QUCS math functions

[faustdownunder]

Hi
I noticed today that the two functions related to the decibel pseudo-unit require some work.

dB(x) is declared as "voltage decibel".

Decibel is however always related to a power ratio.
If we have two voltages measured across the same resistor, the power ratio is then the square of the voltage ratio because P = ( V^2)/R or P_dB = 20 x log10 (V2/V1).

I believe the definition is dB(x) = dB(V2/V1) where both voltage are across the same resistor. The function should therefore probably be called "voltage ratio to decibel (R1 = R2)" denoting a limitation to identical resistors. A bit pedantic for some but definitely correct and necessary. I would not call this function dB(x) for the reasons explained above. Instead, it should perhaps be

dBv(x).

Secondly, I see

"dBm(x) converts voltage into power in dBm"

We can convert a voltage ratio (R1 = R2) to a power ratio by squaring the voltage ratio.

dBm(x) = 20 x log10(V/V_1mW) (R1 = R2)

which makes clear what the function does. Otherwise, less experienced users might take two voltages measured across different resistances and get the wrong answer.

Since dBm is always defined as 10 x log10(P2/1mW), we should probably call the function

dBmv(x).

with best regards

Dieter

[csrabak]

Whereas the definition above for "voltage decibel" is not completely correct in all realms, it is widely used in electronics, and a lot of references, circuit simulators, maths SW, like the Matlab e compatible open source variety, make use of this definition.

So for active filter design it is the definition used in the craft.

[faustdownunder]

Thanks for your response.
Yes, I am aware of this. However, dB is and was always the log10 of a power ratio and we should attempt to use the pseudo-unit dB in that sense. Otherwise we open all doors to misinterpretation and mistakes.

[felix-salfelder]

On Sun, Apr 16, 2023 at 11:37:43PM -0700, faustdownunder wrote: Yes, I am aware of this.

There are obvious problems with "dB" in Qucs. - dB is not a function. - It is implemented and used as a function, - There is some kind of incomplete unit system. The first one follows from [1], for example. The second, watch out for "dB(...)" in the discussion board or manual. The other -- read the code. In some places, variable names are used to defer type, and some wild overloading heuristics are applied, to pretend it's there. This does not imply that the use of the string "dB" should be discouraged. To illustrate the point, in a normal programmling language, you'd type double ratio = 2.; printf("my ratio is %f dB\n", log(ratio)); // (*) Without overloading, you can still have different context dependent variants. Here's the recipe. double voltage_ratio = 2.; double power_ratio = 17.; printf("my voltage ratio is %f dB\n", dB_v(voltage_ratio)); printf("my power ratio is %f dB\n", dB_p(power_ratio));

However, dB is and was always the log10 of a power ratio

This may be true, but does not imply that dB is a function or that this function takes a real number argument. Removing the "dB function" will solve this puzzle. No such function is used to implement the functionality displayed in (*). [1] https://en.wikipedia.org/wiki/Decibel

[faustdownunder]

I don't understand the programming part but let me add the following:

If you look at the ever-so-professional MS Excel, even the natural constant Pi is defined as an "argumentless function"

PI()

Pi is most certainly not a function in any way - even if Microsoft say so.

So, QUCS would be doing better than Microsoft if it defined a dB function, I guess.

log10(x) is itself already a mathematical function of x, so why not call the whole dB thing a function? Maybe we call it

dB_level(x) instead of just dB (dB is a pseudo-unit)

Relative power level / dB = dB_level(x) = 10 x log10 (P2 / P1) (P2/P1) = x

with dB = 1 for correctness' sake.

And for voltages across the same resistance

dB_level_v

Relative power level / dB = dB_level_v(x) = 20 x log10 (V2 / V1) (V2/V1) = x R1 = R2

I hope this helps a little bit. If not, then I'm sorry.

[csrabak]

I've two comments on this:

1. The dB "always has been..." in the pertaining books if you don't look at the neighborhood. Open loop gain of operational amplifiers has been quoted in "voltage decibels" for more than fifty years and I could post here a plethora of links of named firms, which see, employ this 'incorrect' way in their datasheets¹!

2. The attempt to go to the purist view of "being a function" can have our feet blown if we don't look at the current practice. Even programming languages like C can use macros which at the thousand feet the programmers as a user of it don't distinguish easily, fact that requires some books to remember that max in C being a macro would call the argument (if it happens to be a post or pre incremented variable or even a function that is not reentrant, with consequences) twice, etc.

So in recollection, whereas I agree that "... open all doors to misinterpretation and mistakes.", it is not "us", but the plain historical fact it is that this boat sailed very long ago... please read in the Wikipedia article the paragraph on which J. W. Horton in 1954 argued in these lines, but as we see without success.

We've to refrain to think too much qucs-s as a programming language, but rather an environment to ease our analysis of electrical circuits.

As a closing note, some circuit simulators that have some canned solutions for recurrent tasks, like Bode plots, etc., sometimes go to the absurd of putting impedances in dB!!!

my 0.019999....

Footnotes

1. I concede on the onset that there is a mixed practice in this industry depending upon, who knows what as it can be found in the same company the gain is expressed in dB, sometimes in mV/V, etc... ↩