The voltage conversion equation M = Vo/Vi in a buck power source or a boost power source is ideally given by the following equations. Here, M and V are variables and the subscripts o and i are labels. Buck: MD = D [<1] (8.1) Boost: MU = 1/(1 – D) = 1/D¢ [>1] (8.2) Here, D is a variable that is the duty ratio and the subscripts D and U are labels. In a real power source, the switching elements, coil internal resistance, and load resistance R influence the circuit operation, and the voltage conversion ratio can be expressed by the following, more complex, equations: Buck: MD¢¢ = D/(1 + Zo/R) [<MD ] (8.3) Boost: MU¢ = 1/D¢◊(1 + Zo¢/R) [<MU ] (8.4) Here, Zo is the various internal resistance. When rL is taken to be the coil internal resistance, rD is the diode connection resistance and rS is the switch connection resistance, and then Zo can be represented using the equations below: Zo = rL + D◊rS + D¢◊rD (8.5)

Zo¢ = (rL + D◊rS + D¢◊rD)/D¢2 (8.6) Here, r is a variable and the subscripts L, S, and D are labels. Therefore, when outputting a fixed voltage, the actual input voltage range must have a further margin and the voltage gap expands more. Voltage conversion equation in the mixed-control

methodThe voltage conversion ratio in a buck and boost power source using the mixed-control method can be considered as follows using the state space averaging method. In a mixed state, both the buck voltage and the boost voltage are regulated to their maximum values in the duty ratio in the voltage gap. Therefore, if the respective voltage conversion ratios are designated as MUM and MDM, and the mixing ratio (buck:boost) is M:N, then the voltage conversion equation using buck-boost operation is given as follows: MUD = M◊MUM + N◊MDM/(M + N) (8.7) Here, M and N are variables and the subscripts UM and DM are labels. 8.1.3 DS Modulated Mixed-Control MethodIn the mixed-control method, detection of the voltage gap and control of the mixed ratio in the gap are essential. In this case, the mixing ratio must be controlled in sequence, and the circuit configuration and control procedure are complicated. Thus, we evaluated a DS modulated mixed-control method that uses a DS modulator circuit in the U/D controller (the configuration is the same as that in Fig 8.2). Utilizing this method, it is not necessary to detect the voltage gap, and the mixing ratio is automatically switched across the entire input voltage range. 8.1.4 Dual DS Modulated Control Method Configuration of the dual DS modulated methodIn the DS modulated mixed-control method in Fig. 8.2, both switches S1 and S2 are switched and controlled separately using the PWM

signal. With respect to the operation of each switch, buck-boost operation becomes possible by primarily operating S1 for buck switching and S2 for boost switching, even when controlling the switches individually in the PWM cycle. Thus, we evaluated a method of controlling the switches by setting up two independent DS modulation circuits, as shown in Fig. 8.3. Note that the response speed is improved by using the clock in both modulation circuits as the inverse phase. In the configuration shown in Fig. 8.3, the circuit parameters are L = 1.6 µH and C = 200 µF, and the DS modulation clock set to fck = 2 MHz. First, the operation of buck-boost control is checked using an open loop. Figure 8.4 shows the output pulse (metal-oxidesemiconductor field-effect transistor [MOSFET] gate control pulse) in each modulation circuit and then the output voltage when the same sine wave is added to the input edge of each DS modulation circuit. Here, the MOSFET is on when the pulse is at the H level. On the basis of the figure, the on state for both MOSFETs is long when the output voltage is in boost mode, and the off state for both MOSFETs is sustained for a long time in buck mode. The minimum pulse width and clock cycle are both the same, 0.5 µs.