Circuit design considerations

This is the essence of learning and comparison summarized by a technical engineer. I share it here with you who want to understand circuit design. It can be helpful to you at work or study~

1.Voltage and current

The reference direction of the current can be specified arbitrarily. During analysis: if the reference direction is consistent with the actual direction, then i>0, otherwise i<0. The reference direction of the voltage can also be specified arbitrarily. During analysis: if the reference direction is consistent with the actual direction, then u>0 and vice versa u<0.

2. Power balance In a practical circuit, the power emitted by the power supply is always equal to the power consumed by the load.

3. Ohm’s law for the whole circuit: U=E-RI

4. The meaning of load size: The greater the current of the circuit, the greater the load. The greater the resistance of the circuit, the smaller the load.

5. Circuit break and short circuit, circuit break: I=0, U≠0 and circuit short circuit: U=0, I≠0.

Kirchhoff's Law:

1. Several concepts: Branch: It is a branch of the circuit. Node: The connection point of three (or more than three) branches is called a node. Loop: A closed path consisting of branches is called a loop. Mesh: A loop that has no other branches passing through it is called a mesh.

2. Kirchhoff’s current law:

(1) Definition: At any time, the algebraic sum of the current flowing into a node is zero. In other words: the current flowing in is equal to the current flowing out.

(2) Expression: i-in sum = 0 or: i-in = i-out

(3) can be extended to a closed surface. 3. Kirchhoff’s Voltage Law (1) Definition: Through any closed path, the voltage rise is equal to the voltage drop. In other words: in a closed loop, the algebraic sum of voltages is zero. In other words: In a closed loop, the sum of the voltage drops across the resistors is equal to the sum of the electromotive force of the power supply.

The concept of potential

(1) Definition: The potential at a certain point is equal to the voltage from that point to the reference point of the circuit.

(2) The potential of the reference point is specified to be zero. called grounding.

(3) Voltage is represented by the symbol U, and potential is represented by the symbol V

(4) The voltage between two points is equal to the difference in potential between the two points.

(5) Pay attention to the simplified drawing of the power supply.

Ideal voltage source and ideal current source

1.Ideal voltage source

(1) Regardless of the size of the load resistance and the size of the output current, the output voltage of the ideal voltage source remains unchanged. The output power of an ideal voltage source can reach infinity. (2) An ideal voltage source does not allow short circuits.

2.Ideal current source

(1) Regardless of the size of the load resistance and the size of the output voltage, the output current of the ideal current source remains unchanged. The output power of an ideal current source can reach infinity. (2) An ideal current source is not allowed to open circuit.

3. Series and parallel connection of ideal voltage source and ideal current source

(1) When an ideal voltage source and an ideal current source are connected in series, the current in the circuit is equal to the current of the current source, and the current source works. (2) When an ideal voltage source and an ideal current source are connected in parallel, the voltage across the power supply is equal to the voltage of the voltage source, and the voltage source works.

4. Series and parallel connection of ideal power supply and resistor

(1) An ideal voltage source is connected in parallel with a resistor, and the resistor can be removed (disconnected) without affecting the analysis of other circuits. (2) The ideal current source is connected in series with the resistor, and the resistor can be removed (short-circuited) without affecting the analysis of other circuits.

5. The actual voltage source can be represented by the series connection of an ideal voltage source and an internal resistance.

branch current method

1. Significance: A method of solving equations using the branch current as the unknown quantity.

2. Method of formulating equations:

(1) There are b branches in the circuit, and a total of b equations need to be listed. (2) If there are n nodes in the circuit, first use Kirchhoff's current law to list n-1 current equations. (3) Then select b-(n-1) independent loops and use Kirchhoff’s voltage law to formulate the voltage equation of the loop.

3. Note: If a branch in the circuit contains a current source, the current of the branch is known, and one less equation can be listed (one less circuit voltage equation).

superposition principle

1. Significance: In a linear circuit, the voltage and current everywhere are the result of the superposition of the separate effects of multiple power supplies. 2. Solution method: When considering a certain power supply acting alone, other power supplies should be removed, other voltage sources should be short-circuited, and current sources should be disconnected. 3. Attention: During the final superposition, the direction of the current generated by each power source independently and the total current should be considered. The superposition principle is only suitable for linear circuits, not nonlinear circuits; it is only suitable for the calculation of voltage and current, not suitable for the calculation of power.

Thevenin's theorem

1. Meaning: A complex two-terminal network containing a source is equivalent to a resistor and a voltage source.

2. How to find the equivalent power supply voltage: Disconnect the load resistor and find the open circuit voltage UOC of the circuit. The equivalent supply voltage UeS is equal to the open circuit voltage UOC of the two-terminal network.

