Channelman
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Post by Channelman on Sept 24, 2006 5:04:59 GMT -5
Sorry, but after hearing that 'passive circuits can only reduce the output' in my last topic, I couldn't resist showing some simulations to prove this wrong. The attached simulations are for a typical guitar PU an average cable capacitance, and a typical amplifier input.......Anything above zero dB IS a Boost. Volume control has been swept 15% to 95%. Channelman
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Post by Mike Richardson on Sept 24, 2006 7:01:00 GMT -5
Your graph simply shows the peak in response at the pickup's resonant frequency, and the reduction in the peak as the volume control is lowered. The "0dB" on your graph actually represents the pickup's average response over it's frequency range. It does not, however, indicate an increase in output voltage.
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Channelman
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Post by Channelman on Sept 24, 2006 10:39:59 GMT -5
> It does not, however, indicate an increase in output voltage...MRBut the output at 4.5kHz is larger than that being generated. OK, it is due a resonant peak but not the pickup's self resonant frequency but due to the extra capacitance added by the 'treble bleed' cap and the cable cap in series. [glow=red,2,300]If you are getting an output at a higher level than that being generated then it is boosted.[/glow] Without the 'treble bleed' the same setup sims as shown below. First slight peak at 3 kHz only occurs at max vol. Pickup's own natural resonace is shown at 7kHz and is much lower. Channelman
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Post by sumgai on Sept 24, 2006 15:49:25 GMT -5
Channelman,
Jeez, you just aren't gonna get it one take, are you?
TANSTAAFL!
If you can prove Robert Heinlein was wrong, then I will personally show up on the downtown courthouse steps in the county of your choice, and commit a lewd and lascivious act that will likely land me in jail! You can even have an hour to draw a crowd!
It just ain't gonna happen. So the airlines aren't getting my money today. ;D
Now, you blew off M.R. rather summarily, and that was a lack of discipline on your part. You simply must distinguish between 'peak' and 'average' before you go any further, or your credibility with us will be hugely diminished. You need to prove, beyond the shadow of a doubt, that the pickup is generating something by itself, and that some magic combination of following componentry is indeed increasing the pickup's output - at any frequency, let alone a peak.
Your first assignment - model the output of a pickup without any additional componentry coming after it. Any 'peaks' visible? Then they are to be considered as the zero dB point, and not as some point above zero dB. In the wonderful world of electronics, that is the definition of resonance, and you can't change it to suit your desires.
Next assignment - model as you have above, but with a volume control.... any value will do. Now what do you see? If there's a peak above the dB level noted earlier, can you display it for all to see? And if so, then where does the rest of the response curve lay on the graph? Don't forget, loading a generating device changes its output characteristics, but that doesn't give you permission to change the reference points - leave the zero dB point right where it was, please.
And finally, insert a tone control of any design, again your choice. With or without a volume control. Model it, and display the results. Is there now, suddenly and miracously, a peak greater than whatever occurred before? Or is the rest of the response curve now "down" a bit from before? And not coincidentally, is the 'peak' resting at the same spot it had all along?
Bonus question: If cable capacitance, a treble bleed cap, or other stray capacitance anywhere in the guitar, could enhance the treble response, essentially giving us free harmonic content, then don't you think that by now, all the engineers in the world would have figured this out, and rushed to market with "new and improved" guitar models, extolling the virtues of getting something for nothing? And wouldn't you kind of wonder why we've been trying to get rid of these capacitances as a detriment all along, instead of harnessing them for better sound, as you seem to want us to do?
And finally, if you 'swept from 95% down to 5%", then go back and do it all over again. No guitarist plays an entire gig without going to '10' at least once in awhile. You simply must include the maximum volume and tone positions in your experiments, or you will have left out a significant portion of the control's range that is used most often by most guitarists.
I repeat, There Ain't No Such Thing As A Free Lunch.
sumgai
p.s. Even expensive SPICE programs can give you inaccurate results.... they are meant to be a starting point in the design process, and not the be-all, end-all tool that replaces the physical breadboard. Reputable engineers don't send product out the door without getting their hands dirty!
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Post by JohnH on Sept 24, 2006 15:53:33 GMT -5
EDIT Chanelman is right in this case - and Im now going to collect my free cheese sandwich.
Its true - its a resonant effect. There are lots of mechanical analogies in real life, such as bouncing on a trampoline, pushing a kid on a swing and earthquake engineering, where a small input on each cycle builds up over a number of cycles at resonance, to a much greater response.
