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First, the basic knowledge of the circuit
1. Definition: The sum of electrical equipment and components connected in some way to provide a path for current circulation is called a circuit, also known as a network.
Example: The simplest circuit: the circuit of flashlight.
Actual circuit and equivalent circuit diagram.
2, the composition of the circuit
A. power supply: equipment or device that provides electric energy;
B. Load: components or equipment that convert electric energy into other forms of energy;
C. Intermediate links: wires, switches, etc.
3, the role of the circuit
1. Transmission, distribution and use of electric energy; Such as a power supply circuit.
B. transmission and processing of electrical signals. Such as radio, television and satellite communication circuits.
Second, all kinds of circuit types
(1) linear circuit: A circuit consisting of linear passive components, linear controlled sources and independent power sources is called a linear circuit.
(2) Resistance circuit: If all the linear passive components constituting the circuit are linear resistors, the circuit is called linear resistance circuit (referred to as resistance circuit for short).
(3) DC circuit: When the independent power supplies in the circuit are all DC power supplies, this circuit is called a DC circuit. Inductance is equivalent to short circuit in DC circuit, and capacitance is equivalent to open circuit in DC circuit.
Third, equivalent transformation.
(1) Equivalence condition: If the volt-ampere characteristics of two one-port network are exactly the same, then two one-port network are equivalent.
(2) The characteristics of equivalence transformation: external equivalence.
The parallel connection of voltage sources and the series connection of current sources should satisfy Kirchhoff's law.
(3) The method steps of equivalent transformation of two power supply circuit models: (a) Draw the corresponding power supply circuit model and pay attention to the reference direction; (b) determining the resistance value; (c) Determine the power supply voltage and current of the independent power supply in the power supply circuit model according to the formula.
Fourth, the general analysis of resistance circuit
Number of independent equations of KCL and KVL
(Number of independent equations of KCL: For a circuit with n nodes, (n- 1) independent KCL equations can be obtained at any (n- 1) nodes.
(b) The number of b)KVL independent equations: use the concept of "tree" to determine the independent loop group. For a circuit with n nodes and b branches, (b-n+ 1) independent KVL equations can be obtained.
Verb (abbreviation of verb) Thevenin theorem
(1) Thevenin equivalence is a method to simplify the circuit, and Thevenin theorem is suitable for linear circuits.
(2) Thevenin theorem can be expressed as: a port with independent power supply, linear resistor and controlled power source can be equivalently replaced by a series combination of voltage source and resistor. The source voltage of the voltage source is equal to the open circuit voltage of the port, and the resistance is equal to the input resistance of all independent power supplies of the port after clearing.
Six, Norton theorem
(1) Norton equivalence is a method to simplify circuits, and Norton theorem is applicable to linear circuits.
(2) Norton equivalent circuit can be simply obtained from Thevenin equivalent circuit through power equivalent transformation.
(3) Norton's theorem can be expressed as: a port with independent power supply, linear resistance and controlled power source can be equivalently replaced by a parallel combination of current source and conductance. The source current of the current source is equal to the short-circuit current of the port, and the conductance is equal to the input conductance of all independent power supplies at the port after zeroing (for the same port, the input resistance of Thevenin equivalent circuit is the same as that of Norton equivalent circuit).
(4) Maximum power transmission: the port containing the source is externally connected with an adjustable resistor (load). When the load resistance is equal to the input resistance of a port, the resistance will get the maximum power. At this time, it is said that this resistance matches the input resistance of a port.
Seven, superposition theorem
1, superposition theorem: In a linear resistance circuit, any voltage or current is the superposition of the voltage or current generated there when each independent power supply in the circuit acts alone.
(1) superposition theorem is the most important theorem that embodies the essence of linear circuits.
