Summary of knowledge points for electronic information engineering professional course review: (1) Basics of circuit analysis

Be prepared to ask questions in the pre-interview-free professional courses later. It mainly covers some basic conceptual questions in each subject and does not involve calculation problems.

Chapter 1: Basic concepts and circuit laws of circuits

1. Actual circuit and circuit model:

A real circuit refers to a real-world circuit consisting of actual electronic components (such as resistors, capacitors, inductors, etc.). Real circuits have various characteristics and limitations, such as resistors generating heat, capacitors having a certain charge discharge rate, etc.

A circuit model is a simplified description of an actual circuit, usually represented by symbols, equations, or graphics. Circuit models can help analyze and design circuits and predict their behavior and performance. The ideal circuit model assumes that all electronic components are perfect, without any internal resistance, inductance or capacitance, etc. Through the ideal circuit model, some complex circuit characteristics can be ignored and the analysis and calculation of the problem can be simplified.

2. Lumped circuit: The actual circuit meets the conditions of centralization, that is, the geometric size of the circuit is smaller than the wavelength corresponding to the operating frequency, and can be processed as a lumped circuit.

3. Current: The amount of charge passing through the cross-section of a conductor per unit time.
The direction in which the positive charge moves is the actual direction of the current flow.
Current is divided into direct current (the magnitude and direction do not change with time) and alternating current (the magnitude and direction change with time).

4. Voltage: The potential difference from point A to point B in the circuit.
The direction in which the potential decreases is the direction of the voltage

5. Power:
Instantaneous power: the energy consumed by the circuit per unit time.
Absorbed power and generated power: related to the associated reference direction.

6. Linear time-invariant resistance: Linearity means that the resistance value of a resistive element is proportional to the current passing through it . That is, according to Ohm's law, there is a linear relationship between the voltage of a resistive element and the current flowing through it .

Time invariance means that the resistance value of the resistive element does not change with time. No matter how the voltage or current in the circuit changes, the resistance value of the resistive element remains the same.

7. Open circuit and short circuit:

An open circuit prevents current from flowing through the circuit, so the current flowing through the component at the open circuit is zero. An open circuit can be used to disconnect a certain part of a circuit so that it does not participate in the transmission of current and voltage.

A short circuit causes current in the circuit to flow directly from one node to another, so the voltage across the component at the short circuit is zero. A short circuit can be used to connect two nodes in a circuit so that they are at the same potential.

8. A voltage source refers to an electronic device or component that can provide a constant voltage output. Its characteristic is to provide a fixed voltage in the circuit, and the output voltage remains unchanged regardless of how the load in the circuit changes. Common voltage sources include batteries, voltage regulators, etc.

A current source refers to an electronic device or component capable of providing a constant current output. Its characteristic is to provide a fixed current in the circuit. No matter how the load in the circuit changes, the output current remains unchanged. Common current sources include current source circuits, constant current sources, etc.

A controlled source refers to an electronic device or component whose output characteristics are controlled by external input quantities. Its output voltage or current is related to and controlled by the input signal. Common controlled sources include voltage controlled voltage source (VCCS), current controlled current source (CCCS), voltage controlled current source (VCVS) and current controlled voltage source (CCVS).

9. Kirchhoff’s Law

Kirchhoff's Current Law (KCL): At a certain moment, for a circuit node, the algebraic sum of all currents flowing in or out is always zero.

Kirchhoff's Voltage Law (KVL): At a certain moment, the algebraic sum of the voltages of each component on any circuit is always 0.

Chapter 2: Equivalent Transformation of Resistor Circuits

1. Series equivalent of resistors
2. Parallel equivalent
3. Bridge circuit: When R1R4=R2R3 (opposite resistance), a balanced state is reached.
4.Y-shaped equivalent: Connect three resistors together to form a Y-shaped circuit. The current in the Y-shaped circuit is divided through each resistor with the same voltage. The total resistance of a Y-shaped circuit is equal to the reciprocal of the sum of the reciprocals of the individual resistances.
5. Triangular equivalent: Triangular equivalent refers to connecting three resistors together to form a triangular circuit. Current in a delta circuit has only one path through all the resistors, while the voltage is distributed across the individual resistors.