I believe that if you did this as a transient analysis, feeding in a sine wave at the resonant frequency, you would see that the peak response takes a number of cycles to build up. I havn't tried this, but it might be interesting.
There is no boost in power from the pickup, hence no defying of physics, because the impedance at resonance is higher and hence less current can be drawn from the passive set up. But the amp is mainly just detecting voltage - being high impedance itself - and once in the amp, the extra power can be released.
John
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Channelman
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Post by Channelman on Sept 24, 2006 17:53:40 GMT -5
Sorry Kids, I think I just got up this morning in a devilish mood, wanting a bit of bother. When I've worked out what sumgai is asking me to do (lot of words there mate), I'll have a go but the 0dB level is always the same in my sims defined by the input level, it's not a relative level. If the output comes out at 0dB then there's no boost or cut. JohnH's transient analysis idea is also interesting. I'll try to find time to try both suggestions tomorrow. Channelman
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Post by sumgai on Sept 24, 2006 17:59:53 GMT -5
John, I don't know whether or not to be surprised at your response. The point here is not "free" anything, but where the reference point sits. Allow me to repeat: The given output of a device is it's maximum at any peak, due to resonance or otherwise, and that is the maximum, period. There may be an amount of time necessary to reach that point, and one could expect that to be true wherever one encounters inductance and/or capacitance. The SPICE simulator, as in the real world, has already taken that effect into account - the steady-state waveform has already built up, as evidenced by the existance of the peak in the first place. Your examples, such as pushing a kid on a swing, break down because we never say "The first push was the maximum distance the kid moved away from BDC (Bottom Dead Center), or standing perfectly still. We say "The kid reached a maximum deviation of X-number of degrees", or perhaps we might say "the kid swung out from the bottom-most position such that he was X-number of feet off the ground", or whatever, but the point is, we didn't immediately jump to any conclusions after measuring only one "kid push", we waited until we had pushed so many times that we could no longer perceive a difference in our efforts, and had observed that the kid wasn't going to go any further in his excursions. Indeed, if we pushed until he went around the top, we'd be seeing a helluva a deviation from the bottom, but we'd note that point as the maximum extension from standing still (which in this case is limited by physical constraints), we would not call the average distance of travel his maximum, now would we? Equally to the point, you stated that "There is no boost in power from the pickup, hence no defying of physics, because the impedance at resonance is higher and hence less current can be drawn from the passive set up." Well now, isn't that an interesting phenomenon...... And here I thought that the SPICE program was showing us the total output. While you and I know that a pickup is gonna be used for one thing, the SPICE program doesn't know that. Or did you specifically set a constraint that it should not concern itself with current? I hate to say it, but someone is now gonna have to go back and make their SPICE simulations graph out either total power, or current versus voltage response curves. And I really hate to say this, but your cheese sandwich just melted all over your lap! "But the amp is mainly just detecting voltage....... and once in the amp, the extra power can be released." I'm sorry, but I must reject any attempt to introduce an outside factor into this discussion, such as a guitar amp. We haven't used one in this simulation up until now, so why bring it in now, this late in the game? sumgai
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Post by JohnH on Sept 24, 2006 20:29:08 GMT -5
Sumgai - You have written a lot of words, so I hope you are hungry. I’m sticking to what I said for now, but I’ll chip in again in a couple of days, if needed. J
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Post by sumgai on Sept 24, 2006 20:37:57 GMT -5
(sung to the tune of "They Call Me The Breeze", by J.J. Cale, as performed by Lynyrd Skynyrd)
They call me the Verbose, I keep spittin' out those words. They wish I'd just close, my mouth, and stop spittin' out...... words!
.........
