An analysis of circuit for quick understanding

introduction

Don't worry, iron sons , This article will start from the most basic , Suitable for children's shoes that just touch Electronics , Even lying in bed , After reading this article for more than ten minutes, you will have a painless and comprehensive understanding of circuit analysis ！
I will elaborate on the very basic concept , I will try to explain some advanced concepts in words , So I will cover all the knowledge points involved in circuit analysis , It aims to let you see the whole picture of circuit analysis first , Lay a foundation for future study ！
The following figure shows all the basic concepts of circuit analysis , I'll talk about Brown in detail , You can master it immediately , I will try to make the knowledge of blue clear in language . Hopefully that helped .

 

Text

What children's shoes who study electronics cannot escape from entering university is circuit analysis This lesson , seeing the name of a thing one thinks of its function , This course is about analyzing circuits , To put it bluntly , Namely Give you a complicated circuit , You can find its current by some means 、 voltage 、 Input and output resistance 、 Performance, etc. . So in order to achieve this goal , You need a lot of means , It can be understood as many weapons , Is there only such a weapon in your arsenal now ？

Hahaha, it's normal , In high school, he can solve almost all problems , But in College , That's not enough .
Circuit analysis is a course that constantly teaches you how to solve circuits , Expand your arsenal .OK, The following contents are closely linked , This matter should not be delayed , Let's do something about it ！
 

KCL、KVL

KCL It's Kirchhoff's law of current ,KVL It's Kirchhoff's voltage law , This may be the two laws you use most later , Very, very important ！
So-called KCL That is to say , At any moment , For any node in the circuit , The current flowing in is equal to the current flowing out ！
The following figure clearly explains KCL.

So-called KVL That is to say , For any circuit in the circuit , After you choose a direction , In this circuit, the algebraic sum of the voltage is equal to 0！
Look at the picture below , After I choose the counterclockwise direction , about U2 and U4 I am a Go through their negative pole first , So voltage algebra is negative ！ namely -U2+U4-U3+U1=0.

KCL、KVL It's that simple ！
 

Branch current method

But now you just know KCL、KVL These two important concepts , If we give you a circuit right away, actually calculate it , How do you use these two concepts to solve problems ？
We thus extend a method , Branch current method ！
It is a versatile method , Namely Give you a circuit , You just list all its nodes KCL equation , All circuits are listed KVL equation , Then solve all the equations , Then you can see all the current and voltage of this circuit , So it is omnipotent hahaha , very “ violence ”, It's very simple .
Sometimes your goals are clear , It's like finding three unknowns , For example, in the following figure $I_1、I_2、I_3$ , Then we only need to list three equations ok, Yes a The node lists one KCL, Yes Ⅰ、Ⅱ There are two loops KVL, Get it done .

 

Node voltage method 、 Mesh current method

The branch current method is very simple , But the price is to list many equations , When a circuit becomes complex , There will be many nodes , Many circuits , At this time, if you use it again, it will be very complicated , But if your computing power can , The exam can also be used like this, haha , It can also be solved , It's just trouble , So there must be more efficient methods for complex circuits ！
Node voltage method 、 Mesh current method emerge as the times require , In fact, the actual situation is that we use these two methods very often , On the contrary, branch current method is rarely used . When there are few nodes, it is suggested to use the node voltage method , When there are few mesh circuits, it is recommended to use mesh current method , These two can have an impression first .
 

Superposition theorem

Superposition theorem It is a powerful tool for solving linear circuits , Linear means that there is no diode in the circuit 、 capacitance 、 Inductance these three nonlinear elements , That is linear circuit . You see a linear circuit , Conditional reflection should think of superposition theorem .
First look at what the textbook says ：

To put it bluntly , Namely The total response of multiple power supplies Acting on a branch , It is equal to separating the power supply , The sum of the responses generated separately in this branch .
There is another rule of the game when using the superposition theorem , That is when we analyze a single power supply , For other power supplies , We want to The voltage source is short circuited , Current source open circuit .（ Because the ideal voltage source internal resistance is 0, The internal resistance of an ideal current source is infinite , So it's simply short circuit and open circuit .）
For example, the circuit on the left below , It can be divided into two parts on the right , Left split analysis U1, Right split analysis U2, Using the superposition theorem, we can get $I_1^{\prime }and{I}_1^{\prime \prime }$ The algebraic sum of these two responses yields $I_1$ This total response , $I_2$ , $I_3$ The same is true .（$I_1^{\prime \prime }$ In the opposite direction , So it's negative ）

Let's practice a circuit ：
Look at this circuit, there are three power supplies , Two current sources and one voltage source , Direct analysis can be a headache , Try the superposition theorem ！

The figure in the upper left corner can be decomposed into the right 3 Subtext , Analyze separately 3 Add up the responses of the power supplies , Is the total response ！
 

Power equivalent conversion

Do you know about power supply 5 Number ,7 Battery No ？ This is usually Voltage source , That is, the voltage applied to the load is constant . Another important branch of the circuit is Current source ！ That is, the current applied to the load is constant , Isn't that amazing , There are many ways to do this , Let's start with a concept .
Voltage source and current source can also be transformed into each other ！ It can be used for Circuit simplification .
A voltage source is connected in series with a resistor , It can be equivalent to A current source is connected in parallel with a resistor .
As shown in the figure below ：

The following is the formula of transformation ：

For some circuits , It will be much easier to use the tool of power equivalent transformation .
 

