First, the capacitor charge and discharge time calculation 1. The L and C components are called "inertial components". That is, the current in the inductor and the voltage across the capacitor have a certain "electrical inertia" and cannot suddenly change. The charge and discharge time is not only related to the capacity of L and C, but also related to the resistance R in the charge/discharge circuit. “How long does the 1UF capacitor charge and discharge it?†and cannot answer without resistance. Time constant of RC circuit: τ=RC When charging, uc=U×[1-e^(-t/τ)] U is the power supply voltage; when discharging, uc=Uo×e^(-t/τ) Uo is the voltage on the capacitor before discharge Time constant of RL circuit: τ=L/R LC circuit connected to DC, i=Io[1-e^(-t/τ)] Io is the final steady current; the short circuit of the LC circuit, Io is the current in L before the short circuit 2. Let V0 be the initial voltage value on the capacitor; V1 is the voltage value that the capacitor can be charged or put into; Vt is the voltage value on the capacitor at time t. Then: Vt = V0 + (V1-V0) × [1-exp (-t/RC)] or t = RC × Ln [(V1 - V0) / (V1 - Vt)] For example, the battery with voltage E passes R charges the capacitor C with an initial value of 0, V0 = 0, V1 = E, so the voltage on the capacitor when charged to t is: Vt = E × [1-exp(-t/RC)] Again, the initial voltage The capacitor C for E is discharged through R, V0 = E, V1 = 0, so the voltage on the capacitor when placed at t is: Vt = E × exp (-t/RC) Another example is that the initial value is 1/3Vcc capacitor C charges through R, the final charging value is Vcc. What is the time required to charge 2/3Vcc? V0=Vcc/3, V1=Vcc, Vt=2*Vcc/3, so t=RC×Ln[(1-1/3)/(1-2/3)]=RC×Ln2=0.693RC Note: The above exp() denotes the exponential function with e as the base; Ln() is the logarithm function with e as the base 3. Provide a common formula for constant current charge and discharge: ?Vc=I*?t/C. Then provide a common formula for capacitor charging: Vc=E(1-e-(t/R*C)). In the RC circuit charge formula Vc=E(1-e-(t/R*C)): -(t/R*C) is the negative exponent term of e. The capacitor used for the delay capacitor is relatively good and cannot be generalized. The actual capacitance is added with parallel insulation resistance, series lead inductance and lead resistance. There are more complicated modes - causing adsorption effects and so on. for reference. E is the magnitude of a voltage source. By closing a switch, a step signal is formed and the capacitor C is charged through the resistor R. E can also be a high-level amplitude of a continuous pulse signal whose amplitude changes from a low level of 0V to a high level. The variation of the voltage Vc across the capacitor with time is the charging formula Vc=E(1-e-(t/R*C)). Among them: -(t/R*C) is the negative exponent term of e, which cannot be shown here and requires special attention. Where t is the time variable and e is the natural exponent term. For example: When t=0, e is 0 to 0, and Vc is calculated as 0V. Meet the law that the voltage across the capacitor cannot be abruptly changed. The common formula for constant current charge and discharge is: Vc=I*?t/C, which is derived from the formula: Vc=Q/C=I*t/C. For example: Let C = 1000uF, I is a constant current source of 1A current amplitude (ie: its output amplitude does not change with the output voltage) to charge or discharge the capacitor, according to the formula can be seen, the capacitor voltage increases or decreases linearly with time, Many triangular waves or sawtooth waves are produced in this way. According to the set value and formula can be calculated, the rate of change of the capacitor voltage is 1V/mS. This means that the 5V capacitor voltage change can be obtained in 5mS; in other words, it is known that Vc changes by 2V, and it can be calculated that it has gone through a 2mS time history. Of course, both C and I in this relation can also be variables or reference quantities. Details can refer to the relevant materials to see. for reference 4. First set the capacitor plate charge at t is q, the voltage between the plates is u. According to the loop voltage equation can be: Uu = IR (I represents the current), and because u = q / C, I =dq/dt (where d is the derivative), after substitution, we get: Uq/C=R*dq/dt, that is, Rdq/(Uq/C)=dt, and then we get the indefinite integral on both sides, and use the initial condition: t =0, q=0 gives q=CU [1-e^-t/(RC)] This is the function of the charge on the capacitor plate over time t. By the way, electrical engineering often calls RC a time constant. Correspondingly, using u = q/C, the function of the plate voltage over time is immediately obtained, u = U [1-e^-t/(RC)]. Judging from the formulas obtained, only when the time t approaches infinity, the charge and voltage on the pole plate reach stability, and the charging is finished. However, in practical problems, since 1-e ^-t/(RC) tends to move toward 1 soon, after a short period of time, the change in charge and voltage between the capacitor plates is negligible, even if we use very high sensitivity. The electrical instrument is also unaware that the q and u changes slightly, so at this point it can be assumed that