Basic Concepts of Circuit Analysis-電路學筆記

Shih Jiun Lin Lv4
  2023-01-21 16:00 2023-01-21 16:00 Created   2023-02-04 17:23:34 2023-02-04 17:23:34 Updated      886 Words  5 Mins  

一定愛配陳晏笙教授的開放課程食用: 課程連結

Basic Concepts of Circuit Analysis

Presumptuions in Circuit Analysis

No Time Delay

  • Time delay leads to transmission line theory (Wiki ).

No Radiation

  • Radiation loss = Energy loss.

  • KVL and KCl are based on Energy Convervation.

Linerity

  • All components exhibit a linear relationship between the current input and the voltage output. =>

Circuit Variables

Current

  • Definition: the rate of charge flow.
  • Current is the motion of charge that creates electric fluid.
  • current has sign, indicates the direction of current flow.
    • : the current in amperes.
    • : the charge in coulombs.
    • : the time in seconds.
    • SI unit: ampere (A).

Voltage

  • Definition: the energy per unit charge created by charge separation.
    • : the voltage in volts.
    • : the energy in joules.
    • : the charge in coulombs.
    • SI unit: volt (V).
  • Voltage is the electrical potential difference between two points.
  • Voltage has polarity, which implies voltage drop and raise.

Power

    • : the power in watts.
    • : the voltage in volts.
    • : the current in amperes.
  • Passive Sign Convention
    • The electric fluid flowing out of the circuit into an electrical component as positive, and flowing into the circuit out of a component as negative.

Energy

  • A duration of time:
    • : the function of power in watts.
    • : the energy in joules.
    • : the time in seconds.
  • A single moment:
    • : the function of power in watts.
    • : the energy in joules.
    • : the time in seconds.

Ex:

Circuit Components: Active Components

Describing a Component

  • Defined by the terminal voltage and current.
  • If two components have the same relationship between terminal voltage and current => they are identical in circuit analysis.
  • Component = Element = Branch

Ideal Basic Circuit Component

  • Definition:

    • Only two terminals.
    • Can be described mathematically in terms of current and voltage.
    • Cannot be subdivided into other elements.

  • We only focus on this part:

Active Components

  • Ideal Independent Voltage Source

    • It maintains a prescribed voltage regardless of the current.
    • The current is the function of the circuit.

  • Ideal Independent Current Source

    • It maintains a prescribed current regardless of the voltage.
    • The voltage is the function of the circuit.

  • Ideal Dependent Voltage Source

    • Voltage-controlled Voltage Source

      • : controlling parameter.
      • is known => we can calculate the value of source voltage and current.

    • Current-controlled Voltage Source

      • : controlling parameter.
      • is known => we can calculate the value of source voltage and current.

  • Ideal Dependent Current Source

    • Voltage-controlled Current Source

      • : controlling parameter.
      • is known => we can calculate the value of source voltage and current.

    • Current-controlled Current Source

      • : controlling parameter.
      • is known => we can calculate the value of source voltage and current.

DC vs. AC

  • Direct Current(DC)
    • The direction of the electric flow does not alter with respect to time.
  • Alternating Current(AC)
    • The direction of the electric flow alters with respect to time.

  • Time-variant and Time-invariant
    • DC can be time-variant or time-invariant.
    • AC is always time-variant.

Circuit Components: Passive Components

Passive Components

  • Resistor

    • Definition of Resistence
      • A measure of the opposition current flow in a circuit.
    • Definition of Resistor
      • The circuit components used to model this behavior.
    • (Resistance), Unit: Ohm()
    • (電導), Unit: Siemens()
      1. : Resistivity().
      2. : Conductivity().

