# Step-down converter and ceramic minimum ESR capacitor

I'm building a step-down converter, based on the TI TPS5450, which provides a reference design and various considerations on the capacitor. Even on the minimum ESR required. But when states

"The minimum ESR of the output capacitor should also be considered. For good phase margin, the ESR zero when the ESR is at a minimum should not be too far above the internal compensation poles at 24 kHz and 54 kHz."

And talks about this zero in other parts of the datasheet. How can I find this zero introduce with the C and the ESR? I did something like this:

$$Resr = \frac{1}{(2*\pi*f_z*Co)}$$

where the Co is the output capacitor, f_z the target zero freqeuncy which should be not so far over the indicated pole frequency.

The problem is that I will need a ceramic capacitor, because the regulator will work in a high vacuum condition, and the polarized ones like tantalium can have problems. But when searching for a ceramic capacitor, it is not stated the information about the ESR, but only the dielectric type (for example the X5R).

• Tantalum capacitors in power supplies where you do not have COMPLETE control over spikes, surges and voltage transients are an invitation to grief sorrow disaster smoke flame bad-smells shrieking and explosion. (I've seen all of the last 5 in one incident with a single cap :-) ). Be pleased you cannot use one here and resolved to not use them if at all possible elsewhere. The less know SOLID Aluminum do not have the same issues and are about as good. Jun 17, 2015 at 13:56

You can assume the ESR of the ceramic capacitor is $0\Omega$ in that frequency range and add a series resistor to put the zero right where you want it. Usually a fraction of an ohm up to an ohm or two will do it.

Here, for comparison, from an AVX paper, is the ESR of a 4.7uF ceramic capacitor vs. a tantalum.

As you can see, $0\Omega$ is a pretty good approximation for the ceramic part when you want total ESR to make it look more like a tantalum part.

Edit: Note that the very high capacitance X5R MLCC caps you have in mind typically have a horrible voltage coefficient. The stated capacitance is achieved at a bias of 500mV, which is probably lower than you are using.

For the same zero frequency your ESR must be higher by the capacitance ratio so if your '220uF' cap is only 80uF at temperature extreme and 5V bias you might need to have more like 150m$\Omega$ series resistance to maintain the same stability as the 330uF tantalum cap in the eval board.

You should be able to find these specs for the Samsung parts.. the above graph is from an NIC guide.

• In my case the ESR of the tantalum used is 40mOhm. Searching around seems a comparable value of the ceramic one. I can try with this w/out a serie resistor of 30/40mOhms. Moreover, that graph seem to be acceptable in terms of minimum ESR. Unfortunately, I can't find something similar for my capacitor (a Samsung CL32A227MQVNNNE) Jun 17, 2015 at 16:38
• I saw just now yout update. The maximum ESR at 220uF should be 40mV for a given ripple. I know the capacitance reduction issue, and seems that using TWO of them in parallel solves the problem and the ESR equivalent seems to be higher than the minimum. Assuming that the cap is halving, the minium ESR is around 10mOhms. And, including the PCB resistance, could be a reasonable compromise. But things must be tested. I will search, hopelessly, for an ESR indications. The TPS regualator works at constant frequency of 500kHz, keeping an ESR not so low...usually. Jun 22, 2015 at 16:35