the balance has been reached and the charge is over. To give a practical example, suppose that U = 10 volts, C = 1 picofarad, and R = 100 ohms. Using our formula, we can calculate that after t = 4.6 * 10 ^ (-10) seconds, the voltage of the plate has reached 9.9 volts. It can be said that it is a moment of speed. Second, the choice of capacitance When the general Electrolytic capacitor is in use, if there is no large ripple, the withstand voltage can be as large as 20% of the actual value, that is, the output of the 7805 is already very enough with 10V, 6V is also OK; 7809 with 16V is enough, with 10V will not There is a big problem, the output of the three-terminal regulator does not need to take a large capacitor, depending on the actual load, the general 100mA then 47-100uF can be, 1A then 470-1000uF, preferably a further 0.01-0.1uF Small tiles or monolithic capacitors. Main filter capacitor In general, the role of electrolytic capacitor is to filter out the low-frequency signal in the current, but even the low-frequency signal, the frequency is divided into several orders of magnitude. Therefore, in order to be suitable for use at different frequencies, electrolytic capacitors are also divided into high-frequency capacitors and low-frequency capacitors (where high frequencies are relative). Low-frequency filter capacitor is mainly used for mains filter or transformer rectification filter, its operating frequency is consistent with the city power is 50Hz; and high-frequency filter capacitor mainly works in the switching power supply rectification filter, its operating frequency is several thousand Hz to several Million Hz. When we use low-frequency filter capacitors for high-frequency circuits, because of the poor high-frequency characteristics of low-frequency filter capacitors, it has a large internal resistance at high frequency charge and discharge, and the equivalent inductance is high. Therefore, during use, large amounts of heat are generated due to the frequent polarization of the electrolyte. The higher temperature will vaporize the electrolyte inside the capacitor and the pressure in the capacitor will increase, eventually causing the capacitor to bulge and burst. The selection of the filter capacitor is followed by a pulsed DC after the rectification bridge, which has a large range of fluctuations. Behind the general use of the size of two capacitors, large capacitors used to stabilize the output, it is well known that the voltage across the capacitor can not be mutated, it can make the output smooth; small capacitors are used to filter out high-frequency interference, so that the output voltage is pure. The smaller the capacitance, the higher the resonant frequency and the higher the filterable interference frequency. 1. Capacity selection: (1) Large capacitance, the heavier the load, the stronger the ability to absorb current, the larger the capacity of this large capacitor; (2) Small capacitance, based on experience, generally 104 can. Other people's experience 1. Capacitance-to-ground filtering requires a small parallel capacitor to ground to provide a ground path to high-frequency signals. 2. The capacitor should be as close as possible to the ground in the power filter. 3. Theoretically, the larger the power filter capacitor, the better. Generally, the large-capacitor filter filters low-frequency waves and small capacitors filter high-frequency waves. 4. The reliable method is to connect two capacitors, one large and one small, in parallel. Generally, the difference is more than two orders of magnitude to obtain a larger filter frequency band. Specific Case: After the AC220-9V is fully bridged, what filter capacitor should be added? What is the capacitance after 78LM05? The former capacitor withstand voltage should be greater than 15V, and the capacitor capacity should be greater than 2000 micro-fails or more. The latter capacitor voltage should be greater than 9V, the capacity should be greater than 220 micro-fails. 2. A single-phase Bridge Rectifier circuit with capacitor filtering, with an output voltage of 24V and a current of 500mA. Requirements: (1) choose rectifier diodes; (2) select filter capacitors; (3) another: capacitor filter is step-down or booster? (1) Because the bridge is full-wave, each diode current will only reach half of the load current, so the maximum diode current is greater than 250mA; the output voltage of the capacitor-filtered bridge rectifier is equal to 1.2 times the effective value of the input AC voltage. Therefore, the effective value of the AC voltage input by your circuit should be 20V, and the maximum backpressure the diode can withstand is twice the voltage of this voltage. Therefore, the diode withstand voltage should be greater than 28.2V. (2) Select the filter capacitor: 1, the voltage is greater than 28.2V; 2, the size of C: the formula RC ≥ (3--5) × 0.1 seconds, in this question R = 24V/0.5A = 48 ohm, so can be drawn C≥(0.00625--0.0104)F, that is, the value of C should be greater than 6250μF. (3) Capacitor filtering is increasing voltage. Filter capacitor selection principle In the power supply design, the filter capacitor selection principle is: C ≥ 2.5T/R; where: C is the filter capacitor in UF; T is the frequency in units of Hz; R is the load resistance in units Ω. Of course, this is only a general selection principle. In practical applications, if conditions (space and cost) allow, C≥5T/R is selected. 