# With 3000 words, 11 pictures, take you to know the capacitor!

2020-12-05 03:03:54

I don't say much nonsense , Go straight to the point .

### brief introduction

A high-end smartphone has 800~1000 Chip multilayer ceramic capacitors , Capacitors are also used most in general circuits , It can be seen that the function of capacitance is great , This paper mainly introduces some basic knowledge of capacitance .

Two conductors close to each other , A dielectric interlayer that is not conductive , This makes up the capacitor . Capacitors have two very important characteristics , No sudden change of voltage is allowed , So it's often used in filter circuits 、 Bootstrap circuit 、 In circuits such as tuning .

The basic unit of capacitance is F（ Farah ）, The common unit is uF、nF and pF, The conversion relation is ：1uF=1000nF=1000000pF

because F The unit is larger ,1F=1000000uF, Generally do not use .

### Naming rules

There are many manufacturers of capacitors , Different manufacturers have different naming rules , Let's take a look at Murata's naming rules .

Such as GRM representative ：Chip Multilayer Ceramic Capacitors for General Purpose.
18 For size ：1.6x0.8mm, English 0603 encapsulation .
In this part, you can check the model selection manual of the corresponding manufacturer .

### Series parallel calculation formula

Capacitance is the same as resistance , It can also be connected in series or in parallel .

Two capacitors C1 and C2 parallel connection , The equivalent capacitance is ：

C e q = C 1 + C 2 C_{eq}=C1+C2

If C1 Far greater than C2, The equivalent capacitance can be reduced to ：

C e q = C 1 + C 2 ≈ C 1 C_{eq}=C1+C2≈C1

Two capacitors C1 and C2 Series connection , The equivalent capacitance is ：

C e q = C 1 C 2 C 1 + C 2 C_{eq}=\frac{C1C2}{C1+C2}

If C1 Far greater than C2, The equivalent capacitance can also be reduced to ：

C e q = C 1 C 2 C 1 + C 2 ≈ C 1 C 2 C 1 = C 2 C_{eq}=\frac{C1C2}{C1+C2}≈\frac{C1C2}{C1}=C2

It can be seen from the above formula that , The series and parallel connection of capacitors is the opposite of resistance .

### The formula for flat plate capacitors

Capacitors store electricity and energy （ Electric potential energy ） The elements of , The formula of flat plate capacitor is ：

C e q = Q U A − U B = ξ r S 4 π k d C_{eq}=\frac{Q}{U_A-U_B}=\frac{\xi_rS}{4\pi kd}

among Q Q The charge stored for a capacitor , U A − U B U_A-U_B Is the potential difference between the two plates , ξ r \xi_r Relative permittivity , S S It is the area opposite to the plate , d d Is the distance between the two plates . Larger area , The smaller the distance , The larger the volume value .

### Standard and common volume values

The standard capacitance of a capacitor is in accordance with E6,E12,E24 Numerical standards , as follows ：

• E6 Series values ：1.0、1.5、2.2、3.3、4.7、6.8 multiply 10 Of n Power ;
• E12 Series values ：1.0、1.2、1.5、1.8、2.2、2.7、3.3、3.9、4.7、5.6、6.8、8.2 multiply 10 Of n Power ;
• E24 Series values ：1.0、1.1、1.2、1.3、1.5、1.6、1.8、2.0、2.2、2.4、2.7、3.0、3.3、3.6、3.9、4.3、4.7、5.1、5.6、6.2、6.8、7.5、8.2、9.1 multiply 10 Of n Power ;

In everyday circuit design , We often use the capacity of ：

• frequently-used pF Level ：39、43、47、51、56、100、150、200、220、270、300、330、390、470、560、680 etc. .
• frequently-used nF Level ：1、1.2、1.5、2.2、2.7、3.3、10、22、33 etc. .
• frequently-used uF Level ：0.1、0.15、0.22、0.33、0.47、1、2.2、10uF etc. .

### Capacitance classification

There are many kinds of capacitors , According to the material , The commonly used ones can be divided into the following , The tantalum electrolytic capacitor is generally called tantalum capacitor .

The following is the characteristic comparison of several capacitors given by Murata .

According to the different characteristics of capacitance , The use of the occasion is not the same .

