hurtz,
Normally I wouldn't bother trying to explain this much. But you seem like a very bright person for whom it might be worth doing. I'm sorry if you already know about all of the following. I got the impression that you didn't and thought that it might eventually provide a significant benefit to you, and possibly some enjoyable intellectual stimulation.
It is very important (and potentially empowering) to understand that (almost) every signal can be mathematically decomposed into a superposition (summation) of a large number of sinusoids, in the time domain, which also correspond to the signal's spectrum content in the frequency domain.
Then, also realize that any linear system's response (and "system" is a VERY broad term, here) to a general signal is the summation of its responses to all of the sinusoidal components of the signal.
In that light, I think that you might enjoy researching "Fourier Series".
For simplicity, those are limited, technically, by the math used, to looking at periodic signals of infinite extent in both directions in time. But later developments have taken care of those limitations.
If you have studied calculus, and hopefully differential equations, or even if you haven't, you might then also look at the "Fourier Transform", and then the "Laplace Transform".
Laplace is the more-general case, since it also includes transient components of signals and system responses (in addition to the steady-state sinusoidal components).
Just to give some background:
Laplace also enables us to fully describe the complete (i.e. both the transient and steady-state components of the) behavior of any linear system with an algebraic expression called the system's Transfer Function, which, when multiplied by the Laplace transform of an input signal, provides the Laplace transform of the output signal (which is a lot more useful than it might sound).
One of the many beauties of the Laplace Transform is that it enables us to easily transform differential equations (in the time domain) into algebraic equations (in the frequency/Laplace domain). We can then solve them algebraically(much easier; almost feels like cheating), which gives the solution in the Laplace/frequency domain (which is extremely useful, by itself). BUT, then we can also "inverse transform" the solution and get the time-domain solution to the original differential equation!
Sorry to have blatherd-on about all of that, for so long. Enjoy!
Regards,
Tom
aparatusonitus,
Thank you!
It looks like that website has a lot of other good stuff, too!
Cheers,
Tom
Dont forget that the powerpoint above is for laying out small signal boards, when it comes to boards with both small signals and powerdriving a more creative method of provideing return current control has to be employed (not a fan of the term star grounding, it oversimplifies what can be a very complex and critical part of the layout.)It is a common problem not only with audio but with numerous designs that involve control and driving, be it speakers, motors, the magnets on a synchrotron or LHC. Component placement is critical to seperate the low andhigh current areas and provide a layout that best optimeses the signal integrity of both areas. This is best achieved with ground planes for the low signal areas and for the high current drives. The low signal areas are to provide the optimum return paths for a signal, as illustrated in the John Wu article, and the high current areas to provide the current carying capacity and low impedance.
Multi layer PCB's are used extensively for high reliability and critical designs, though for simple chip amps two layers can suffice, though 4 gives you more freedom, also the small distances involved help. With SMD devices its amazing how small you can make a chip amp, especially if you use active heatsinking (thermal pipes etc).
For Gootee, just spent a week in Munich learning andplaying with this software:
CADSTAR Power Integrity Advance | Zuken
When I get time I will provide more info on the decoupling thread we were involved in a few moons back.
Multi layer PCB's are used extensively for high reliability and critical designs, though for simple chip amps two layers can suffice, though 4 gives you more freedom, also the small distances involved help. With SMD devices its amazing how small you can make a chip amp, especially if you use active heatsinking (thermal pipes etc).
For Gootee, just spent a week in Munich learning andplaying with this software:
CADSTAR Power Integrity Advance | Zuken
When I get time I will provide more info on the decoupling thread we were involved in a few moons back.
Thanks gootee for the extensive explanation!
Especially about the grounding-scheme(s)! Very insightful
I've done a little bit of research on laplace transformation during my bachelor thesis, but thanks for the explanation anyway. However when I talked about matching impedances/capacitances for both rails I made an error by thinking both rails would be stressed at the same time, but this is of course not the case. Now to the relevancy of matched rails, the argument is still valid that matched rails should give equal sagging thus better signal consistency.
However now back to the sinusoidal signal. Even though any signal can be broken into one, in a regular piece of music the positive excitation will mostly not be equal to the following negative excitation. The exception being music where not a lot is going on... well you know what I mean. Thus it would be interesting to follow this doing some measurements with the amplifier (under load) comparing output vs input of a sinus signal and seeing how much an unmatched rail offers difference in positive vs negative excitation.
I wonder if it is possible to measure runtime differences in the wires from the PSU at such short length'.
cheers,
hurtz
Especially about the grounding-scheme(s)! Very insightful
I've done a little bit of research on laplace transformation during my bachelor thesis, but thanks for the explanation anyway. However when I talked about matching impedances/capacitances for both rails I made an error by thinking both rails would be stressed at the same time, but this is of course not the case. Now to the relevancy of matched rails, the argument is still valid that matched rails should give equal sagging thus better signal consistency.
However now back to the sinusoidal signal. Even though any signal can be broken into one, in a regular piece of music the positive excitation will mostly not be equal to the following negative excitation. The exception being music where not a lot is going on... well you know what I mean. Thus it would be interesting to follow this doing some measurements with the amplifier (under load) comparing output vs input of a sinus signal and seeing how much an unmatched rail offers difference in positive vs negative excitation.
I wonder if it is possible to measure runtime differences in the wires from the PSU at such short length'.
cheers,
hurtz
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