In 555 astable multivibrator, R a= 22 k, R b= 39 K and C = 0.01 μf. Calculate the width of the positive pulse.

Question

In 555 astable multivibrator, R a= 22 k, R b= 39 K and C = 0.01 &mu;f. Calculate the width of the positive pulse.

Prepp Team · Accepted Answer

Calculating Pulse Width in a 555 Astable Multivibrator

The 555 timer IC is a versatile integrated circuit commonly used in various timer, pulse generation, and oscillator applications. When configured as an astable multivibrator, it produces a continuous output signal switching between a high and a low state, effectively generating a square or rectangular wave.

In the astable mode, the 555 timer's timing is determined by two external resistors, \(R_a\) and \(R_b\), and an external capacitor, \(C\). The output signal has a specific frequency and duty cycle, which are controlled by these components.

Understanding the 555 Astable Circuit Parameters

The key parameters for a 555 astable multivibrator are:

\(R_a\): Resistance connected between the supply voltage (Vcc) and pin 7 (Discharge).
\(R_b\): Resistance connected between pin 7 (Discharge) and pin 6 (Threshold) and pin 2 (Trigger).
\(C\): Capacitor connected between pin 6 (Threshold) and pin 2 (Trigger) and ground.
\(T_{high}\) (Pulse Width / ON Time): The duration for which the output is high.
\(T_{low}\) (OFF Time): The duration for which the output is low.
\(T\) (Period): The total time for one cycle (\(T = T_{high} + T_{low}\)).
Frequency (\(f\)): The number of cycles per second (\(f = 1/T\)).

Formula for 555 Astable Pulse Width (\(T_{high}\))

The width of the positive pulse, or the ON time (\(T_{high}\)), for a 555 astable multivibrator is determined by the time it takes for the capacitor to charge from 1/3 Vcc to 2/3 Vcc through resistors \(R_a\) and \(R_b\). The formula is:

T_{high} = 0.693 \times (R_a + R_b) \times C

Where:

\(R_a\) and \(R_b\) are in Ohms (\(\Omega\))
\(C\) is in Farads (F)
\(T_{high}\) is in seconds (s)

Step-by-Step Calculation of Pulse Width

We are given the following values for the 555 astable multivibrator:

\(R_a = 22 \text{ k}\Omega\)
\(R_b = 39 \text{ k}\Omega\)
\(C = 0.01 \text{ }\mu\text{F}\)

First, convert the component values to their base units (Ohms and Farads):

\(R_a = 22 \text{ k}\Omega = 22 \times 10^3 \Omega\)
\(R_b = 39 \text{ k}\Omega = 39 \times 10^3 \Omega\)
\(C = 0.01 \text{ }\mu\text{F} = 0.01 \times 10^{-6} \text{ F}\)

Now, plug these values into the formula for \(T_{high}\):

T_{high} = 0.693 \times (R_a + R_b) \times C

T_{high} = 0.693 \times (22 \times 10^3 \Omega + 39 \times 10^3 \Omega) \times 0.01 \times 10^{-6} \text{ F}

Sum the resistances:

R_a + R_b = (22 + 39) \times 10^3 \Omega = 61 \times 10^3 \Omega

Substitute the sum back into the \(T_{high}\) formula:

T_{high} = 0.693 \times (61 \times 10^3 \Omega) \times (0.01 \times 10^{-6} \text{ F})

Rearrange and calculate:

T_{high} = 0.693 \times 61 \times 0.01 \times 10^3 \times 10^{-6} \text{ s}

T_{high} = 0.693 \times 61 \times 0.01 \times 10^{-3} \text{ s}

T_{high} = 0.693 \times 0.61 \times 10^{-3} \text{ s}

T_{high} \approx 0.42273 \times 10^{-3} \text{ s}

Rounding the result to three significant figures, we get:

T_{high} \approx 0.423 \times 10^{-3} \text{ s}

Since \(10^{-3}\) seconds is equal to 1 millisecond (ms), the pulse width is:

T_{high} \approx 0.423 \text{ ms}

Result and Conclusion

The calculated width of the positive pulse (\(T_{high}\)) for the given 555 astable multivibrator circuit is approximately 0.423 ms.

Comparing this result with the provided options:

0.423 \(\mu\)s (0.423 \(\times 10^{-6}\) s)
0.423 ns (0.423 \(\times 10^{-9}\) s)
0.423 s
0.423 ms (0.423 \(\times 10^{-3}\) s)

The calculated value matches the option representing 0.423 ms.

Revision Table: 555 Astable Formulas

Parameter	Formula	Notes
Positive Pulse Width (\(T_{high}\))	\(0.693 \times (R_a + R_b) \times C\)	ON time, capacitor charges through \(R_a\) and \(R_b\)
Negative Pulse Width (\(T_{low}\))	\(0.693 \times R_b \times C\)	OFF time, capacitor discharges through \(R_b\)
Period (\(T\))	\(T_{high} + T_{low}\) or \(0.693 \times (R_a + 2R_b) \times C\)	Total time for one cycle
Frequency (\(f\))	\(1/T\) or \(1.44 / ((R_a + 2R_b) \times C)\)	Number of cycles per second
Duty Cycle (%)	\((T_{high} / T) \times 100\%\) or \(((R_a + R_b) / (R_a + 2R_b)) \times 100\%\)	Percentage of time the output is high

Additional Information: 555 Astable Multivibrator Operation

The 555 timer in astable mode constantly switches between two states, generating a free-running square wave. The operation relies on charging and discharging an external capacitor between 1/3 Vcc and 2/3 Vcc.

When the capacitor voltage is below 1/3 Vcc, the internal comparator sets the flip-flop, making the output high and turning off the discharge transistor (pin 7). The capacitor charges through \(R_a\) and \(R_b\).
When the capacitor voltage reaches 2/3 Vcc, the internal comparator resets the flip-flop, making the output low and turning on the discharge transistor. The capacitor discharges through \(R_b\) and the discharge pin (pin 7).
When the capacitor voltage drops back down to 1/3 Vcc, the cycle repeats.

The values of \(R_a\), \(R_b\), and \(C\) directly control the charging and discharging times, thus determining the frequency and duty cycle of the output waveform. Note that \(R_a\) must not be zero, as this would short-circuit the power supply when the discharge transistor is on.