Three kinds of ripple-based control method of buck converter including hysteretic control, constant on-time control and constant off-time control are introduced in this section.
2.3.1 Hysteretic Control Method
The hysteretic controller is shown in Fig. 12 [16], the main control method is generating a hysteresis window. By controlling the upper and lower boundary to regulate the output voltage, when the feedback voltage touch to the hysteretic upper boundary, the power N-type MOSFET will turn on and power P-type MOSFET will turn off to discharge the inductor current and feedback voltage will decrease. At the same time, the hysteretic
22
window will change to the lower boundary. While the feedback voltage touch to the hysteretic lower boundary, the power P-type MOSFET will turn on and the power N-type MOSFET will turn off to charge the inductor current and feedback voltage will increase.
The hysteretic window which is calculating by superposition theorem can be expressed as follows.
2 1 2 1
1 2 1 2 1 2 1 2
( ) ( )
H uppper lower REF IN REF IN
R R R R
V V V V V V V
R R R R R R R R
(14)
The features of hysteretic controller are described as follows; firstly, the main control circuit is comparator and the error amplifier does not be used, so it is no problem about system compensation. Secondly, without using any clock generator, the switching frequency of hysteretic controller is generated by system itself. The following is the calculation of feedback voltage variation, as expressed as follows.
0 (1 ) 0
The voltage VFBAVG is the average voltage of feedback voltage, ideally is DVIN, the parameter D is the duty ratio of buck converter. And the hysteresis window variation (VH) equals to feedback voltage variation (ΔVFB). Combining the Eq. (14) and Eq. (15), the switching frequency can as expressed as follows.
1 0 2
By controlling the resistor R, capacitor C and the ratio of resistors R1 and R2 can define the switching frequency. However, as line and load conditions change, the hysteretic regulator operates over a wide frequency range that depends on the input and output voltages, the output filter inductance, the hysteresis window and ESR of output capacitor.
Finally, because the output ripple has been defined, it can’t choose the low ESR capacitor to
23
Fig. 12. The block diagram of hysteretic control method.
2.3.2 Constant On-time Control Method
As shown in Fig. 13, the basic constant on-time control structure consists of a comparator and one-shot on-time timer, with the output voltage feedback compared with an internal reference. The constant on-time control method is a modification of hysteretic control that operates at a relative constant frequency without an oscillator. It controls the high side power MOSFET switch whose on-time varies inversely with the input supply voltage.
In normal operation, the system initiates an on-time period when the feedback voltage VFB falls below the reference voltage VREF, which can be viewed as a valley voltage. The high side power P-type MOSFET stays on for the programmed on-time, causing the feedback voltage to rise above the reference voltage. After the on-time period, the power
24
P-type MOSFET remains off until the feedback voltage falls below the reference voltage.
Besides, the one-shot on-time timer provides a period that is inversely proportional to input supply voltage for constant frequency operation over input supply voltage variation.
Fig. 13. The block diagram of constant on-time control method.
In continuous conduction mode (CCM) the frequency depends only on duty cycle and on-time period. This is in contrast to hysteretic regulators where the switching frequency is determined by the output inductor and capacitor. In discontinuous conduction mode (DCM), experienced at light loads, the frequency will vary according to the load condition, similar to the operation in PFM mode [17]. This leads to high efficiency and good transient response.
25
Fig. 14. Inductor current and feedback voltage waveforms in DCM operation of constant on-time control.
Fig. 14 shows the waveforms of constant on-time control in DCM operation, inductor current IL raises to peak value during the fixed on-time period, and it falls back to zero before feedback voltage VFB reaches valley voltage VREF for constant on-time control.
When VFB reaches VREF, the next on-time period is introduced. Therefore, the off-time period of constant on-time control is dependent on load current condition in DCM operation.
2.3.3 Constant Off-time Control Method
The approach of constant off-time control is similar to constant on-time control. In normal operation, the system initiates an off-time period when the feedback voltage VFB
rises above the reference voltage VREF, which can be viewed as a peak voltage. However, constant on-time control is more popular than constant off-time control in application of
26
power management system. The reason is that the switching frequency in DCM operation of constant off-time control is inversely proportional to the load current.
Fig. 15. Inductor current and feedback voltage waveforms in DCM operation of constant off-time control.
As shown in Fig. 15, the off-time period of constant off-time control is fixed, which is independent of load current condition. However, the voltage difference ΔV is proportional to output current. As the ΔV becomes larger, the VFB needs to extend on-time period to reach VREF to cause the decrease of the switching frequency. The switching frequency increases as output current decreases in the DCM. It deteriorates the system efficiency. Thus, constant on-time control is widely used in practice [18].
27
Chapter 3
Topology of Constant On-time Control DC-DC Buck Converter without ESR Compensation
In this chapter, the system stability analysis and operation of proposed constant on-time control DC-DC buck converter are presented. The system stability analysis of conventional constant on-time control converter is shown in section 3.1. In section 3.2, the system operation is introduced.