If the switching frequency of a boost converter is high enough, an average lin- ear model...

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If the switching frequency of a boost converter is high enough, an average lin- ear model of the converter is often used. One such average model is shown below where the equivalent inductance Le is related to the actual inductance L by the relation Le = L/(1-D)² where D is the duty cycle of the switching and Vin and Vout are incremental changes in voltage from some nominal input and output, respectively. The capacitor C' is included to filter the ripple in the output voltage, and the load is modeled as a simple resis- tance R₁. L₂ R₁ SV The transfer function for the above converter for an input of 8Vin and an output of 8Vout is AVout (8) R₂ AVin (8) R₂CL² + $Le + Ri (a) Let R₁ = 1000, C = 10 x 10- F, L = 200 x 10-6 H and D = 0.50. For these parameters, estimate the peak time tp, the settle time t,, and the maximum percent overshoot M, for a unit step change in the input voltage. are constants. (b) Sketch a rough graph of the response of Vout for unit step input, that is, &Vin = 1(t). (c) How would the step response be affected if the numerator of the above transfer function was somehow changed to R + sL? Note, no calculations are needed. (d) It is often desirable to consider the change in duty cycle 6D to be the input to the converter. For this input, the transfer function becomes the following where Vin and D AVOut (8) Vin R₁- sLe AD(s) (1-D)2 RCLs2 + sLe + Ri Describe how the character of the step response of this transfer function would be dif- ferent than the transfer function in Part (c). Again, no calculation is necessary. If the switching frequency of a boost converter is high enough, an average lin- ear model of the converter is often used. One such average model is shown below where the equivalent inductance Le is related to the actual inductance L by the relation Le = L/(1-D)² where D is the duty cycle of the switching and Vin and Vout are incremental changes in voltage from some nominal input and output, respectively. The capacitor C' is included to filter the ripple in the output voltage, and the load is modeled as a simple resis- tance R₁. L₂ R₁ SV The transfer function for the above converter for an input of Vin and an output of Vout is AVout (8) R₂ AVin (8) R₂CL² + $Le + Ri (a) Let R₁ = 1000, C = 10 x 10- F, L = 200 x 10-6 H and D = 0.50. For these parameters, estimate the peak time tp, the settle time t,, and the maximum percent overshoot M, for a unit step change in the input voltage. are constants. (b) Sketch a rough graph of the response of Vout for unit step input, that is, &Vin = 1(t). (c) How would the step response be affected if the numerator of the above transfer function was somehow changed to Ri + sL? Note, no calculations are needed. (d) It is often desirable to consider the change in duty cycle 6D to be the input to the converter. For this input, the transfer function becomes the following where Vin and D AVOut (8) Vin R₁- sLe AD(s) (1-D)2 RCLs2 + $Le + Ri Describe how the character of the step response of this transfer function would be dif- ferent than the transfer function in Part (c). Again, no calculation is necessary. If the switching frequency of a boost converter is high enough, an average lin- ear model of the converter is often used. One such average model is shown below where the equivalent inductance Le is related to the actual inductance L by the relation Le = L/(1-D)² where D is the duty cycle of the switching and Vin and Vout are incremental changes in voltage from some nominal input and output, respectively. The capacitor C' is included to filter the ripple in the output voltage, and the load is modeled as a simple resis- tance R₁. L₂ R₁ SV The transfer function for the above converter for an input of 8Vin and an output of 8Vout is AVout (8) R₂ AVin (8) R₂CL² + $Le + Ri (a) Let R₁ = 1000, C = 10 x 10- F, L = 200 x 10-6 H and D = 0.50. For these parameters, estimate the peak time tp, the settle time t,, and the maximum percent overshoot M, for a unit step change in the input voltage. are constants. (b) Sketch a rough graph of the response of Vout for unit step input, that is, &Vin = 1(t). (c) How would the step response be affected if the numerator of the above transfer function was somehow changed to R + sL? Note, no calculations are needed. (d) It is often desirable to consider the change in duty cycle 6D to be the input to the converter. For this input, the transfer function becomes the following where Vin and D AVOut (8) Vin R₁- sLe AD(s) (1-D)2 RCLs2 + sLe + Ri Describe how the character of the step response of this transfer function would be dif- ferent than the transfer function in Part (c). Again, no calculation is necessary. If the switching frequency of a boost converter is high enough, an average lin- ear model of the converter is often used. One such average model is shown below where the equivalent inductance Le is related to the actual inductance L by the relation Le = L/(1-D)² where D is the duty cycle of the switching and Vin and Vout are incremental changes in voltage from some nominal input and output, respectively. The capacitor C' is included to filter the ripple in the output voltage, and the load is modeled as a simple resis- tance R₁. L₂ R₁ SV The transfer function for the above converter for an input of Vin and an output of Vout is AVout (8) R₂ AVin (8) R₂CL² + $Le + Ri (a) Let R₁ = 1000, C = 10 x 10- F, L = 200 x 10-6 H and D = 0.50. For these parameters, estimate the peak time tp, the settle time t,, and the maximum percent overshoot M, for a unit step change in the input voltage. are constants. (b) Sketch a rough graph of the response of Vout for unit step input, that is, &Vin = 1(t). (c) How would the step response be affected if the numerator of the above transfer function was somehow changed to Ri + sL? Note, no calculations are needed. (d) It is often desirable to consider the change in duty cycle 6D to be the input to the converter. For this input, the transfer function becomes the following where Vin and D AVOut (8) Vin R₁- sLe AD(s) (1-D)2 RCLs2 + $Le + Ri Describe how the character of the step response of this transfer function would be dif- ferent than the transfer function in Part (c). Again, no calculation is necessary.

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Question a Given R 1000 C 10 F L 200 H D 05 Estimate Peak time tp Settle time ts Maximum percent overshoot Mp To estimate the peak time settle time an... View the full answer