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# Arrangement of circuit analysis notes (analog electronic circuit)

2022-05-15 07:48:00【Cold foam】

## 1. introduction （ Understanding level ）

At this stage, the object of circuit analysis is the DC steady-state circuit with only power supply and resistance ： The circuit has been working long enough , So that the voltage and current at each point in the circuit can remain unchanged . For DC , The capacitance is equivalent to an open circuit , Inductance is equivalent to short circuit , Therefore, both of them do not need to be considered in the Tianlu analysis for the time being .

## 2. Equivalent transformation of circuit （ Understanding level ）

① Any circuit can be regarded as having two ports to input and output the same amount of current respectively , Call such a model a two terminal circuit .

② If the port current voltage relationship between the two ends of the circuit （VCR） identical , The two circuits are called equivalent , The equivalent transformation can simplify the circuit and facilitate calculation .

## 3. Series and parallel connection of resistors （ Application level ）

① Series connection ： The current is the same , Voltage addition , Resistance addition , Power addition .

② parallel connection ： The current is added , Same voltage , Conductance addition , Power addition .

③ In series and parallel ： That is, the resistance in the circuit exists in series and parallel at the same time , This is also the focus of this chapter .

## 4. Series parallel connection of ideal voltage source and current source （ Understanding level ）

① Ideal voltage source ： The series voltage is equal to the sum of the respective voltages ; Only the same voltage source can be connected in series , The series voltage remains unchanged, but the output power becomes larger , The current through the voltage source is uncertain .

② Ideal current source ： The parallel current is equal to the sum of the respective currents ; Only the same current source can be connected in parallel , The parallel current remains unchanged, but the output power becomes larger , The voltage at both ends of each current source is uncertain .

## 5. Two models of actual power supply and their equivalent conversion （ Key points and difficulties ）

① The actual voltage source can be regarded as an ideal voltage source connected in series with internal resistance . The internal resistance of the actual voltage source is small , Short circuit is not allowed to prevent excessive current from burning the power supply .

② The actual current source can be regarded as an ideal current source in parallel with the internal resistance . The internal resistance of the actual current source is large , Open circuit is not allowed to avoid excessive voltage burning the power supply .

③ The actual voltage source and the actual current source can be converted equivalently . The magnitude of internal resistance during the conversion process remains unchanged , The current of the equivalent current source or the voltage of the equivalent voltage source can be obtained by calculation . The ideal voltage source and the ideal current source cannot be converted to each other , The actual independent power supply and controlled power supply can be equivalent converted .

There are also analysis methods without simplification in circuit analysis , Including branch current method 、 Mesh current method 、 Loop current method and node voltage method , These general analysis methods are more general and universal .

## 1.KCL And KVL Independent equation

For having n The circuit of nodes has n-1 Independent KCL equation ; For having m A mesh circuit has m Independent KVL equation ; For having b A branch circuit , independent KCL Equations and KVL The equation has a total of n individual , These equations together constitute the whole circuit equation .

## 2. Branch current method

① Specific steps ： There is n A node and m In a mesh circuit , choice n-1 List... Nodes KCL Equation combination m A mesh to write m individual KVL equation . If the circuit contains a controlled source , First list the equations as independent sources, and then look for supplementary equations （ There are several branches, and finally several equations are needed to solve ）.

② Method features ： The logic of this method is simple , Clear and intuitive , But there are many equations , It is suitable for use when there are few branches in the circuit .

## 3. Mesh current method （ Personally, I feel that it is easier to make mistakes than the branch current method ）

① The basic idea ： Suppose that each mesh in the circuit has a loop current , In this way, the current of each branch can be expressed by the linear combination of mesh current . This method is only applicable to planar circuits .

② The specific methods ： Take the current of each mesh as the unknown quantity , List... For each mesh KVL The equations are solved after solving the equations . In a circuit without a controlled source, the coefficient matrix of the equation is a symmetric matrix .

③ Self resistance and mutual resistance ： The sum of all the resistances in each mesh is called self resistance , The resistance shared by multiple meshes is called mutual resistance , When the current direction in all meshes is the same （ Both are clockwise or counterclockwise ）, All mutual resistances are negative .

## 4. Loop current method

① The basic principle ： The basic principle of loop current method is similar to mesh current method , It can be regarded as a generalization of the mesh current method . This method still needs to select the circuit with the same number of meshes in the circuit , However, the selected circuit is no longer limited to mesh, but can be selected arbitrarily . This method can not only be used in planar circuits , The same applies to non planar circuits .

