Understanding currents in DC/DC buck converter enter capacitors

All buck converters want capacitors on the enter. Truly, in an ideal world, if the provision had zero output impedance and infinite present capability and the tracks had zero resistance or inductance, you wouldn’t want enter capacitors. However since that is infinitesimally unlikely, it’s finest to imagine that your buck converter will want enter capacitors.

Enter capacitors retailer the cost that provides the present pulse when the high-side swap activates; they’re recharged by the enter provide when the high-side swap is off (Determine 1).

Determine 1 The above diagram reveals simplified present waveform within the enter capacitor present in the course of the buck DC/DC switching cycle, assuming infinite output inductance. Supply: Texas Devices

The switching motion of the buck converter fees and discharges the enter capacitor, inflicting the voltage throughout it to rise and fall. This voltage change represents the enter voltage ripple of the converter on the switching frequency. The enter capacitor filters the enter present pulses to attenuate the ripple on the enter provide voltage.

The quantity of capacitance governs the voltage ripple, so the capacitor should be rated to resist the root-mean-square (RMS) present ripple. The RMS present calculation assumes the presence of just one enter capacitor, with no equal collection resistance (ESR) or equal collection inductance (ESL). The finite output inductance accounts for the present ripple on the enter facet, as proven in Determine 2.

Determine 2 Enter capacitor ripple present and calculated RMS present are displayed by TI’s Energy Stage Designer software program. Supply: Texas Devices

Present sharing between parallel enter capacitors

Most sensible implementations use a number of enter capacitors in parallel to supply the required capacitance. These capacitors usually embody a small-value, high-frequency multilayer ceramic capacitor (MLCC), for instance, 100 nF. A number of bigger MLCCs (10 µF or 22 µF) are used, and typically accompany a polarized large-value bulk capacitor (100 µF).

Every capacitor is performing related but completely different capabilities; the high-frequency MLCC decouples quick transient currents attributable to the MOSFET switching course of in DC/DC converter. The bigger MLCCs supply the present pulses to the converter on the switching frequency and its harmonics. The majority capacitor provides the present required to reply to output load transients when the impedance of the enter supply implies that it can not reply as shortly.

The place used, a big bulk capacitor has a major ESR, which supplies some damping of the enter filter’s Q issue. Relying on its equal impedance on the switching frequency relative to the ceramic capacitors, the capacitor may additionally have important RMS present on the switching frequency.

The datasheet of a bulk capacitor specifies a most RMS present ranking to forestall self-heating and be sure that its lifetime just isn’t degraded. The MLCCs have a a lot smaller ESR and correspondingly a lot much less self-heating due to the RMS present. Even so, circuit designers typically overlook the utmost RMS present laid out in ceramic capacitor datasheets. Subsequently, it is very important perceive the RMS currents in every of the person enter capacitors.

If you’re utilizing a number of bigger MLCCs, you may mix them and enter the equal capacitance into the current-sharing calculator for calculating RMS currents in parallel enter capacitors. The calculation of RMS present considers the elemental frequency solely. Nonetheless, this calculation instrument is a helpful refinement of the one enter capacitor RMS present calculation.

Take into account an software the place V_IN = 9 V, V_OUT = 3 V, I_OUT = 12.4 A, f_SW = 440 kHz and L = 1 µH. The three parallel enter capacitors might then be 100 nF (MLCC), ESR = 30 mΩ, ESL = 0.5 nH; 10 µF (MLCC), ESR = 2 mΩ, ESL = 2 nH; and 100 µF (bulk), ESR = 25 mΩ, ESL = 5 nH. The ESL right here contains the PCB monitor inductance.

Determine 3 reveals the capacitor current-sharing calculator outcomes for this instance. The 100-nF capacitor attracts a low RMS present of 40 mA as anticipated. The bigger MLCC and bulk capacitors divide their RMS currents extra evenly at 4.77 A and 5.42 A, respectively.

Determine 3 Output is proven from TI’s Energy Stage Designer capacitor current-sharing calculator. Supply: Texas Devices

In actuality, the precise capacitance of the 10-µF MLCC is considerably decrease due to the voltage utilized. For instance, a 10-µF, 25-V X7R MLCC in an 0805 bundle would possibly solely present 30% of its rated capacitance when biased at 12 V, through which case the big bulk capacitor’s present is 6.38 A, which can exceed its RMS ranking.

The answer is to make use of a bigger capacitor bundle dimension and parallel a number of capacitors. For instance, a 10-µF, 25-V X7R MLCC in a 1210 bundle retains 80% of its rated capacitance when biased at 12 V. Three of those capacitors have a complete efficient worth of 24 µF when used for C2 within the capacitor current-sharing calculator.

Utilizing these capacitors in parallel reduces the RMS present within the giant bulk capacitor to three.07 A, which is extra manageable. Inserting the three 10-µF MLCCs in parallel additionally reduces the general ESR and ESL of the C2 department by an element of three.