Chapter 3: General analysis methods of resistive circuits

1. KCL and KVL equations
2. Power supply equivalent
Voltage source
in series Current source in parallel Any
component connected in parallel with the voltage source becomes a voltage source Any
component connected in series with the current source becomes a current source
Voltage source series resistance and current source parallel resistance can be equivalent to each other
3. High-order analytical circuit methods
① Branch voltage method: Branch Voltage Method is a method used to solve the voltage of each branch in the circuit, also known as the node voltage method. It is a common technique in circuit analysis and is suitable for solving voltage and current distribution problems in complex circuits.

The basic idea of ​​the branch voltage method is to decompose the circuit into multiple branches, and then apply Kirchhoff's voltage law (KVL) to each branch to establish the branch voltage equation. By solving these equations, the voltage values ​​of each branch in the circuit can be obtained.

That is to say, for example, if there is a public node, for each branch connected to this node, KVL is used to establish equation solving parameters.

The steps of branch voltage method are as follows:

Label the nodes in the circuit: Select one node as the reference node (usually the ground node) and number the other nodes.
Mark branch voltage: Mark a voltage variable for each branch, usually the voltage between the two endpoints of the branch is selected as the voltage of the branch.
Write the branch voltage equation: Apply Kirchhoff's voltage law to each branch and write the branch voltage equation. The form of the equation is that the difference between the branch voltages is equal to the sum of the voltage drops caused by the voltage source and the resistive element.
Form a system of equations: Combine all branch voltage equations into a system of equations, which includes unknown branch voltage variables and known voltage sources.
Solving the system of equations: By solving the system of equations, the voltage values ​​of each branch in the circuit can be obtained.
Calculate current: Based on the known voltage value and resistance value, the current value of each branch can be calculated.
②Loop Current Method
The Loop Current Method is a method used to solve the loop current in the circuit. It is also called the loop analysis method. It is a common technique in circuit analysis and is suitable for solving current and voltage distribution problems in complex circuits.

The basic idea of ​​the loop current method is to establish the loop current equation by assuming that there is a set of loop currents in the circuit, and then applying Kirchhoff's voltage law (KVL) and Ohm's law. By solving these equations, the value of each loop current in the circuit can be obtained.

That is to say, we define the current in each loop ourselves, such as i1, i2, etc., and then use Kirchhoff's law to establish the KCL equation for each loop to solve the relevant parameters.

The steps for the loop current method are as follows:
Label the loops in the circuit: Select one loop as the reference loop and then number the other loops in the circuit.
Assume loop currents: Assume a current variable for each loop that represents the current in each loop in the circuit.
Write the loop current equation: Apply Kirchhoff's voltage law and Ohm's law to each loop and write the loop current equation. The form of the equation is that the sum of the loop voltages is equal to the sum of the voltage drops caused by the voltage source and the resistive element.
Form a system of equations: Combine all loop current equations into a system of equations, which includes unknown loop current variables and known voltage sources.
Solving the system of equations: By solving the system of equations, the values ​​of the currents in each loop in the circuit can be obtained.
Calculate voltage: Based on the known current value and resistance value, the voltage value of each branch can be calculated.

Chapter 4: Circuit Theorem

1. Superposition theorem

Superposition theorem is a basic theorem in circuit analysis and is used to simplify the analysis of complex circuits. It allows us to consider the effects of multiple independent power or signal sources separately, calculate the impact of each source on the current and voltage in the circuit separately, and then add them to get the final result.

The basic idea of ​​the superposition theorem is to apply each independent source in the circuit (commonly a voltage source or current source) to the circuit separately, and set other independent sources to zero or short circuit. The effect of each source on the current and voltage in the circuit is then calculated separately. Finally, these partial results are added together to get the final results for the current and voltage in the circuit.

Apply each independent source in the circuit to the circuit separately, and set other independent sources to zero or short-circuit them. For a voltage source, set it to zero (short circuit), for a current source, set it to zero (open circuit).
Calculate the effect of each source on the current and voltage in the circuit. The calculation can be performed using the branch voltage method or the loop current method.
These partial results are added together to get the final results of the current and voltage in the circuit. For current, just add it directly. For voltage, add them up to get the total voltage.

2. Substitution theorem

Thevenin's Theorem is a circuit analysis method used to simplify complex circuits and find equivalent circuits. It is based on the principle that any linear circuit can be replaced by an equivalent single voltage source and a series resistor.

According to the substitution theorem, the circuit can be decomposed into two parts: the Thevenin equivalent voltage source and the Thevenin equivalent resistance.

