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?
Best Answer
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.