3. How to find the equivalent internal resistance of the power supply:

(1) Disconnect the load resistor and remove the power supply in the two-terminal network (the voltage source is short-circuited and the current source is open-circuited). The resistance seen from both ends of the load is the internal resistance R0 of the equivalent power supply. (2) Disconnect the load resistor and find the open circuit voltage UOC of the circuit. Then, short-circuit the load resistor and find the short-circuit current ISC of the circuit. Then the internal resistance of the equivalent power supply is equal to UOC/ISC.

Norton's theorem

1. Significance: A complex two-terminal network containing a source is equivalent to a parallel circuit of a resistor and a current source. 2. How to find the equivalent current source current IeS: short-circuit the load resistor and find the short-circuit current ISC of the circuit. Then the current IeS of the equivalent current source is equal to the short-circuit current ISC of the circuit. 3. How to find the internal resistance of the equivalent power supply: The same as the method of finding the internal resistance in Thevenin’s theorem.

Route changing rules:

1. The principle of switching circuits is: When switching circuits: the voltage across the capacitor remains unchanged, Uc(o+) =Uc(o-). The current in the inductor remains constant, Ic(o+) = Ic(o-). The reason is: the energy storage of the capacitor is related to the voltage across the capacitor, and the energy storage of the inductor is related to the current passing through it.

2. When changing circuits, handle the inductor and capacitor

(1) Before changing the circuit, when the capacitor has no energy storage, Uc(o+)=0. After changing the circuit, Uc(o-)=0, the voltage across the capacitor is equal to zero, and the capacitor can be regarded as a short circuit.

(2) Before changing the circuit, when the capacitor has stored energy, Uc(o+)=U. After changing the circuit, Uc(o-)=U, the voltage across the capacitor remains unchanged, and the capacitor can be regarded as a voltage source.

(3) Before switching, when the inductor has no energy storage, IL(o-)=0. After changing the circuit, IL(o+)=0, the current passing through the inductor is zero, and the inductor can be regarded as an open circuit.

(4) Before switching, when the inductor has energy stored, IL(o-)=I. After changing the circuit, IL(o+)=I, the current on the inductor remains unchanged, and the inductor can be regarded as a current source. Based on the above principles, the initial values ​​of voltage and current everywhere in the circuit can be calculated after circuit change.

Basic concepts of sinusoidal quantities

1. The three elements of sinusoidal quantity (1) represent the size of the quantity: effective value, maximum value

Quantities that represent the speed of change: period T, frequency f, angular frequency ω. Quantities representing the initial state: phase, initial phase, phase difference.

Basic knowledge of complex numbers:

1. Complex numbers can be used to represent directed line segments. The module of the complex number A is r and the argument is Ψ.

2. Three ways of expressing complex numbers: 1. Algebraic expression 2. Trigonometric expression 3. Exponential expression 4. Polar coordinate expression

3. Addition and subtraction of complex numbers are performed using algebraic expressions. Multiplication and division of complex numbers are performed using exponential or polar coordinates.

4. The meaning of the imaginary unit j of a complex number: any vector rotates forward (counterclockwise) after multiplying by +j, and rotates backward (clockwise) after multiplying by -j.

Phasor representation of sinusoidal quantities:

1. The meaning of phasor: Use the module of a complex number to represent the magnitude of the sinusoidal quantity, and use the argument of a complex number to represent the initial phase of the sinusoidal quantity. A phasor is a complex number used to represent a sinusoidal quantity. To distinguish it from ordinary complex numbers, a small dot is added to the symbol of the phasor.

2. Maximum phasor: Use the modulus of a complex number to represent the maximum value of a sinusoidal quantity.

3. Effective value phasor: Use the modulus of a complex number to represent the effective value of a sinusoidal quantity.

4. Pay attention to the problem: the sine quantity has three elements, while the complex number has only two elements, so the phasor only shows the size and initial phase of the sine quantity, but does not show the cycle or frequency of the alternating current. Phasors are not equal to sinusoids.

5. Use phasors to express the meaning of sinusoidal quantities:

After using phasors to represent sine, the addition, subtraction, multiplication, division, integration and differential operations of sine quantities can be transformed into algebraic operations of complex numbers.

6. The addition and subtraction of phasors can also be implemented using the graphic method. The method is the same as the parallelogram method and triangle method of complex number operations.

