From 6f12a41cc6fc61d62bfd862f454e63b0652823fc Mon Sep 17 00:00:00 2001 From: jaseg Date: Mon, 12 Jun 2017 13:03:18 +0200 Subject: Add resistor calculation script --- hw/chibi/chibi_2024/rcalc.py | 127 +++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 127 insertions(+) create mode 100644 hw/chibi/chibi_2024/rcalc.py (limited to 'hw/chibi/chibi_2024') diff --git a/hw/chibi/chibi_2024/rcalc.py b/hw/chibi/chibi_2024/rcalc.py new file mode 100644 index 0000000..3bba342 --- /dev/null +++ b/hw/chibi/chibi_2024/rcalc.py @@ -0,0 +1,127 @@ +#!/usr/bin/env python3 +""" + MBI5026 current set resistor calculations + + The MBI5026's output current is set by a current set via a single resistor + connected to its R_ext pin. + + To get a larger inter-frame dynamic range Megumin can switch between + four different current ranges. The ratio between one current range and the + next smaller one is r=1:8 (eq. -lg(r)=3 bit). This means at b=12bit BCM range we + get a minimum of + + bmin = b+lg(r) = 8bit @ r=1:16, b=12bit + + worst-case in the intermediate ranges using a static current setting. + Megumin uses BC847 small-signal NPN transistors to switch between three + current ranges: + + ┌─────────┐ + │ MBI5026 │ + │ │ + │ Rext─┼──┬──┤R1├───────────GND + │ │ │ + └─────────┘ ├──┤R2├──┤BC847├──GND + │ + ├──┤R3├──┤BC847├──GND + │ + └──┤R4├──┤BC847├──GND + + The transistors are used to select either or none of {R2, R3, R4}. This means + the R_ext pin sees either R1, R1||R2, R1||R3 or R1||R4. We don't do a full + R-2R or similar DAC configuration as we only have to maintain the ratio r + between ranges. + + Megumin's smallest BCM period is tb=250ns resulting in a base BCM rate of + 4MHz minus control overhead. This results in a BCM period and frame rate of + + Tm = tb*(2**b) = 1.024ms @ tb=250ns, b=12bit. + fm = 1/Tm ≈ 1kHz + + Now, if we want to modulate the display at a current range in between two + of the preset ranges, we can switch between both ranges with a ratio of + sqrt(r)=1:4 and still get a frame rate of + + f = fm/sqrt(r) = 250Hz @ fm=1kHz, r=1:16 + + Normalized to the larger of the two ranges (here r1=1) we get the following + equation for the ratio of the resulting modulated range: + + r_im1 = sqrt(r)*r1 = 0.25 @ r=1:16, r1=1 + r_im_tot = r_im1 + (1-sqrt(r))*r2 = 0.297 @ r2=r*r1 + + Including the 2 bit gained by inter-frame modulation this results in the + following basic ranges at framerate f=250Hz with a slight mid-range + discontinuity at the mixed ranges: + + Range max │ Total bits + ───────────┼────────────────────── + 1.000 │ 14 + 0.297 | 16 (14 at mid-range) + 0.250 | 14 + + The resistances of the resistors R1, R2, R3, R4 used are calculated in this + script. +""" + +prefixes = {' ': 1, 'k': 1e3, 'M': 1e6, 'm': 1e-3, 'μ': 1e-6, 'n': 1e-9} +def format_unit(val): + for prefix, magnitude in prefixes.items(): + if 1.0 <= val/magnitude < 1000.0: + return val/magnitude, prefix + else: + if val<1: + return val/10e-9, 'n' + else: + return val/10e6, 'M' + +def print_var(name, val, unit, **kwargs): + scaled, prefix = format_unit(val) + print('{} = {: >7.3f}{}{}'.format(name, scaled, prefix, unit), **kwargs) + +r = 1/16 +stages = 3 +mod_r = 1/8 +I_max_led = 0.01 +n_boards = 20 +n_digits_per_board = 8*4 +n_leds = n_boards*n_digits_per_board*8 +V_fw = 1.9 # V + +print('r = 1:{:.0f}'.format(1/r)) + +I_min_led = I_max_led*(r**(stages-1)) # A +I_max_mod = I_max_led/mod_r +I_min_mod = I_min_led/mod_r +print_var('I_max_led', I_max_led, 'A') +print_var('I_max_mod', I_max_mod, 'A') +print_var('I_min_mod', I_min_mod, 'A') +if (I_max_mod > 0.09): + print('\033[91mError: The MBI5026 has a maximum output current of 90mA!\033[0m') + +Vrext = 1.26 # V +# Iout = 15 * Vrext/Rext | acc. to MBI5026 datasheet +R1 = 15*Vrext/I_min_mod +Itot_1 = n_leds * mod_r * I_min_mod +Ptot_1 = Itot_1 * V_fw +print_var('R1', R1, 'Ω', end='\t') +print_var('I1', I_min_mod, 'A', end='\t') +print_var('Itot_1', Itot_1, 'A', end='\t') +print_var('Ptot_1', Ptot_1, 'W') + +for i in range(stages-2, -1, -1): + # Rpar = 15*Vrext/(I_max_mod*r) + # R1||R2 = 1/(1/R1 + 1/R2) =!= Rpar = 15*Vrext/(I_max_mod*r) + # ⇒ 1/R1 + 1/R2 = 1/(15*Vrext/(I_max_mod*r)) + # ⇒ 1/R2 = 1/(15*Vrext/(I_max_mod*r)) - 1/R1 + # ⇒ R2 = 1/((I_max_mod*r)/(15*Vrext) - 1/R1) + In = I_max_mod*(r**i) + Rn = 1/(In/(15*Vrext) - 1/R1) + Itot_n = n_leds * mod_r * In + Ptot_n = Itot_n * V_fw + scaled, prefix = format_unit(Rn) + print_var('R{}'.format(stages-i), Rn, 'Ω', end='\t') + print_var('I{}'.format(stages-i), In, 'A', end='\t') + print_var('Itot_{}'.format(stages-i), Itot_n, 'A', end='\t') + print_var('Ptot_{}'.format(stages-i), Ptot_n, 'W') + -- cgit