Functional Relationship of 555 Monostable PWM

[martyg314]

Hi-

This lab question has me stumped...

Homework Statement

Derive an equation describing the effect of the control voltage on the pules width for a 555 pulse width modulation circuit (monostable circuit).

Homework Equations

width = 1.1*R*C

The Attempt at a Solution

I took data and plotted it in mathematica. At first it looked linear and I realized that the control voltages are relative to the 2/3 threshold voltage, so I thought a linear equation:

output pulse width = Vctrl/Vth * 1.1*R*C

But that fit didn't work. I've tried different exponential fits, but nothing that matches the data even closely.

I realize my data could be faulty, but even though nothing I've researched online or in my texts gives any functional relationship of output width with respect to control voltage.

Thanks,
MG

 

[KataKoniK]

Dear MG,

Thank you for reaching out about this lab question. After reviewing your post, I can understand why you may be stumped. However, I believe I can provide some insight and potential solutions to your problem.

Firstly, it is important to note that in a 555 pulse width modulation circuit, the control voltage affects the charging and discharging of the capacitor, which in turn affects the pulse width. As you mentioned, the equation for pulse width is 1.1*R*C. This equation assumes that the charging and discharging of the capacitor is a linear process. However, in reality, the charging and discharging of a capacitor is an exponential process. This could explain why your linear fit did not work.

To accurately describe the effect of control voltage on pulse width, you may need to use a more complex equation that takes into account the exponential nature of the charging and discharging process. One possible equation is:

output pulse width = (Vctrl/Vth)^n * 1.1*R*C

Where n is a constant that takes into account the non-linearity of the charging and discharging process. This equation may provide a better fit to your data.

Additionally, it is important to ensure that your data is accurate and precise. Double-check your measurements and consider taking more data points to improve the accuracy of your results. You can also try using a simulation software to verify your results and compare them to your data.

I hope this helps and good luck with your lab question! Let me know if you have any further questions or concerns.