The Thevenin equivalent voltage source is the result of measuring the voltage across two endpoints after setting all sources in the circuit (independent voltage sources and current sources) to zero. The polarity of this equivalent voltage source is consistent with the direction of the measured voltage.

Thevenin equivalent resistance is the result obtained by setting all power supplies to zero, disconnecting the external load, and measuring the equivalent resistance between the two endpoints. This equivalent resistance is equal to the equivalent resistance of all resistive elements in the circuit between the two endpoints.

The steps for the substitution theorem are as follows:

Select two endpoints in the circuit you want to simplify, call them point A and point B.
Zero out all power sources (voltage and current sources) in the circuit.
Use an appropriate method (such as the branch voltage method or the loop current method) to calculate the voltage between point A and point B. This will be the voltage of the Thevenin equivalent voltage source.
Disconnect the external load and measure the equivalent resistance between point A and point B. This will be the Thevenin equivalent resistance.
According to Thevenin's theorem, connecting the Thevenin equivalent voltage source and the Thevenin equivalent resistance results in an equivalent circuit that behaves the same as the original circuit between point A and point B.

3. Thevenin’s law

Generally, when the electrical parameters (such as current, voltage) of a specific component (such as resistor, capacitor, inductor, a certain branch) are required, it can be processed using Thevenin's law: Based on the experience of doing the questions: ① Find the
open
circuit Voltage: Disconnect the required component and find the open circuit voltage at the disconnection point.
② Find the equivalent resistance: Find the equivalent resistance of the remaining circuit. This is more difficult. You need to talk about independent sources (voltage source short circuit, current source open circuit) and controlled sources for calculation.
③Use the substitution theorem and regard the original circuit as a series connection of a voltage source and an equivalent resistance, and you can calculate it relatively quickly.

4.Norton’s Law

Norton's law is similar to Thevenin's. The core is the substitution theorem: replace the original circuit with an equivalent current source + an equivalent resistance. Which component's electrical parameters are also required?
① Find the short-circuit current
② Find the equivalent resistance
③ Substitute the law into a simple circuit calculation

5. Maximum power transmission theorem

The Maximum Power Transfer Theorem is an important theorem in circuit theory. It states that in a given circuit, maximum power transfer will be achieved when the external load resistance is equal to the conjugate value of the power supply resistance .

According to the maximum power transfer theorem, in order to achieve maximum power transfer, the external load resistor should match the conjugate value of the power supply resistor. This means that the impedance of the load resistor should be equal to the complex conjugate of the impedance of the supply resistor.

The mathematical expression of the maximum power transfer theorem is as follows: Maximum power transfer will be achieved when the load resistance RL = RS*, where RS* is the complex conjugate value of the power supply resistance RS.

6. Tellegen’s theorem

①The algebraic sum of the power absorbed by each branch in the circuit is always zero.
② For any two centralized parameter circuits with b paths and n nodes, their branch structures are different, but their topological structures are the same.

7. Reciprocity theorem

Three conditions: ①Linear resistor
②An excitation source
③The power supply is set to zero (voltage source short circuit, current source open circuit) topology remains unchanged

8. Duality theorem

Duality Theorem is an important theorem in circuit theory, which describes the dual relationship between voltage and current in a circuit.

According to the duality theorem, for a linear circuit, if the positions of the voltage and current sources are swapped, and the resistance and conductance are swapped, the behavior and characteristics of the circuit will remain the same.

Specifically, the duality theorem can be divided into the following aspects:

Voltage and Current: In a dual circuit, the roles of voltage and current are reversed. A voltage source in the original circuit corresponds to a current source in the dual circuit, and a current source in the original circuit corresponds to a voltage source in the dual circuit.
Resistance and Conductance: In dual circuits, resistance and conductance are interchanged. The resistance in the original circuit corresponds to the conductance in the dual circuit, and the conductance in the original circuit corresponds to the resistance in the dual circuit.
Equivalence: Primitive and dual circuits have the same circuit characteristics and behavior. For example, the properties of the voltage and current relationships, power distribution, etc. in the two circuits are the same

Chapter 7 Energy Storage Components-Capacitors and Inductors

1. Capacitor

A capacitor is a passive electronic component used to store and release electrical charge . It consists of an insulating material (called a dielectric) separated between two metal plates (called electrodes).

