Sources of voltage ripple in buck converter

[CoolDude420]

I am reading a book 'Fundamentals of Power Electronics' - Erickson. The book begins with a buck converter and the assumptions that we use so that we do not have to deal with 2nd order equations. I will first explain what the book says

What the book says?​

The book says that the LC filter of a buck conveter should be designed so that the cut-off is lower than the switching frequency of the converter. This is to remove any ripples at the switching frequency or its harmonics. Of course, you cannot fully eliminate them, you can only attenuate with the LC filter, so there will be a small ripple. The small ripple approximation assumes that the output of the LC filter (= output of buck converter) is just the DC output voltage and that we can neglect these ripples. Ok, makes sense. Let's move on.

The book now draws the inductor current waveform. It provides an equation for the inductor ripple current. The DC portion of this current goes to the resistive load, thereby generating a fixed output voltage. The AC portion goes to the output capacitor.

Why am I confused?​

The AC portion that goes to output capacitor will cause the output capacitor voltage to increase. The output capacitor voltage IS the output voltage of the converter, hence there will be a ripple on the output voltage due to the AC current of the inductor flowing into the cap. This contradicts the small-ripple approximation we made at the start, that the output voltage is fixed.

I am very confused. We started with an assumption that the output voltage is fixed, we used that assumption to get the equation for the inductor current. The AC part of this current flows to the cap, which creates an AC ripple on the output. This is a contradiction.

Neglect ESR's, ESLs, on-resistances, parasitics, etc.

 

[Averagesupernova]

I think you are assuming that the capacitor will charge to peak as it does directly after a rectifier. The ideal LC filter removes all but the DC. If you are able to simulate it in Spice I would recommend simulating just the LC portion and a load to see the behavior.

 

[DaveE]

The AC portion that goes to output capacitor will cause the output capacitor voltage to increase. The output capacitor voltage IS the output voltage of the converter, hence there will be a ripple on the output voltage due to the AC current of the inductor flowing into the cap.

Yes, but it is small and can be approximated as DC.

This contradicts the small-ripple approximation we made at the start, that the output voltage is fixed.

Why? It wasn't a zero ripple approximation. You can think of this as a sort of successive approximation process. After you model it as DC it may be good to verify that that was a "good enough" approximation.

Of course you could build a circuit that had a large amount of ripple; it's not common, but people do that. There are many second order effects in SMPS if you look for them. However the analysis of truly non-linear systems is very difficult. It's best either in course work or in practice to work through the switched linear models and then worry about the errors due to the approximations you made.

 

[Averagesupernova]

I recall troubleshooting a switcher once that we couldn't get rid of the ripple. Great care needed to be taken as to where the bypass capacitors and the freewheeling diode (yes, your circuit has one) were placed on the board. Very small inductance in the PCB traces was significant.

 

[DaveE]

The ideal LC filter removes all but the DC. If you are able to simulate it in Spice I would recommend simulating just the LC portion and a load to see the behavior.

This a great way to think of the buck SMPS topology, a chopper followed by a LPF (of any sort). You can then think of the input signal a square(ish) wave with the fundamental and harmonics filtered out. That's how I do it.

However, it is best to first do it like Erikson does, because it will teach you how to approach other, more complex topologies, like boost, flyback, sepic, etc.

I recall troubleshooting a switcher once that we couldn't get rid of the ripple. Great care needed to be taken as to where the bypass capacitors and the freewheeling diode (yes, your circuit has one) were placed on the board. Very small inductance in the PCB traces was significant.

Again, a great point here. In practice there are so many things that will mess up the textbook version of a SMPS. For example, you asked about the capacitor voltage but said to ignore ESR. In my experience, ESR is often the single most important spec for the PS caps. (no, not capacitance). In many PS designs, ESR is the most important component of the output ripple. The other big component are spikes from switching stray (parasitic) L's and C's in the real design.

But, you need to learn the textbook version first, the simple linear models that are easy to analyse. Then you can (and will) start to consider these practical and second order effects.

PS: That is a great textbook for this subject.

 

[Averagesupernova]

In my experience, ESR is often the single most important spec for the PS caps. (no, not capacitance).

Ding ding ding ding! There is the winner statement of this thread. I was a bit of a newb back in the day when I troubleshoot the switcher in my example. That's why I remember it. Another thing I remember was multiple capacitors in parallel. Reducing the ESR of the capacitor network as much as possible. I still recall how easy it seemed after moving the caps. The next morning my coworker said: How'd you get rid of the ripple?

