In-depth understanding of the equivalent series resistance (ESR) of capacitors, the role of multiple small capacitors in parallel to replace large electrolytic capacitors

Equivalent series resistance ESR of capacitance

The prevailing view is that an external capacitance of relatively large capacity with a small equivalent series resistance (ESR) can well absorb the peak (ripple) current at fast conversion. However, sometimes such a choice can cause the voltage regulator (especially the linear regulator  ldo) instability, so it is necessary to choose a reasonable capacitance of small capacity and large capacity. Always remember that a voltage regulator is an amplifier that can appear in various situations where the amplifier may appear. Because the  DC/DC  converter responds relatively slowly, the output decoupling capacitor plays a leading role in the initial phase of the load step, so additional capacitance is required to slow down the fast conversion to the  DC/DC  converter. At the same time, high-frequency capacitance is used to slow down the rapid transformation of large capacitance. In general, the equivalent series resistance of a large capacitance capacitor should be selected as the appropriate value so that the output voltage spikes and glitches are within the device's dasheet  requirements. In high-frequency conversion, the small capacitance capacitor can meet the requirements in  0.01μF  to 0.1μf . Surface-mount Ceramic capacitors or multilayer ceramic capacitors (MLCCS) have a smaller  esr. In addition, their volume and  BOM  cost are reasonable under these allowances. If the local low frequency decoupling is not sufficient, then the input voltage will be reduced when converting from low frequency to high frequency. The voltage drop process can last for several milliseconds, depending on the regulator's tuning gain and the time it takes to provide a large load current. It is certainly more cost-effective to use a  ESR  large capacitance in parallel with a single capacitor that is so low in  ESR . However, this requires that you seek a tradeoff between the  PCB  area, the number of devices, and the cost.

In-depth understanding of capacitor equivalent series resistance (ESR)

The main technical specifications of capacitors are electrical capacity, pressure value, temperature resistance value. In addition to these three main indicators, the more important of the other indicators is the equivalent series resistance (ESR). Some capacitors have a gold ribbon line printed with a large hollow letter "I", which indicates that the capacitor belongs to the LOW ESR low loss capacitance. Some capacitors also have an ESR value (equivalent series resistance), the lower the ESR, the smaller the loss, the greater the output current, the higher the quality of the capacitor. The esr  is the abbreviation for Equivalent series resistance, the equivalent series resistor. The ideal capacitor itself will not have any energy loss, but in fact, because the material that makes the capacitance has a resistor, the capacitance of the insulating medium is lossy. This loss is external and behaves like a resistor in series with a capacitor, so it is called an "equivalent series resistor". Another concept similar to ESR is ESL, which is the equivalent series inductance. Early coil inductors often have very high ESL, and the larger the capacitance, the greater the ESL is generally. ESL is often a part of ESR, and ESL can cause a series resonance. However, compared to the electrical capacity, the proportion of ESL is very small, the probability of problems is very small, and later due to the increase in the production of capacitors, and now gradually ignore ESL, and the ESR as the addition of capacity, pressure, temperature resistance of the main reference factor of the choice of capacitors.  

     series equivalent resistance ESR is in milli-ohm (MΩ) units. Tantalum capacitors typically have an ESR of less than 100 milli-ohms, while aluminum electrolytic capacitors are higher than this, and some types of capacitors can  esr even up to several ohms. The ESR is related to the capacitance, voltage, frequency and temperature of the capacitor, and when the rated voltage is fixed, the larger the capacity  ESR the lower. Similarly, when the capacity is fixed, the selection of high rated voltage varieties can also reduce  ESR; so the use of high-pressure capacitor does have many advantages, low-frequency ESR, high-frequency ESR, high temperature will also cause an increase in ESR.  

     now electronic technology is moving towards the design direction of low voltage high current circuit, The voltage supplied to the components is trending down, but the power requirements are not reduced. According to the P=UI formula, to obtain the same power, the voltage is reduced, it is necessary to increase the current. For example, Intel, AMD's latest CPU, the voltage is less than 2V, and the previous 3,  4v voltage compared to much lower. But on the other hand, because of the proliferation of transistors and frequencies, the power consumption of these chips is increasing, and the demand for electric current is higher. For example, both power is 70W  cpu, the former voltage is 3.3V, the latter voltage is 1.8V. The former, then, is i=p/u=70w/3.3v=21.2a, while the latter's current is i=p/u=70w /1.8v=38.9a, nearly twice times the former current. In the case of a higher current through the capacitance, if the capacitance of the ESR value can not be maintained in a small range, then the higher ripple voltage (the ideal output DC voltage should be a horizontal line, and the ripple voltage is the crest and trough of the horizon), so that the engineer in the design, To use the smallest ESR capacitor.  

the relationship between the ESR value and the ripple voltage can be expressed in equation V=r (ESR) XI. The V in this formula represents the ripple voltage, and R indicates that the esr,i of the capacitor represents the current. It can be seen that when the current increases, the ripple voltage increases exponentially even when the ESR remains constant, so capacitors with lower ESR values are imperative. In addition, even the same ripple voltage, the effect on the low voltage circuit is greater than in the case of high voltage. For example, 3.3V CPU, 0.2V ripple voltage accounted for a small proportion, not enough to form a big impact, but for the 1.8V CPU, the same 0.2V ripple voltage, the proportion of which is enough to cause the digital circuit judgment error.

