Answered step by step
Verified Expert Solution
Link Copied!

Question

1 Approved Answer

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

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

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) 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 R. L R SV The transfer function for the above converter for an input of 8Vin and an output of 8Vout is AVout (8) R AVin (8) RCL + $Le + Ri (a) Let R = 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 R- 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) 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 R. L R SV The transfer function for the above converter for an input of Vin and an output of Vout is AVout (8) R AVin (8) RCL + $Le + Ri (a) Let R = 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 R- 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.

Step by Step Solution

There are 3 Steps involved in it

Step: 1

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... blur-text-image

Get Instant Access to Expert-Tailored Solutions

See step-by-step solutions with expert insights and AI powered tools for academic success

Step: 2

blur-text-image

Step: 3

blur-text-image

Ace Your Homework with AI

Get the answers you need in no time with our AI-driven, step-by-step assistance

Get Started

Recommended Textbook for

Income Tax Fundamentals 2013

Authors: Gerald E. Whittenburg, Martha Altus Buller, Steven L Gill

31st Edition

1111972516, 978-1285586618, 1285586611, 978-1285613109, 978-1111972516

More Books

Students also viewed these Accounting questions

Question

If y= (cos-x), then (1-x)x-xy-2 is

Answered: 1 week ago

Question

What is meant by Career Planning and development ?

Answered: 1 week ago

Question

What are Fringe Benefits ? List out some.

Answered: 1 week ago