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1. Linearize the power stage of the boost converter using the method. Find the equation between the following smallsignal perturbations: voltage port voltage, current port voltage, voltage port current, current port current, and duty cycle.

2. Draw a smallsignal model for the Boost converter based on the results from question 1

4.3.2 Linearizing the Power Stage of DC-DC Converters in CCM To design feedback controllers, the power stage of the converters must be linearized around the steady state de operating point, assuming a small-signal disturbance. Figure 4.6a shows the average model of the switching power-pole, where the subscript vp refers to the voltage-port and cp to the current-port. Each average quantity in Figure 4.6a can be expressed as the sum of its steady state dc value (represented by an uppercase letter) and a small-signal perturbation (represented by a ~ on top): d(t) =D+ (t) Fvp(t) = Vp + Fxp(t) Vcp(t) = Vcp + cp (t) ivp(t) = Ivp + ivp(t) icr(t) = Icp + icp(t) (4.9) Utilizing the voltage and current relationships between the two ports in Figure 4.6a, and expressing each variable as in Equation 4.9, Vcp + Vcp = (D+ )(Vvp + vp) (4.10a) and, Ivp + ivp = (D+ ) (Icp + icp) (4.10b) Equating the perturbation terms on both sides of the above equations fp(t) =DF + Vga + dep (4.11a) 4.3.2 Linearizing the Power Stage of DC-DC Converters in CCM To design feedback controllers, the power stage of the converters must be linearized around the steady state de operating point, assuming a small-signal disturbance. Figure 4.6a shows the average model of the switching power-pole, where the subscript vp refers to the voltage-port and cp to the current-port. Each average quantity in Figure 4.6a can be expressed as the sum of its steady state dc value (represented by an uppercase letter) and a small-signal perturbation (represented by a ~ on top): d(t) =D+ (t) Fvp(t) = Vp + Fxp(t) Vcp(t) = Vcp + cp (t) ivp(t) = Ivp + ivp(t) icr(t) = Icp + icp(t) (4.9) Utilizing the voltage and current relationships between the two ports in Figure 4.6a, and expressing each variable as in Equation 4.9, Vcp + Vcp = (D+ )(Vvp + vp) (4.10a) and, Ivp + ivp = (D+ ) (Icp + icp) (4.10b) Equating the perturbation terms on both sides of the above equations fp(t) =DF + Vga + dep (4.11a)

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