volts and i(t) in amps.
Inductance: property of a conductor and its local environment (a coil with an air core or an iron
core) that relates the time derivative of a current through the conductor to an induced voltage across
the ends of the conductor.
Insulator: a material that opposes the easy movement of electrons.
Farad: a measure of capacitance in which a charge of 1 coulomb produces a 1-V potential
difference.
Faraday's law of induction: law asserting that, for a coil of wire sufficiently distant from any
magnetic material, such as iron, the voltage induced across the coil by a time-varying current is
proportional to the time derivative of the current; the constant of proportionality, denoted L, is the
inductance of the coil. Faraday's law is usually stated in terms of flux and flux linkages, which are
discussed in physics texts.
Filter: network (circuit) that passes frequencies within a specified frequency range, while
attenuating frequencies outside this range.
Floating source: source, neither of whose nodes is connected to the reference node.
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Frequency response: ratio of the phasor output to the phasor input of a circuit as a function of
frequency. A graph of the frequency response of a circuit consists of two parts: a graph of the
magnitude of the phasor ratio and a graph of the angle of the phasor ratio.
Henry: the unit of inductance; equal to 1 V-sec/amp.
Highpass circuit: circuit with a frequency response such that the high-frequency content of the
input signal is passed, while the low-frequency content of the input signal is attenuated.
Kirchhof’s current law (KCL): law asserting that the algebraic sum of the currents entering a
node of a circuit consisting of lumped elements is zero for every instant of time. In general, for
lumped circuits, the algebraic sum of the currents entering (leaving) a Gaussian surface is zero at
every instant of time.
Kirchhoffs voltage law (KVL): law asserting that for lumped circuits, the algebraic sum of the
voltage drops around any closed path in a network is zero at every instant of time. In general, for
lumped connected circuits, the algebraic sum of the node-to-node voltages for any closed node
sequence is zero for every instant of time.
Linearity property: let the responses due to inputs u1 and u2, each acting alone, be y1 and у2. When
the scaled inputs α1u1 and α2u2 are applied simultaneously, the response is у = α1u1+α2u2. Linearity
implies both superposition and proportionality, and vice versa.
Linear resistive element: an n-terminal circuit element whose terminal voltage and current
relationships are described by a set of linear homogeneous algebraic equations.
Linear resistive network (circuit): a network consisting of only linear resistive elements and
independent voltage and current sources.
Linear matrix equation: an equation of the form Ax = b, where A is an n x n matrix, x is an n vector of unknowns, and b is an n -vector of constants.
Linearly dependent: a set of equations is linearly dependent if and only if one of the equations is a
scaled sum of the remaining equations, e.g., Fn = a1F1 + …+- an-1Fn-1 . The constants a1,..., an-1 that
scale the equations F1, ..., Fn-1 are real numbers.
Linearly independent set of equations: the set of equations [F1(x1,x2,…xn,)..., F1(x1,x2,…xn) = 0] is
linearly independent if no one equation can be expressed as the scaled sum of the remaining
equations.
Loop (closed path): a contiguous sequence of branches that begins and ends on the same node and
touches no other node more than once.
Loop analysis: an organized method of circuit analysis for computing loop currents in a circuit.
Knowledge of the loop currents allows one to compute the individual element currents and,
consequently, the element voltages.
Loss: effect then absorbed power is dissipated as heat.
Lossless device: device in which energy can only be stored and retrieved and never dissipated.
Lossy device: a device, such as a resistor (with positive R), that dissipates energy as some form of
heat or as work.
Lumped circuit element: circuit element whose dimensions are small compared to the wavelength
of frequencies that excite the element.
Magnitude (modulus):,
(a 2 + b 2 )
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where a and b are real numbers making up the complex number z = a + jb. Also denoted |z|.
Maximum power transfer theorem: let an adjustable resistor RL be connected to a practical power
source represented by an ideal voltage source VS in series with a fixed source resource RS. Then
maximum power is absorbed by the resistor when its value is adjusted to RL = RS.
Maxwell's equations: a set of mathematical equations governing the properties of electric and
magnetic fields and their interaction.
Memory: property of a device whose voltage or current at a particular time depends on the past
operational history of the device; e.g., the current through an inductor at time to depends on the
history of the voltage excitation across the inductor for t 5 to.
Mho: unit of conductance; equal to inverse ohm. (See Siemens.)
Multimeter or volt-ohmmeter (VOM): an instrument capable of measuring voltage, current, and
resistance.
Node: the end point of a branch that represents the terminals of a circuit element. In general, a node
is a point of connection between two or more circuit elements (branches).
Node voltage: the voltage drop from a given node to the reference node.
