maximum frequency component of a square wave

[praveenkumardr]

maximum frequency

what is the maximum frequency component in a typical practical square wave with rise time : "Tr". Most of the engineers say it is
F max = 0.3 / Tr.

please explain!

 

[FvM]

0.35/tr bandwidth

You get 0.35/tr bandwidth for a first order lowpass. The expression has been derived more than once at edaboard, I think. The -3 dB bandwidth of a lowpass doesn't mean maximum frequency component, however. There are higher frequency components present as well.

 

[praveenkumardr]

frequency = 0.3/tr

Right, But if you look at these documents, they say,

It can be shown that the highest frequency component we usually need to be concerned with (in a practical sense) on our board can be approximated by
1/(3*Tr), (I've also attached these documents for your reference)

https://www.polarinstruments.com/support/cits/Critical_length.pdf
https://www.ultracad.com/articles/whensignalintegritymatters.pdf

Could you please explain this in more detail, or send me the link or may be the document , deriving this relation.

 

[AdvaRes]

rise time relation to maximum frequency

Hi all,
The maximum frequency that you can get with Tr is 1/(3*Tr).
Actually a square wave can be defined by: Rise time Tr, Fall time Ft, pulse width and the period P. So, Max frequency is reached when the pulse width is zero and (P-(Tr+Ft+Tr))=0;

Generally Tr=Ft so, the max frequency is reached when P=3*Tr.

 

[Thanhlongbin]

frequency components of a square wave

Hi all,
The maximum frequency that you can get with Tr is 1/(3*Tr).
Actually a square wave can be defined by: Rise time Tr, Fall time Ft, pulse width and the period P. So, Max frequency is reached when the pulse width is zero and (P-(Tr+Ft+Tr))=0;

Generally Tr=Ft so, the max frequency is reached when P=3*Tr.

Hi,
More correctly : Minimum Periode P=Tr when Hold time=Fall time=0.
In this case, you have true "sawtooth wave".
Refer to
https://en.wikipedia.org/wiki/Fourier_series
you get the 2-nd harmony coefficient equ to 50% value of the 1-st one! So 6dB bandwidth is BW =2/Tr !
Is that wright?:|

 

[FvM]

Personally, I prefer models that are closer to common signal parameter specifications in analog electronics and measurement technique.

In this field rise time is usually specified between 10 to 90 % relative amplitude levels. If you apply it to a first order low pass (exponential step response), you get the said low pass frequency.

 

[Thanhlongbin]

@FvM
But for 1-st order LPF, max frequency must be 1/Tr insteed of 0.3/Tr!
OK?

 

[LvW]

Hi praveenkumardr,

I´m satisfied with no answer given to you up to now.
Starting with the documents referenced by you, I think the statement in doc 1 is false (or too simplified) as - according to the FOURIER series - there is no "maximum" frequency within a non-sinusoidal periodic wave.

Doc 2 is more accurate:
It can be shown that the highest
frequency component we usually need to be con-
cerned with (in a practical sense) on our board can
be approximated by 1/(3*T ), where T is the rise
time of the pulse.

Emphasis is on "need to be concerned..in a practical sense" !

My summary is as follows:
Take an ideal square wave and filter it with a first order lowpass having a 3-dB-frequency of Fg. Then, the rise time of the filtered pulse is Tr=0.35/Fg (as stated correctly earlier in this thread).
And now, the question is: What are your requirements as far as your "practical sense" is concerned. Because there are (theoretically) infinite frequency lines in the spectrum. Do you consider an attenuation of only 60 or 80 dB as negligible ?

You can calculate by yourself: The frequency lines of the ideal squarewave decay with 20 dB/dec and the attenuation of the 1st order LP with another 20 dB/dec (above the corner frequency). Which frequency of the spectrum do YOU consider as still important for your specific application ?

Finally, I think an engineer should be able to recalculate some "rules of thumb" and not blindly believe some written statements (even when they are printed in a textbook!).

Regards
LvW

 

[dipnirvana]

Well as said above and again repeating , there is no meaning to "Maximum" frequency component. It's your application which defines the maximum frequency and acceptable level of amplitiude.