This is what all of us: 70+, other seniors, and kids (south of 60) have to look forward to!! This is something that happened at an assisted living center.
The people who lived there have small apartments but they all eat at a central cafeteria. One morning one of the residents didn't show up for breakfast so my wife went upstairs and knocked on his door to see if everything was OK. She could hear him through the door and he said that he was running late and would be down shortly so she went back to the dining area.
An hour later he still hadn't arrived so she went back up towards his room and she found him on the stairs. He was coming down the stairs but was having a hell of time. He had a death grip on the hand rail and seemed to have trouble getting his legs to work right. She told him she was going to call an ambulance but he told her no, he wasn't in any pain and just wanted to have his breakfast. So she helped him the rest of the way down the stairs and he had his breakfast.
When he tried to return to his room he was completely unable to get up even the first step so they called an ambulance for him. A couple hours later she called the hospital to see how he was doing. The receptionist there said he was fine, he just had both of his legs in one leg of his boxer shorts.
Please Take Home A Small Stranger By Anthony C.Wonfor
Jimmy was small for his age and really quite skinny. Apart from a few days at his Grandmother's house in the country he had had no real peace in his life. As a severe chronic asthmatic, he had spent hours struggling for his life's breathe and it had left its mark. He was still of school age but his bad health and the bombing hadn't improved things for him. It would be only four years before he would be thrust out to work so that he could make a small contribution to an ailing home economy. It was decided that if he was to grow old at all he would have to leave home with the next batch of evacuee children to be taken far away from the harassment of war.
They were to meet at North Street Junior school where buses would take all these hundreds of children of all ages, shapes and sizes to an unknown destination. At least it was unknown to all the mums and some dads who had come to say goodbye to the bewildered objects of this mass exodus.
Each Child carried their own case filled with the clothes which matched the list supplied by the authorities. One pair of boots for boys, one over coat, three pairs of socks two shirts, three pairs of underpants and so on. Tied to each small lapel was a label giving its bearer's name, an age and its school. Some of the schools teachers had agreed to go with the children and each small party was assigned to its teacher leader. Jimmy's teacher was Miss Milne, a quiet spoken young woman who was well liked by all the kids. She understood that young Jimmy wasn't the healthiest of lads and somehow managed to be somewhere close by most of the time.
The children were told to leave their cases a pile so that they could be loaded with their owners on the buses which were to take them to the station. Goodbyes were said and tears were shed. Neither children nor their parents knew whether or not they would ever meet again, for this was the time of the V2 Rockets when at night whole families disappeared in the piles of rubble which were once their homes. Some of the pain of leaving home and loved ones was offset by the excitement of going away on a train, something rarely done in this time of war.
The convoy of red buses soon arrived at the local railway station. The train was waiting. But first each child had to locate and retrieve its case and take it with them on to the train. For Jimmy this was a formidable task, but with his lungs bursting he somehow struggled enough to deposit his case on to the luggage rack. The compartment was soon filled with then children all wedged five aside like cheap cigarettes squashed into a tiny packet on to two seats each designed to carry three adults in luxury.
Many of the children still desperately clung to their gas masks, slung around their necks on a piece of string, each in its little cardboard box. The others most treasured possession was a bag containing their two sandwiches and an apple which was to last them for the journey. During most of the six hour journey the children slept, ate their food or drank the watery orange drink provided by two visits from a controlling teacher.
As the train pulled into Snowhill station nobody had any idea where they were. The unwashed, tined and bedraggled groups were ushered on to double decker buses and dispensed across the City of Birmingham. Jimmy with his group of a bout fifty children found themselves in College Road School in Sparkhill, although they at that time still didn't know where they were. Rows of mattresses had been laid on the floor of the school assembly hall and that's where they were to sleep. Each covered by a single rough blanket. The floor felt hard through the slim mattress and the night was cold but at least this was a night where Adolf Hitler's cronies didn't break up your nights sleep and send you scurrying to the air raid shelters at the bottom of the garden.
Throughout the following day, Sunday, Strange men and women came and selected the child they wanted to foster for 10 shillings and 6 pence a week. Then with their forlorn acquisitions just walked away and they were never seen again. Jimmy was very homesick and continually crying; nobody took any notice. By early evening he and a few other children were still at school when a very motherly lady spotted him and after trying hard to reconcile him, she collected his small case and took home to meet her family.
Mum Lilley as she was later known, understood his plight. From that day on until the end of the war Jimmy was loved, nursed through illness and am accident, taken on holiday and treated as one of her family. Two weeks after VE day she took Jimmy back to his own family and they said their goodbyes. Jimmy never forgot that he was the luckiest of all the evacuees and carries the memories of those war time days into his old age,
Alas the lovely lady, "Our Mum", is no longer with us but is remembered for he love, compassion and understanding for a small lonely boy far away from home.
Fundamental Understanding of the Transmission line
Metallic bond and its effect on signal propagation
The propagation of signal through an element is directly affect by the atomic makeup of that element. Atoms are made up of the nucleolus and a cloud of electrons. The cloud of electrons are usually represented by energy levels, where the electrons with the highest energies hang out in the outer layer while the weaker ones are closer to the core. Valance electron is the electron that hangs in the outer most rim of the electron cloud. In order to conduct current, which is the transfer of energy from one electron to another, or you can call it drift current, the valance electron must be able to move around. Metallic bound, unlike covalent or ionic bound, do not restrict the movement of their valance electrons. Although semiconductors are the exception with covalent bound (that's another topic all together). So why is one metal a better conductor than the other? The simple answer is the more levels of energy a given metal has, the better it conducts electricity. The easier and less restrictive the movement of the electron the better it conduct electricity. One of the most important reasons is that when valance electrons are further from the core, there is less positive force pulling on it and since the valance electrons are usually the stronger ones that jumped from the level below, it has enough energy to 'swim' around the cloud. When an electric field is applied to the element, the energy is transferred from one electron to another and from one atom to another down the chain. Ag is a larger atom than Cu, but both have 2 valance, so they are pretty good conductors, with Ag being the better of the 2. Al, on the other hand, is pretty bad. It has 3 valance electrons and the atom is small. So the electric energy is freely passed in Ag and Cu, but is no so in Al.