The low capacitance of the 100-nF MLCC and its comparatively excessive ESR imply that this capacitor performs little half in sourcing the present on the switching frequency and its lower-order harmonics. The operate of this capacitor is to decouple nanosecond present transients seen on the switching instants of the DC/DC converter’s MOSFETs. Designers usually confer with it because the high-frequency capacitor.

With a purpose to be efficient, it’s important to put the high-frequency capacitor as shut as potential to the enter voltage and floor terminals of the regulator utilizing the shortest (lowest inductance) PCB routing potential. In any other case, the parasitic inductance of the tracks will stop this high-frequency capacitor from decoupling the high-frequency harmonics of the switching frequency.

It’s additionally necessary to make use of as small a bundle as potential to attenuate the ESL of the capacitor. A high-frequency capacitor with a price of <100 nF might be helpful for decoupling at a selected frequency when in comparison with its ESR and impedance curve. A smaller capacitor may have a better self-resonance frequency.

Equally, at all times place the bigger MLCCs as shut as potential to the converter to attenuate their parasitic monitor inductance and maximize their effectiveness on the switching frequency and its harmonics.

Determine 3 additionally reveals that, though the general RMS present within the total enter capacitor (have been it a single equal capacitor) is 6 A, the sum of RMS currents within the C1, C2 and C3 branches is >6 A and doesn’t observe Kirchhoff’s present legislation. The legislation solely applies to the instantaneous values, or to the advanced addition of the time-varying and phase-shifted currents.

Utilizing PSpice for TI or TINA-TI software program

Designers who want greater than three enter capacitor branches for his or her purposes can use PSpice for TI simulation software program or TINA-TI software program. These instruments allow extra advanced RMS present calculations, together with harmonics alongside the elemental switching frequency and using a extra refined mannequin for the capacitor, which captures the frequency-dependent nature of the ESR.

TINA-TI software program can compute the RMS present in every capacitor department within the following means: run the simulation, click on the specified present waveform to pick it, and from the Course of menu possibility within the waveform window, choose Averages. TINA-TI software program makes use of a numerical integration over the beginning and finish show instances of the simulation to calculate the RMS present.

Determine 4 reveals the simulation view. For readability on this instance, we omitted the 100-nF capacitor as a result of its present may be very low and contributes to ringing on the switching edges. The Energy Stage Designer software program evaluation of the whole enter capacitor present waveform for the converter calculates the enter present (I_IN), which is 6 A_RMS, the identical worth as for Determine 2.

Determine 4 Output from TINA-TI software program reveals the capacitor department present waveforms and calculated RMS present in C2. Supply: Texas Devices

The capacitor present waveforms in every department are fairly completely different in comparison with the idealized trapezoidal waveform that ignores their ESR and ESL. This distinction has implications for DC/DC converters such because the TI LM60440, which has two parallel voltage enter (V_IN) and floor (GND) pins.

The mirror-image pin configuration allows designers to attach two similar parallel enter loops, that means that they will place double enter capacitance (each excessive frequency and bulk) in parallel near the 2 pairs of energy enter (PVIN) and energy floor (PGND) pins. The 2 parallel present loops additionally halve the efficient parasitic inductance.

As well as, the 2 mirrored-input present loops have equal and reverse magnetic fields, permitting some H-field cancellation that additional reduces the parasitic inductance (Determine 5). Determine 4 means that if you happen to don’t rigorously match the parallel loops in capacitor values, ESR, ESL and format for equal parasitic impedances, then the present within the parallel capacitor paths can differ considerably.

Determine 5 Parallel enter and output loops are proven in a symmetrical “butterfly” format. Supply: Texas Devices

Software program instrument use issues

To appropriately specify enter capacitors for buck DC/DC converters, you need to know the RMS currents within the capacitors. You possibly can estimate the currents from equations, or extra just by utilizing software program instruments like TI’s Energy Stage Designer. It’s also possible to use this instrument to estimate the currents in as much as three parallel enter capacitor branches, as generally utilized in sensible converter designs.

Extra advanced simulation packages akin to TINA-TI software program or PSpice for TI can compute the currents, together with harmonics and basic frequencies. These instruments also can mannequin frequency-dependent parasitic impedance and plenty of extra parallel branches, illustrating the significance of matching the enter capacitor combos in mirrored enter butterfly layouts.

Dr. Dan Tooth is Member of Group Technical Workers at Texas Devices. He joined TI in 2007 and has been a discipline software engineer for over 17 years. He’s chargeable for supporting TI’s analog and energy product portfolio in ADAS, EV and numerous industrial purposes.

Dr. Jim Perkins Senior Member of Technical Workers at Texas Devices. He joined TI in 2011 as a part of the acquisition of Nationwide Semiconductor and has been a discipline software engineer for over 25 years. He’s now primarily chargeable for supporting TI’s analog and energy product portfolio in grid infrastructure purposes akin to EV charging and good metering.