② Method features ： Selecting different circuits will have different amount of calculation , And it is more difficult to identify the mutual resistance in this method , It is easy to be missed .

③ matters needing attention ： If there is a controlled source in the circuit , The equations are still listed in the same way , Then find the supplementary equation according to the problem conditions and solve it .

## 5. Node voltage method ：

① The node voltage method is a method of formulating equations with the node voltage as an unknown quantity , It is applicable to the case with few nodes .

② The self conductance of a node refers to the sum of conductance of all branches connected by the node ; The mutual conductance of nodes refers to the conductance of the branch between two nodes , Mutual conductance must be negative .

③ The basic steps of node voltage method ： selected n-1 Nodes , List the basic equations and solve them （ On the left is the linear combination of conductance and node voltage product , On the right is the current flowing into the node from the power supply , If there is no controlled source in the circuit, the coefficient matrix is symmetrical ）. If there is an unaccompanied voltage source branch in the circuit, it is necessary to introduce a new variable and list a supplementary equation . Be careful ： The resistance connected in series with the current source does not need to consider conductivity .

④ Milman's theorem ： If there are only two nodes in the circuit and all branches are connected between the two nodes , Then the node voltage method can be simplified to calculate the voltage value of another node ：U= The sum of the current flowing into the node / Sum of conductance of each branch .

## 6. Superposition theorem

① Definition ： The current or voltage of any branch in the circuit can be regarded as the algebraic sum of the current or voltage generated in the branch when each independent power supply in the circuit acts alone . This theorem can simplify the analysis of multi power supply circuits .

② matters needing attention ： The theorem is only applicable to linear circuits ; A zero voltage source is equivalent to a short circuit , A zero current source is equivalent to an open circuit ; Power cannot be superimposed ; If there is a controlled source in the circuit, the controlled source must be retained at all times .

③ The specific stacking method is arbitrary , How to make the calculation simple is how to stack . One independent source at a time can act alone , Multiple independent sources can also act at the same time .

④ Homogeneity principle ： In linear circuits , All independent sources increase or decrease by a multiple , Then its response （ Voltage and current ） Also increase or decrease the same multiple .

## 7. Substitution theorem

① Definition ： If the port voltage and current of a two terminal circuit are known , Then the two terminal circuit can be replaced by a voltage source with the same voltage or a current source with the same current, or a resistance with a resistance value equal to the ratio of port voltage to current , The rest of the total circuit remains unchanged . The substitution theorem can be used in both linear and nonlinear circuits .

② Difference from equivalent circuit ： The substitution theorem requires that the current and voltage of the two ports of the two terminal circuit are known , The equivalent circuit can meet this requirement , That is, the use threshold is lower .

## 8. Equivalent power theorem

① Davining's theorem ： For any active two terminal linear circuit , For the external circuit, it can be equivalent to the series form of an ideal voltage source and internal resistance , The voltage of the ideal voltage source is the open circuit voltage of the two terminal circuit , The equivalent internal resistance is the resistance between the two ports after setting all independent power supplies in the two terminal network to zero .

② Norton's theorem ： For any active two terminal linear circuit , For the external circuit, it can be equivalent to an ideal current source in parallel with the internal resistance , The current of the ideal current source is equal to the short-circuit current , Equivalent internal resistance is the resistance between two ports after all independent current sources in the two terminal network are set to zero .

③ Solution method of equivalent internal resistance ： For the circuit without controlled source in the network, the equivalent resistance can be obtained directly from the connection law of resistance , However, when there is a controlled power supply in the two terminal network, another three methods need to be used . Open circuit short circuit method ： First, calculate the open circuit voltage of the two terminal circuit , Then the short-circuit current is calculated , The equivalent internal resistance can be obtained by dividing the short-circuit current by the open circuit voltage ; Additional incentive method ： For controlled voltage sources , External excitation current source , The relationship between the applied current source and the excitation is obtained , For controlled current sources , External excitation voltage source , The relationship between the applied voltage source and the excitation is obtained ; In addition, the measurement method is often used to calculate the equivalent resistance in the laboratory .

④ If the equivalent resistance of a one port network is zero , Then there is only Thevenin equivalent circuit ; If the equivalent resistance of a one port network is infinite , Then only Norton equivalent circuit .

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