Small-signal Analysis and Design of Constant-on-time V2 Control for Ceramic Caps

Recently, constant-on-time V2 control is more and more popular in industry products due to features of high light load efficiency, simple implementation and fast transient response. In many applications such as cell phone, camera, and other portable devices, low-ESR capacitors such as ceramic caps are preferred due to small size and small output voltage ripple requirement. However, for the converters with ceramic caps, the conventional V2 control suffers from the sub-harmonic oscillation due to the lagging phase of the capacitor voltage ripple relative to the inductor current ripple. Two solutions to eliminate sub-harmonic oscillations are discussed in [39] and the small-signal models are also derived based on time-domain describing function. However, the characteristic of constant-on-time V2 with external ramp is not fully understood and no explicit design guideline for the external ramp is provided. For digital constant on-time V2 control, the high resolution PWM can be eliminated due to constant on-time modulation scheme and direct output voltage feedback [43]. However, the external ramp design is not only related to the amplitude of the limit-cycle oscillation, but also very important to the stability of the system. The previous analysis is not thorough since numerical solution is used. The primary objective of this work is to gain better understanding of the small-signal characteristic for analog and digital constant-on-time V2 with ramp compensations, and provide the design guideline based on the factorized small-signal model.

First, constant on-time current-mode control and constant on-time V2 control are reviewed. Generally speaking, constant-on-time current mode control does not have stability issues. However, for constant-on-time V2 control with ceramic caps, sub-harmonic oscillation occurs due to the lagging phase of the capacitor voltage ripple. External ramp compensation and current ramp compensation are two solutions to solve the problem. Previous equivalent circuit model extended by Ray Ridley's sample-and-hold concept is not applicable since it fails to consider the influence of the capacitor voltage ripple. The model proposed in [39] successfully considers the influence from the capacitor voltage ripple by using time-domain describing function method. However, the characteristic of constant-on-time V2 with external ramp is not fully understood. Therefore, more research focusing on the analysis is needed to gain better understanding of the characteristic and provide the design guideline for the ramp compensations.

After that, the small-signal model and design of analog constant on-time V2 control is investigated and discussed. The small-signal models are factorized and pole-zero movements are identified. It is found that with increasing the external ramp, two pairs of double poles first move toward each other at half of switching frequency, after meeting at the key point, the two double poles separate, one pair moves to a lower frequency and the other moves to a higher frequency while keeping the quality factor equal to each other. For output impedance, with increasing the external ramp, the low frequency magnitude also increases. The recommended external ramp is around two times the magnitude at the key point K. When Duty cycle is larger, the damping performance is not good with only external ramp compensation, unless very high switching frequency is used. With current ramp compensation, it is recommended to design the current ramp so that the quality factor of the double pole is around 1. With current ramp compensation, the damping can be well controlled regardless of the circuit parameters.

Next, the small-signal analysis and design strategy is also extended to digital constant on-time V2 control structure which is proposed in [43]. It is found that the scenario is very similar as analog constant on-time V2 control. The external ramp should be designed around the key point to improve the dynamic performance. The sampling effects of the output voltage require a larger external ramp to stabilize digital constant-on-time V2 control while suffers only a little bit of damping performance. One simple method for measuring control-to-output transfer functions in digital constant-on-time V2 control is presented. The experimental results verify the small-signal analysis except for the high frequency phase difference which reveals the delay effects in the circuit. Load transient experimental results prove the proposed design guideline for digital constant on-time V2 control.

As a conclusion, the characteristics of analog and digital constant-on-time V2 control structures are examined and design guidelines are proposed for ramp compensations based on the factorized small-signal model. The analysis and design guideline are verified with simplis simulation and experimental results.