For example, "E-News" 2007 26th issue 17 version of the "12V, 1A switching power supply" by NCP1200, the switch transformer secondary diode rectifier lowpass Type filter Capacitor C6, C7 requirements is "to choose the equivalent series resistance small high-quality electrolytic capacitors, The equivalent resistance affects not only the conversion rate but also the output ripple voltage. ”

ESR is an equivalent "in series" resistor, in series with two capacitors, which increases the ESR value and decreases in parallel. Therefore, in cases where lower ESR is required, while low ESR high capacitance is relatively expensive, it is common to create a low ESR high capacitance capacitor in parallel with multiple ESR-higher aluminum electrolytic capacitors. Many switching power supply to take the capacitor parallel strategy to sacrifice a certain amount of PCB space, in exchange for the reduction of the cost of the device.

However, there are some good aspects in the existence of the equivalent series resistors. For example, in the voltage regulator circuit, there is a certain ESR capacitance, when the load transients, will immediately generate fluctuations and trigger feedback circuit action, the rapid response to sacrifice a certain transient performance at the expense of the subsequent rapid adjustment, especially the power tube response speed is relatively slow, but also in the volume of the capacitor, Severely limited capacity. This situation is more common in some three-terminal regulators or similar circuits where the MoS tube is used as an adjustment tube, but a low ESR capacitor can reduce overall performance.

The role of multiple small capacitors in parallel replacing large electrolytic capacitors

This usage is common in the switching power supply section, which acts as a high frequency filter. Multiple capacitor parallel is mainly to reduce the equivalent impedance of the capacitance, because in parallel. The electrolytic capacitance is replaced by a small capacitance ceramic capacitor, which increases the life expectancy. Electrolytic capacitors have a lifetime of only thousands of hours, while ceramic capacitors have a lifespan of hundreds of thousands of hours. The principle of preventing the faddish effect is to increase the surface area of the wire. Multiple capacitors can only reduce line reliability, but not the high frequency performance of large capacitors is poor. Usually the larger the capacitance, the lower the resonant frequency. Once the resonant frequency is exceeded, the capacitance will be represented as an inductor, completely does not have the function of filtering, if with n small capacitance in parallel, because each small capacitance resonant frequency is very high, there is no such problem , the same capacitance, the more small capacitors in parallel, the better the pressure value, temperature, capacitance, ESR (equivalent resistance) is a number of important parameters of the capacitor, for ESR is naturally lower the better. ESR is related to capacitance capacity, frequency, voltage, temperature, and so on. When the voltage is fixed, the larger the capacity, the lower the ESR. In the board design to adopt a number of small capacitors and even more is out of the limitations of the PCB space, so some people think, the more parallel small resistors, the lower the ESR, the better the effect. Theoretically so, but to consider the capacitance of the solder joint point impedance, the use of multiple small capacitors in parallel, the effect is not necessarily prominent.

The lower the ESR, the better the effect.

In combination with the improved power supply circuit above, the input capacitance is a bit larger for the input capacitance. Relative capacity requirements, the ESR requirements can be appropriately reduced. Because the input capacitance is mainly voltage withstand, followed by the switching pulse absorption MOSFET. For the output capacitance, the pressure requirements and capacity can be properly reduced a little. The ESR requirement is a bit higher because there is enough current to be guaranteed. However, it is important to note that ESR is not as low as possible, and low ESR capacitors can cause the switching circuit to oscillate. The complexity of the damping circuit also leads to increased costs. Board design, here is generally a reference value, this as a component selection parameters, to avoid the elimination of vibration circuit and lead to increased costs.

A good capacitor stands for high quality.

"Only capacitance theory" once flourished, some manufacturers and the media have deliberately made this thing a selling point. In the board design, the circuit design level is the key. And some manufacturers can use two-phase power supply than some manufacturers using four-phase power supply more stable products, blindly using high-priced capacitors, not necessarily can make good products. Measurement of a product, must be all-round multi-angle to consider, should not be the role of capacitance unintentionally exaggerated.

Ripple voltage, output capacitance ESR

The output ripple voltage of the switching power supply is divided into two parts, One is the capacitive ripple voltage generated by the capacitor charge and discharge, and the other is the resistive ripple voltage generated by the capacitance ESR.   In order to get a smaller ESR-generated resistive ripple voltage, I heard that multiple capacitors can be used in parallel, I do not know how the total ESR of a number of capacitors in parallel, how specific changes, smaller I can understand, but become what value?   For example, a 470uF electrolytic capacitor ESR is 0.1 kohm, that two electrolytic parallel up ESR is not 0.05 euro I have some doubts now, I do not know that with low ESR ceramic capacitors in parallel with the electrolytic capacitor, there is no same effect. For example, I output, after calculation, ripple requirements capacitance ESR less than 0.01 kohm, that according to the previous idea, may require several electrolytic capacitors to meet the requirements, if I choose to use an electrolytic capacitor, and then give it a number of ceramic capacitors in parallel 103 or 104, there is no effect.

