Posts tagged python
Computers must represent real numbers with some finite precision (ignoring symbolic algebra packages), and sometimes that precision limit ends up causing problems that you might not expect. Here are a couple examples.
The function \(f(x) = \exp(x) - 1\) is kind of fun – by subtracting one from the exponential, it removes the only constant term in the Maclaurin series of \(\exp(x)\):
The distribution of the sum of N uniformly distributed variables came up in a recent RdTools PR. The approach taken there was to just sample each distribution and sum the samples, but I wondered how it could be done analytically. This notebook is inspired by this StackExchange post and extends the derivation from just summing two uniform distributions on \([0,1]\) to two distributions with arbitrary bounds.
Given two independent random variables \(A\) and \(B\) with probability densities \(f_a(x)\) and \(f_b(x)\), the probability density \(f_c(x)\) of their sum \(A + B = C\) is given by the convolution \(f_a * f_b\):
This post will work through a simple power electronics problem. An ideal boost converter uses only lossless components (L, C) and no lossy components (R). However, real inductors will have nonzero resistance in its wiring. This copper loss has a strong effect on the converter’s ability to boost voltage. This follows the approach of Chapter 3 of Fundamentals of Power Electronics, 2e by Erickson and Maksimović.
First let’s draw the boost converter we’ll be modeling. Note that in this context, the precise switching circuit (PWM driver, MOSFET, etc) is irrelevant and represented by an ideal switch.