A detailed discussion on capacitors, which are indispensable in power supply design

　　Power supply is often the most easily overlooked link in the circuit design process. In fact, as an excellent design, power supply design should be very important, which greatly affects the performance and cost of the entire system.

　　Here, we will only introduce the use of capacitors in circuit board power supply design. This is often the most easily overlooked part in power supply design. Many people are engaged in ARM, DSP, and FPGA. At first glance, they seem to be very advanced, but they may not be able to provide a cheap and reliable power supply solution for their own system. This is also a major reason why our domestic electronic products are rich in functions but poor in performance.

　　1 Important parameters of capacitors

　　Okay, let's get back to the point. Let me introduce capacitors to you. First, you need to have a general understanding of capacitor brands. Domestic capacitors on the market include Sanhuan Capacitors, Fenghua Capacitors and other brands, Taiwan's leading YAGEO Capacitors (i.e. Yageo Capacitors), and foreign imported brands such as TDK Capacitors, SAMSUNG Capacitors and MURATA Capacitors are all relatively well-known brands.

　　Most people's concept of capacitors is still at the ideal capacitor stage. They generally think that a capacitor is a C. However, they don't know that capacitors have many important parameters, nor do they know the difference between a 1uF ceramic capacitor and a 1uF aluminum electrolytic capacitor.

　　The actual capacitor can be equivalent to the following circuit form:

　　C: Capacitance. Generally refers to the value measured at 1kHz, 1V equivalent AC voltage, and 0V DC bias, but there are many different environments for capacitance measurement. But one thing to note is that the capacitance value C itself will change with the environment.

　　ESL: Capacitor equivalent series inductance. The pins of the capacitor have inductance. In low-frequency applications, the inductance is small, so it can be ignored. When the frequency is higher, this inductance must be considered. For example, a 0.1uF chip capacitor in a 0805 package has an inductance of 1.2nH per pin, so the ESL is 2.4nH. It can be calculated that the resonant frequency of C and ESL is about 10MHz. When the frequency is higher than 10MHz, the capacitor will show inductive characteristics.

　　ESR: Capacitor Equivalent Series Resistance. No matter what type of capacitor, there will be an equivalent series resistance. When the capacitor works at the resonant frequency, the capacitive reactance and inductive reactance of the capacitor are equal, so it is equivalent to a resistor, which is the ESR. It varies greatly due to different capacitor structures. The ESR of aluminum electrolytic capacitors generally ranges from a few hundred milliohms to a few ohms, while that of ceramic capacitors is generally tens of milliohms. Tantalum capacitors are between aluminum electrolytic capacitors and ceramic capacitors.

　　Let's look at the frequency characteristics of some X7R ceramic capacitors:

　　Of course, there are many other parameters related to capacitors, but the most important ones in design are C and ESR.

　　The following is a brief introduction to the three types of capacitors we commonly use: aluminum electrolytic capacitors, ceramic capacitors and tantalum capacitors.

　　1) Aluminum capacitors are made of aluminum foil that is grooved and oxidized, then rolled with an insulating layer, and then immersed in electrolyte. The principle is chemical. The charging and discharging of capacitors depends on chemical reactions. The response speed of capacitors to signals is limited by the movement speed of charged ions in the electrolyte. They are generally used in filtering situations with low frequencies (below 1M). ESR is mainly the sum of aluminum foil resistance and electrolyte equivalent resistance, and the value is relatively large. The electrolyte of aluminum capacitors will gradually evaporate, resulting in a decrease in capacitance or even failure, and the evaporation rate will accelerate as the temperature rises. The life of electrolytic capacitors will be halved for every 10 degrees increase in temperature. If a capacitor can be used for 10,000 hours at room temperature of 27 degrees, it can only be used for 1,250 hours at 57 degrees. Therefore, aluminum electrolytic capacitors should not be too close to heat sources.

　2) Ceramic capacitors store electricity through physical reactions, so they have a very high response speed and can be applied to G-level occasions. However, ceramic capacitors also show great differences due to different dielectrics. The best performance is the capacitor made of C0G material, which has a small temperature coefficient, but the material has a small dielectric constant, so the capacitance cannot be too large. The worst performance is the Z5U/Y5V material, which has a large dielectric constant, so the capacitance can be tens of microfarads. However, this material is seriously affected by temperature and DC bias (DC voltage will cause the material to polarize and reduce the capacitance). Let's take a look at the effects of ambient temperature and DC working voltage on the three types of capacitors: C0G, X5R, and Y5V.

　　It can be seen that the capacitance of C0G does not change with temperature, the stability of X5R is slightly worse, and the capacitance of Y5V material becomes 50% of the nominal value at 60 degrees.