• Ceramic capacitors are small in size （ The smallest 01005 encapsulation ）, Nonpolarity , Cheapness ,ESR low （ Lower than tantalum and aluminum electrolytic capacitors ）, The disadvantage is that the capacity is not as large as electrolytic capacitance , Poor toughness , The impact is fragile , Generally used in small consumer electronic products , Such as mobile phone .
• The electrolytic capacitor has a large capacity , Large size , The price is relatively cheap , It's mostly used in power supply and automotive electronics ;
• Tantalum has a large capacitance , Small volume , Compared with aluminum electrolytic capacitor, its stability is higher , It's mostly used in power supply and automotive electronics ;
• High withstand voltage of thin film capacitor , Good frequency characteristic , High voltage applications are preferred .

### Ceramic capacitor

according to EIA and IEC Recommended standards , Ceramic capacitors can be divided into two categories ,Class1 and Class2, That we use a lot X5R and X7R All belong to Class2;

Class1 and Class The dielectric materials are different , Murata gives two contrasts .

C0G It's warm tonic , You can see that as the temperature changes , The rate of change of electrostatic capacity is almost 0

High inductivity series capacitors (B/X5R、R/X7R characteristic ), Due to the application of DC voltage , Its electrostatic capacity sometimes differs from the nominal value , As can be seen from the figure below , The greater the DC voltage applied , The lower the actual electrostatic capacity .

For temperature compensation capacitors (CH、C0G Characteristics, etc. ) , The main raw material is often induced ceramics , The electrostatic capacity does not change due to the DC voltage characteristics .

C0G The advantage of capacitance like is that the capacitance change caused by temperature is small , The disadvantage is low capacitance , There can't be a lot of capacity .

X5R The advantage of capacitance like is high capacitance , Can have large capacitance , The disadvantage is that the capacity change caused by temperature is large .

### Tantalum capacitance

Tantalum capacitors usually look like this , Compared with aluminum electrolytic capacitors , It's still small .

The advantage of tantalum capacitors is ：

• Small size, large capacity
• The leakage current is small
• At higher frequencies ESR low , But no MLCC low
• It has the ability of self-healing under low current （ Depend on the handle MnO2 become MnO, Fix the defective location ）

The disadvantage is that the ability to withstand voltage and current is relatively weak , Overpressure is easy to explode , Failure of the capacitor may cause open fire .

### Capacitor charging and discharging

The time constant must be mentioned when the capacitor is charged or discharged τ e = R C \tau_e=RC , One τ e \tau_e Represents that the capacitor is charged to the supply voltage 63% Time spent .

The formula of capacitor charging is ：

V c = V 0 + ( V u − V 0 ) ∗ ( 1 − e − t R C ) V_c=V_0+(V_u-V_0)* (1- {\rm e}^{-{\frac{t}{RC}}})

among V 0 V_0 It's the starting voltage of the capacitor , V u V_u It's the voltage at which the capacitor is fully charged , Capacitance from 0V Start filling , namely V 0 = 0 V V_0=0V , Then the above formula can be simplified as ：

V c = V u ∗ ( 1 − e − t R C ) V_c=V_u*(1- {\rm e}^{-{\frac{t}{RC}}})

When time is a τ e \tau_e , We can get the following , That is, the capacitor voltage is charged to 63% The origin of , among e e =2.71828

V c = V u ∗ ( 1 − 1 e ) = 0.63 V u V_c=V_u*(1-{\frac{1}{e}})=0.63V_u

Empathy ,2 individual τ e \tau_e The time can be charged to the power supply voltage 87%,3 individual τ e \tau_e It can be charged to the supply voltage 95%.

The formula of capacitance discharge is ：

V c = V u ∗ e − t R C V_c=V_u*{\rm e}^{-{\frac{t}{RC}}}

among V u V_u It's the voltage on the capacitor before discharge .

### The function of capacitance

In circuit design, capacitors are often placed in the power supply 、 radio frequency 、 Audio and other places .