When a capacitor is connected to a power source, positive charge collects on one electrode and negative charge collects on the other electrode. This creates an electric field between the electrodes of the capacitor, the strength of which depends on the voltage of the power supply and the characteristics of the capacitor .

The capacitance of a capacitor (called capacitance) is measured in farads (F). The larger the capacity, the greater the amount of charge the capacitor can store.

The capacitance of a capacitor can be calculated by the following formula: C = Q/V

Among them, C represents the capacity of the capacitor (Farads), Q represents the amount of charge stored in the capacitor (Coulombs), and V represents the voltage across the capacitor (Volts).

Capacitors have some important properties:

Charging and Discharging: When a capacitor is connected to a power source, it charges and charge accumulates between the capacitor's electrodes. When the power is disconnected, the capacitor discharges, releasing the stored charge.
Energy Storage: Capacitors can store electrical energy and release it when needed. This makes capacitors very useful in circuits where they are needed to smooth voltage and store energy.
Frequency Dependence: The behavior of a capacitor is affected by frequency. At low frequencies, the capacitor can be considered an open circuit and does not conduct electricity. At high frequencies, the capacitor can be considered conductive.

2.Inductor

An inductor is a passive electronic component capable of storing and releasing magnetic energy . It consists of one or more coils or coil windings, usually made of conductors.

When current passes through an inductor, it creates a magnetic field around the inductor. This magnetic field stores the energy of the current flowing through the inductor.

The inductance value of an inductor (called inductance) is measured in Henrys (H). The magnitude of the inductance depends on the geometry of the inductor, how the coil is wound, and the materials used.

The inductance value of the inductor can be calculated by the following formula: L = Φ/I

Among them, L represents the inductance of the inductor (Henry), Φ represents the magnetic flux passing through the inductor (Weber), and I represents the current through the inductor (amps).

Inductors have some important properties:

Self-inductance: When the current changes through the inductor, the inductor will generate a self-inductance electromotive force, which hinders the change of current. This self-inductance is critical to transient and frequency response in circuits.
Energy Storage: Inductors are capable of storing magnetic energy and releasing it when needed. This makes inductors very useful in circuits where they are required to smooth current flow and store energy.
Frequency Dependence: The behavior of an inductor is affected by frequency. At low frequencies, the inductor can be considered conductive. At high frequencies, the inductor can be considered an open circuit.
Inductors have a wide range of applications in electronic circuits, such as filtering, coupling, transformers, and oscillators. They play an important role in circuits such as power supplies, amplifiers, filters, transmission lines, and electromagnetic induction.

3. The series-parallel equivalent of capacitors and inductors

Capacitors and inductors have different equivalent properties when connected in series and in parallel.

Series equivalent:
Capacitor series equivalent: When multiple capacitors are connected in series, their equivalent capacitance values ​​are equal to the sum of their reciprocals. That is, C_eq = 1/(1/C1 + 1/C2 + … + 1/Cn).
Inductor series equivalent: When multiple inductors are connected in series, their equivalent inductance value is equal to their algebraic sum. That is, L_eq = L1 + L2 + … + Ln.
Parallel equivalent:
Capacitors in parallel equivalent: When multiple capacitors are connected in parallel, their equivalent capacitance value is equal to their sum. That is, C_eq = C1 + C2 + … + Cn.
Equivalent inductors in parallel: When multiple inductors are connected in parallel, their equivalent inductance values ​​are equal to the sum of their reciprocals. That is, 1/L_eq = 1/L1 + 1/L2 + … + 1/Ln.

Chapter 8 Time Domain Analysis of Dynamic Circuits

1. Related basic concepts

① Time domain and frequency domain: Time domain and frequency domain are two commonly used representation methods in signal processing. The time domain represents the change of the signal over time, and you can see the waveform of the signal over time. The frequency domain represents the distribution of signals in frequency, and the spectral characteristics of the signal can be seen.

②Dynamic circuit: A dynamic circuit refers to a circuit composed of components such as capacitors, inductors, and variable resistors, in which the state of the components changes with time. The behavior of dynamic circuits is affected by changes in voltage and current as well as the characteristics of components such as capacitance and inductance.

③Time constant: The time constant is an important parameter describing the response speed of a dynamic circuit. For an RC circuit, the time constant (τ) is equal to the capacitance value (C) multiplied by the resistance value (R) and represents the time required for the circuit response to reach a steady state from the initial state.