　　It can be seen that when the 50V withstand voltage Y5V ceramic capacitor is used at 30V, the capacity is only 30% of the nominal value.

　　Ceramic capacitors have a big disadvantage, which is that they are fragile. So you need to avoid bumping them and keep them away from places where the circuit board is prone to deformation.

　　3) Tantalum capacitors are like batteries in both principle and structure. Below is a schematic diagram of the internal structure of a tantalum capacitor:

　　Tantalum capacitors have the advantages of small size, large capacity, fast speed, low ESR, etc., and the price is relatively high. The size of the raw material tantalum powder particles determines the capacity and withstand voltage of tantalum capacitors. The finer the particles, the larger the capacitance can be obtained. If you want to get a higher withstand voltage, you need thicker Ta2O5, which requires the use of tantalum powder with larger particles. Therefore, it is very difficult to obtain a tantalum capacitor with high withstand voltage and large capacity of the same volume. Another point that needs to be paid attention to tantalum capacitors is that tantalum capacitors are more likely to break down and show short-circuit characteristics, and have poor surge resistance. It is very likely that a large instantaneous current will cause the capacitor to burn out and form a short circuit. This needs to be considered when using ultra-large capacity tantalum capacitors (such as 1000uF tantalum capacitors).

　　From the above, we can understand that different capacitors have different applications, and the higher the price is not necessarily better.

　　2 The role of capacitors in power supply design

　　In power supply design applications, capacitors are mainly used for filtering and decoupling/bypass.

　　Filtering mainly refers to filtering out external noise, while decoupling/bypass (a type of decoupling effect achieved in the form of bypass, hereinafter referred to as "decoupling") is to reduce the external noise interference of the local circuit. Many people tend to confuse the two. Let's look at a circuit structure:

　　The switching power supply in the figure supplies power to A and B. After passing through C1, the current passes through a section of PCB trace (temporarily equivalent to an inductor. It is wrong to analyze this equivalence using electromagnetic wave theory, but for the convenience of understanding, this equivalence method is still used.) and is divided into two paths to supply A and B respectively. The ripple from the switching power supply is relatively large, so we use C1 to filter the power supply to provide a stable voltage for A and B. C1 needs to be placed as close to the power supply as possible. C2 and C3 are both bypass capacitors, which play a decoupling role. When A needs a large current at a certain moment, if there are no C2 and C3, the voltage at the A end will become lower due to the line inductance, and the voltage at the B end will also be affected by the voltage at the A end and decrease. Therefore, the current change of the local circuit A causes the power supply voltage of the local circuit B, thereby affecting the signal of the B circuit. Similarly, the current change of B will also interfere with A. This is "common-path coupling interference".

　　After adding C2, when the local circuit needs a large current for a moment, capacitor C2 can temporarily provide current for A. Even if the common inductance exists, the voltage at the A end will not drop too much. The impact on B will also be greatly reduced. Therefore, the current bypass plays a role of decoupling.

　　Generally, large-capacity capacitors are mainly used for filtering. The speed requirement is not very fast, but the capacitance requirement is relatively high. Aluminum electrolytic capacitors are generally used. When the surge current is small, it will be better to use tantalum capacitors instead of aluminum electrolytic capacitors. From the above example, we can know that as a decoupling capacitor, it must have a very fast response speed to achieve the effect. If the local circuit A in the figure refers to a chip, then the decoupling capacitor must be a ceramic capacitor, and the capacitor should be as close to the power pin of the chip as possible. If "local circuit A" refers to a functional module, ceramic capacitors can be used. If the capacity is not enough, tantalum capacitors or aluminum electrolytic capacitors can also be used (the premise is that each chip in the functional module has a decoupling capacitor-ceramic capacitor).

　　The capacity of the filter capacitor can often be calculated from the data sheet of the switching power supply chip. If the filter circuit uses electrolytic capacitors, tantalum capacitors and ceramic capacitors at the same time, put the electrolytic capacitors as close to the switching power supply as possible to protect the tantalum capacitors. Put the ceramic capacitors behind the tantalum capacitors. This will achieve the best filtering effect.

　　Decoupling capacitors need to meet two requirements, one is the capacity requirement, the other is the ESR requirement. That is to say, the decoupling effect of a 0.1uF capacitor may not be as good as that of two 0.01uF capacitors. Moreover, 0.01uF capacitors have lower impedance in higher frequency bands. In these frequency bands, if a 0.01uF capacitor can meet the capacity requirement, it will have a better decoupling effect than a 0.1uF capacitor.

　　Many high-speed chip design manuals with more pins will give the requirements for decoupling capacitors in power supply design. For example, a BGA package with more than 500 pins requires a 3.3V power supply with at least 30 ceramic capacitors and several large capacitors with a total capacity of more than 200uF.