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Roy, W7EL wrote:
"I`m sure that somewhere in one of your texts you can find the definition of linear as applied to networks." Right. From "The Penguin Desk Encyclopedia of Science and Mathematics": "Linear (algebra) An equation or function of the form ax + by + c = 0 or f(x) = mx +b is called linear because its graph is a line. This has been generalized to a concept called linear combination, which is the sum of 2 or more entities with each multiplied by some number (with not all numbers being 0). Linear combinations of vectors, equations, and functions are commonly employed." I think that definition is broad enough to cover the representations I made in my postings. Best regards, Richard Harrison, KB5WZI |
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I can only hope that some of the readers understand.
Roy Lewallen, W7EL Richard Harrison wrote: Roy, W7EL wrote: "I`m sure that somewhere in one of your texts you can find the definition of linear as applied to networks." Right. From "The Penguin Desk Encyclopedia of Science and Mathematics": "Linear (algebra) An equation or function of the form ax + by + c = 0 or f(x) = mx +b is called linear because its graph is a line. This has been generalized to a concept called linear combination, which is the sum of 2 or more entities with each multiplied by some number (with not all numbers being 0). Linear combinations of vectors, equations, and functions are commonly employed." I think that definition is broad enough to cover the representations I made in my postings. Best regards, Richard Harrison, KB5WZI |
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Richard Harrison wrote: Roy, W7EL wrote: "I`m sure that somewhere in one of your texts you can find the definition of linear as applied to networks." Right. From "The Penguin Desk Encyclopedia of Science and Mathematics": "Linear (algebra) An equation or function of the form ax + by + c = 0 or f(x) = mx +b is called linear because its graph is a line. This has been generalized to a concept called linear combination, which is the sum of 2 or more entities with each multiplied by some number (with not all numbers being 0). Linear combinations of vectors, equations, and functions are commonly employed." I think that definition is broad enough to cover the representations I made in my postings. Best regards, Richard Harrison, KB5WZI You're right in a certain mathematical sense, but that definition isn't correct, as Roy pointed out, in defining superposition. 73, Tom Donaly, KA6RUH |
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OK, you guys can stop now... wx is improving and i found something more fun
to play with anyway.... try this site out: The links don't mail well, but if you go to this link... http://local.live.com/?v=2&sp=aN.42.....022505_k1ttt_ and then do this.... After the page above displays the road view, in the control pad at the top left click on 'bird's eye'... then wait for it to redraw. Then click on the 'W' on the compass rose to view toward the west which seems to be the closest view of my place. Then click on the big set of buildings in that control panel to zoom in. by this point you won't see the station at all, but in the 'scratch pad' control on the right side click on the 'k1ttt' link and it should swing it around and show you a view of my station looking toward the west. the photo is at least 3 to 4 years old now as you can see the 6 element 20m and 8 element 15m yagi's still up that have been replaced. David Robbins K1TTT web: http://www.k1ttt.net AR-Cluster node: 145.69MHz or telnet://dxc.k1ttt.net |
neat aerial photo site... was FIGHT! FIGHT! FIGHT!
OK, you guys can stop now... wx is improving and i found something more
fun to play with anyway.... try this site out: The links don't mail well, but if you go to this link... http://local.live.com/?v=2&sp=aN.42.....022505_k1ttt_ and then do this.... After the page above displays the road view, in the control pad at the top left click on 'bird's eye'... then wait for it to redraw. Then click on the 'W' on the compass rose to view toward the west which seems to be the closest view of my place. Then click on the big set of buildings in that control panel to zoom in. by this point you won't see the station at all, but in the 'scratch pad' control on the right side click on the 'k1ttt' link and it should swing it around and show you a view of my station looking toward the west. the photo is at least 3 to 4 years old now as you can see the 6 element 20m and 8 element 15m yagi's still up that have been replaced. David Robbins K1TTT web: http://www.k1ttt.net AR-Cluster node: 145.69MHz or telnet://dxc.k1ttt.net |
FIGHT! FIGHT! FIGHT!
Oh my goodness! The critical qualification and definition has been provided
by Roy. Roy and Richard then proceeded to nail the subject to the proverbial wall. It is time to pause in grading exams to remind that analytic geometry and circuit theory are not the same thing. In circuit theory (and practice) a circuit/network/or-whatever is linear if, and only if, superposition is satisfied. If superposition is satisfied, then the circuit in question is linear. This concept also has utility in some mechanical structures. In English, it is not uncommon for a word to have quite different meanings depending on where it is used. We all know this. Even when discussing active devices such as BJTs and FETs one finds the word "saturation" used differently depending on the device. Obviously, large enough signals applied to any network that appears to be linear with smaller signals will melt same - letting out the smoke that was placed therein at the factory. Obviously, there are degrees of linearity. A footnote is always understood to say: such-and-such network is acceptably linear for signals larger than A and smaller than B. ... thus ends the lesson. 73, Mac N8TT -- J. Mc Laughlin; Michigan U.S.A. Home: "Roy Lewallen" wrote in message ... I can only hope that some of the readers understand. Roy Lewallen, W7EL |
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On Tue, 23 May 2006 19:11:00 -0400, "J. Mc Laughlin"
wrote: Dear Richard: I have had occasion to note to students that some of what they call music would not be noticeably modified by being amplified by a amplifier having a great deal of distortion. Your point is right on target. Hi Mac, My point may have been on target, but the specifics left an escape for those quick enough to pick up on it. In fact, I would speculate that most audio (as do RF) amplifiers exhibit the gain characteristic of f(x) = y = mx + b and this is called class AB. When you build an amp employing two of them in a push-pull configuration the constants b negate each other and the 2mx remains. Of course, the push-pull configuration is built to nullify the distortion of this "linear" curve. The single power supply Op Amp also suffers from f(x) = y = mx + b with the output floating at half the supply voltage - this has got to be an application killer if it goes straight to the speakers without removing the b with a capacitor. 73's Richard Clark, KB7QHC |
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Tom, KA6RUH wrote:
"You`re right in a certain mathematical sense, but that definition isn`t correct as Roy pointed out in defining superposition." Or in conjugate matching for that matter. The discussion was: Is an antenna a linear device, meaning does it produce amplitude distortion? Amplitude distortion comes from a nonlinear relation between imput and output. It has nothing to do with has the amplitude grown larger or smaller in the antenna? I think the majority of antennas have an output which is a reasonable approximation in form to their input. That goes for frequencies too. The response won`t be the same for all frequencies, but you`re not likely to find new frequencies on the output of the antenna that aren`t on its input. Superposition says that when a number of voltages (distributed in any manner throughout a linear network) are applied to the network simultaneously, the current that flows is the sum of the component currents that would flow if the same currents had acted individually. As Cecil said, nonlinearity produces new frequencies. Good antennas don`t do that, superposition or not. Best regards, Richard Harrison, KB5WZI |
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