④Zero input response: Zero input response refers to the response caused by the internal energy of circuit components without the action of external input signals. It depends on the initial conditions of the circuit and the characteristics of the components, and has nothing to do with external input signals.

⑤Zero-state response: Zero-state response refers to the response of the circuit to an external input signal without initial energy storage. It depends on the characteristics of the external input signal and the transfer function of the circuit.

⑥ Full response: Full response refers to the total response of the dynamic circuit to the external input signal, including the superposition of zero input response and zero state response.

⑦Impulse response: The impulse response refers to the response of the circuit to the unit impulse signal (impulse function). It is usually represented by an impulse response function and can be calculated through a convolution operation.

⑧Step response: Step response refers to the response of the circuit to the unit step signal (step function). It is usually represented by a step response function and can be calculated through a convolution operation.

⑨First-order circuit: A first-order circuit refers to a circuit composed of a capacitor or an inductor and a resistor. Its response characteristics can be described by a first-order differential equation, with one pole. First-order circuits are commonly used in applications such as filtering, clocking circuits, and signal processing.

2. Circuit switching rule and circuit initial state solution

Switching theorem: Transient analysis of dynamic circuits, usually known t=0- and the old steady state. Then:
(1) Uc(0+)=Uc(0-)
(2)iL(0+)=iL(0-)
Then the capacitor voltage and inductor current at t=0+ are known. Using the substitution theorem, we can Replace the capacitor with a voltage source and the inductor with a current source to obtain an equivalent circuit.

3. Zero input, zero state, full, step and impulse response of first-order circuit

① Zero input response: As the name suggests, when the circuit changes paths (such as opening and closing a switch), if the circuit itself has no excitation source, it only relies on certain states of its own to operate.

For example, in this picture, when the switch is not closed, the capacitor already has a voltage, indicating that charge is stored. After the switch is closed, the circuit has no excitation source and relies on the initial energy storage of the capacitor itself to be discharged through the resistor R. Therefore, although there is no external excitation source, the initial energy storage still makes the circuit have electrical properties, which is called zero input response.

②Zero state response: the response generated by external excitation when t>=0+ after changing paths. Then there must be an initial voltage source, current source, and controlled source in the circuit, and then Uc0+=UC0-=0 (it means that the capacitor has not stored electrical energy before).

③Full response: The circuit has both initial energy storage of dynamic components and external stimulation.

Ask for y0+, y∞, and the time constant.

④Step response

This is the step jump at t=0. If it is at t=t0, it will change accordingly.
The zero-state response of a circuit under unit step voltage or unit step current excitation is called unit step response.
It is equivalent to the zero-state response of a unit DC power supply connected to the circuit at t=0, and is still solved using three elements.

⑤Impulse response:

The zero-state response of a circuit under the excitation of unit impulse current or voltage is called unit impulse response. When finding the impulse response, it is a zero-state response when t0- to t0+ changes, but after t>0+, the excitation source is 0, so it is a zero-state response at this time.

Chapter 9 Sine and Phasor

The previous questions were all about direct current. Now we need to discuss sinusoidal alternating current, because this is the most basic form of alternating current.

1…Basic concepts of sinusoidal alternating current

Three elements of sine:

The positive or negative of the phase difference of the sine quantities reflects the lead or lag of the phases of the two sine quantities.

2. Phasor representation of sinusoidal quantity

A sinusoidal quantity is only equal to the real part of a complex vector.
For circuit components, the phasor method can be used to analyze:

Chapter 10 Sinusoidal Steady State Circuit Analysis

Starting from the complex impedance and complex conductance of components, analyze the complex circuits of R, L, C in series and parallel.

1. Complex impedance, complex admittance

Complex impedance (complex impedance) refers to the impedance displayed by circuit components on the alternating current in an AC circuit, and its expression form is a complex number. Complex impedance consists of a real part and an imaginary part. The real part represents the resistance and the imaginary part represents the reactance.

Complex admittance (complex admittance) is the reciprocal of complex impedance, which represents the admittance exhibited by circuit components in the conduction of alternating current. The complex admittance also consists of a real part and an imaginary part. The real part represents the conductance and the imaginary part represents the susceptance.

2. Phasor analysis method of sinusoidal steady-state circuit

All analytical methods that apply to resistive circuits still apply to sinusoidal steady-state circuits, but the rules of complex arithmetic must be followed.
Special: In the mesh current method, mutual resistance is replaced by mutual impedance, and self-resistance is replaced by self-impedance. In the node voltage method, mutual conductance is replaced by mutual admittance, and self-conductance is replaced by self-admittance.