 

[DaveE]

Ding ding ding ding! There is the winner statement of this thread. I was a bit of a newb back in the day when I troubleshoot the switcher in my example. That's why I remember it. Another thing I remember was multiple capacitors in parallel. Reducing the ESR of the capacitor network as much as possible. I still recall how easy it seemed after moving the caps. The next morning my coworker said: How'd you get rid of the ripple?

AKA "ripple current rating". In many designs where you may not care too much about ripple, you still don't want the caps to fail. It's the ESR that makes the heat that kills the cap. This is really useful when you looking through a table of cap choices. If you want low ESR but that's not there, look for high current, and vice-versa.

EDIT: Oh, yea, then read the whole G%$ D!@# data sheet for the ones you'll buy.

 

[berkeman]

For example, you asked about the capacitor voltage but said to ignore ESR. In my experience, ESR is often the single most important spec for the PS caps. (no, not capacitance). In many PS designs, ESR is the most important component of the output ripple.

I agree as well. We invest in low-ESR caps in our DC-DC converters just for this reason (our mixed signal circuits that are powered by the converters are sensitive to power supply ripple).

BTW, if you have a circuit like a radio receiver or some other circuit that is sensitive to PS ripple (because it is running with 80dB+ of dynamic range), you can follow the low-ripple switching circuit with a low-dropout linear regulator and be careful about your power distribution start grounding layout.

 

[CoolDude420]

I think you are assuming that the capacitor will charge to peak as it does directly after a rectifier. The ideal LC filter removes all but the DC. If you are able to simulate it in Spice I would recommend simulating just the LC portion and a load to see the behavior.

I think I am getting confused between voltage ripple and current ripple.

The LC filter will severely attenuate voltage ripple at the switching frequency and the harmonics, for any bit of voltage ripple left over, we use the small-ripple approximation and say it is zero.

However, the current ripple flows to the cap, the cap charges up and creates another voltage ripple?

Could you please help me in distinguishing between the two?

 

[berkeman]

However, the current ripple flows to the cap, the cap charges up and creates another voltage ripple?

Via its ESR...

 

[CoolDude420]

Via its ESR...

Why do you need an ESR for the capacitor to create a voltage ripple? Just the capacitor on its own receiving the AC component of the inductor current will charge it up, thereby creating a voltage ripple.

 

[berkeman]

Why do you need an ESR for the capacitor to create a voltage ripple? Just the capacitor on its own receiving the AC component of the inductor current will charge it up, thereby creating a voltage ripple.

If you do the calculations with real numbers from real datasheets for a design you are doing, you quickly find that the voltage ripple from the ESR of the output cap dominates the output voltage ripple. The triangular input current ripple and any output current ripple create voltage ripple across the output cap's ESR. Do you think my company would pay twice as much for those capacitors (in high volume production) if I didn't have to?

 

[DaveE]

Why do you need an ESR for the capacitor to create a voltage ripple? Just the capacitor on its own receiving the AC component of the inductor current will charge it up, thereby creating a voltage ripple.

Yes, there is a sort of sinusoidal ripple voltage due solely to the capacitance at the switching frequency. But in practice every time the cap current changes polarity, at the min and max cap voltage, the ESR causes a quick step which is often larger than the capacitor ripple.

In this photo (which I stole at random from the web) you will see three main features of the SMPS output ripple & noise.
- The high frequency spikes are created by the switching and parasitic stuff, what @Averagesupernova referred to. Device selection, PCB layout, and snubber design are a huge issue with these.
- The rising and falling slopes are from the LC filter showing a bit of the fundamental (switching) frequency getting through the filter.
- The step like feature between the rising and falling capacitor voltage is due to the cap ESR. It is because the cap current switches direction, sometimes that Ic⋅ESR voltage adds to the output, other times it subtracts.

PS: Notice the scale at 5mV/div for a 3.3V PS that is 0.15%/div, which is why we start the analysis by pretending it's zero.

 

[DaveE]

Could you please help me in distinguishing between the two?

This would be a great time to use (or learn) a simple simulator. I like LTSpice; it's good and free. This question is really about the different functions of the output filter components. All of your questions could be answered in a simulation with a pulsed source voltage plus a simple LCR LPF. You'll learn it better if you play around with it yourself.

PS: Probably the only time you'll hear me say this. Normally I think simulators are used way too much in place of textbook, conceptual, learning.