Hehehe, I'm up for this. ;D
sumgai
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Post by sumgai on Sept 24, 2006 21:00:05 GMT -5
Channelman, Ya know, come to think of it, I see where you've made me have to apologize to John. You've put cable capacitance into the equation, and to top it off, you've introduced an amplifier's input impedance. [glow=red,2,300]WHAT?[/glow] Now why would you wanna do that? Your first circuit, shown in Suggestion For Improved Tone Control didn't do that.... why the change? I thought we were discussing the action of a tone control vis-a-vis a pickup, weren't we? If we wanted to include cables and amps, then we're really in trouble. How do you identify an ideal cable? An average one? An acceptable one? And then we have to deal with amplifier inputs. 1MΩ is pretty high, don't you think? I'd start with something more on the order of 68KΩ, and maybe let it drop down to as low as 33KΩ. If you really need to, you might let it rise to as high as 100KΩ but I doubt many real world examples of that exist. If it's all the same to you, I'd rather that we stayed with a signal source, a volume control, and a tone control circuit, if you don't mind. Please? I just don't want to go around looking at scores of amplifiers, combined with dozens of cables, trying to find one that follows the simulation model you've built. Not many players have the time, money, or inclination to do that, I know I sure don't. But my guitar never changes from one amp to the next, hence my request to keep the sim simple - limit it to what can be controlled, meaning the guitar by itself. Please? Thank you. sumgai
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Channelman
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Post by Channelman on Sept 25, 2006 4:08:16 GMT -5
sumgaiI did mention in the thread 'Suggestion For Improved Tone Control' that I was trying not to confuse the issue by adding any extras like PU, cable & amp because they are always going to be in circuit and the 'Improved Tone Control ' suggestion was going to add or subtract from whatever 'qualites' the pickup, cable and amplifier already had. This is a separate thread to contest a point raised in the Tone Control thread in connection with the fact that it is possible to boost the treble end of the spectrum without adding active electronics to a guitar. Of course, I can miss out the amplifier input impedance. I only put it in because I thought somebody would say, "It's not going to happen in practice, because you've missed the amplifier input impedance out". The cable capacitance is a different matter. It's always going to be there and is playing a crucial part in this resonance boost. The reason for the 5% to 95% sweep limit in the simulations is at the 'less than 5% end' this corresponds to -26dB, 1% would be -40dB and 0% would be -infinity dB. I chose 5% as a sensible range to display without 'cramping up' the part we really want to see. Also at 0% the simulator 'falls over' trying to get to grips with infinity. At the top end (and I can't explain why, this time), the simulator also hits a snag at 100% on the sweep range. I can use up to 99%, but not 100%. Again I chose 95 % since I can then step in 10% increments from 5% to 95%. I'll try to do some sims in accordance with your suggestions sometime today. Channelman
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Post by sumgai on Sept 25, 2006 12:35:27 GMT -5
Channelman, (Nice avatar - I hope to live long, although prosper is out of the question! ;D) I've had a chat with unklmickey, and I've had some sleep, so I'm not feeling so 'plucky' this morning. I'm pretty sure we'll remain on a civil basis.... I was starting to get out of hand, wasn't I? Questions for you, just to make your heart skip a beat. In a tank circuit, we generally use a steady-state generator to represent the signal source. This is usually a black box, we don't qualify it in any way. From that we observe the results of various components as they respond to, and interact with, the generator. It is quite possible that with no other components hooked up, the generator will "produce" some given quantity of voltage, current, and therefore, power. But when we hook up 'stuff', we see that the generator has changed some, or all, of its output readings. Question: Why is that? Number Two: Is a steady-state generator in anyway comparable to a pickup that has all manner of anomolies in its output? I personally don't see any similarity between the two, beyond the fact that they are both signal sources, for our purposes. (Actually, like you, I want to be thorough..... a pickup is not a source, strictly speaking, it is a transducer - the string was the true source.) Number Three: What is the proper model for a pickup? When I measure a coil at rest, I can find only DC resistance, no AC was introduced in any fashion, so there is no impedance. Shouldn't that DC resistance show up in parallel with the output of the coil in action? Why would it only be in series? And capacitance..... I'm pretty sure that vector analysis will show us that some capacitance is in series with the output of the coil, not just in parallel. In short, pickups are not steady-state generators. By comparison, they are fickle as all get-out, and I can just imagine the difficulty in modeling their actual properties and actions as they respond to an outside influence (the string and magnet). Hysteresis alone is enough to make me blanch in trying to make sense of what's going on in there. Eddy currents, leakage coupling, just about every phenomenon except skin effect is probably at play here. The final question becomes, at what point do we accept on blind faith those factors we choose not to simulate, for the sake of simplicity and perhaps quicker results? Take your time, there is no penalty for making me wait on pins and needles. (© The Searchers, 1965) ;D sumgai
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Post by sumgai on Sept 25, 2006 14:12:15 GMT -5