Davinan 、 Norton's theorem

For what a complex circuit , We can all be regarded as a black box （ I don't know the internal structure , Only two lines lead out ）.
Davinan said , We can directly equivalent this black box to a series connection of a voltage source and a resistor ;
Norton said , We can directly equivalent this black box to a parallel connection of a current source and a resistor .
As for how to solve the value of power supply and resistance , There is a set of rules of the game , There's no verbosity here , Let's have an impression first .

 

First order 、 Time domain analysis of second-order circuit

We didn't touch the diode in front 、 Capacitance and inductance are three components , But the actual household circuit 99% There are three of them . Using only one capacitor or inductor, we call it a first-order circuit , When capacitance and inductance are used, we call it a second-order circuit . Here are two recommended b Stop video BV1ax411q7rG ,BV1sx411B7Hf, If you don't know about capacitance and inductance, you can go and have a look first .
There will be a complete set of methods for the analysis of these nonlinear circuits , Time domain analysis means that abscissa is time , It's your daily way of thinking , See how the circuit response changes over time .
Zero input response ： Think of input as 0, Only analyze the response caused by the state of the circuit .
Zero input response ： Regard the state of the circuit as 0, Only analyze the response caused by input .
Overall response Is equal to Zero input response add Zero input response ！ This is very similar to the idea of superposition theorem .

 

Phasor method

In nature , Many inputs can be written as a stack of sine waves （ The Fourier transform ）, How to respond efficiently after many sine waves enter our circuit ？ At this time, the phasor method is introduced , Study how to solve the circuit systematically when the input is sine and cosine .

 

three-phase circuit

Power generation and transmission in our country are three-phase , That is equivalent to three power supplies , Transmission through three lines , The efficiency of this will be much higher than that of single-phase and two-phase .

 

Frequency response

Here we mainly study how the input of different frequencies will affect the circuit . Here we introduce a concept ： resonance . The first time I listen to this word, I'm sure I don't know what to say , In fact, when the input reaches the resonant frequency of the circuit , The capacitive reactance and inductive reactance in the circuit will cancel each other , The equivalent resistance of capacitance and inductance is 0, The total resistance of the whole circuit will be greatly reduced ！ Therefore, after reaching the resonant frequency, the current of the circuit will suddenly increase , What is it? ？ This is filtering ！ Different frequency inputs come in , High current , That is, the resonant frequency is selected .
What is the use of filters ？ On the radio , Why can I only receive the sound of this channel when I can tune to a channel ？ In fact, it has received signals from all stations , Just because filter , It selects the desired signal . So the circuit is very interesting .
 

Frequency domain analysis

The time domain analysis we mentioned earlier , Take time as abscissa , It's the normal way we look at the world . But try to Abscissa becomes frequency , Then our whole view of the world will be different , It's a new world , Some extremely complex inputs are surprisingly simple after being converted into frequency domain , For example, the frequency is 2HZ, The magnitude is 1 The sine wave of , There are continuous curves in the time domain , But in the frequency domain, the abscissa is 2 A discrete value at 1！ It also teaches us to look at signals from another angle , Look at the world .
The following figure is from Baidu , It's a The black curve is decomposed into three sine waves of red, green and pink （ The Fourier transform , Any signal can be equivalent to the addition of several sine waves ）, Then in the frequency domain, there are three discrete values ,easy！

If you study deeper , You will know Laplace transform and Z Transformation , Can be derived from Fourier transform , They are the two major killers in the frequency domain . But these are the knowledge of signal and system .
 

Two port network

The black box in the aforementioned davinam equivalent , Because it led two feet out , So it can be regarded as a two port network , We can study the output equation of this network , Various parameters ...
 

END

Finally, review all the concepts of the whole circuit analysis , Brown is a little more detailed , The blue one is simple to understand the concept , I hope it can help you form a general understanding of circuit analysis .
 

expand

You remember KCL、KVL Well , This is what we think is omnipotent after learning circuit analysis , The law of the cornerstone , Is it really effective for all circuits ？ Just like Newtonian mechanics only applies to the low-speed macro world ,KCL、KVL There are also limitations , That is, only applicable to low-frequency signal analysis . When the frequency of the signal reaches 30Mhz—30Ghz, We call these high-frequency signals RF signals ,KCL,KVL, Even Ohm's law, which is popular in high school, doesn't work with these signals . The reason can be simply stated , When the frequency of the signal is higher , The shorter the wavelength , When the wavelength is shorter than the physical size of the resistance , You are not sure about the exact voltage of the resistor , Ohm's law naturally doesn't work .
The circuit learned earlier is called Lumped parameter circuit , The circuit works at high frequency , It's called Distributed parameter circuit . For the analysis of distributed parameter circuit , Need Transmission line theory Knowledge , This is a 《 Radio frequency signal 》 The knowledge of this book , Take it as science popularization , In recent years, the salary of RF engineers is often high , It's certainly not a loss to study when you have time .

Attach links to two other articles 《 A quick understanding of analog electricity 》,《 A quick understanding of digital 》.