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Capacitance of decoupling radius calculation

by:SMiLer     2021-01-26
An important problem capacitance of decoupling is the decoupling capacitor radius. Most data will be mentioned in capacitance is put as much as possible close to the chip, most information are from the Angle of the reduce the loop inductance to talk about the problem of distance. Indeed, decrease the inductance is an important reason, but there is also a most important reason why data don't mention, that is radius of capacitance decoupling problem. If the capacitance is put far from chips before, beyond its decoupling radius, capacitance will lose its decoupling effect. The best way to understand the decoupling radius is to review the phase relationship between noise and capacitor compensation current. When chip demand for current changes, the power plane of a small local area voltage disturbance, capacitance to compensate the current ( Or voltage) , you must first perceive the voltage disturbance. It takes time to signal propagation in a medium, so from local voltage changes to capacitance sensing to a time delay between the disturbance. Similarly, compensation of capacitance current to the district of disturbance also needs a delay. Therefore cause noise and phase on the inconsistent between the capacitance compensation current. Specific capacitance, with it since the resonant frequency of the same noise compensation effect is best, we measured in the frequency of the phase relationship. For example: 0. 001 uf ceramic capacitors, if the total parasitic inductance after installed to the circuit boards of 1. The resonance frequency of the 6 nh, after its installation for 125. 8 MHZ, resonant cycle for 7. 95ps。 Assumes that the signal on the circuit board at the rate of 166 ps/inch, the spread of the wavelength of 47. 9 inches. Capacitance decoupling radius of 47. 9/50 = 0. 958 inches, about equal to 2. 4 cm. Set the resonant frequency to f, corresponding wavelength L, compensation current expression can be written as: among them, A is current amplitude, R for the needs of the area to the capacitance compensation distance, C for signal transmission speed. When the disturbance zone to the distance to the capacitance L / 4, the phase compensation current PI = 3. 14, and phase noise just sent 180 degrees, namely completely reversed phase. The compensation current no longer work, decoupling function failure, the energy compensation cannot be delivered in a timely manner. To transfer to compensate the energy effectively, should make noise and offset current phase difference as small as possible, had better be in phase. The closer distance, phase difference is smaller, the more compensation energy transfer, if the distance to 0, the compensation one hundred percent energy transfer to the disturbance area. This requires a noise source capacitance as much as possible close, far less than L / 4. In practical application, the distance from the best control between L / 40 ~ 50 L /, which is an empirical data. In this case capacitance can only around 2 for it. 4 cm within the scope of the power supply noise compensation, namely its decoupling radius 2. 4 cm. Different capacitance, the resonance frequency is different, different radius of decoupling. For large capacity, because of its resonance frequency is low, the corresponding wavelength is very long, thus decoupling radius is large, and this is why we are not too concerned about the cause of the large capacitance on the circuit board is placed. For small capacitance, for decoupling the radius is very small, as near as possible to the need of decoupling chip, this is what most of the materials will be repeatedly stressed that the small capacitor as close as possible to place close to the chip.
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