3. The size of the filter capacitor selection PCB plate capacitance selection There are contactors, relays, buttons and other components in the printed board. When operating them, large spark discharges are generated, and an RC absorption circuit must be used to absorb the discharge current. General R takes 1~2kΩ, C takes 2.2~4.7μF, general 10PF capacitors are used to filter out high-frequency interference signals, 0.1UF or so is used to filter out low-frequency ripple interference, and can also be used as a regulator. The role. What capacitance value is chosen by the filter capacitor depends on the main operating frequency on your PCB and the harmonic frequency that may affect the system. You can check the capacitor data of the relevant manufacturer or refer to the database software provided by the manufacturer and choose according to the specific needs. . As for the number is not necessarily, to see your specific needs, plus one or two is also very good, temporarily useless can not paste, according to the actual debugging situation and then choose the value. If the main operating frequency on your PCB is relatively low, you can add two capacitors, one to eliminate ripple and one to eliminate high-frequency signals. If there is a relatively large instantaneous current, it is recommended to add a larger tantalum capacitor. In fact, the filter should also include two aspects, that is, you say the large value and small value, decoupling and bypass. Principle I will not say, practical point, the general digital circuit decoupling 0.1uF can be used for 10M or less; 20M above with 1 to 10 uF, remove high-frequency noise better, probably by C = 1 / f. The bypass is generally relatively small, generally based on the resonant frequency is generally 0.1 or 0.01uF. When it comes to capacitance, various names can make people dizzy, bypass capacitors, decoupling capacitors, filter capacitors, etc. In fact, regardless of how they are called, the principle is the same, that is, the use of AC signals. The low-impedance characteristic can be seen by the equivalent impedance formula of the capacitor: Xcap = 1/2 лfC, the higher the operating frequency, the larger the capacitance is, the smaller the impedance of the capacitor is. In the circuit, if the main role of the capacitor is to provide a low-impedance path for the AC signal, it is called the bypass capacitor; if it is mainly to increase the AC coupling of the power supply and the ground and reduce the influence of the AC signal on the power supply, it can be called Decoupling capacitors; if used in the filter circuit, it can also be called filter capacitor; In addition, for DC voltage, the capacitor can also be used as a circuit to store energy, the use of red discharge to play the role of the battery. In actual situations, the role of the capacitor is often multifaceted. We don't have to spend too much thought on how to define it. In this article, we uniformly refer to these capacitors used in high-speed PCB designs as bypass capacitors. The essence of the capacitor is to communicate with AC and DC. In theory, the larger the power filter capacitor, the better. However, due to lead wires and PCB layout, in practice, the capacitor is a parallel circuit of inductance and capacitance (the resistance of the capacitor itself cannot be ignored). This introduces the concept of resonant frequency: ω=1/(LC)1 /2 The capacitor is capacitive below the resonant frequency, and the capacitor above the resonant frequency is inductive. As a result, large capacitors filter low-frequency waves and small capacitors filter high-frequency waves. This can also explain why the capacitive filtering frequency of the same capacitance STM package is higher than the DIP package. A more reliable approach is to connect two capacitors, one large and one small, in parallel, generally requiring a difference of more than two orders of magnitude to obtain a larger filter band. In general, large capacitors filter low-frequency waves, and small capacitors filter high-frequency waves. The capacitance value is inversely proportional to the square of the frequency you want to filter out. The choice of a specific capacitor can be determined by using the formula C=4Pi*Pi/(R*f*f). How to choose the filter capacitor for the power supply? It is not difficult to master its essence and method. 1) Theoretically ideal capacitor's impedance decreases with increasing frequency (1/jwc), but due to the inductance effect of the pin at both ends of the capacitor, the capacitor should be seen as a LC series resonant circuit, and the self-resonant frequency The device's FSR parameter, which means that when the frequency is greater than the FSR value, the capacitor becomes an inductor. If the capacitor is filtered to ground, when the frequency exceeds FSR, the suppression of interference is greatly reduced, so a smaller capacitor is needed in parallel to ground. , can you think about why? The reason is that small capacitors, SFR value, provides a ground path for high-frequency signals, so we often understand this in the power supply filter circuit: large capacitors account for low frequencies, small capacitors account for high frequencies, fundamental The reason is that the value of SFR (Self Resonance Frequency) is different, but of course you can also think about why. If you think from this point of view, you can understand why the capacitance of the power supply filter is as close as possible to the ground. 