• The capacitance of power supply terminal is mainly filter , The larger the volume value , The more stable the output voltage is , The ripple is small .
• The capacitance at the RF end , It is mainly used for power supply and energy storage of radio frequency , In order to prevent instantaneous high current caused by RF power failure , Because of tantalum capacitor ESR Affect efficiency , So for capacitors ESR The requirements are quite high .
• The main function of the series capacitor of audio frequency is to isolate , Larger capacity , The greater the range of audio you pass through , The better the bass effect ,ESR The lower the , The smaller the impact on the output power , The more efficient , But because of the smaller impedance relative to the earphone , So right. ESR Not very demanding .

Capacitance has a wide range of functions , The above is just a few examples .

### The actual equivalent model

The ideal capacitor doesn't exist in practice , The actual model of capacitance is a ESR A series of ESL, Another capacitor in series ,ESR Is the equivalent series resistance ,ESL Is the equivalent series inductance ,C It's the ideal capacitor .

So the complex impedance of the above model is ： Z = E S R + j 2 π f E S L + 1 j 2 π f c = E S R + j ( 2 π f E S L − 1 2 π f c ) Z=ESR+j2\pi fESL+\frac1{j2\pi fc}=ESR+j(2\pi fESL-\frac1{2\pi fc})

• 2 π f E S L < < 1 2 π f c 2\pi fESL<<\frac1{2\pi fc} when , The capacitor behaves as capacitive ;
• 2 π f E S L > > 1 2 π f c 2\pi fESL>>\frac1{2\pi fc} when , Capacitors behave as perceptual , So there is a saying that capacitance is no longer capacitance at high frequency , It's an inductance , This inductance doesn't mean that a capacitor becomes an inductor , It means that the capacitor has the similar characteristics as the inductance .
• 2 π f E S L = 1 2 π f c 2\pi fESL=\frac1{2\pi fc} when , The capacitive reactance vector is equal to the inductive reactance vector , The total impedance of the capacitor is the smallest , It shows pure resistance characteristic , At this time f It's called the self resonant frequency of a capacitor .

The self resonance frequency point is the dividing point between capacitance and sensibility , Above resonance point “ A capacitor is no longer a capacitor ”, So decoupling will decrease . The actual capacitor has a certain operating frequency range , Within the operating frequency range , The capacitor has a good decoupling effect .ESL It is the fundamental reason that the decoupling function of the capacitor is weakened after it is higher than the self resonant frequency point .

The figure below shows the frequency characteristics of the actual capacitor .

The actual equivalent model of capacitance can be read from the author's previous article ： Seeing is not necessarily believing ！ resistance 、 Practical equivalent model of capacitance and inductance

### Capacitance parameters and selection

Capacitor selection mainly considers the following parameters .

• Capacity ： At room temperature 25℃, The capacity measured under an AC signal of a certain frequency and amplitude .
• Rated voltage ： It refers to the maximum effective value of DC voltage that can be continuously applied to the capacitor at the lowest ambient temperature and rated ambient temperature , Generally, derating is required , Such as derating 80% refer to 6V Capacitance at rated voltage , The value of DC voltage added to it should not exceed 4.8V; But there is one caveat , The rated voltage of the actual capacitor is made with a certain margin , Such as rated voltage 6V, The actual withstand voltage value may reach its rated voltage 1.5 About times .
• Leakage current ： The test conditions are generally at rated voltage , Work 5 Average leakage current per minute . The standard value of DC leakage current is not specified , But the insulation resistance is the specified value , Through the specified value of insulation resistance and rated voltage of the product , Using the formula I=V/R Calculate the leakage current , That is, the greater the insulation resistance of the capacitor , The smaller the leakage current .
• Insulation resistance ： At room temperature , Charge the capacitor at rated voltage 1 minute /2 minute , Divide the voltage value by 1 minute /2 The average leakage current per minute is used to obtain the insulation resistance value .
• ESR： It refers to the equivalent series resistance of a capacitor , Its parameters can be SPEC View in ,ESR The value of affects the power ripple and PDN Simulation ,MLCC Of ESR It's usually very small ,mΩ Level , Tantalum capacitors and aluminum electrolytic capacitors are generally Ω Level .

### Common capacitor brands

Common capacitor brands such as Murata MURATA、 sis KEMET、AVX、TDK、 Weishi VISHAY、 Yuyang 、 National giant Yageo etc. .

This is the end of today's article , I hope it helps you , There should be another article about capacitors , I'll see you in the next issue .

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