serial-bench one bench, five serial buses - read-only archive

serial-bench / calculators

Two bench calculators

Calc Bench Archive

The two sums I run before touching a bus, taped to a page so I stop re-deriving them: a UART baud-error budget from two reference clocks, and an I²C rise time from pull-up and bus capacitance. Both run in your browser and send nothing; with scripts off, the formula and a reference table under each one give the same answer by hand.

---

UART baud-rate error

A classic UART divides its reference clock by sixteen and then by an integer, so it can only produce f / (16 × N). Rounding N leaves an error. Two ends work only if their combined error stays well inside half a bit cell over a frame - the hard ceiling is 0.5 / 9.5 = 5.26 %, and I refuse anything above 4 %. Full write-up: the seven-per-cent baud error.

Reference A, MHz Reference B, MHz Target baud

-

UART formula and divider table (works without scripts)

N = round(f / (16 × baud)), actual = f / (16 × N), error = (actual − baud) / baud. Add the magnitudes of the two ends.

Divider error by reference clock, N rounded to nearest integer

Reference	9600	57600	115200
8 MHz	+0.16 %	−3.55 %	+8.51 %
11.0592 MHz	0.00 %	0.00 %	0.00 %
12 MHz	+0.16 %	+0.16 %	−7.00 %
16 MHz	+0.16 %	+2.12 %	−3.55 %
18.432 MHz	0.00 %	0.00 %	0.00 %

---

I²C rise time

The pull-up resistor charges the bus capacitance through an RC curve. The time from 0.3 to 0.7 of the supply is t = ln(0.7 / 0.3) × R × C = 0.847 × R × C, and it must stay under the limit for the bus speed. Full write-up: 310 pF and the rise time I ignored.

Pull-up R, kΩ Bus capacitance, pF Bus speed Standard, 100 kHz (1000 ns) Fast, 400 kHz (300 ns) Fast-mode plus, 1 MHz (120 ns)

-

I²C formula and rise-time table (works without scripts)

t_rise = 0.847 × R × C, with R in ohms and C in farads. Lower the resistor to speed the edge; the floor is the current the open-drain output can sink, roughly V_DD / R.

Rise time (ns) against the 300 ns Fast-mode limit, 0.847 × R × C

R \ C	100 pF	220 pF	310 pF	400 pF
1.0 kΩ	85	186	263	339
1.8 kΩ	152	335	473	610
2.2 kΩ	186	410	578	745
4.7 kΩ	398	876	1234	1593

---

Both calculators use the same arithmetic as the posts they link to, so if a number here disagrees with a number there, the post is the one I stand behind - write to ivo@rawsocket.cloud.