3. Power of sinusoidal steady-state circuit

Several concepts:
① Instantaneous power:
② Average power (active power):
③ Reactive power:
④ Apparent power:
⑤ Complex power:
⑥ Superposition and conservation of power
⑦ Power factor
⑧ Maximum power transmission

①Instantaneous power: Instantaneous power is the power value at a certain moment, indicating the energy consumed or provided by the circuit or device at that moment.

②Average power (active power): Average power is the average power within a cycle, indicating the energy consumed or provided by a circuit or device within a certain period of time. Average power is also called active power, which refers to the true energy conversion efficiency in the circuit. P=UIcosθ

③Reactive power: Reactive power refers to the power that flows back and forth between the power supply and the load in the AC circuit. Reactive power is usually associated with capacitive and inductive components and is used to maintain circuit stability and power factor adjustment. P=UIsinθ

④Apparent power: Apparent power is the total power in the AC circuit, indicating the total energy flow in the circuit. Apparent power is a maximum value and also a valid value. P=UI.

⑤Complex power: Complex power is power represented by a complex number. The product of the voltage phasor and the current conjugate phasor is called complex power.

⑥ Superposition and conservation of power: Instantaneous power, active power, and reactive power satisfy superposition and conservation, that is, in the correlation direction, the algebraic sum of power absorbed by the entire circuit is zero. The problem is that the apparent power does not satisfy the superposition and conservation properties.

⑦Power factor cosθ: Power factor refers to the absolute value of the ratio of active power to apparent power in an AC circuit. Power factor can be used to measure the proportion of useful power in a circuit, and its value ranges from 0 to 1. The closer the power factor is to 1, the higher the proportion of useful power in the circuit and the higher the energy utilization efficiency. Increasing the power factor or reducing the power factor angle can improve energy utilization.

⑧Maximum power transmission: Maximum power transmission refers to the conditions under which maximum power output can be achieved in the circuit. Maximum power transfer usually occurs when the source resistance matches the load resistance. At this time, the load resistance and source resistance are equal, and maximum power transfer can be achieved.

Chapter 11 Sinusoidal Steady-State Circuit Containing Magnetic Coupling Components

1. The concept of magnetic coupling

In a transformer, there are two or more coils (usually windings) connected together by a magnetic material (such as an iron core). When the current in one winding changes, the magnetic field generated will be transmitted to other windings through the iron core, and the change in this magnetic field will generate induced electromotive force in other windings, thereby realizing energy transmission and voltage conversion.

The concept of the same terminal:
If the currents i1 and i2 flow from one end of the two coupled inductor coils, so that the reference direction of the mutual inductance flux linkage and the self-inductance flux linkage are the same, they are called the same terminal.

2. Coupled inductor circuit analysis

1. Series connection:
serial connection in series: L=L1+L2+2M
reverse series connection: L=L1+L2-2M
2. Parallel connection
3. T-type equivalent decoupling: after decoupling, the inductor becomes an ordinary inductor without mutual inductance voltage is affected. If decoupling is not performed, the influence of mutual inductance voltage must also be considered when analyzing the circuit.

3.Air core transformer

Air-core transformer is a special type of transformer, which is mainly composed of one or more hollow coils instead of the traditional solid coils.

In an air-core transformer, there are mainly two air-core coils, one as the main coil and the other as the secondary coil. These coils are usually wrapped in insulating material and have no direct electrical connection to each other. Air-core coils often adopt a planar helical shape to better utilize magnetic field coupling.

In terms of working principle, air-core transformers are similar to traditional solid-core transformers. When an alternating current flows through the primary coil, the generated magnetic field will be transmitted to the secondary coil through the air, thereby generating an induced electromotive force in the secondary coil. According to the principle of magnetic coupling, the voltage in the secondary coil is proportional to the voltage in the primary coil, realizing voltage conversion.

Air-core transformers have several advantages over traditional solid-core transformers. First, due to the design of the air-core coil, the capacitive coupling between coils can be reduced, thereby reducing current leakage. Secondly, the design of the air-core coil can improve the auto-coupling ratio (auto-transformation ratio) of the transformer, allowing the transformer to achieve a higher transformation ratio.

