System-on-chip (SoC) applications require accurate designs of their power-management circuits. One good example of this concept is represented by the DC/DC converter voltage regulators that are able to control and regulate the voltage to a load inside a integrated circuit.
One important parameter of a switching regulator (SWR) is the conversion ratio—the ratio between the output regulated voltage and the input supply voltage of the converter. The interesting aspect of the conversion ratio parameter is that it depends on the duty cycle—the ratio between the tON, the time interval in which the power flows from the input to the output and the switching period TS, the time interval in which there is the complete commutation of the power switches of the SWR (Figure 1).
Depending on the relationship between the convertion ratio and the duty cycle there are different types of SWR, mainly divided in three categories:
All of these types of converters include an inductor, a linear element which voltage-current relationship is differential as shown in Equation 1.
If we assume that the current flowing in the inductor doesn’t fall to zero during the switching period– (mode called CCM, Continuous Conduction Mode) the inductor current will also be periodic of period TS. Because we have a linear circuit element, the current in the inductor is periodic and therefore by applying equation 1 we obtain (Equation 2):
In part 1 we introduced the relationships between the tON and tOFF time intervals and the period of switching TS (Equation 3)
We will use the equations 1, 2, and 3 to obtain the voltage conversion ratio in CCM for each type of SWR. In part 3, you’ll see the final for the VOUT/VIN ratios are respectively:
The type of relationship between VIN and VOUT lets an SoC designer choose the power circuit. For example, if there is a memory block inside the SoC requiring voltages greater than the supply voltage for the write operations, a step-up voltage regulator is the best choice among the possible configurations of standing wave ratio (SWR).
Furthermore, the conversion ratio for each type of SWR shows that the output voltage can be accurately controlled by a well designing of a logic circuitry to control the duty cycle D of the power switches of the SWR as shown in Figure 2.
In part 3, we derive the voltage conversion ratio for each type of switching voltage regulator under the hypothesis of CCM mode of operation.