[PWM using 555 timer]

I found a circuit that is very close to what I am trying to do:

This is from http://www.saburchill.com/tech/electronics/elect039.html



This circuit uses a sound sensor to vary the brightness of a lightbulb.

I also figured out some timing formulas based on threshold voltage (Vth) and triggering voltage (Vtr).  As you know, normally, Vth = 2/3Vcc and Vtr = 1/3 Vcc.  These values result in the "standard" timing formulas.  Applying the control voltage, Vc, to pin 5 directly affects these values.  It is applied directly to the 2/3 point on the voltage divider.  3 equal-valued resistors make up this voltage divider.  The reference voltage for the threshold comparator is b/n the first and second resistor (hence 2/3Vcc) and the ref voltage for the trigger comparater is b/n the 2nd and 3rd resistor (hence 1/3Vcc).  If I can figure out how the control voltage affects these reference voltages, the following formulas should work.

In monostable mode:
(pulse width) T = [ln(Vcc) - ln(Vcc-Vth)] * R * C

In astable mode:
T1 = -ln[1 - (Vth - Vtr)/(Vcc - Vtr)] * (R1 + R2) * C
T2 = [ln(Vth) - ln(Vtr)] * R2 * C
(pulse width) T = T1 + T2
(frequency) f = 1 / (T1 + T2)
(duty cycle) % = T1 / (T1 + T2)

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I plugged in values Vth = 2/3Vcc and Vtr = 1/3Vcc and got the same values that would result from using the "standard" formulas (discounting some roundoff errors).


Thanks again.  :)

Darrin

Darrin:
I am interested in knowing how you derive the above equations.

Can you tell me how?

Besides, how does the control voltage affect these reference voltages (threshold and trigger voltages)
ie. what is the relationship between Vc , Vth and Vtr  ?