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This is more of mathematical problem, but I think there is an electrotechnical engineer that can help me.

So I was reading about I2C pull-up values in the Texas Instruments SLVA689 I2C Bus Pullup Resistor Calculation document and stumbled upon these equations and partial explanation:

Page of formulas from TI SLVA689 I2C Bus Pullup Resistor Calculation

What I don't understand is where does the yellow marked value of 0.8473 come from?

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1 Answer 1

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When you solve the eponential equation for times t1 and t2, i.e. how long it takes for the RC waveform to rise from 0 to 0.3×Vdd, and from 0 to 0.7×Vdd, then you can calculate the time how long it takes for the RC waveform to rise from 0.3×Vdd to 0.7xVdd, then you get ln(0.7)-ln(0.3) and that's 0.8473 and that is the coefficient for the RC rise time from 0.3 to 0.7.

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  • \$\begingroup\$ Thanks for the answer! I am weak in mathematics and these kind of step skipping confuses me a lot. \$\endgroup\$
    – ves_el
    May 26 at 6:14

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