Question About Duty Cycle and Average Value of a Square Wave

It's possible that they mean something else, like the peak-to-peak voltage, but it's not clear.In summary, the first conversation discusses determining the value of resistor R2 for a 555 timer circuit with a specified output duty cycle of 0.7. The second conversation involves finding the average value of a square wave with a minimum value of 0 volts, maximum value of 10 volts, and a duty cycle of 73%. The proposed equation for the average value may not be correct, and the answer of 2.7 volts may need to be reversed to 7.3 volts.
  • #1
Mohamed Abdul

Homework Statement


[/B]
1. Using the Schematic of a 555 in astable mode from the Wikipedia entry on '555 Timer IC," resistor R1 = 8 kOhms and capacitor C = 3 micro-Farads. Determine the value of R2 so that the output duty cycle is D = 0.7. Note that D is not expressed as a percentage here for simplicity. Express your answer in kOhms.

2. Determine the average value of a square wave whose minimum value is 0 Volts, whose maximum value is V = 10 Volts and whose duty cycle D = 73 %. Express your answer in Volts.

Homework Equations



DC = high time/low time
high time = ln(2)*C*(R1+R2)
low time = ln(2)*C*R2

average value = D*V1 + (1-d)*V2 <= Not sure if this is the right equation

The Attempt at a Solution



For number 1, I set my high time and divided it by the low time. I managed to cancel out the ln(2)*C and got that duty cycle was (R1+R2)/(R1+2R). After setting that equal to .7, I got that R2 was 6kOhms.

For number 2, I plugged in my values for the last equation, using O volts as V1 and 10 volts as V2. This gave me an answer of 2.7 volts.
 
Physics news on Phys.org
  • #2
Mohamed Abdul said:
2. Determine the average value of a square wave whose minimum value is 0 Volts, whose maximum value is V = 10 Volts and whose duty cycle D = 73 %. Express your answer in Volts.
Mohamed Abdul said:
For number 2, I plugged in my values for the last equation, using O volts as V1 and 10 volts as V2. This gave me an answer of 2.7 volts.

73% of the time at 10 volts, and 27% of the time at 0 volts. Would this average 2.7 volts?
 
  • #3
Asymptotic said:
73% of the time at 10 volts, and 27% of the time at 0 volts. Would this average 2.7 volts?
] Looking at what you said, it'd make sense that the number should be higher, so should I just reverse the voltages in the equation and get 7.3 volts instead?
 
  • #4
Mohamed Abdul said:
] Looking at what you said, it'd make sense that the number should be higher, so should I just reverse the voltages in the equation and get 7.3 volts instead?
Yes, an answer of 7.3 volts fits with how I'm interpreting question #2.
 

What is the duty cycle of a square wave?

The duty cycle of a square wave is the percentage of time that the signal is in its "on" state compared to its total period. It is typically represented as a percentage or decimal value between 0 and 1.

How is the duty cycle calculated?

The duty cycle can be calculated by dividing the duration of the "on" state by the total period of the signal and multiplying by 100. For example, if a square wave has a period of 10 milliseconds and the signal is "on" for 6 milliseconds, the duty cycle would be (6/10)*100 = 60%.

What is the relationship between duty cycle and average value of a square wave?

The average value of a square wave is directly proportional to its duty cycle. This means that as the duty cycle increases, the average value of the square wave also increases. On the other hand, as the duty cycle decreases, the average value decreases as well.

Can the average value of a square wave be negative?

Yes, the average value of a square wave can be negative if the duty cycle is less than 50%. In this case, the signal spends more time in its "off" state, resulting in a negative average value.

How is the average value of a square wave calculated?

The average value of a square wave can be calculated by taking the sum of all the instantaneous values of the signal over one period and dividing by the total period. This can also be represented as an integral of the signal over one period divided by the total period.

Similar threads

RMS of square wave and alternating currents
    • Introductory Physics Homework Help
Replies
2
Views
979
Question about circuits with transistors (current, voltage)
    • Introductory Physics Homework Help
Replies
4
Views
1K
Question about output voltages and impedances
    • Introductory Physics Homework Help
Replies
5
Views
1K
NASA NASA - Bimodal NTP/NEP with a Wave Rotor Topping Cycle
    • Aerospace Engineering
Replies
1
Views
2K
Vectors: Displacement, average velocity & speed
    • Introductory Physics Homework Help
Replies
7
Views
1K
Carnot Engine cycle on PV Diagram
    • Introductory Physics Homework Help
Replies
5
Views
1K
Interpreting questions like this (About waves)
    • Introductory Physics Homework Help
Replies
11
Views
1K
Circuit Analysis: Current and Voltage Ranking
    • Introductory Physics Homework Help
Replies
10
Views
2K
Expressing expectation values of a particle moving in a periodic potential
    • Introductory Physics Homework Help
Replies
1
Views
1K
Sine Wave Questions: Wavelength, Frequency, Speed
    • Introductory Physics Homework Help
Replies
2
Views
3K

Hot Threads

Recent Insights

Back
Top