Answer: If the ESR is required to be very low, it is generally important to select a large MLCC (multilayer CERAMIC CHIP capacitor), which does not need to be parallel in N 104.

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More than 1 parallel, can actually reduce the specific calculation method of ESR, in parallel with the resistor.

2 can choose low ESR electrolysis, but the price is more expensive.

3 film capacitors can also be selected instead.

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Different types of capacitors in parallel. The equivalent ESR and capacitance values are associated with frequency. It's not a simple esr/n,cxn. Usually small ESR small volume and large ESR, large capacitance in parallel. Both ESR and capacitance are in between.

You said that the electrolytic capacitor and low ESR porcelain, to reduce the ripple is effective.

Filter circuit a few capacitors in parallel and a large capacitance (equal capacity) what is the difference?

Answer: both capacitance capacities are equal. But in reality the capacitance is a parasitic parameter of the equivalent series inductance and the equivalent series resistance, and a capacitor can be seen as a model

, a large capacitance of ESL and ESR is larger than the capacitance of small capacity, and in the same capacity ESL and ESR values the smaller the filter capacity of the capacitor is stronger, so a plurality of capacitors in parallel and a large capacitance equivalent of the main difference is that multiple capacitors in parallel with the ESL and ESR is much lower than a large capacitance equivalent capacity , the filtering ability is stronger. You might think that the small capacitance (assuming 100u) of the ESL and ESR is equivalent to the large capacitance (200u) of ESL and ESR, and then the two small capacitors in parallel with the equivalent capacitance equal to 200U, but its ESL and ESR because of parallel and halved, so the two small capacitors in parallel filtering capability is stronger. If this is four parallel, then ESL and ESR are one-fourth of the large capacitance. I hope I can help you.

A brief talk on the misunderstanding of capacitor use

1. The bigger the capacitance, the better?

Many people often love to use large capacitance in the replacement of capacitors. We know that the greater the capacitance, the greater the ability to compensate for the current provided by the IC. It does not say that the increase in capacitance increases the volume, increasing the cost while also affecting the air flow and cooling. The key is that there is parasitic inductance on the capacitor, and the capacitance discharge circuit will resonate at a certain frequency point. At the resonant point, the capacitance has a small impedance. Therefore, the impedance of the discharge circuit is minimal and the effect of replenishing energy is the best. However, when the frequency exceeds the resonant point, the impedance of the discharge circuit begins to increase, and the capacitance supply current capability begins to decline. The larger the capacitance, the lower the resonant frequency, and the smaller the frequency range of the capacitor to compensate the current effectively. From the point of view of the ability of the capacitor to provide high-frequency current, the larger the capacitor the better the view is wrong, the general circuit design has a reference value.

2. Capacitance of the same capacity, the more in parallel with the smaller capacitance the better?

Voltage, temperature, capacitance, ESR (equivalent resistance) are some of the important parameters of the capacitance, for ESR is naturally lower the better. ESR is related to capacitance capacity, frequency, voltage, temperature, and so on. When the voltage is fixed, the larger the capacity, the lower the ESR. In the board design to adopt a number of small capacitors and even more is out of the limitations of the PCB space, so some people think, the more parallel small resistors, the lower the ESR, the better the effect. Theoretically so, but to consider the capacitance of the solder joint point impedance, the use of multiple small capacitors in parallel, the effect is not necessarily prominent.

3.ESR Lower, the better the effect?

Relative capacity requirements, the ESR requirements can be appropriately reduced. Because the input capacitance is mainly voltage withstand, followed by the switching pulse absorption MOSFET. For the output capacitance, the pressure requirements and capacity can be properly reduced a little. The ESR requirement is a bit higher because there is enough current to be guaranteed. However, it is important to note that ESR is not as low as possible, and low ESR capacitors can cause the switching circuit to oscillate. The complexity of the damping circuit also leads to increased costs. Board design, here is generally a reference value, this as a component selection parameters, to avoid the elimination of vibration circuit and lead to increased costs.

4. Good capacitance represents high quality?

"Only capacitance theory" once flourished, some manufacturers and the media have deliberately made this thing a selling point. In the board design, the circuit design level is the key. And some manufacturers can use two-phase power supply than some manufacturers using four-phase power supply more stable products, blindly using high-priced capacitors, not necessarily can make good products. Measurement of a product, must be all-round multi-angle to consider, should not be the role of capacitance unintentionally exaggerated.

In-depth understanding of the equivalent series resistance (ESR) of capacitors, the role of multiple small capacitors in parallel to replace large electrolytic capacitors