OK, I've thought this over some more..... Resonance of a tank circuit is not what I'm d1ckering over here, I hope I'm clear on that. What this thread's title refers to, and what I'm at odds over, is a boost in the treble area of a guitar's overall output signal. To me, this is not the same thing as finding a short, sharp peak in the response curve. I'll grant that such may be noticible to the listener, given all other factors being 'neutral', and for some listeners, it may stand out quite a bit. Fine, I have no problem with that, nor with them (the listeners who feel they are hearing "more treble"). Where I'm having a big beef, and I probably should let it go, is the claim that the 'treble' is boosted, where in fact, only a tiny fraction of the overall spectrum shows a comparative peak. Like I said, this doesn't jibe with my reality. Perhaps I've made a mountain out of a molehill, hmmmm? In that vein, I'd like to say, Channelman, you have brought great controversy to this forum, and we all thank you for it, myself included. There is no better way to learn than to take a position and defend it. While most others here have been sitting quietly, waiting to see which giant falls, they have also been learning, even if only passively by comparison. Know that before your coming, I've often had to re-align my thinking after finding that the world has passed me by in some aspects, most usually when I wasn't paying attention. But this time I intend to see it through to the end. Can you convince me that bringing in all the outside influences is pertinent to the title of this thread? I'm sure others also want to know! ;D Respectfully, sumgai
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Post by UnklMickey on Sept 25, 2006 15:07:33 GMT -5
i think it's amazing that a structural engineer can be soooooooo insightful on matters such as this. although, i really think this wording, really confused things a bit: ...But the amp is mainly just detecting voltage - being high impedance itself - and once in the amp, the extra power can be released. the idea behind this is valid, but the way you expressed it, is wobbly at best. you guys can all you want about no free lunch,perpetual motion, etc. but............. the internal inductance of a pickup and external capacitors can often result in a situation where the voltage and current have a differing phase relationship. so much so, that the VOLTAGE is much greater at certain points than the voltage without the capacitor. this will also be true for the current. but since the voltage peak and the current peak occur at different times, the power will not exceed the power being applied. yes, John, there is no such thing as a free lunch. (except for the cheese sandwich you earned) the POWER seen at any point in the circuit we described will not exceed what it put into it. but since the VOLTAGE IS greater than the voltage put into it, that does indeed give us more volume. an amplifier rarely presents much of a load to the input signal, it responds to the voltage of the signal. also noteworthy, the more " boost" we get at the resonant frequency, the more loss we see at frequencies away from the resonance. unk
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Post by JohnH on Sept 25, 2006 15:55:45 GMT -5
Well there we have it! - all straight now I think
John
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Post by sumgai on Sept 25, 2006 15:57:44 GMT -5
Agreed!
sumgai
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Channelman
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Post by Channelman on Sept 25, 2006 17:50:16 GMT -5
>first assignment - model the output of a pickup without any additional componentry coming after it. >Any 'peaks' visible? Then they are to be considered as the zero dB point, and not as some point above >zero dB. In the wonderful world of electronics, that is the definition of resonance, and you can't change >it to suit your desires.This is the response of the pickup ALONE…no volume control…no cable. It shows is the pickup's self resonant frequency. We can't use this because we need a cable. It's not a practical usable peak unless active electronics are used with a very high input impedance. I did try this once in a guitar and it sounded reeee……eeealy 'bright'. This first assignment Mk2 is a 'straight' guitar….like I said earlier it has to be fed into a cable and since it's always going to be there and crucial to this demo…there it is at 800pF. I've left the amp off. The volume sweep is up to 99%, again for reasons mentioned earlier. Note at max volume a peak due to the inductance and the cable capacitance. As the volume is turned down the peak is killed. It's this peak which is exploited in the last circuit. Also note the pickup's own self resonant frequency around 7kHz which gets well and truly clobbered by the cable. This is a realistic sim of a 'straight' guitar. So any increase on these levels at the various volume settings is a boost.>Next assignment - model as you have above, but with a volume control.... any value will do. Now >what do you see? If there's a peak above the dB level noted earlier, can you display it for all to see? >And if so, then where does the rest of the response curve lay on the graph? Don't forget, loading a >generating device changes its output characteristics, but that doesn't give you permission to change >the reference points - leave the zero dB point right where it was, please.All I've added here is the 'treble bleed' capacitor. This links the cable capacitance to the inductance and gives a peak at all volume settings. Also it's at a much more pleasant and useful 4.5 kHz. So, take (for example) the middle sweep. In the 'straight guitar' at 4kHz it is at -9dB. In the last circuit at 4kHz the same middle sweep is at +3dB or 12dB higher which is actually four times the voltage level. A treble boost in my book.Hope that's all my 'homework' done for the weekend, sumgai ;D ALL 0dB levels on graphs are the same level. ALL volume control sweeps are up to 99%. ALL levels are voltage levels. NO power, as such, is taken from the pickup. NO laws of physics have been broken. NO animals or humans have been harmed in these simulations Channelman
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Post by UnklMickey on Sept 25, 2006 18:05:11 GMT -5
