The following diagram shows the use of a 555 timer as a monostable polytuned oscillator. This is the basic mode of operation of the IC 555, which requires only two additional components to make it work as a monostable polytuned oscillator: a resistor and a capacitor.
In this case, pins 1 and 8 are connected to ground and power supply VCC), respectively, and the output is made at pin 3. To avoid accidental reset of the circuit, pin 4 is connected to VCC. pin 5 is the control voltage
The input should be grounded when not in use. To filter out noise, it is grounded through a small capacitor with a capacitance of 0.01uF.
Operating Procedure
The monostable mode is also known as a "one-shot" pulse generator. The event sequence starts when a negative trigger pulse is applied to the trigger comparator. When the trigger comparator detects a short negative trigger pulse just below the reference voltage (1/3 VCC), the device triggers and the output goes high.
The discharge transistor is switched off and the capacitor C, which is connected to its collector, starts to be charged to its maximum value by means of a positive R. When the charge on the capacitor reaches its maximum value, it is charged to its maximum value. The HIGH output pulse ends when the charge on the capacitor reaches 2/3 VCC.The internal connection of the IC 555 to the RC timing circuit in monostable mode is shown below.

Initially, the trigger is RESET, which saturates the discharge transistor. A capacitor C connected to the open collector (drain in the CMOS case) of the transistor sets up a discharge path. Thus the capacitor is completely discharged and the voltage across its terminals is 0. The output of pin 3 is low (0).
When a negative trigger pulse input is applied to the trigger comparator (Comparator 2), it is compared with the reference voltage of 1/3 VCC. The output remains low until the trigger input is greater than the reference voltage. When the trigger voltage falls below 1/3 VCC, the output of the comparator goes high, which sets the trigger. As a result, the output of pin 3 will go high
At the same time, the discharge transistor turns off and capacitor C will begin to charge, with an exponential rise in voltage across its terminals. This is nothing but the wink voltage on pin 6. This is supplied to comparator 1 along with the reference voltage of 2/3 VCC The output of pin 3 will remain high until the voltage across the capacitor reaches 2/3 VCC.
In the event that the sniff voltage (voltage across the capacitor) becomes greater than the reference voltage, the output of comparator 1 goes high. This resets the flip-flop so that the output of pin 3 drops to a low level (logic 0), i.e. the output returns to its steady state. As the output goes low, the discharge transistor is driven to saturation and the capacitor will be fully discharged.
As a result, the output of pin 3 goes low at startup, high when the trigger becomes less than 1/3 VCC, and low when the value voltage is greater than 2/3 VCC until the next trigger pulse occurs. A rectangular pulse is generated at the output. The time for which the output remains high or the width of the rectangular pulse is controlled by the timing circuit, i.e., the charging time of the capacitor depends on the time constant RC.
Pulse Width Derivation Process
The voltage across the capacitor C increases exponentially. Therefore, the equation for the capacitor voltage VC can be written as: VCC = VCC(1 - e -t/RC When the capacitor voltage is 2/3 VCC, then we have.

Therefore, the pulse width of the output rectangular pulse is W = 1.1 RC.Also, the waveform for monostable operation is shown below
Application of 555 Timer Monostable Multi-Harmonic Oscillator
Frequency Divider
When IC 555 is used as a monostable polytuned oscillator, a positive rectangular pulse will be supplied at the output when a short duration negative pulse is applied at the hair input. The device can be made to operate as a frequency divider circuit by adjusting the time interval t of the charging or timing circuit.
If the time interval t is slightly greater than the time period of the input pulse trigger pulse), the device can be used as a three-way frequency divider circuit. The time interval can be controlled by appropriately selecting the values of the electropositive R and capacitor C in the timing circuit. The waveforms of the input and output signals corresponding to the bifurcation circuit are shown below.

