Circuit Analysis and Linear Systems, Part I Flashcards
circuit model
a representation of circuit device made up of ideal circuit elements
- A real circuit does not behave as an ideal linear device but it can be approximated as one or more ideal to produce a mathematical model
- a mathematical model is used to predict the behavior of the circuit with acceptable accuracy for practical applications
Kirchoff’s Laws
- fundamental concepts about circuits
- needed for loop and nodal analysis
Kirchhoff’s Voltage Law (KVL)
KVL is about conservation of force
- for every action, there is an equal and opposite reaction
- a voltage source exerts force to move electrons
- the sum of the response forces must equal the source
DC Circuits
- a voltage source moves electrons in one direction
- the circuit components react to the force in such a way that the electron completes the circuit with no energy, to be accelerated again by the voltage source
AC Circuits
- A voltage source moves electrons back and forth
- The effect of the force transfers through the circuit, and the circuit components react in the same way with a DC Circuit
voltage divider
works on the principle of an equal and opposite reaction for every action
- voltage sources causes electrons to flow in form of current
- resistors in voltage divider react to force, cause voltage drops
- voltage across resistor 2 is
v2= v (R2/ (R1 + R2))
current divider
works on the principle of favoring the path of least resistance
- current is flow of electrons
- flow favors the path of least resistance
-
Joule’s law
P= V I = V^2/R = I^2 * R
gives the power P, that is dissipated in
- and individual component with resistance R
- a circuit with an equivalent resistance R
resistive power
power in a circuit that is converted to heat
P = dw/ dt = dW/dq dq/dt = V i = i^2 R
loop analysis and node analysis
systematic methods for representing circuits as a system of n equations and n unknowns
- loop current method: determining unknown current
- node voltage method: determining unknown voltage
loop current circuit analysis
1) select one less than the total number of loops (n-1)
2) Assume current directions for the chosen loops
3) Write Kirchoff’s voltage equation around each loop
4) Solve for the current by using the simultaneous equations generated
Node voltage circuit analysis
- Convert all current sources to voltage sources
- Choose one node as reference (usually ground)
- Identify unknown voltages at other nodes compared to reference
- Write Kirchoff’s current equation for all unknown nodes except reference node
- Write all currents in terms of voltage drops
- Write all voltage drops in terms of the node voltages
superposition theorem
net current is the sum of all currents caused by each current source
net voltage is the sum of the voltages caused by each voltage sum
Thevenin’s theorem
a linear, two terminal network with dependent and independent sources can be represented by a Thevenin equivalent circuit consisting of a voltage source in series with a resistor
Norton’s theorem
A linear, two-terminal network with dependent or independent sources can be represented by an equivalent circuit consisting of a single source current source and resistor in parallel
maximum power transfer theorem
- A circuit is most efficient when the maximum power available from a source is transferred to a load resistance RL
Maximum power transfer theorem
the power transfererred to RL is maximized when the derivative of the load power function taken with respect to RL equals zero
two-port equivalent circuit models
- Linear or piecewise linear three- or four terminal devices such as transformers and transistors can be modeled as two-port networks
- A two-port network may be represented by equivalent circuit using a set of two-port parameters, regardless of how the network is actually wired
- commonly used parameters are impedance, admittance, and hybrid parameters
impedance model
represents input voltage and output current as functions of input current and output voltage
The network is modeled as
- an input impedance in series with a dependent voltage source and
-an output admittance in parallel with a dependent current source
admittance model
represents input and output currents as functions of input and output voltages
The network is modeled as
- an input admittance in parallel with a dependent current source, and
- an output admittance in parallel with a dependent current source
two-port hybrid model
represents the input voltage and output current as functions of the input current and output voltage
The network is modeled as
- an input impedance in series with a dependent voltage source, and
- an output admittance in parallel with a dependent current source
sinusoid
waveform simlilar to sine function
may be shifted to left or right
frequency, f of sinusoid is reciprocal of period T
angular frequency w, is frequency expressed in radians per second
phase shift
- difference between peaks of sinusoids for voltage and current
- due to capacitors and inductors in circuit
phase angle
- magnitude of phase shift (in radians)
- by convention, voltage taken as reference
phasor
graphically represents a cosine wave as a line in the complex plane
contains all the information contained in the time domain diagram of the waveform
presents this information in a form that makes it easier to calculate the real and reactive power in the system
especially useful for three-phase systems
waveform analysis
many characteristics of periodic waveforms can be used to determine other characteristics of the system
- average value relates to the charge exchanged by the waveform
- root-mean-square (rms) values relate to the power of the waveform
- Frequency and wavelength of periodic waveforms are inversely related
- phase gives a time comparison of that waveform to the rest of the system, usually as compared with a reference waveform
effective value
- a single voltage value that characterizes an alternating waveform for use in power calculations
- equivalent to DC voltage with same heating effect
- also called root-mean-square value or rms value
impedance, Z
- describes the combined effect circuit elements have on current magnitude and phase
- units of ohms
- a complex quantity with a magnitude and an angle
- usually written in polar form
series AC circuit
consists of circuit elements connected along single path
- the same current flows through all elements
- the voltage drop across each element is found from Ohm’s law (all calculations are complex algebra)
- Kirchoff’s voltage law applies to AC circuits (also with complex algebra)
- Loop analysis can be used for simple stead-state series AC circuits
series RL circuit
- consists only of resistors and inductors in series
- magnitude and phase of impedance found from complex algebra
series RC circuit
- consists only of resistors and capacitors
- magnitude and phase of impedance found from complex algebra
parallel AC circuit
consists of circuit elements connected so that the same voltage appears simultaneously across all elements
- the current through each element can be found from Ohm’s law (all calculations are complex algebra)
- Kirchhoff’s current law applies
- Nodal analysis can be used for simple steady-state parallel AC circuits
- It is convenient to convert all known circuit element impedances to rectangular admittance form
parallel RL circuit
- consists only of resistors and inductors in parallel
- magnitude and phase of admittance found from complex algebra
parallel RC circuit
- consists only of resistors and capacitors in parallel
- magnitude and phase of admittance found from complex algebra
GLC circuit
- is in parallel RLC circuit
- consists of capacitors, inductors, and resistors in parallel
- can be lagging or leading
transient behavior
- process of changing to a new steady state after a change in configuration of circuit
- observed when sources or components are added or removed from a circuit
first-order circuit
contains one energy-storing component: one capacitor or one inductor
bandwidth
range of frequencies between the half-power points in a circuit or signal
half-power points
points where the power is half that of the power at the peak
resonant circuit
- at some frequency, called resonant frequency, inductive reactance and capacitance reactance exactly cancel
- at resonant frequency, the circuit is purely resistive
- Circuits can become resonant when frequency is adjusted, circuit elements are adjusted so that inductive reactance cancels capacitive reactance
parallel resonance
also known as band reject filter
mathematical transforms
used to analyze time functions by converting them to the frequency domain
laplace transforms
used for electronic circuits and control systems