....Hope that's all my 'homework' done for the weekend, sumgai ;D ... me too, cause i just laid out the framework for your Masters Thesis. unk
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Post by sumgai on Sept 26, 2006 13:33:18 GMT -5
I wonder why I'm missing the boat on this one. Seems to me that I've taken on the air of a professor who doesn't like being contradicted, and wants to tell the student to either sit down and shut up, or get out. I never did that in the classroom, and I don't intend to start doing it here and now. I will devote as much time as necessary to see this thing through, it's that important to me that no one goes away from here with faulty knowledge. But I am going to tell you all that this is a hard nut for me to crack, a lot of "inertial stubbornness" has built up. Huh. I'm always up for a challenge, I was born ready. ;D Here's the real meal deal, as I have experienced it since 1958 (you'll have to guess how old I was at the time, but certainly old enough to start in on learning to become a HAM operator, accomplished in 1959.) When a steady-state generator emits a signal, said signal is complex in terms of impedance, frequency, current and voltage. As capably noted before, such a generator will have a particular point in the overall frequency spectrum where it would like to work... it finds that point to be the easiest for it to produce a signal. You could say that the generator is loafing at that particular point, which is called, of course, resonance. Fine. But the rub is, how do we reference that peak, and particularly, how do we reference the overall output spectrum. In terms of raw power, taking the whole complex situation into account, we most often use mW (or µW), but that is cumbersome for nearly any comparison to other components in a circuit. We generally use V (or mV) to denominate the output of a generator, although there are many cases where current is the desired measurement medium. (IOW, a current source might be more desirable than a voltage source.) Back to the point..... John has, so far, been the only one to provide a graph referenced in terms of a known quantity, the Volt. I have great problems with the scale of his graphs, but at least they are in concrete units. Not so with Channelman's output. These are done in dB, and I prefer that for my purposes - I am intending to make comparisons, not measure raw output. But Channelman has perverted that capability by using dB as if it were a concrete unit of measure. Sorry, it's not. dB's are meant for relativity only, not for absoluteness. So what, you say, what's my point, you ask. My point is, you can set the zero point of dB wherever you wish, it is not set in stone. Returning to the generator..... The output of any device that transduces energy (It didn't come out of thin air, bunky!) can be measured, and then shown or displayed in a graph. By our design, we have chosen to have the graph represent volts for us, usually on the vertical axis. At this point, we have concrete evidence of what's happening, and the evidence is repeatable under nearly any circumstances, given most if not all other parameters. And now to watch the rubber hit the road. ;D Since we can elect to place the starting value for our comparisons anywhere on the chart, we are constrained by good manners to use what the vast majority of us agree is a valid starting point.... that means, the zero dB point is placed where we ( the world, not we, the GuitarNutz) agree to place it. And if you haven't guessed where that point is by now, according to the IEEE and other bodies of engineers, then I really am pissing in the wind here. It's not the average output, spitfire, it's the max that has been chosen to be the defining point for zero dB. A steady-state geneator (why do I keep using that term?) wants to do the least work necessary, it wants to work at resonance. We can certainly force it to do otherwise, but at resonance, it is putting out its maximum output. Any argument to the contrary is null and void, and presents the arguer in a highly unfavorable light. At all other points on the spectrum of its output, the strength of the signal, measured in volts or otherwise, is less than that of resonance. Are we clear on this so far? Good. So, I'm here to tell you, that if you place zero dB at some point other than the maximum output, you're welcome to do so. After all, it's only for reference purposes, right? Even I agree on that one. But if you do place it below the maximum, and then you state "Look, I got better than zero dB output at this peak", then I'm gonna call Bojer on you. While you're playing games with numbers, you've forgotten that you can't back them up with repeatability by others who have no vested interest in making you look good. Final note: tell your SPICE program to put the zero dB point at the maximum output, and go from there. If it refuses to let you do that, then you're using the wrong program. And that's my final answer. sumgai
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Channelman
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Post by Channelman on Sept 26, 2006 15:28:45 GMT -5
>>> And that's my final answer.......sumgaiI'll bet it isn't In ALL my graphs the 0dB level is the level of the source at all frequencies. Anything higher than that is at a level higher than the source. I have not "perverted that capability by using dB as if it were a concrete unit of measure".Here's the same simulation with an input source voltage of 1 volt and the output as a log scale in volts. This is what simulators do...the input voltage is the reference whether it's 1volt or 0db with the output being displayed relative to the input. i.e. If the input is 1 volt and the output 4 volts then it will display on the graph as +12dB. P.S. I passed the Radio HAM Exam the year before you and became a C.Eng M.I.E.E. in the 1970's...so you can guess my age as well. Regards, Channelman
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Post by sumgai on Sept 26, 2006 19:50:31 GMT -5
You want a changed answer - you got it, Red Rider!
