5A Constant Frequency Hysteretic Synchronous Regulator
Output Capacitor Selection
Output capacitor is basically decided by the amount of the output voltage ripple allowed during
steady state (DC) load condition as well as specification for the load transient. The optimum design
may require a couple of iterations to satisfy both conditions. The amount of voltage ripple during
the DC load condition is determined by the following equation:
∆퐼ꢂꢃ푃푃퐿퐸
∆푉ꢂꢃ푃푃퐿퐸 = ꢄꢅ푅 × ∆퐼ꢂꢃ푃푃퐿퐸
+
8 × 퐹 × ꢆ푂푈푇
푆
Where ESR is the output capacitors' equivalent series resistance, COUT is the value of output
capacitors. Typically when ceramic capacitors are selected as output capacitors, DC ripple spec is
easy to be met, but multiple ceramic capacitors are required at the output to meet transient
requirement.
Compensator Design
Due to the double pole generated by LC filter of the power stage, the power system has 180° phase
shift, and therefore, is unstable by itself. In order to achieve accurate output voltage and fast
transient response, compensator is employed to provide highest possible bandwidth and enough
phase margin. Ideally, the Bode plot of the closed loop system has crossover frequency between
1/10 and 1/5 of the switching frequency, phase margin greater than 50° and the gain crossing 0dB
with 20dB/decade.
Power stage output capacitors usually decide the compensator type. If electrolytic capacitors are
chosen as output capacitors, type II compensator can be used to compensate the system, because
the zero caused by output capacitor ESR is lower than crossover frequency. Otherwise type III
compensator should be chosen.
A. Type III Compensator Design
For low ESR output capacitors, typically such as Sanyo Os-Con and Poscap, the frequency of ESR
zero caused by output capacitors is higher than the crossover frequency. In this case, it is
necessary to compensate the system with type III compensator.
The following figures and equations show how to realize the type III compensator by
transconductance amplifier.
1
퐹푍1
퐹푍2
=
=
2 × 휋 × 푅4 × ꢆ2
1
2 × 휋 × (푅2 + 푅3) × ꢆ3
1
퐹푃1
퐹푃2
=
=
2 × 휋 × 푅3 × ꢆ3
1
ꢆ1 × ꢆ2
2 × 휋 × 푅4 ×
ꢆ1 + ꢆ2
Where, FZ1, FZ2, FP1, and FP2 are poles and zeros in the compensator. Their locations are shown in
figure 10. The transfer function of type III compensator for transconductance amplifier is given by:
1 − 푔푚 × ꢇ푓
푉
푒
=
푉푂푈푇 1 + 푔푚 × ꢇ푖푛 + ꢇ푖푛/푅1
For the voltage amplifier, the transfer function of compensator is
−ꢇ푓
ꢇ푖푛
푉
푒
=
푉푂푈푇
12