Draw the circuit of a one-shot using a 555 timer to provide one time period of \(20 \mu \mathrm{s}\). If \(R_{A}=7.5 \mathrm{k} \Omega\), what value of \(C\) is needed?

In electronics, a monostable multivibrator is a circuit that, when triggered, changes state temporarily before returning to its original stable state. This type of multivibrator is also referred to as a 'one-shot' pulse generator because it produces a single output pulse of a defined duration in response to a triggering event.

A typical example of this is the 555 timer used in the one-shot configuration. When the 555 timer is triggered by a falling edge signal at its trigger input, its output goes high and stays high for a time period determined by the external components (usually a resistor and a capacitor) connected to it. After the time has elapsed, the output goes back to low, and the circuit is ready to be triggered again.

A monostable multivibrator can be used in various applications such as timers, pulse generation, and even as a debounce circuit to clean up noisy signals from mechanical switches.

Designing circuits, particularly with a 555 timer, involves understanding the function of the timer and how external components influence its operation. The 555 timer is versatile and can be used in astable, bistable, or monostable configurations. In the one-shot monostable arrangement, two main components are critical: a resistor (denoted as R) and a capacitor (denoted as C).

These components are selected based on the duration of the output pulse you require. For precision timing, the values of the resistor and capacitor must be accurately calculated and chosen. In our example, with a given resistance value (\( R_A = 7.5 k\text{\textOmega} \)), we are designing the circuit to produce a pulse of 20 microseconds. It is essential to follow a proper design process to ensure the circuit meets the desired specifications.

Determining the duration of the output pulse in a monostable 555 timer circuit boils down to a relatively simple formula: \( T = 1.1 \times R_A \times C \) where \( T \) is the time period of the pulse, \( R_A \) is the resistance, and \( C \) is the capacitance. In the step-by-step solution, the formula is rearranged to solve for \( C \) as this is the unknown we want to discover.

By inserting the known values into the rearranged formula \( C = \frac{T}{1.1 \times R_A} \) and performing the calculation, you can find the exact value of capacitance needed for the desired pulse duration. This formula is essential when designing monostable circuits with a 555 timer, as it directly relates the timing components to the output pulse width.