Well, seeing as you're now the grand old man of these here forums, and you have all the wisdom attending such honors, I hereby bequeath to you my marbles, I won't be needing them any more.
No strongly worded message will follow. ;D
sumgai
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Channelman
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Post by Channelman on Sept 27, 2006 4:05:59 GMT -5
>>I hereby bequeath to you my marbles, I won't be needing them any more.....sumgai
C'mon, lighten up sumgai. If there isn't room on this forum for another 'Old Timer' with some knowledge of electronics then just say so....and I'll p*ss off. Channelman
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Post by ChrisK on Sept 29, 2006 12:05:58 GMT -5
Aside from some specific physical units, all else is relative (including the words in a dictionary).
A simple operation can easily show the absoluteness of our relative discussion here. Presuming that pSpice is the tool, voltage probe and include in the graph the generator as a reference trace.
The simulation assumes that the pickup and string is a simple AC generator. It is not. However, for a relative simulation of the relative effects of the tone control, this will suffice.
With said graphing of the generator output (irrespective of the inherent basis for such baseline), we would see the relatively relative effect of the tone control components. And yes, 100% output is most meaningful, for therein lies the maximum relative peaking effect.
PLEASE ensure that the generator model has NO internal resistance or capacitance, and include these most important terms as external components. Internal resistance must be modeled as series (a parallel model can be used, but it must be converted from the series model, and hence its use is moot) and internal capacitance must be modeled as parallel (a series model can be used, but it must be converted from the parallel model, and hence its use is also moot).
A lumped line analysis of the generator winding leads to this series/parallel model.
Such model basis will allow the graphical probing of the base generator without the effect of its internal series resistance and parallel capacitance (which, in conjunction with the external load components, will affect the baseline output) as well as with same.
This addresses the simple semantics issue.
And, most unfortunately, ALL external loads such as the cable capacitance, amp input capacitance and resistance structures including the input capacitance and the reflected to grid effects of input impedance from the first preamp stage (or that solid-state equivalent stuff) must be included to see the more accurate relative effect of the tone control, since these will present the actual load "seen" by the generator in conjunction with its internal terms AND the tone control circuit.
When I modeled the effect of a 1,000 pF "peaking" capacitor, the inclusion of said effects substantially affected the response in magnitude, frequency, and phase. One would expect such when adding an additional 1,000 pF of capacitance and 100K or less of parallel load resistance (and what's all this feldergarb aboot 250K vs 500K volume/tone pots when facing such loading, ). To truly emulate the "vintage tone" of our hero's, we all must employ the 25 foot coil cord.
Only when a proper "brick wall" is used in the form of an isolating amplifier stage (with ALL input side model terms (direct and reflected) present), can actual isolation from the "bi-directional" effects within a discrete AC circuit occur, allowing the discarding of down-stream (over the wall) effects.
All of this "stuff", is a common discrete component circuit and AC circuit analysis rules rule.
Period.
While we may see relative effects without such completeness, the actual effect may/will vary by quite a lot.
Now, it appears to me that "we'all" are arguing about the same thing from different relative perspectives. In a sense, from our individual perspectives, we're all more correct than incorrect.
Individual perspectives breed diversity, and diversity breeds individuality. A wider gene/perspective pool serves us'all well.
Those of us long of tooth/opinion must appear to be pretty pi$$y to the newbies.
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Post by Runewalker on Sept 30, 2006 10:02:44 GMT -5
Whewwww and D@mn.
"Can't we all just get along?'
- Rodney King.
I thought entrophy was the natural resolution of the universe, not implosion.
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