# Why does the MCP1650 datasheet give such a low value for the inductor in a boost converter?

I'm currently designing an SMPS around an MCP1650. In the datasheet (see page 4), the recommended value of inductor is 3.3uH. However, all the inductor size calculations I've come across (here and elsewhere) give a much greater value:

Inductor frequency ~= 750kHz

Vout = 12V

Iout = 0.1A

And using the 10% rule of thumb (i.e. ripple current = 0.1*output current), this should give a first approximation of 1.6mH. Why is there such a large discrepancy here? I'm assuming the designer is using a decent value of ripple current of course, I think with the inductor specified the ripple current was approx. 35% of output current, but to my mind this is excessive. What gives?

• The "recommended" value might be a "catch-all" for a wide range of power supply characteristics. In your linked calculation, the author even says they are "quick and dirty", so it's still just someones approximation of what is "correct". I think the best way to arrive at an optimal value is start with the approximation, but then build a circuit and test it under typical operating parameters. Try different values and keep notes, until the power supply operates within your required parameters. – dext0rb Apr 2 '15 at 17:27
• Have you read the design considerations page ? – efox29 Apr 2 '15 at 17:28
• @dextorb gives some good advice in general and I'm not a designer of SMPSs, but in most situations outside Astronomy nearly three orders of magnitude is somehwat remarkable and surely needs another explanation than it just being a part of the rough and tumble of life? – Dan Sheppard Apr 2 '15 at 17:31
• @DanSheppard Ooops...I did misread 1.6mH as 1.6uH! – dext0rb Apr 2 '15 at 17:34
• The calculation you link to is for a buck converter, and it's not a great calculation since it ignores the duty cycle. You're talking about a boost converter. With a more reasonable ripple ratio of 0.3, I got on the order of 100 uH for continuous conduction mode with your parameters. As Olin and The Photon said, it's most likely a DCM circuit. – Adam Haun Apr 2 '15 at 18:04

With a boost regulator, although the same characteristic inductor equation is used, it is used in a different context and a different way than in the buck. In a boost, everything is kind of backward from the buck. For example in the buck, output ripple current is important because it's the dominant determinant of output ripple voltage. But, in the boost the inductor ripple current shows up on the input rather that the output. In fact, for part of the cycle, the inductor is not connected to the output and the capacitor alone must provide energy to the load, so the capacitor is the dominant determinant of output voltage ripple.

Another difference with the boost is the extreme change in circuit dynamics between the discontinuous conduction mode (DCM) and continuous conduction mode (CCM) of the inductor. With DCM you effectively end up with 1 pole to compensate, until the Nyquist frequency shows up. DCM mode is basically stable by itself. While with CCM you have 2 complex high Q poles, and a wandering right half plane zero (RFPZ)to contend with.

Because of the easier control dynamics, DCM is often preferred. The problem with DCM is that for a given power level, peak currents (switch, inductor, and capacitor) are higher. So, DCM is usually limited to lower powers, like under ~20W, with notable exceptions.

It is very important to choose DCM or CCM operation. You especially do not want to design for DCM operation, and then have it wander into CCM because that would be a stability nightmare.

The first step in design of a boost is finding the critical inductance or current, which defines the boundary between DCM and CCM. For that I'll use another equation that doesn't include duty cycle:

$L_c$ = $\frac{V_{\text{out}}}{16 I_{\text{crit}} f_s}$

In this case with $V_{\text{out}}$ = 12V, $I_{\text{out}}$ = 0.1A, and $f_s$ = 750kHz, $L_c$ would be $10 \text{\mu H}$. So, for DCM operation you wouldn't want an inductor value greater than $10 \text{\mu H}$. In fact you wouldn't want to get near that, so $3.3 \text{\mu H}$ or $4.7 \text{\mu H}$ something like that. Less is OK, but not more.

The MCP1650 is, from my 5 minute read of the datasheet, a hysteretic controller. These types of controllers don't use linear feedback techniques, but instead put out a fixed width pulse where either the frequency or pulse count is varied to regulate the output. When the output voltage gets low, the control will deliver a few pulses to raise back to regulation. So, you don't have to worry about compensating an error amplifier. But, because of the kick of fixed width pulses, hysteretic control is not the friend of high Q power modulators, like a boost in CCM can be. This type of control tends to be prone to ringing at the high Q frequency. For DCM, boost power modulator Q is ~0.5, and so doesn't tend to ring. That may be why the datasheet is tilted to DCM operation.

Note that this IC switches at 750 kHz and maximum input voltage is only 5.5 V. A pulse half of the period long is only 670 ns.

(5.5 V)(670 ns)/(3.3 µH) = 1.1 A

So it's not like the current in the inductor will build up to ridiculous values over reasonable switch on times.

As for the ripple current, this unit is apparently not designed primarily for continuous mode operation. I only looked at the datasheet briefly, but it apparently uses one of two duty cycles. If so, then it must enable/disable the pulses as needed. In other words, it appears to be a pulse on demand system.

As for your comment about ripple current should be 10% of average current, I can't think of any law of physics that says it must be so. We do engineering here. Justifying something based on religious dogma you heard somewhere is silly. According to your "rule", discontinuous mode switchers should never exist. Also, even applying your rule, 1.6 mH seems way too high.

• I've seen the 10% rule of thumb used in a lot of places so I assumed it was useful as a good first approximation... Sorry for being ignorant I guess? – Alex Freeman Apr 2 '15 at 18:53
• @AlexFreeman I've seen and used 30% many times before as the "thumb of ruling" so I guess every thumb is different – KyranF Apr 2 '15 at 21:20

using the 10% rule of thumb

If you go to the Design Considerations section on page 18, you'll see they are not using this rule of thumb. It seems they are targeting an operating point on the boundary between continuous and discontinuous operation; meaning they allow 100% ripple or higher. That is, they are trying to choose the maximum inductor value possible while remaining in discontinous mode.

• From what I've heard, a 30% - 40% ripple ratio is more common for CCM anyway. – Adam Haun Apr 2 '15 at 17:59
• @AdamHaun I'm not SMPS expert, but I guess it's a trade-of between inductor value and saturation current specs. This particular controller is good for situations where you can find high Isat relative to L. – The Photon Apr 2 '15 at 18:09
• For example, looking at a randomly selected inductor family, Coilcraft XFL2006. The 3.3 uH part has 0.4 A Isat, allowing 0.2 A average current with 100% ripple. The 33 uH part has 0.11 A I sat, allowing only about 0.1 A average current with low ripple. – The Photon Apr 2 '15 at 18:11
• That makes sense, but I'm confused as to why they're insisting on using discontinuous. I have read that this is best used for boost ratios greater than 6:1, and reduces efficiency (and increases EMI) when used, so why have they chosen to do this? – Alex Freeman Apr 2 '15 at 18:55
• @AlexFreeman, read through the Design Considerations section. Much of it is about getting higher boost ratios. They even talk about getting 100 V out. Also, lower inductor values typically means less board real estate. – The Photon Apr 2 '15 at 19:21