  • Capacitor

    • Definition of Capacitance
      • The ability of a system to store an electric charge.
    • Definition of Capacitor
      • The electrical component consists of two conductors seperated by an insulator.
    • (Capacitance), Unit: Farad()
      1. : permitivity(電容率)().
      2. : The area of the conductors.
      3. : The length between two conductors.
    • (Improper Integral)

  • Inductor

    • Definition of Inductance
      • The tendency of an electrical conductor to oppose a change in the electric current flowing through it.
    • Definition of Inductor
      • The electrical component composed of a coil of wire wound around a supporting core.
    • (Inductance), Unit: Henry()
      • : Permeability(導礠率)()
      • : How many coils.
      • : The area of the inductor.
      • : The length of the inductor.
    • (Magnetic Flux)
      • : How many coils.
      • : Magnetic flux.
    • Definition of Inductance
    • , 感應電壓
    • (Improper Integral)

How to Solve a Circuit?

Three Laws in Circuit Analysis

Node, Branch, Loop and Mesh

  • Node: A point where two or more components contact.
  • Branch: component.
  • Loop: A closed path in a circuit without passing through any intermediate node more than once.
  • Mesh: A loop that does not enclosed any other loops.

KCL (Kirchhoff's Current Law)

  • The sum of the current leaving any node in a circuit equals to 0. ()

  • KCL is based on the conservation of charge.

    • => =

  • Ex:

KVL (Kirchhoff's Voltage Law)

  • The sum of the voltagedrops equals to 0. ()

  • KVL is based on the conservation of energy.

    • => =
      • D: Dropping.
      • R:Ｒising.

  • Ex:

Basic Approach to Solve a Circuit(2B法)

Simple Resistive Circuit

Equivalent Resistance for Series Connection

  • Can be proved with KVl, KCL and Component Model.

Equivalent Resistance for Parallel Connection

  • Can be proved with KVl, KCL and Component Model.

Voltage Divider Circuit

  • Can be proved with KVl, KCL and Component Model.

Generalized Voltage Divider

Current Divider Circuit

  • Can be proved with KVl, KCL and Component Model.

Generalized Current Divider

Example of Voltage Divider and Current Divider

Circuit or Circuits?

  • can be transformed into without distrubing the equivalence of the two configuration.

Circuits or Circuits?

  • can be transformed into without distrubing the equivalence of the two configuration.

-Y Equivalent Circuits

  • By changing the topology of the circuit, the analysis procedure can be simplified.

  • transformation

    • If ,

  • transformation


    • If ,

  • Proof of equivalence

  • Example of transformation

  • Example of transformation

  • Title: Basic Concepts of Circuit Analysis-電路學筆記
  • Author: Shih Jiun Lin
  • Created at : 2023-01-21 16:00:00
  • Updated at : 2023-02-04 17:23:34
  • Link: https://shih-jiun-lin.github.io/2023/01/21/Basic Concepts of Circuit Analysis/
  • License: This work is licensed under CC BY-NC-SA 4.0.
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Basic Concepts of Circuit Analysis-電路學筆記
  1. Basic Concepts of Circuit Analysis
    1. Presumptuions in Circuit Analysis
      1. No Time Delay
      2. No Radiation
      3. Linerity
    2. Circuit Variables
      1. Current
      2. Voltage
      3. Power
      4. Energy
      5. Ex:
    3. Circuit Components: Active Components
      1. Describing a Component
      2. Ideal Basic Circuit Component
      3. Active Components
      4. DC vs. AC
    4. Circuit Components: Passive Components
      1. Passive Components
    5. How to Solve a Circuit?
      1. Three Laws in Circuit Analysis
      2. Node, Branch, Loop and Mesh
      3. KCL (Kirchhoff's Current Law)
      4. KVL (Kirchhoff's Voltage Law)
      5. Basic Approach to Solve a Circuit(2B法)
    6. Simple Resistive Circuit
      1. Equivalent Resistance for Series Connection
      2. Equivalent Resistance for Parallel Connection
      3. Voltage Divider Circuit
      4. Generalized Voltage Divider
      5. Current Divider Circuit
      6. Generalized Current Divider
      7. Example of Voltage Divider and Current Divider
      8. Circuit or Circuits?
      9. Circuits or Circuits?
      10. -Y Equivalent Circuits