2. Several problems that should be paid attention to when applying superposition theorem.
The research object of (1) superposition theorem is independent power supply. (2) The control quantity of controlled power source is the voltage or current on the controlled power source circuit elements. (3) In each sub-circuit, the inactive independent voltage source should be set to zero, and the independent voltage source should be replaced by short circuit; Zero the invalid independent current source and replace it with an open circuit at the independent current source. (4) The power of the original circuit is not equal to the sum of the powers calculated by each sub-circuit. (5) The superposition theorem is applicable to linear circuits, but not to nonlinear circuits.
8. Time domain analysis of first-order circuit and second-order circuit
A circuit containing dynamic elements is called a dynamic circuit. The characteristic of dynamic circuit is that when the circuit is switched, there will be a transition process. First-order circuits usually contain a dynamic element, which can be described as a first-order differential equation of voltage or current. Second-order circuits usually contain two dynamic components, which can be described by a second-order differential equation of voltage or current.
Zero-state response: refers to the zero-input response of the transient circuit after switching without external power supply, and its response is caused by the initial value of the energy storage element.
Zero-state response: refers to the zero initial value of the energy storage element, and the response of the circuit after switching is caused by the external power supply, which is called the zero-state response of the transient circuit.
Full response: the response after switching is caused by the initial value of the energy storage element and the external power supply, which is called the full response of the transient circuit.
Nine, phasor method
Phasor analysis/phasor method: For sinusoidal circuits containing L and C, the basic description equation should be calculus equation. Although the derivative and integral of sine are still sine, it is still very troublesome to directly operate trigonometric functions. In sinusoidal steady-state circuits, current and voltage are sinusoidal time functions with the same frequency, and our task is only to analyze and determine the effective value (or maximum value) and initial phase of these physical quantities. Phasor contains two elements, namely modulus and angle. We introduce phasor representation and vector diagram of sine, which can be used as a mathematical tool to analyze sine steady-state circuit. This analysis method is called phasor analysis/phasor method.
The essence of phasor method is a mathematical transformation, which transforms the operation in time domain (sine time function) into complex operation in frequency domain.
Ten, three-phase circuit
The symmetrical three-phase voltage source is provided by a three-phase generator (the power frequency of the three-phase system in China is 50Hz, the household voltage is 220V, and the household line is one of the three phases and the ground wire, 60Hz in the United States and Europe, 1 10V, and 50Hz and 60Hz in Japan, 1 10V).
In the actual three-phase circuit, the power supply is symmetrical, and the three-phase load is not necessarily symmetrical.
Eleven, sine phasor representation:
1, the meaning of phasor: the magnitude of sine is expressed by the module of complex number, and the initial phase of sine is expressed by the angle of complex number.
Phasor is a complex number, which is used to represent sine quantity. In order to distinguish it from general complex numbers, a dot is added to the sign of phasor.
2. Maximum phasor: the maximum value of sine is expressed by the modulus of complex number.
3. Effective value phasor: the effective value of sine is expressed by the modulus of complex number.
4. Three elements of sine quantity
(1) Quantity indicates size: valid value, maximum value.
(2) Quantities indicating the speed of change: period t, frequency f and angular frequency ω.
(3) Quantities representing initial state: phase, initial phase and phase difference.
5, pay attention to the problem:
Sinusoidal quantity has three elements, while complex number has only two elements, so phasor only indicates the magnitude and initial phase of sinusoidal quantity, not the period or frequency of alternating current. Phasor is not equal to sine.
6, with phasor said the meaning of sine:
After sine is expressed by phasor, the addition, subtraction, multiplication, division, integration and differential operations of sine can be transformed into algebraic operations of complex numbers.
7. Addition and subtraction of phasor can also be realized by graphic method, which is the same as parallelogram method and triangle method of complex number operation.
XII. Non-sinusoidal periodic current circuit and signal spectrum
The effective value of non-sinusoidal periodic current is equal to the square root of the sum of the square of the constant component and the square of the effective value of each harmonic. This conclusion can be extended to other non-sinusoidal periodic quantities.
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