Right, welcome to appnotes. They're always top quality, as you see.
As for a ground-up understanding, consider what happens as the switch goes on and off. When on, Vin is applied to the inductor. According to the inductor equation,
V = L dI/dt
if V and L are momentarily fixed, then dI/dt is also fixed: current is rising at a constant slope. It starts from whatever the initial current was, then by the time the switch turns off, has reached some higher peak value.
Likewise if the inductor discharges into a clamp diode and very large capacitor, Vout is essentially fixed (i.e. ripple is a small fraction of Vout), so a voltage of Vin - Vout is applied to the inductor, and thus the current ramp is negative during this phase.
We get one more condition, where if I drops to zero, the diode ceases conduction, and the switch node rings down to Vin. This is DCM (discontinuous current mode). The waveform during this phase is an RLC resonance between L, and switch and diode capacitances, and whatever loss resistance is present. Starting from an initial amplitude of Vout - Vin and ringing down. So there's a first downward swing of that waveform, which can approach 0V, which is a particularly opportune time to turn on again; this is exactly the operation of QR (quasi-resonant) boost/flyback controllers, and therefore operate in BCM (boundary). If the switch turns on before inductor current reaches zero, then it does so in hard switching (switch turns on with substantial voltage across it, and some fraction of full load current -- whatever the current remaining is), and operation is CCM (continuous).
Now consider the control type. TPS61040 is a hysteretic control. The block diagram shows a current sense and Max On Time which turn off the switch, and a feedback comparator and Min Off Time to turn it on. There is a comparator, not an error
amplifier, and there is no compensation R+C. These devices are prone to high output ripple -- some ripple is necessary to cross the comparator's thresholds; and to erratic behavior, as limitations due to the fixed timers, and response of the circuit around it, cause alternate short and long pulses, or burst mode operation, or etc. So, the output ripple / emissions can be richer in harmonics/noise, which is more difficult to filter. The only thing you are guaranteed with a hysteretic control, is that the ripple will never be better or worse than some margin (determined by thresholds, min/max timing, and inductance and capacitance, and maybe further factors). Also, being an instantaneous sort of control, transient response is very good: within one cycle.
Another popular type is peak current mode control. This has a similar block diagram, but instead of a fixed current limit, the limit is adjustable, proportional to the output of an error amplifier. Instead of an error comparator starting the switch, a fixed oscillator turns it on every cycle (also briefly blanking the switch at the end of every cycle, to ensure it doesn't get stuck into 100% duty). This has very predictable emissions -- the output ripple is fixed frequency, and it can be filtered arbitrarily low because no ripple voltage is needed by the control. Control is very simple, in that it's basically a 2nd-order feedback loop that only needs two components (R+C) to fully tune the stability / transient response. UC3843 is an archetype of this control. Downsides are, potentially slower transient response (due to the continuous-time feedback loop responding gradually over time), and values must be chosen correctly to avoid subharmonic oscillation, or chaos.
Aside: peak current mode control is, in fact, an electronic implementation of a chaotic iterated system, the
logistic map. For small values of the parameter, stable operation results. At large values, operation
bifurcates into two, four, etc. (and so on, hyperbolically?), operating states. In the logistic map, these are simply the sequence of numbers in a cycle; for the peak current mode control, the parameter is ripple fraction (>100% (DCM) is stable, CCM is unstable), and the states are pulse widths. So at the onset of chaos, you get alternate long and short pulse widths; you get one long cycle which, because it spent most of its time on, hardly has any time to discharge before the next cycle begins; then the next cycle starts with a lot of initial current so is on only briefly before turning off, but is then able to discharge the inductor pretty well.
Operationally, the consequence of chaos is somewhat increased losses, and increased input/output ripple -- particularly at low (subharmonic) frequencies. Frequencies that may be audible from the inductor or capacitors, hence a whine or hiss sound as well. (This is different from the whine of a burst-mode control, which is more or less proportional to load current.)
Subharmonic oscillation can be avoided by slope compensation (adding some of the RC timing ramp into the current ramp signal), which makes it a hybrid voltage/current mode PWM system. This worsens current regulation (so the switch current at low duty cycles (heavy load, fault, startup conditions) can be much higher than the nominal current limit), so can only go so far before design issues take over. Typically, these controls are good down to 50 or 33% ripple fraction. Which is pretty good.
Also, the point about ripple fraction is, the higher it is, the higher losses are -- more peak currents drawn from the capacitors, more flux swing in the inductor, relative to the amount of power you're getting. Which makes this control unappealing past 100W or so (at which point, forward and resonant converters take over).
For arbitrarily low ripple fractions, a different tack can be used: regulate inductor current directly, then servo that with a voltage error amp. This is average current mode control. Downsides are yet slower operation -- roughly speaking, the inductor current can't change any faster than Fsw * [ripple fraction] (intuitively; think about it!), and at light load or high ripple fraction, can be prone to subharmonic oscillation (but only period doubling AFAIK, not the whole logistic map!). They're also easy to make from discrete components, and easy to adapt to synchronous rectification, to get lower losses at full load (but, somewhat harder to do with that, AND get good performance at light load).
So, thinking about the waveforms a bit, and what triggers on/off switching, or determines Fsw, etc., should give you some ideas about the applicability of those equations. Point in case: the second equation is backwards for a hysteretic control: you can't simply assume some frequency; rather, the frequency depends on everything else -- it should be rearranged with Fsw on the left, if anything!
Tim
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