Air-core transformers are commonly used in applications such as high-frequency electronics, communications equipment, and power amplifiers. Due to its special design, it can meet the requirements of efficient energy transmission and voltage conversion within a specific frequency range.

4.Ideal transformer

An ideal transformer refers to a transformer model that theoretically fully conforms to the working principle and characteristics of a transformer. It is an idealized concept used to simplify analysis and calculations to better understand the basic principles of transformers.

In an ideal transformer, it is assumed that there are no losses such as resistance, permeability loss and magnetic leakage. Therefore, an ideal transformer has the following characteristics:

Constant transformation ratio: The transformation ratio of an ideal transformer is constant, that is, the ratio between the input voltage and the output voltage always remains the same.

Current transformation: An ideal transformer transfers energy only through magnetic coupling, and the transformation of current only depends on the transformation ratio of the transformer. The ratio between input current and output current is equal to the transformation ratio between output voltage and input voltage.

Ideal Efficiency: An ideal transformer has no resistance and permeability losses, so its efficiency is 100%. The power input is equal to the power output.

No magnetic leakage: There is no magnetic leakage phenomenon in an ideal transformer, that is, the magnetic field is completely transmitted to the secondary coil through the iron core, and no leakage of the magnetic field occurs.

Chapter 14 Frequency Characteristics of Sinusoidal AC Circuits

1.Network functions

Frequency is the independent variable, which is the ratio of the circuit output phasor to the input phasor when the frequency changes.

The network function is represented by amplitude-frequency characteristics and phase-frequency characteristics.

2. Resonant circuit

1. The concept of resonance

Resonance refers to the phenomenon that in a physical system, when the external excitation frequency is equal to or very close to the natural frequency of the system, the system will show the maximum response or amplitude amplification.

Under resonant conditions, the vibration or oscillation of the system reaches its maximum value. This is because when the external excitation frequency matches the natural frequency of the system, the energy transfer efficiency is highest, allowing the system to absorb or amplify more energy.

Resonance can appear in various physical systems, including mechanical systems, circuit systems, and optical systems. The resonance phenomena of different systems may have different characteristics, but their basic principles are similar.

For example, in a mechanical system, when a system of spring and mass vibrating is subjected to a periodic external force, if the frequency of the external force is equal to the natural frequency of the system, the spring and mass system will exhibit the maximum amplitude. This resonance phenomenon can be observed in mechanical systems such as tuning forks, pendulums, and bridges.

In a circuit system, resonance occurs when the voltage or current in a resonant circuit composed of a capacitor and an inductor reaches its maximum value. This resonance phenomenon is widely used in radio and communication systems, such as in tuned radios, where tuning to specific frequencies can be achieved by adjusting the values ​​of capacitors and inductors.

In optical systems, resonances can be observed in optical resonant cavities, where light waves are reflected multiple times within the cavity, depending on the cavity length and the wavelength of the light. When the wavelength of the light wave matches the natural frequency of the optical resonant cavity, the resonance phenomenon occurs, causing the light wave to be amplified or enhanced within the cavity.

2.RLC series resonance and parallel resonance

RLC series resonance and parallel resonance refer to two different ways to achieve resonance phenomena in the circuit by adjusting the values ​​of the inductor (L), capacitor (C) and resistor (R).

RLC Series Resonance: In an RLC series resonance circuit, inductors, capacitors and resistors are connected in series. When external AC power is applied to the circuit, if the values ​​of the inductor, capacitor and resistor can meet the resonance conditions, that is, the natural frequency of the circuit is equal to the external excitation frequency, the resonance phenomenon will occur.
In a series resonant circuit, the combination of an inductor and a capacitor forms a resonant circuit, where the inductor provides the ability to store energy and the capacitor provides the ability to release energy. When the natural frequency of the circuit matches the external excitation frequency, the current in the circuit will reach its maximum value and the voltage will also reach its maximum value.

RLC parallel resonance: In an RLC parallel resonance circuit, inductors, capacitors and resistors are connected in parallel. When external AC power is applied to the circuit, if the values ​​of the inductor, capacitor and resistor can meet the resonance conditions, that is, the natural frequency of the circuit is equal to the external excitation frequency, the resonance phenomenon will occur.
In a parallel resonant circuit, the combination of an inductor and a capacitor forms a resonant circuit, where the inductor provides a path for current and the capacitor provides a path for voltage. When the circuit's natural frequency matches the external excitation frequency, both the current and voltage in the circuit will reach their minimum values.