The circuit will trigger the first negative pulse of the trigger input. As a result, the output will go high. The output will remain high for a time interval t. During this interval, even if a second negative trigger pulse is applied, the output will not be affected and will continue to remain high because the timing interval is greater than the time period of the trigger pulse. On the third negative trigger
pulse, the circuit is retriggered.
The circuit will therefore trigger on each alternating negative trigger pulse, i.e. one output pulse for every two input pulses, so it is a bisecting circuit. By adjusting the time interval, monostable circuits can be made to produce integer portions of the input frequency.
Pulse Width Modulator
The monostable mode of operation of the C 555 can be converted to a pulse width modulator by applying a modulating signal as a control voltage on pin 5. The circuit for a pulse width modulator using a monostable polytuned oscillator is shown below.
The control signal will modulate the sniff value voltage and thus the output pulse width. As the control voltage varies, the break-in voltage, the input to the comparator 1, varies. As a result, the time to charge the capacitor to the level of the sniff value voltage will vary, thereby generating a pulse width modulating waveform at the output. The waveforms of the input, output and modulating signals are shown below.
Due to the application of the control signal, the upper break-in voltage level of the capacitor will vary. The new upper breakout level UTL is given by: UTL = 2/3 VCC + VMOD where VMOD is the voltage of the modulating signal.
Due to the new break-in level, the output pulse width is given by:W = -RC In (1 - UTL/VCC)
Where the time period of the output is the same as the time period of the input
Linear Ramp Generator
The monostable polytuned oscillator will act as a linear ramp generator with the addition of a constant current source. A current mirror consisting of a diode and a PNP transistor is used as a constant current source and this constant current source is placed at the location of the timing resistor. The linear ramp generator circuit with IC 555 in monostable mode is shown below.

Current 1C from the constant current source will charge the peak voltage (VCC) at a constant rate, resulting in a linear rising ramp. When the voltage across the capacitor reaches 2/3 VCC, comparator 1 will drive the discharge transistor to saturation. As a result, the capacitor begins to discharge. When discharging, as the voltage across the capacitor drops to 1/3 VCC, comparator 2 will switch off the discharging capacitor.
As a result the capacitor will start charging again. The discharge time of the capacitor is very short compared to the charging time. As a result, the downward slope is very steep (almost immediate discharge). Therefore, the time period of the ramp output is actually equal to the charging time of the capacitor. The time period of the ramp output is approximately given by the following equation.
T = (2/(3 ) Vcc Re (R1+R2)C)/(R1 Vcc - Vbe(R1+R2)) The ramp output and pulse output waveforms of the ramp generator are shown below.
Driving Relays
A monostable polytuned oscillator can be used to drive a relay in the circuit shown below.
These circuits are called time delay relays. In this circuit the relay once activated stays on for some time. The time for which the relay is switched on can be between 0 and 20 seconds.
It depends on the values of R and C in the timing circuit.
For example, if the relay is to be switched on for 10 seconds in order to supply power to an external device, the values of the anode and capacitor can be calculated using the formula t = 1.1 RC as follows Assuming that the value of the capacitor is the smallest possible value through the capacitor, i.e., 10uF, and that the value of the resistor is 10 = 1.1R*10uF
i.e.: R = 909090.9090 = 909KQ
The potentiometer can be used to adjust the resistor and thus the time delay
Missing pulse detector
The missing pulse detector circuit is shown below, with a PNP transistor connected to a capacitor and an input trigger pulse sequence supplied to the base terminal of the transistor and pin 2 of the 1IC 555
Trigger Input.

The trigger pulse sequence will continuously reset the timing period so that the output is always high. If any trigger pulse is missing, the device detects this missing pulse and the output goes low.
The process works as follows: when the input is 0, the PNP transistor turns on, the voltage across the capacitor is clamped to 0.7 V, and the output is HIGH. when the input trigger voltage is high, the diode cuts off and the capacitor starts to charge.
If the input trigger signal goes low again before the timing cycle is completed, the voltage across the capacitor drops to 0.7 V before reaching the value voltage 2/3 VCC) and the output continues to be HIGH. If the input trigger signal does not go low before the timing cycle is completed due to a missing pulse, it allows the capacitor to charge to the break-in value voltage and the output will go low.
In order for the circuit to operate as a missing pulse detector, the time period of the input trigger signal should be slightly less than the timing interval. Thus, successive negative input pulses will not allow the capacitor to charge to the glancing voltage and the output will continue to remain high. In the case of a change in the input frequency or loss of pulses, the capacitor will charge to the LangValue voltage and aim for the output to drop. The input pulse waveform, capacitor voltage waveform and output signal waveform are shown below.

Summary
As you know, a monostable oscillator, also known as a self-excited polytuned oscillator, is a circuit part. In a circuit, a monostable polytuned oscillator has only one steady state. When a trigger input is applied, a pulse is generated at the output and returns to the steady state after a period of time. And in practice, the 555 timer is used as a common IC device to build a monostable oscillator.