File:Transmission line pulse reflections.gif
![File:Transmission line pulse reflections.gif](http://upload.wikimedia.org/wikipedia/commons/thumb/5/50/Transmission_line_pulse_reflections.gif/800px-Transmission_line_pulse_reflections.gif)
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Original file (900 × 330 pixels, file size: 1.87 MB, MIME type: image/gif, looped, 240 frames, 12 s)
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Summary
DescriptionTransmission line pulse reflections.gif | English: 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. |
Date | |
Source | Own work |
Author | Sbyrnes321 |
Licensing
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The person who associated a work with this deed has dedicated the work to the public domain by waiving all of their rights to the work worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law. You can copy, modify, distribute and perform the work, even for commercial purposes, all without asking permission. http://creativecommons.org/publicdomain/zero/1.0/deed.enCC0Creative Commons Zero, Public Domain Dedicationfalsefalse |
Source code
""" (C) Steven Byrnes, 2014-2016. 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 arrow_color = (140,0,0) # 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 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): """ 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, arrow_color, tup_round((x, tail_y)), tup_round((x, triangle_middle_y)), arrow_width) pg.draw.polygon(surf, arrow_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_params[i] 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) #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_list[frame]) 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()
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File history
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Date/Time | Thumbnail | Dimensions | User | Comment | |
---|---|---|---|---|---|
current | 19:05, 18 March 2024 | ![]() | 900 × 330 (1.87 MB) | MrAureliusR | Larger size, tweaks made to diagram to make it easier to understand, added labels |
02:04, 29 May 2016 | ![]() | 300 × 110 (442 KB) | Sbyrnes321 | all arrows are red, to reduce image complexity | |
14:47, 15 November 2014 | ![]() | 300 × 110 (605 KB) | Sbyrnes321 | User created page with UploadWizard |
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