[SOLVED] PWM output equation for 555 timer

[kishore3677]

hi

can anyone explain the relationship between control voltage and pwm output of a 555 timer.
searched a lot but could not get one.

 

[alexan_e]

Check this link 555 and 556 Timer Circuits
all the modes are explained and the equations to calculate the frequency or duty

Alex

 

[kishore3677]

Actually I am looking for a PWM varying control voltage, not with pot as shown in the link you suggested.

 

[ckshivaram]

check these discussion
PWM with control Voltage using 555 timer IC
Control motor PWM schematic | Scientific, embedded, biomedical, electronics contents.

**broken link removed**

 

[kishore3677]

ya checked out the site, but can anybody clearly explain mathematically the relation between control voltage and pwm output.

 

[mister_rf]

Actually I am looking for a PWM varying control voltage, not with pot as shown in the link you suggested.

In this case need to use a specially-designed PWM ICs, to include separate settings for the oscillation frequency and enabling external control voltage.

 

[kishore3677]

Any further advice and links

 

[KerimF]

If you have an example to start with, it could be possible to find a formula for it when used as PWM circuit.

 

[kishore3677]

could you explain it further

 

[KerimF]

I mean... did you start with something?
That is, did you have a specific circuit in which the main IC is 555 and you like to find out, for example, the relation between the voltage on its pin 5 and its output waveform on its pin 3?
Or you are just asking a general question?

 

[kishore3677]

yes I wired 555 as per the data sheet. Trigger in pin 2 and modulating input at pin 5. Getting PWM output , but unable to establish any direct relationship between control voltage and pulse width. Not able to relate mathematically.

 

[KerimF]

I see... You use the 555 as a monostable.
Just to be sure, does your trigger signal has a constant frequency (same intervals)?

For instance, which is the voltage of the power supply? Is it regulated?

Since you wired the circuit, which values you selected for RA and C?

Sorry for asking too much questions... I use to calculate to build real circuits. The general form of any formula, for educational purpose, needs more work to include all possible conditions :grin:

 

[kishore3677]

yes my trigger has a constant frequency with pulse width 50us. The value of R -10K and C-10nF.
Yes my power supply is linear one , not SMPS. I have also decoupled with 0.01uf. Now any clues.

 

[KerimF]

I don't see values :wink:
Trigger frequency
and
Supply voltage

If you are not sure about their values, you may give any ones you prefer. I like to work with formulas from which I can get numerical results for one or more examples. So that one can verify his work on a real circuit.

 

[kishore3677]

trigger frequency 50hz, supply voltage 12V.

 

[KerimF]

Now we are ready for work...

Let us examine what is behind pin5. There is a voltage divider. Its upper resistor is 5K and the lower one 10K (actually 5K+5K).
So the pin5 voltage if open should be:
Vctl = Vcc * 10 / (5 + 10) = Vcc * 2/3
In our example:
Vct = 12 * 2/3 = 8V

Now, when the trigger signal arrives (its hi to low edge), C will be released from oin7 and be charged via RA.


To be continued...

Note: when I am on edaboard pages my internet cut off randomly... so I need to restart it.

 

[kishore3677]

I tried to use following equation Vc = VCC(1-e(-t/RC)). Substituted Vc for various control voltages ( 4 to 8V) and tried to find corresponding T, theoretically. Now by experimenting , I am unable to get anywhere near theoretical values.

 

[KerimF]

Even at pin5 = 7V for example

It is good that you did some tests... can you share your results so that we can analyze them together.

 

[kishore3677]

yes I will share some of the results:

practical R values= 9.83K c= 15nF.

Control voltage = 4 V ----> PW= 56us
CV = 5V------> PW= 78us
CV= 6V-------> PW= 102us
CV= 7v--------> PW= 133us
CV= 8V--------> PW= 171us

 

[KerimF]

Ok... so let us consider your measured t (PW) as the given data and find out C that 555 IC really sees.
I assume you can verify that RA has indeed the value 10K.

I just noticed the real values of RA and C... sorry

C_tot = T/R/ln [ Vcc/(Vcc-Vctl) ]

It seems that C_tot (seen by 555) is about 12 nF (sorry this is wrong )

14.05nF @4V
14.72nF @5V
14.97nF @6V
15.45nF @7V
15.83nF @8V

So I think we have to add another factor in the C formula to include the Vsat of pin 7:

Vc(t) - Vc(0) = [ Vmax - Vc(0) ] * [ 1 - e^( -t/RC ) ]
Where
Vc(0) = Vsat (at time 0)

T = RC * ln [ (Vcc - Vsat) / (Vcc - Vctl) ]

It is better to isolate Vsat first.

Vsat = Vcc - (Vcc - Vctl) * e^(T/RC)

This didn't work too :sad:

If this happens to me... I won't sleep till I get the missing keys :smile:

I am not sure how much the delays from trigger to output (low to high) and from Vc = Vctl to output (high to low) contribute on the measured pulse width.

In any case, since we have 12V, I prefer to charge C with constant current instead.
I think you already saw how to do it on the next paragraph "Linear Ramp".