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| Keywords: Transmission line pulse reflections.gif en Transmission lines terminated by an open circuit top and a short circuit bottom A pulse reflects off the termination Black dots represent electrons and arrows show the electric field 2014-11-15 own Sbyrnes321 other versions cc-zero Source code <source lang python> C Steven Byrnes 2014 This code is released under the MIT license http //opensource org/licenses/MIT This code runs in Python 2 7 or 3 3 It requires imagemagick to be installed; that's how it assembles images into animated GIFs Use Python 3 style division a/b is real division a//b is integer division from __future__ import division import subprocess os directory_now os path dirname os path realpath __file__ import pygame as pg from numpy import linspace from math import erf exp frames_in_anim 240 animation_loop_seconds 12 time in seconds for animation to loop one cycle bgcolor 255 255 255 background is white ecolor 0 0 0 electrons are black wire_color 200 200 200 wire color is light gray split_line_color 0 0 0 line down the middle is black pygame draws pixel-art not smoothed Therefore I am drawing it bigger then smoothly shrinking it down img_height 330 img_width 900 final_height 110 final_width 300 ~23 megapixel limit for wikipedia animated gifs assert final_height final_width frames_in_anim < 22e6 transmission line wire length and thickness and y-coordinate of the top of each wire tl_length int img_width 9 tl_thickness 27 tl_open_top_y 30 tl_open_bot_y tl_open_top_y + 69 tl_short_top_y 204 tl_short_bot_y tl_short_top_y + 69 tl_open_center_y int tl_open_top_y + tl_open_bot_y + tl_thickness / 2 tl_short_center_y int tl_short_top_y + tl_short_bot_y + tl_thickness / 2 wavelength 1 1 tl_length e_radius 4 dimensions of triangular arrow head this is for the longest arrows; it's scaled down when the arrow is too small arrowhead_base 9 arrowhead_height 15 width of the arrow line arrow_width 6 number of electrons spread out over the transmission line top plus bottom num_electrons 130 max_e_displacement is defined here as a multiple of the total electron path length roughly twice the width of the image because we're adding top + bottom max_e_displacement 0 0194 num_arrows 30 max_arrow_halflength 24 def rgb_from_V V voltage V varies -1 to +1 Return a color as a function of V Color is a 3-tuple red green blue each 0 to 255 This is just an arbitrary function which makes colors that I like return 70+70 V 70-70 V 70-70 V def tup_round tup round each element of a tuple to nearest integer return tuple int round x for x in tup def draw_arrow surf x tail_y head_y color 0 0 0 draw a vertical arrow Coordinates do not need to be integers calculate dimensions of the triangle; it's scaled down for short arrows if abs head_y - tail_y > 1 5 arrowhead_height h arrowhead_height b arrowhead_base else h abs head_y - tail_y / 1 5 b arrowhead_base h / arrowhead_height if tail_y < head_y downward arrow triangle tup_round x head_y tup_round x - b head_y - h tup_round x + b head_y - h triangle_middle_y head_y - h/2 else upward arrow triangle tup_round x head_y tup_round x - b head_y + h tup_round x + b head_y + h triangle_middle_y head_y + h/2 pg draw line surf color tup_round x tail_y tup_round x triangle_middle_y arrow_width pg draw polygon surf color triangle 0 def pulse c t open_or_short c is a coordinate c 0 is the left side of the image c 1 is the terminal t is time with t 0 at the beginning of the animation t 1 at the end This calculates two things Displacement of an electron in the top wire relative to its equilibrium position i e integral of I x t' from t' -infty to t' t in arbitrary units Charge on the top wire at that location in arbitrary units assert c < 1 We imagine that c>1 is a mirror-world beyond the terminal which will not be actually drawn Then we can add up a leftward-traveling pulse and a rightward-traveling pulse using the superposition principle pulse_speed 3 pulse_width 0 2 if open_or_short 'open' pulses 'center' 1 + pulse_speed t - 0 5 'sign' +1 'center' 1 - pulse_speed t - 0 5 'sign' +1 else pulses 'center' 1 + pulse_speed t - 0 5 'sign' +1 'center' 1 - pulse_speed t - 0 5 'sign' -1 displacement 0 charge 0 for pulse in pulses center sign pulse'center' pulse'sign' displacement + erf c - center / pulse_width sign charge + exp - c - center 2 / pulse_width 2 sign return 'displacement' displacement 'charge' charge/2 def e_path_open param time param is an abstract coordinate that goes from 0 to 1 as the electron position goes right across the top wire then left across the bottom wire time goes from 0 to 1 over the course of the animation This returns a dictionary 'pos' is x y the coordinates of the corresponding point on the electron dot path; 'displacement' is the displacement of an electron at this point relative to its equilibrium position between -1 and -1 ; and 'charge' is the net charge