AC circuit with resistive elements

1. The relationship between the instantaneous values ​​of voltage and current: u=Ri, u and i are in the same phase.

2. Ohm's law in the form of maximum value (the relationship between the maximum value of voltage and current)

3. Ohm’s law in the form of effective value (relationship between voltage and current effective value)

4. Ohm's law in the form of phasor (relationship between voltage phasor and current phasor) phase and phase are in phase.

AC circuit with inductive components

1. The relationship between the instantaneous values ​​of voltage and current: u and i are in different phases, u leads i

2. Ohm's law in the form of maximum value (the relationship between the maximum value of voltage and current)

3. Ohm’s law in the form of effective value (relationship between voltage and current effective value)

4. Inductive reactance of inductor: unit: ohm

5. Ohm's law in the form of phasor (the relationship between voltage phasor and current phasor) is obtained from equation 1 and equation 2: the phase leads the phase of the phase.

6. Reactive power: used to represent the amount of energy exchange between the power supply and the inductor Q=UI=XL. The unit is: Var.

AC circuit with capacitive element

1. The relationship between the instantaneous values ​​of voltage and current u and i are in different phases, u lags behind i.

2. Ohm's law in the form of maximum value (the relationship between the maximum value of voltage and current)

3. Ohm’s law in the form of effective value (relationship between voltage and current effective value)

4. Capacitive reactance of capacitor: unit: ohm

5. Ohm's law in phasor form (relationship between voltage phasor and current phasor) The phase lags behind the phase of the phase.

6. Reactive power: used to indicate the amount of energy exchange between the power supply and the capacitor. In order to distinguish it from the reactive power of the inductor, the reactive power of the capacitor is specified as negative. Q=-UI=-XC The unit is: Var

1. Series circuit of impedance:

(1) The currents on each impedance are equal: (2) The total voltage is equal to the sum of the voltages on each impedance: (3) The total impedance is equal to the sum of each impedance: (4) Voltage division formula: When multiple impedances are connected in series, there is Similar properties to two impedances in series.

2. The parallel circuit of impedance is as shown in the figure:

(1) The voltage on each impedance is equal: (2) The total current is equal to the sum of the currents on each impedance: (3) Shunt formula: When multiple impedances are connected in parallel, they have similar properties to two impedances in parallel.

3. Calculation of complex AC circuits

In electrical engineering, the calculation of complex AC circuits is generally not discussed. For complex AC circuits, the calculation methods learned in DC circuits can still be used, such as: branch current method, node voltage method, superposition principle, Thevenin's theorem, etc.

AC circuit power

1. Instantaneous power: p=ui=UmIm sin(ωt+φ) sinωt=UIcosφ-UIcos(2ωt+φ)

2. Average power: P= = =UIcosφThe average power is also called active power, where cosφ is called the power factor. The active power in the circuit is the power consumed by the resistor.

3. Reactive power: Q=ULI-UCI= I2(XL-XC)=UIsinφ The reactive power in the circuit is the power exchanged back and forth between the inductor, capacitor and power supply.

4. Apparent power: S=UI The unit of apparent power is volt-ampere (VA), which is often used to express the capacity of power supply equipment such as generators and transformers.

5. Power triangle: P, Q, S form a triangle, where φ is the impedance angle.

circuit power factor

1. The meaning of power factor can be seen from the power triangle, power factor. Power factor is the ratio of the circuit's active power to the total apparent power. A high power factor means that the proportion of active power in the circuit is large and the proportion of reactive power is small.

2. Reasons for low power factor:

(1) Inductive load asynchronous motors are widely used in production and life. Washing machines, electric fans, and fluorescent lamps are all inductive loads. (2) The motor operates with light load or no load (large horse-drawn cart)

When the asynchronous motor is no-load, cosφ=0.2~0.3, and when the rated load is used, cosφ=0.7~0.9.

3. The significance of improving power factor:

(1) Improve the utilization rate of power generation equipment and transformers

Power supply equipment such as generators and transformers have a certain capacity, called apparent power. Improving the power factor of the circuit can reduce reactive power output, increase active power output, and increase equipment utilization.

(2) Reduce line losses

When the power transmitted by the line is constant and the transmission voltage of the line is constant, increasing the power factor of the circuit can reduce the current of the line, thereby reducing the power loss on the line, reducing the voltage drop on the line, improving the quality of power supply, and also using a larger Thin wires save construction costs.

(3) Parallel capacitor method: connecting capacitors in parallel at both ends of the inductive load can compensate for the reactive power consumed by the inductor and improve the power factor of the circuit.

Summary: Learning these essential notes is very helpful for beginners, and you can lay a solid foundation step by step. I believe that everyone will have a certain appreciation after reading it.