Circuit Principles
Arithmetic : calculation of numbers
Algebra : use variables and functions to represent numbers
Calculus : the accumulated effect and the rate of change of variables
Circuits:
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Source (generator , photovoltaic(pv) cell,mic…) [ˌfəʊtəʊvɒlˈteɪɪk]
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Load (motor , speaker, screen…)
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Energy or/and signal processing circuits (transformer, filter , amplifier…)
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Switch and line (circuit board, transmission line)
How to regard circuits?
Load 1.Resistive 2.Dynamic —> Interesting period [ 1. Transient 2.Steady state]
Source 1.DC 2.AC [1.sine 2.periodical]
Model
- Ideal circuit elements
Actual circuit element —by abstracting—> simple u-i relationship
Basic ideal circuit elements (two terminal) :
resistor inductor capacitor source
- Circuit modeling
Classification
- Linear and nonlinear
Linear elements: linear relationship of stimulations and its corresponding response
Linear circuits: all loads are linear , expressed by linear equations
Nonlinear circuits : one of more loads are nonlinear , expressed by nonlinear equations
- Planar and non-planar
Planar circuits can be draw on a plane without any intersection of elements
Non-planar circuit will always have intersections
Variables
1.Current
Time variance rate of charges
Unit: A (ampere)
Direct Current Alternating Current
Ideal dc current Sinusoidal ac current
2.Voltage
The work provided by electric field force while moving unit positive charge
Unit: V (Volt)
3.Potential
The voltage from some point to the reference point
The potential of the reference point is ZERO
Symbol: (or U) Unit: V(Volt)
The voltage between two points = the difference of the potential of these two points
4.Electromotive force
The work provided by non-electric field force while moving unit positive charge
eBA=UAB
5.Capital and small letter for variables
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Capital for constant variables --U, I
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Small for changeable variables --u, i
Reference direction
Associated reference directions / Non-associated reference directions
Power
Resistors
Resistance : The opposition of a body or substance to current passing through it, resulting in a change of electrical energy into heat or another form of energy
Resistor : A device used to control current in an electric circuit by providing resistance
Conductance : G=1/R i=Gu Unit : S(Siemens)
Resistors always absorb power, regardless of the reference direction.
Independent sources
Ideal independent voltage source :
a. The voltage of $u_s$ is independent of other elements.
b. The current of $u_s$ is determined by outer circuits.
How about short?
Ideal independent current source:
a. The current of $i_s$ is independent of other elements.
b. The voltage of $i_s$ is determined by outer circuits.
How about open?
Port
Two terminals constitute a port if they satisfy the following condition:
The current flowing into one terminal equals to the flowing out of the other.
Two-terminal element are one-port.
Passive sign convention / associated reference direction
Active sign convention / non-associated reference direction
Dependent / controlled elements
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Controlled resistors An example of controlled resistor: switch Another example of controlled resistor : MOSFET
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Dependent sources
(1) Voltage: They have the properties of voltage sources whose voltages are controlled by other voltages or currents in the circuit
(a) Linear Current Controlled Voltage Source (CCVS)
(b) Linear Voltage Controlled Voltage Source (VCVS)
(2)Current~~
VCCS/CCCS
Kirchhoff’s Laws
- Terms
(1) A branch is constituted by the end to end connection of several elements without any divarication.
(2) A node is the connecting point of 3 or more branches.
(3) A path is the branch(es) between two nodes.
(4) A loop is the close path constituted by branches
(5) A mesh is the loop which has no intersections with other branches in the planar circuits.
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Kirchhoff’s Current Laws (KCL) The algebra sum of the currents flowing out of any node is ZERO. The algebra sum of the currents flowing into any node is ZERO.
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KVL The algebra sum of the voltage drop through any loop is ZERO
Generalized KVL : The voltage between any two points in the circuit equals to the algebra sum of the voltages through any path between these two points.
2b method
b branch
2b equation
b current
b voltage
we can list b independent element constraints,
n-1 independent KCLs
b-n+1 independent KVLs
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Serial Connection : the connections without bifurcation
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Parallel Connection : the connections with common nodes
Balanced Bridge
Any resistor between the equipotential points has no effect on branch variables.
