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According the LM555 (google it) datasheet these are the two ecuations you must use:
\[f=\frac{1}{T}=\frac{1.44}{(R_A+2*R_B)*C}\] (1)
\[D=\frac{R_B}{R_A+2R_B}\] (2)
With (2) you can find the relation between RA and RB. You need a 1s pulse (On time) after 20s (Off time), this gives you a total time of 21s, so the duty cycle is \[D=\frac{T_{on}}{Period}=\frac{1s}{21s}=0.0476=4.76%\].
Using (2) \[R_B=\frac{D}{1-2*D}*R_A\], so \[R_B=0.0526*R_A\].
If the total period is 21sec, then \[T=21s {\Rightarrow} f=\frac{1s}{21s}=0.0476 Hz\] and working with the first equation: \[C=\frac{1.44}{(R_A+2*R_B)*f}=\frac{1.44}{(1.105*R_A)*0.0476}=\frac{27.377}{R_A}\]
So, you get these two equations:
\[R_B=0.0526*R_A\]
\[C=\frac{27.377}{R_A}\].
You can choose a value for C, and the find then values of RA and RB. Due to the very low frecuency, you will find that, or you use a very big capacitor, or a very big resistor.
(OR, you can use an CSS555. Check the datasheet to find if it suits your needs.)
To achieve duty cycle other than 50% we add a signal diode across R2
Choose value of R1,R2,C1 accrodingly
Tm = 0.7 × R1 × C1 (ignoring 0.7V across diode)
Ts = 0.7 × R2 × C1 (unchanged)
Where:
Tm :Mark time (output high):
Ts : Space time (output low)
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