MindMap Gallery Circuits and their analysis methods
This is a mind map about circuits and their analysis methods. It summarizes the functions and components of circuits, circuit models, reference directions of voltage and current, reference directions of voltage and current, etc.
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Circuits and their analysis methods
The functions and components of a circuit
The function of circuit
Realize the transmission, distribution and conversion of electric energy
Implement signal transmission and processing
components of a circuit
Power supply: A device that provides electrical energy
Intermediate link: the role of transmitting, distributing and controlling electrical energy
Load: a device that consumes electrical energy
circuit model
In order to facilitate the analysis and calculation of actual circuits, under certain conditions, the secondary factors of the actual component are often ignored and its main electromagnetic properties are highlighted, treating it as an ideal circuit component.
A circuit composed of ideal circuit components is called a circuit model of an actual circuit
Reference directions for voltage and current
reference direction
When analyzing and calculating circuits, any direction of charge is assumed.
How to express the reference direction
Relationship between actual direction and reference direction
The actual direction is consistent with the reference direction, and the current (or voltage) value is positive; The actual direction is opposite to the reference direction, and the current (or voltage) value is negative.
Power supply on-load operation, open circuit and short circuit
Power supply working on load
voltage and current
Power and power balance
Distinguish between power supply and load
Determine based on the actual direction of U and I
Power supply: The actual directions of U and I are opposite, that is, the current flows out from the " " terminal (power is emitted)
Load: U and I have the same actual direction, that is, the current flows out from the "-" terminal (absorbs power)
Determine based on the reference directions of U and I
The reference directions of U and I are different, P = UI > 0, power supply; P = UI < 0, load.
Rated value and actual value
Rating: The specified usage value of electrical equipment during normal operation
Ratings reflect the safety of use of electrical equipment
Ratings indicate the ability of electrical equipment to be used
Three operating states of electrical equipment
Rated working status: I = IN, P = PN (economical, reasonable, safe and reliable)
Overload (overload): I > IN, P > PN (the equipment is easily damaged)
Underload (light load): I < IN, P < PN (uneconomical)
Power supply open circuit
feature
I = 0
U = U0 = E power supply terminal voltage (open circuit voltage)
P = 0 load power
Characteristics of a break somewhere in the circuit
The current in the open circuit is zero; I = 0
The voltage U at the open circuit depends on the circuit conditions
Power short circuit
feature
I=IS=E/R short circuit current (very large)
U = 0 power supply terminal voltage
P = 0 load power
PE = Delta P = I²R0 All the energy generated by the power supply is consumed by the internal resistance
Characteristics of a break somewhere in the circuit
The voltage at the short circuit is equal to zero; U = 0
The current I at the short circuit depends on the circuit conditions
Kirchhoff's Law
Kirchhoff's Current Law (KCL)
i = 0 (for arbitrary waveform current) I = 0 (in DC circuit)
The current law can be generalized to any hypothetical closed surface enclosing part of a circuit. The algebraic sum of the currents passing through any closed surface at any instant is also equal to zero.
Kirchhoff's Voltage Law (KVL)
At any moment, starting from any point in the loop and traveling along the loop for a week, the sum of the potential rises in this direction is equal to the sum of the potential drops.
At any instant, along any loop direction, the algebraic sum of the voltages at each section of the loop is always equal to zero. That is: U = 0
Transient Analysis of Circuits
Calculation of potential in a circuit
Thevenin's theorem
Two models of power supply and their equivalent transformations
power source
Battery
Equivalent transformation of power supply model
superposition theorem
For linear circuits, the current of any branch can be regarded as the algebraic sum of the currents generated in this branch when each power supply (voltage source or current source) in the circuit acts respectively.
The principle of superposition only applies to linear circuits
The current or voltage of a linear circuit can be calculated by the superposition principle, but the power P cannot be calculated by the superposition principle.
Treatment of non-active power supply: E = 0, which means E is short-circuited; Is= 0, which means Is is open-circuited
When solving the problem, the reference directions of current and voltage of each branch should be marked. If the divided current and divided voltage are opposite to the reference directions of the current and voltage in the original circuit, a negative sign must be placed before the corresponding term when superimposing.
When applying the superposition principle, the power supplies can be grouped to solve the problem, that is, the number of power supplies in each branch circuit can be more than one
branch current method
Problem solving steps
1. Mark the reference direction of each branch current in the figure. For the selected circuit Mark the direction of circuit travel
2. Use KCL to list (n-1) independent node current equations for the nodes.
3. Apply KVL to list b-(n-1) independent return voltage equations for the loop (usually mesh list can be used)
4. Solve b equations simultaneously to find the current of each branch.
Resistors in series and parallel
series connection of resistors
Features
The resistors are connected sequentially one after another
The same current passes through each resistor
The equivalent resistance is equal to the sum of the resistances R =R1 R2
The distribution of voltage across a series resistor is proportional to the resistance; the voltage division formula when two resistors are connected in series: U1=R1/(R1 R2) U2=R2/(R1 R2)
application
Voltage reduction, current limiting, voltage regulation, etc.
Resistors in parallel
Features
Each resistor is connected between two common nodes
The voltage across each resistor is the same
The reciprocal of the equivalent resistance is equal to the sum of the reciprocals of each resistance
The distribution of current across a parallel resistor is inversely proportional to the resistance
application
Shunting, regulating current, etc.