2) Then in the actual design, we often have questions, how do I know the SFR of the capacitor? Even if I know the SFR value, how do I choose the capacitance of different SFR values? Is it a capacitor or two capacitors? The SFR value of the capacitor is related to the capacitance value and related to the pin inductance of the capacitor. Therefore, the 0402, 0603 of the same capacitance value or the SFR value of the in-line capacitor will not be the same. Of course, there are two ways to obtain the SFR value. 1) The device data sheet, such as 22pf0402 capacitor SFR value is about 2G, 2) Measure the self-resonant frequency directly through the network analyzer, and think about how to measure the S21? After knowing the SFR value of the capacitor, use software simulation, such as RFsim99, to select one or two circuits to work on the circuit you are supplying. Whether the frequency band has enough noise suppression ratio. After the simulation, that is the actual circuit test, such as debugging mobile phone receiver sensitivity, LNA power supply filtering is the key, good power supply filter can often improve a few dB. Inductance impedance and frequency into In proportion, the impedance of the capacitor is inversely proportional to the frequency. Therefore, the inductor can block the high frequency through, the capacitor can block the low frequency through. The appropriate combination of the two, you can filter a variety of frequency signals. Such as in the rectifier circuit, the capacitor is The AC ripple can be filtered out by placing the inductor in series or on the load. Inductor filter is a current filter, which is based on the current induced electromagnetic induction to smooth the output current, the output voltage is low, lower than the AC voltage rms; suitable for large current, the greater the current the better the filtering effect. Many of the characteristics of capacitors and inductors are exactly the opposite. Under normal circumstances, the role of electrolytic capacitors is to filter out low-frequency signals in the current, but even for low-frequency signals, the frequency is divided into several orders of magnitude. Therefore, in order to be suitable for use at different frequencies, electrolytic capacitors are also divided into high-frequency capacitors and low-frequency capacitors (where high frequencies are relative). Low-frequency filter capacitor is mainly used for mains filter or transformer rectification filter, its operating frequency is consistent with the city power is 50Hz; and high-frequency filter capacitor mainly works in the switching power supply rectification filter, its operating frequency is several thousand Hz to several Million Hz. When we use low-frequency filter capacitors for high-frequency circuits, because of the poor high-frequency characteristics of low-frequency filter capacitors, it has a large internal resistance at high frequency charge and discharge, and the equivalent inductance is high. Therefore, during use, large amounts of heat are generated due to the frequent polarization of the electrolyte. The higher temperature will vaporize the electrolyte inside the capacitor and the pressure in the capacitor will increase, eventually causing the capacitor to bulge and burst. Power filter capacitor size, usually do design, the former with 4.7u, used to filter low frequency, secondary with 0.1u, used to filter high frequency, 4.7uF capacitor function is to reduce output ripple and low frequency interference, 0.1uF The capacitance should be to reduce high-frequency interference due to instantaneous changes in the load current. Generally, the bigger the better, the difference between the two capacitances is about 100 times. Power supply filtering, switching power supply, depends on how large your ESR (equivalent series resistance of the capacitor) is, and the choice of high-frequency capacitance is best at its self-resonant frequency. Large capacitance is to prevent surge, the mechanism is like a large reservoir flood control capability is the same; small capacitor filter high-frequency interference, any device can be equivalent to a resistor, inductor, capacitor series and parallel circuit, also has a self-resonance, Only at this self-resonant frequency, the equivalent resistance is minimal, so filtering is best! The equivalent model of the capacitor is an inductor L, a series connection of a resistor R and a capacitor C, an inductor L is the capacitor lead, a resistor R represents the active power loss of the capacitor, and a capacitor C. So it can be equivalent to series LC loop to find its resonant frequency, the condition of series resonance is L = 1/WC, W = 2 * PI * f, so as to get this formula f = 1/(2pi * LC). The minimum reactance at the center frequency of the series LC loop is pure resistance, so the center frequency plays a filtering effect. The size of the lead inductance is different due to its coarse and short length. The inductance of the grounding capacitor is generally about 1 MM is about 10nH, depending on the frequency of the grounding. The use of capacitor filter design needs to consider the parameters: ESR ESL voltage value resonant frequency filter capacitor range is too wide, here simply talk about the power supply bypass (defect) capacitor. The choice of filter capacitor depends on whether you are using a local or global power supply. For local power, it is to act as a transient power supply. Why add capacitors to power it? This is because the device's current demand changes rapidly with the drive requirements (such as the DDR controller). In the high frequency range, the circuit's distribution parameters must be considered. Due to the presence of distributed inductance, the rapid change of current is hindered, so that the voltage on the chip power supply pin is reduced - that is, noise is formed. Moreover, the current feedback power supply has a reaction time - that is, to wait until the voltage fluctuations have occurred for a period of time (usually ms or us) to make adjustments, for the ns class current demand changes, this kind of Delay also forms actual noise. Therefore, the role of the capacitor is to provide a low inductance (impedance) path to meet the rapid changes in current demand. Based on the above theory, the calculation of the capacitance must be based on the energy that the capacitor can provide to change the current. The type of capacitor chosen needs to be considered in terms of its parasitic inductance—that is, the parasitic inductance is smaller than the distributed inductance of the power path. Discussion issues must start from the essence. First of all, it may be known that the capacitor acts as a galvanic isolation to the DC and the inductor acts the opposite. All are based on basic principles. At this time, the capacitor has the most common two effects. One is used to isolate the DC between poles. It is also known as a coupling capacitor because it isolates the DC but passes the AC signal. The dc path is limited to a few stages, which simplifies the calculation of the operating point that is very complicated and the second is filtering. Basically these two. As a coupling, the value of the capacitor is not strict, as long as the impedance is not too large, so the signal attenuation can be too large. However, for the latter, it is required to consider from the perspective of the filter, such as the power supply filtering at the input, which not only filters out low-frequency (for example, power frequency) noise, but also filters out high-frequency noise, so it needs to be used at the same time. Large capacitors and small capacitors. Some people will say that with large capacitors, what else should be done? This is because of the large capacitance. Since the plate and the pin end are large, the inductance is also large, so it has no effect on the high frequency. The small capacitors are just the opposite. According to this size, the capacitance can be determined. For the pressure resistance, it must be satisfied at any time. Otherwise, it will explode. Even for non-electrolytic capacitors, they sometimes do not explode, and their performance is also reduced. All of them are filters. Aluminum Electrolytic Capacitors have a relatively large capacity and are mainly used to eliminate low-frequency interference. A current of approximately 1mA corresponds to 2 to 3μf, and when the demand is high, 1mA corresponds to 5 to 6μf. Non-polarity capacitors are used to consider high-frequency signals. When used alone, most of them are used. It can sometimes be used in parallel with electrolytic capacitors. The high-frequency characteristics of ceramic capacitors are better, but at a certain frequency (about 6MHz is not clear) is the capacity decline quickly. The parasitic inductance of the capacitor mainly includes the inductance and lead inductance determined by the internal structure. The parasitic inductance of an electrolytic capacitor is mainly determined by the internal structure. In the impression of aluminum electrolytic capacitors in the 20 ~ 30k or more, in addition to the obvious performance of the inductor. Tantalum capacitor is around 1MHz. The high frequency characteristics of ceramic capacitors are much better. However, ceramic capacitors have a piezoelectric effect and are not suitable for the input and output of audio amplifier circuits. This is because of the large capacitance. Since the plate and the pin end are large, the inductance is also large, so it has no effect on the high frequency. The small capacitors are just the opposite. According to this size, the capacitance can be determined. For the pressure resistance, it must be satisfied at any time. Otherwise, it will explode. Even for non-electrolytic capacitors, they sometimes do not explode, and their performance is also reduced. Glass Metal Sealed Cap Glass Metal Sealed Cap YANGZHOU POSITIONING TECH CO., LTD. , https://www.cnfudatech.com