[Questions] power of Square wave vs Sine wave

[jibajam]

Hello, everyone I have a few questions regarding ultrasonic, square wave and sine wave

At a specific range of frequency for ultrasonic, is square wave or sine wave more powerful?
Does this mean that Square/Sine wave is more efficient over the other?
What does the RMS value mean?

Thank you very much!

 

[KlausST]

Hi,

you can´t say whether a square is more powerful than a sine.

It´s like asking:
Is the enclosed area of a circle larger that the enclosed area of a square?
--> it depends on diameter and length.

****
Now you take "RMS" into account.
A sine with 1V RMS connected to a resistor creates the same power like 1V DC to the same resistor.

Indeed RMS is not releated to sine only. It is true for arbitrary signals, too.
Any signal with 1V RMS creates the same power like 1V DC.
Any signal with 5V RMS creates the same power like 5V DC.
Any signal with "X" V RMS creates the same power like "X" V DC.

****
The next point: You say "at a specific range of frequency"
A pure sine consists only of one single frequency. Feed it through a narrow bandpass filter (with same frequency) and the output is the same as the input.

A square wave includes a lot of additional frequencies. With no upper limit. Feed a square wave through a anarrow bandpass filter (with square wave - fundamental - frequency) and the output is a pure sine.

If you go into details the a square wave must not be limited in frequency .. otherwise it is no square wave anymore.

An example: A square wave with 1kHz includes frequencies up to the GHz and above. unlimited. (Theoretically. But not 100% possible in reality)

Klaus

 

[jibajam]

Thank you for your prompt reply, upon googling, i found this.

"Into the same load, a square wave will deliver twice the power as a sine wave of the same peak voltage. This is same as saying the square wave has an RMS voltage equal to its peak value; whereas a sinewave has an RMS value of 0.707 (actually sqrt(2)/2) times the peak value."

so say, at 55khz +/- 5khz is it true that the square wave is more powerful? and that this can be proven by the rms value?

thank you very much

 

[FvM]

If we are talking about driving signals of ultrasonic transducers which have usually small bandwidth, we have to look for the fundamental wave.

To calculate the magnitude of the fundamental sine of a square wave, you can refer to fourier series. It's 4/pi = 1,27 * square wave magnitude. Means a square wave has more fundamental "power" than a sine wave of same magnitude (peak voltage).

I presume your question is addressing ultra sonic driver circuits. The term "efficiency" isn't really clear in this regard. Can you elaborate the actual problem?

Square wave RMS calculations are inappropriate for ultrasonic transducers because they only absorb the fundamental wave.

 

[KlausST]

Hi,

so say, at 55khz +/- 5khz is it true that the square wave is more powerful? and that this can be proven by the rms value?

You answered it already:

"Into the same load, a square wave will deliver twice the power as a sine wave of the same peak voltage.

If you compare both signals with PEAK voltage: Yes, square is more powerful.
And .. like FvM said before .. even if you use a bandpass filter on the square wave you get a sine wave with higher peak value than the square wave peak value. (4/Pi)


Klaus

 

[jibajam]

the actual problem is that i am building an ultrasound speaker. i was wondering if square wave or sine wave would be stronger/ louder. FvM said that RMS calculations are inappropriate for transducers but what about speakers? Which wave is more powerful? with more energy? and why?
thank you

 

[Audioguru]

You must look at the frequency response of your ultrasonic speaker. If it can produce the fundamental and all harmonics up to at least 10 times the fundamental then a squarewave with the same peak voltage as a sinewave at the fundamental frequency will produce twice the power as the speaker playing the only the fundamental sinewave. Because the same amount of power is in the harmonics as in the fundamental.

Please give us a link to the "ultrasound speaker" driver because there are some piezo junk cheap ones that "say" they produce high frequencies but they do not.

What is the purpose of the ultrasound speaker you are making? It will not repel mosquitoes.

 

[c_mitra]

you can´t say whether a square is more powerful than a sine.

You are absolutely correct. I often get puzzled by the more fundamental question about what is a square wave?

Sometimes people consider digital square wave, running from 0 to 1, as the representative square wave. But in the good old days, square wave was also having a negative component- it used to be -1 to +1.

For comparison, we can normalize: the symmetrical square wave as -0.5 to +0.5. After rectification (it will not change the RMS value), it will be a DC of 0.5. They have the same average value (as the digital square wave).

On the other hand, a sine wave and the square wave having the same peak-to-peak value, do not have the same RMS value.

In the same way, sine wave and a square wave with the same RMS value will not have the same peak-to peak amplitude.

 

[albbg]

Sometimes people consider digital square wave, running from 0 to 1, as the representative square wave. But in the good old days, square wave was also having a negative component- it used to be -1 to +1.

For comparison, we can normalize: the symmetrical square wave as -0.5 to +0.5. After rectification (it will not change the RMS value), it will be a DC of 0.5. They have the same average value (as the digital square wave).

Probably I didn't understand correctly what you mean, but a squarewave running from 0 to 1 has a different RMS value of a squarewave running from -0.5 to 0.5

 

[c_mitra]

Probably I didn't understand correctly what you mean, but a square wave running from 0 to 1 has a different RMS value of a square wave running from -0.5 to 0.5

Sorry if I was not clear; a square wave with peak to peak -0.5 to +0.5 has an average value of 0. You shift the base by 0.5 and it will be another square wave with peak to peak of 0 to 1. They look similar in form but has different RMS values.

What I was trying to say that rectification does not change the RMS value but it does change the waveform. That is because the RMS value is computed point by point by squaring and adding...