at this point between -1 and +1 This is for the open-circuit line d is a vertical offset between the electrons and the wires d e_radius + 2 pad is how far to extend the transmission line beyond the image borders since those electrons may enter the image a bit pad 120 path_length 2 tl_length + pad howfar param path_length go right along top transmission line if howfar < tl_length + pad x howfar - pad y tl_open_top_y + tl_thickness - d temp pulse x / tl_length time 'open' displacement temp'displacement' charge temp'charge' return 'pos' x y 'displacement' displacement 'charge' charge go left along bottom transmission line x path_length - howfar - pad y tl_open_bot_y + d temp pulse x / tl_length time 'open' displacement temp'displacement' charge -temp'charge' return 'pos' x y 'displacement' displacement 'charge' charge def e_path_short param time Same as e_path_open above but for the short-circuit line d is a vertical offset between the electrons and the wires d e_radius + 2 pad is how far to extend the transmission line beyond the image borders since those electrons may enter the image a bit pad 120 path_length 2 tl_length + pad + 4 d + tl_short_bot_y - tl_short_top_y - tl_thickness howfar param path_length at the beginning go right along top wire if howfar < tl_length + pad x howfar - pad y tl_short_top_y + tl_thickness - d temp pulse x / tl_length time 'short' displacement temp'displacement' charge temp'charge' return 'pos' x y 'displacement' displacement 'charge' charge at the end go left along bottom wire if path_length - howfar < tl_length + pad x path_length - howfar - pad y tl_short_bot_y + d temp pulse x / tl_length time 'short' displacement temp'displacement' charge -temp'charge' return 'pos' x y 'displacement' displacement 'charge' charge in the middle temp pulse 1 time 'short' charge temp'charge' assert abs charge < 1e-9 displacement temp'displacement' top part of short if tl_length + pad < howfar < tl_length + pad + d x howfar - pad y tl_short_top_y + tl_thickness - d bottom part of short elif tl_length + pad < path_length - howfar < tl_length + pad + d x path_length - howfar - pad y tl_short_bot_y + d vertical part of short else x tl_length + d y tl_short_top_y + tl_thickness - d + howfar-pad - tl_length + d return 'pos' x y 'displacement' displacement 'charge' charge def e_path param time which return e_path_open param time if which 'open' else e_path_short param time def main Make and save a drawing for each frame filename_list os path join directory_now 'temp' + str n + ' png' for n in range frames_in_anim for frame in range frames_in_anim time frame / frames_in_anim initialize surface surf pg Surface img_width img_height surf fill bgcolor ; draw transmission line pg draw rect surf wire_color 0 tl_open_top_y tl_length tl_thickness pg draw rect surf wire_color 0 tl_open_bot_y tl_length tl_thickness pg draw rect surf wire_color 0 tl_short_top_y tl_length tl_thickness pg draw rect surf wire_color 0 tl_short_bot_y tl_length tl_thickness pg draw rect surf wire_color tl_length tl_short_top_y tl_thickness tl_short_bot_y - tl_short_top_y + tl_thickness draw line down the middle pg draw line surf split_line_color 0 img_height//2 img_width img_height//2 12 draw electrons Remember param is an abstract coordinate that goes from 0 to 1 as the electron position goes right across the top wire then left across the bottom wire equilibrium_params linspace 0 1 num num_electrons for which in 'open' 'short' for eq_param in equilibrium_params temp e_path eq_param time which param_now eq_param + max_e_displacement temp'displacement' xy_now e_path param_now time which 'pos' pg draw circle surf ecolor tup_round xy_now e_radius draw arrows arrow_params linspace 0 0 49 num num_arrows for which in 'open' 'short' center_y tl_open_center_y if which 'open' else tl_short_center_y for i in range len arrow_params a arrow_paramsi arrow_x e_path a time which 'pos'0 charge e_path a time which 'charge' head_y center_y + max_arrow_halflength charge tail_y center_y - max_arrow_halflength charge draw_arrow surf arrow_x tail_y head_y color rgb_from_V charge shrink the surface to its final size and save it shrunk_surface pg transform smoothscale surf final_width final_height pg image save shrunk_surface filename_listframe seconds_per_frame animation_loop_seconds / frames_in_anim frame_delay str int seconds_per_frame 100 Use the convert command part of ImageMagick to build the animation command_list 'convert' '-delay' frame_delay '-loop' '0' + filename_list + 'anim gif' subprocess call command_list cwd directory_now Earlier we saved an image file for each frame of the animation Now that the animation is assembled we can optionally delete those files if True for filename in filename_list os remove filename main </source> Uploaded with UploadWizard Transmission lines Animations of electronics Impedance Animations of vibrations and waves Images with Python source code | ||||
