Electrician basics, what is the principle of superposition

The principle of superposition of states: A fundamental principle in quantum mechanics.

It means that in a circuit composed of linear components, the voltage and current on one circuit are superimposed on other voltage sources or current sources on this circuit after acting alone.

Use the superposition theorem.

The following points should be noted:

1) The superposition theorem is only applicable to linear circuits, not to nonlinear circuits.

2) In the superimposed sub-circuits, the voltage source that does not act is set to zero, and the short circuit is replaced at the voltage source; The non-active current source is set to zero, and an open circuit is used at the current source.

In lieu of. 3) All resistors in the circuit are not changed.

4) The reference direction of the voltage and current in each sub-circuit can be taken as the same as that in the original circuit when superimposed. When substituting the number and seeping ridge, pay attention to the "+" sign before each component.

5) The voltage or current of a linear circuit can be calculated by the superposition theorem, but the power p cannot be calculated by the superposition theorem.

6) When applying the superposition theorem, the power supply can be solved in groups, that is, the number of wheel coarse power supplies in each sub-circuit can be more than one.

The superposition theorem is very important in circuit analysis. This theorem applies to independent sources, controlled sources, and passive devices.

resistors, inductors, capacitors) and transformers (time-varying or static).

It should be noted that superposition only applies to voltage and current, not electrical power.

In other words, the sum of the power that each of the other power sources acts on its own is not the power that is actually consumed. To calculate the electrical power, we should first use the superposition theorem to obtain the voltage and current of each linear element, and then calculate the sum of the voltage and current multiplied by the plexus exudation.

1.The superposition principle is an important analysis method of linear circuits, which contains the algebraic sum of the currents (or voltages) generated in each branch of a linear circuit composed of multiple linear resistors and multiple power supplies.

2.Thevenin's theorem: for external circuits, any active two-terminal network can be replaced by a power supply, the electromotive force eo of the power supply is equal to the open-circuit voltage of the two-terminal network collapse, and its internal resistance RO is equal to all power supplies in the active network do not work, only retain its internal resistance, the equivalent resistance (input resistance) at both ends of the network, this is Thevenin's theorem.

3.Norton's theorem: Any active two-terminal network can be replaced by a power supply with an ideal current source for the flow of the electrical strip for IS and a power supply in parallel with the liquid RO of the internal resistor.

Take advantage of the principle of superposition.

The 10V voltage source works separately:

You can send your eyes to the grandson, and the u0 at this time is 5v.

The calculation is as follows: <>

Then, let the dust be over againThe current source operates separately and gives u0 = 4v.

In the end, taken together, u0 is 1v.

The superposition principle only applies to linear circuits.

A linear circuit is a circuit that consists entirely of linear components, independent sources, or linearly controlled sources. There are two physical representations of the component properties of a circuit element. A component is linear if the algebraic relation that characterizes the characterization of the element is linear, and a nonlinear if the algebraic relation that characterizes the element is a nonlinear relation.

Determine linearity and nonlinearity: A nonlinear circuit is a circuit that contains nonlinear components other than a separate power supply. Electricians often use the nonlinearity of certain components.

For example, the non-linear nature of surge arresters is characterized by a reduced resistance value at high voltages, which can be used to protect electrical equipment under lightning.

Characteristics of nonlinear circuits:

Homeostasis is not unique. When the balance key of the DC circuit is disconnected by a knife switch, due to the nonlinearity of the arc, the circuit at this time appears two steady states determined by different starting conditions - one has an arc, so there is a current in the circuit; The other arc goes out, so there is no current in the circuit.

Self-oscillation. In some nonlinear circuits, although the independent power supply is a DC power supply, the steady-state voltage (or current) of the circuit can have a periodic change component, and self-oscillation occurs in the circuit. The self-oscillating circuit of the audio signal generator has a nonlinear element called an amplifier, which can produce periodic oscillations with a waveform close to sinusoidal.

Harmonic wave. When sinusoidal excitation acts on a nonlinear circuit and the circuit has a periodic response, the response waveform is generally non-sinusoidal and contains higher harmonic components or subharmonic components. For example, currents in rectifier circuits often have higher harmonic components.

Jumping phenomenon. In nonlinear circuits, when the parameters (resistance, inductance, amplitude, frequency, etc.) are changed to the bifurcation value, the response will change abruptly, and the phenomenon of jumping will occur. Current jumps occur in ferromagnetic resonant circuits.

Frequency capture. When sinusoidal excitation acts on a self-excited oscillation circuit, if the difference between the excitation frequency and the self-oscillation frequency is small, the response will be synchronized with the excitation. Chaos.

In the 20s of the 20th century, the Dutch bVan der Poel's equation describing the oscillating circuit of an electron tube became a precursor to the study of chaotic phenomena.

Take advantage of the principle of superposition.

Let the 10V voltage source work separately first:The calculation is as follows: <>

It can be concluded that u0 = 5v at this point.

Then, by making the current source work separately, we get u0 = 4v.

In the end, taken together, u0 is 1v.

The above equation is that when 10V acts alone, 8A is set in an open circuit, 6 ohms and (2+4) Euclonium are equivalent to 3 ohms in parallel, the total current = 10 (1+3) =, and the total current is divided equally to 6 ohms and (2+4) ohms, and the terminal voltage of 4 ohms is uO= x 4=5V. The following equation is that when 8A acts alone, 10V is short-circuited to obtain -4V; uo=5-4=1v。

The principle of superposition of electric fields.

If the field source charge is more than one point, the charge is based on the superposition of the charge interaction force, and the field strength of each point in the electric field is the vector sum of the field strength generated by the charge at each point alone, which is the superposition of electric field

Principle of formation. If there are several point charges in space at the same time, then the electric field strength at a point in space is equal to the vector sum of the electric field strength generated at that point if the charges at each point were present alone. A synthetic electric field is formed.

A general approach to superposition.

Superposition follows the law of superposition of vectors – the parallelogram rule. You can also use the vector triangle method, orthogonal decomposition method, etc.

Using the principle of superposition of electric fields, the field strength of any charged body at any point can be calculated theoretically.

For a charged object, when calculating its electric field, it can be divided into a number of small pieces, as long as each small block is small enough, the charge carried by each small piece can be regarded as a point charge, and then the electric field of the whole charged body can be calculated by the method of superposition of the electric field of the point charge, theoretical calculations and experiments can prove that the electric field generated by a uniform charged sphere (or spherical shell) of radius r is the same as the electric field generated by a point charge with an equal charge located in the center of the sphere of the body (or spherical shell), The formula for calculating the electric field strength of each point in the electric field is also e=kq r, where r is the distance from the point to the center of the sphere, r>r, q is the charge carried by the whole sphere.

Superposition meaning. The superposition of electric fields is the difference between electric fields and ordinary matter.

Precautions. The electric fields generated by the individual charges are independent and do not affect each other.

For the electric field strength of the larger charged body that cannot be regarded as a point charge, the charged body can be divided into many small pieces, each of which can be regarded as a point charge, and the electric field superposition of the point charge can be calculated.