Nonlinear resistor: a two-terminal circuit element having a v-i curve that is not a straight line, but
passes through the origin of the v-i plane.
Norton's equivalent circuit: circuit with an independent current source in parallel with a
resistance, equivalent to a two-terminal network consisting of independent sources and linear
resistive elements.
Ohm: unit of resistance. One ohm equals the ratio of 1 V to 1 A.
Ohm's law: for any metallic conductor, the current i through the conductor at any time t is
proportional to the voltage v across the conductor at that time.
Open circuit: n connection of infinite resistance or zero conductance.
Parallel circuit: a side-by-side connection of two-terminal circuit elements whose top terminals are
wired together and whose bottom terminals are wired together.
Passive sign convention: convention by means of which voltage and current reference directions
are indicated. (See figure below.)
Peak-to-peak value: 2A in A cos(ϖt+φ) of an ac waveform.
Peak value: A in A cos(ϖt+φ) of an ac waveform.
Phasor: complex number representation that denotes a sinusoidal signal at a fixed frequency.
Boldface capital letters denote phasor voltages or currents …...
Power: the rate of change of work per unit time.
Proportionality property: property such that when an input to a linear resistive network is acting
alone, increasing the input К times increases the response К times.
Resistance: for a resistor, the proportionality constant R in the formula v(r) == Ri(t). Resistance is
measured in ohms. One ohm means that the voltage is 1 V when the current is 1 ampere.
Resistivity: the resistance of a conductor is proportional to its length and inversely proportional to
its cross section area. The proportionality constant, usually denoted by ρ, is called the resistivity of
the material. The resistivity of copper at 20° С is 1.7 x 10-8 ohm-m.
Resistor (linear): a physical device that obeys Ohm's law. (There are nonlinear resistors that do not
obey Ohm's law.)
Root mean square (rms) or effective value: a measure of ac current; related to the peak value by
the formula rms = 0.7071A, where A cos(ϖt+φ) is the ac waveform.
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Series circuit: a sequential connection of two-terminal circuit elements, end to end.
Short circuit: a connection of zero resistance or infinite conductance.
Siemens: international unit for inverse ohms. mhos, or
Skin effect: as the frequency of sinusoidal current increases, the current flow along the conductor
becomes concentrated on its outer rim. This reduces the effective cross-sectional area and increases
the effective resistance of the conductor.
Source: a device that approximates either an ideal voltage source or an ideal current source.
Source transformation: transformation in which a two-terminal network consisting of an
independent voltage source in series with a resistance is equivalent to another two-terminal Stray
or parasitic capacitance: an unwanted capacitance that exists between two conducting surfaces.
Stray or parasitic inductance: an unwanted inductance affecting a circuit's performance when a
time-varying current flows through a conductor in the circuit.
network consisting of an independent current source in parallel with a resistance.
Superposition property: property such that when a number of inputs are applied to a linear
resistive network simultaneously, the response is the sum of the responses due to each input acting
alone.
Susceptance: the imaginary part of a possibly complex admittance.
v-i characteristic: a graphical or functional representation of a memoryless circuit element.
Thevenin's equivalent circuit: circuit with an independent voltage source in series with a
resistance, equivalent to a two-terminal network consisting of independent sources and linear
resistive elements.
Thevenin's equivalent resistance: the resistance that appears in the Thevenin equivalent circuit of
a two-terminal linear network. It is also the equivalent resistance of the two-terminal network when
all internal independent sources are deactivated.
Two-terminal network: an interconnection of circuit elements inside a box having only two
accessible terminals for connection to other networks. The concept is extendible to n -terminal
networks.
Unbounded voltage or current: a voltage or current whose value approaches infinity as it nears
some instant of time, possible t= /// 211 psl.
Voltage (synonymous with potential difference): measurement obtained when a positive charge
moves from a point of higher potential to a point of lower potential, accompanied by a conversion
of energy. Voltage is measured in volts. The existence of 1 V between two points A and В means
that the energy converted in moving one coulomb of charge between A and В is one joule.
Wattage: a measure of the consumption of power.
Wavelength of a sinusoid: denoted by λ, equals the speed of light divided by the frequency in Hz.
Voltage division: formula showing that each resistor voltage in a series connection is a proportion
of the input voltage that is equal to the ratio of the branch resistance to the total series resistance.
Voltage regulator: circuit that produces a voltage having only a small variation between set limits
for a given range of load variations from a fairly smooth input signal.
// (double slash): notation for combining resistances in parallel. R1//R2 means that R1 and R2 are in
parallel, and R1//R2//R3 means that R1 is in parallel with R2, which is in parallel with R3.