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#!/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')
l = [ (1, [1/2, 1/4, 1/8, 1/16,
1/32, 1/64, 1/128, 1/256,
1/512, 1/1024, 1/2048, 1/4096]),
(1/16, [1/2, 1/4, 1/8, 1/16,
1/32, 1/64, 1/128, 1/256,
1/512, 1/1024, 1/2048, 1/4096]),
(1/256, [1/2, 1/4, 1/8, 1/16,
1/32, 1/64, 1/128, 1/256,
1/512, 1/1024, 1/2048, 1/4096])
]
for v, ls in l:
for e in ls:
print('{:> 12.10f} {:.0f}'.format(e*v, 0.5/(e*v)))
print('\033[93m---\033[0m')
l = [ (1/2**0, [1/2, 1/4, 1/8, 1/16,
1/32, 1/64, 1/128, 1/256,
1/512, 1/1024, 1/2048, 1/4096]),
(1/2**7, [1/32, 1/64, 1/128, 1/256,
1/512, 1/1024, 1/2048, 1/4096]),
(1/2**14, [1/32, 1/64, 1/128, 1/256,
1/512, 1/1024, 1/2048, 1/4096])
]
for v, ls in l:
for e in ls:
print('{:> 5.0f} {:> 12.10f} {:.0f}'.format(0.5/e, e*v, 0.5/(e*v)))
plain = sum(l[0][1])
optimized = sum([e for v, ls in l for e in ls])
overhead_percent = (optimized/plain-1)*100
print(plain, optimized, overhead_percent)
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