Objective: Design the 555 IC as an astable multivibrator for a specified frequency and duty cycle.

Specifications: The circuit with the configuration in Figure 15.41 is to be designed such that the frequency is 50 kHz and the duty cycle is 75 percent.

Choices: A 555 IC circuit is available. A capacitor with a value of C = 1 nF is also available.

Question

Objective: Design the 555 IC as an astable multivibrator for a specified frequency and duty cycle.

Specifications: The circuit with the configuration in Figure 15.41 is to be designed such that the frequency is 50 kHz and the duty cycle is 75 percent.

Choices: A 555 IC circuit is available. A capacitor with a value of C = 1 nF is also available.

Accepted Answer

The frequency of oscillation, as given by Equation (15.102), is

[latex]f = \frac{1}{T} = \frac{1}{T_{C} + T_{D}} = \frac{1}{0.693(R_{A} + 2R_{B})C} [/latex] (15.102)
[latex]f = \frac{1}{0.693(R_{A} + 2R_{B})C} [/latex]
Therefore,
[latex]R_{A} + 2R_{B} = \frac{1}{(0.693) f C} = \frac{1}{(0.693)(50 × 10^{3})(1 × 10^{−9})} ⇒ 28.9 k \Omega[/latex] (15.104)
The duty cycle, given by Equation (15.103), is

Duty cycle = [latex]\frac{T_{C}}{T}[/latex] × 100% = [latex]\frac{R_{A} + R_{B}}{R_{A} + 2R_{B}}[/latex] × 100% (15.103)
Duty cycle = 0.75 = [latex]\frac{R_{A} + R_{B}}{R_{A} + 2R_{B}}[/latex]
which yields
[latex]R_{A} = 2R_{B} [/latex] (15.105)
Combining Equations (15.104) and (15.105), we find that
[latex]R_{A} = 14.5 k \Omega[/latex] and [latex]R_{B} = 7.23 k\Omega[/latex]

Trade-offs: If standard-valued resistors are required, then [latex]R_{A} = 13 k \Omega[/latex] and [latex]R_{B} = 7.5 k\Omega[/latex] would provide a frequency of 51.5 kHz and a duty cycle of 73.2 percent.
Comment: A wide range of oscillation frequencies can be obtained by changing the resistance and capacitance values.

Question 15.11: Objective: Design the 555 IC as an astable multivibrator for...

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