Generate pwm using ic 555

Introduction

IC 555

IC 555 is an astable multivibrator (oscillator).

Frequency: The ON time is defined by the time taken to its capacitor to charge to 2/3 (1/e??) level through pin7 resistor, and the OFF time is the discharging time of the capacitor through pin7, 1/3. See the precise numbers from .

Monostable state. Bistable state.

Theory

${\begin{aligned}T_{\text{on}}&=0.693(R_{1}+R_{2})C\\T_{\text{off}}&=0.693R_{2}C\\f&={\frac {1.44}{(R_{1}+2R_{2})C}}\end{aligned}}$

The $R_{1}$ resistance is much smaller than the resistance of the potentiometer, for example, 1K compared to 100K of the potentiometer. In that way we have 99% control over the charging and discharging resistance in the circuit. See https://electronics.stackexchange.com/questions/175967/how-do-i-use-pin5-to-control-duty-cycle-of-a-555-based-pwm

The output of the 555 timer can source a current of 200mA to the load.

• Use MOSFET (eg TIP122 Darlington transistor; 5A) for driving the motor.

To obtain a zero percent (0%) duty cycle, the oscillator need to stop oscillating. One option is to use a parallel resistor to use some of the current.

Method 1; the simple

• 

  The simple 555 circuit.

• 

  The differences in C and output. Note that more than 50% pwm is not obtained

• 

  The surface and contour plot of the limits of the R₁ and R₂ values.

The capacitor is charging through $R_{1}$ and $R_{2}$ but discharges only through $R_{2}$ using IC 555. Thus $R_{2}$ should be a potentiometer.

The $0.01\mu$F capacitor is to ensure that the CTRL and GND stays on the same voltage level. The CTRL pin of the 555 is to level out any fluctuations in the power supply voltage that might affect the operation.

${\begin{aligned}T_{\text{on}}&=0.693(R_{1}+R_{2})C\\T_{\text{off}}&=0.693R_{2}C\\f&={\frac {1.44}{(R_{1}+2R_{2})C}}\end{aligned}}$

and

${\begin{aligned}{\text{pwm}}\%&={\frac {T_{\text{on}}}{T_{\text{on}}+T_{\text{off}}}}\\&={\frac {0.693(R_{1}+R_{2})C}{0.693(R_{1}+R_{2})C+0.693R_{2}C}}\\&={\frac {0.693C}{0.693C}}{\frac {R_{1}+R_{2}}{R_{1}+2R_{2}}}\\&={\frac {R_{1}+R_{2}}{R_{1}+2R_{2}}}\\\end{aligned}}$

The limits of ${\text{pwm}}\%$

${\begin{aligned}\lim _{R_{2}\to 0}{\text{pwm}}\%&=\lim _{R_{2}\to 0}{\frac {R_{1}+R_{2}}{R_{1}+2R_{2}}}\to {\frac {R_{1}+0}{R_{1}+0}}=1\\\lim _{R_{2}\to \infty }{\text{pwm}}\%&=\lim _{R_{2}\to \infty }{\frac {R_{1}+R_{2}}{R_{1}+2R_{2}}}=\lim _{R_{2}\to \infty }{\frac {R_{2}({\frac {R_{1}}{R_{2}}}+1)}{R_{2}({\frac {R_{1}}{R_{2}}}+2)}}\to {\frac {1}{2}}\\\end{aligned}}$

But note that if $R_{1}$ cannot be zero because then the discharge pin 7 would be shorted to Vcc.

See the attached python file which generates the surface and contour plot shown above: File:555limits.zip. It is a zipped python file.

File:555 simple 300 300.circuitjs.txt is the Falstad file to simulate the circuit. The image above is generated using Falstad circuit simulator.

Caption text

$R_{1}$	$R_{2}$	$C$	$T_{\text{on}}$	$T_{\text{off}}$	pwm%	$f$
300	300	300 nF	0.000125	0.0000624	0.67	5333
300	300	30 nF	0.0000125	0.00000624	0.67	53333
300	300	3 uF	0.00125	0.000624	0.67	533
3000	300	300 nF	0.000686	0.0000624	0.92	1333
300	3000	300 nF	0.000686	0.000624	0.52	762
300	30000	300 nF	0.00630	0.00624	0.50	80

See the file File:555 simple calculations.ods for interactive Libre Office file.

As the resistance of $R_{1}$ becomes much larger than $R_{2}$, the duty cycle increases towards unity (100%) as $R_{2}$ approaches zero. If the resistance of $R_{2}$ increases with respect to $R_{1}$, the duty cycle approaches 50% (or 1:1). It seems to be impossible to obtain less than 50% duty cycle with this system; Thus, only about half range can be achieved.

How to get the pwm% smaller than 50%. Add a diode to short $R_{2}$ during the charge cycle.

Method 2; Longer low time: Add a Diode

File:555 diode 300 300.circuitjs.txt

Method 2; Longer low time: Diodes

The diodes

Note that there exists multiple different placements for diodes! I do not follow all of these, yet.

If needed a shorter high time and longer low time, a diode can be connected across $R_{2}+0$ with cathode on the capacitor side. It is called the PWM mode. The charge and discharge timing of the capacitor $C$ is bifurcated through separate channels using diodes. Also, $R_{2}$ is replaced with a potentiometer.

See for more text. This might be a good: .

Method 3: Transistor

Added a transistor

The 555 can source or sink (supply or pass to ground) around 200mA, thus to drive larger currents we need an output circuit. The 555 will work from 5 to 15 volts, thus a same voltage source can be used. FOr controlling the motor we use TIP31 NPN transistor (max 3A).

Parts

• TIP31 NPN Transistor
• 12V Motor or a dimmable load

https://diyodemag.com/education/fundamentals_versatile_555_timer_pwm_control

• But more diodes

Method 3: MOSFET

Mosfet allows more current (they operate on a totally different electrical principle).

• BJT operation is based on current control. Less efficient (higher power dissipation). Lower input impedance. Superior linearity.
• Mosfet operation is based on voltage control. More efficient. Higher switching speed. Better thermal stability. High input impedance.

Method 2: More Diodes

The diodes are used for direction control and protection of the circuit.

555 internal design and theory

See https://www.electronicshub.org/555-timer-pwm/

and the internal circuit looks like below:

Simulation

Simulation is done using https://www.falstad.com/circuit/circuitjs.html simulation software. The corresponding editable circuit file is downloadable.

References

https://www.homemade-circuits.com/how-to-use-ic-555-for-generating-pwm/

https://www.electronicshub.org/555-timer-pwm/