In theory, the speed of propagation is c (speed of light, 3x10^8m/s), but there is loss in energy when one electron hand over the energy to another electron and to another electron. Thus, the propagation delay is material dependent. Cu has a theoretical propagation of 66.667%c or (2x10^8m/s). This, of course, does not count any boundary electron jump between bonding materials (solder).
So what is phase delay? Phase delay is a shift of the waveform in the time domain.
Voltage drop across transmission line To calculate voltage drop across a transmission line, the propagation delay and the frequency which the signal is traveling at is important.
V1 = V0 cos(w(t-l/c)) where w= 2pif. And c is the speed which the energy travels. and l is the length of the cable
The determining factor in voltage drop is wl/c. By comparing theoretical c to the c of the copper, the power loss is measurable. One also need to taken into account the dispersive effects of the material, which for cu, I am not sure what that is. Dispersive effects are generally thought as different frequency propagate at different speed, so not only do you have phase delay of the superposed waveform, there is a phase delay in different frequency components as well! The effect of short dispersive line is that higher order frequencies are effectively cut off. For example, if you pass a square wave through a short dispersive line, what you see on the scope is a square wave with the rise/fall edge fairly rounded, which indicated some higher order harmonics missing in its structure. Although common intuition tells us that we can't hear the difference, but audiophiles/musicians, unlike 'normal' people have tuned their ear to hear much more information and some are more sensitive than other to this effect.
How to properly calculate RLGC in Coaxial Cable
The Coaxial Cables are constructed with two coaxial conductors separated by dielectrics (of course conventional construction includes an outer layer of shielding).
R = (Rs/(2pi))(1/a+1/b) where a=2r(inner) and b=2r(outer), and Rs= sqrt(pi(f)(uc)(qc)) where uc = magnetic permeability and qc = electric conductivity (sorry no roman letters
As you can see, the resistance is a function of frequency and R is independent of V1 where V1 is the voltage drop due to propagation and again R is not dependent on phase delay and dispersion effects. Also notice the math does not involve any effect of the imperfect dielectric and electron deposition.
L = u/(2pi) x ln(b/a) Again no baring on phase delay
G = (2pi*q)/(ln(b/a))
C = (2pi(e))/ln(b/a)
Notice none of the RLGC is responsible for power loss, phase delay and dispersion effects and R is a function of frequency.
Now if you look the transmission line equation
-dV/dz = (R+jwl)I(z) and -dI(z)/dz = (G+jwC)V(z)
Now if differentiate both sides, you will arrive with (y) or complex propagation constant, which is y=alpha + jbeta
So basically, after doing all the math, the traditional RLC measurements are not only inaccurate, its down right faulty as RLC is a function of frequency at which the wave travels, and is dependent on the electrical permittivity, magnetic permittivity, and electrical conductivity of the individual material. This however does not even consider the power loss or dispersive effects.
I hope the above analysis answers some questions regarding why a manufacturer may want to optimize multiple areas of the cable to give it a lower propagation delay, optimize RLGC with different material and also optimize RLGC with the use of novel geometries. Of course you can ignore this entire discussion and just use your ear.
Dielectric in Coaxial Cable.
In my previous discussion the element of dielectric was assumed to be theoretical but in real life that's not the case. To understand why dielectric behave differently from a conductor one has to look again at the elemental bonding, energy level, and the available valence electrons.
In dielectric material, the outermost shell is bond tightly to the atom. In the absence of electric field, the distribution of the outermost shell is uniform, which means the center of the cloud is where the nucleus is at. This is because the electric generated by the positively charged nucleus cancels out the electric field generated by the electrons.
However, when E(ext) is applied, although the energy normally would not be strong enough to detach any electron from the atom, the E(ext) can nevertheless polarize the atoms or molecules in the material by distorting the center of the cloud and the location of the nucleus, thereby creating a induced electric field or polarization field. One can express this relationship with D=e0E+P where D is the electric flux density (This should look familiar as a modification to one of Maxwell's equations). This equation is further complexed by whether the dielectric medium is either linear or isotropic. Thus P=e0XeE where Xe is the electric susceptibility. Combining the two equations yields D=e0E + e0xeE= eE or e=e0(1+Xe). You can substitute the new e in the C calculation of the lumped element model of the RLGC calculation.
I think with that I have covered the fundamentals of cables.
THIS IS NOT A GENERAL DISCUSSION OR A DISCUSSION ON MERE OPINIONS. PLEASE REFRAIN FROM POSTING IF YOUR REPLY DOES NOT DEAL DIRECTLY WITH ONE OF THE FOLLOWINGS: Frequency Domain Measurement Techniques, Time Domain Measurement Techniques, Modeling Techniques Simulation Techniques for Interconnect, Structures, Electromagnetic Field Theory, Analysis and Modeling of Power Distribution Networks, Propagation Characteristics on Transmission Lines, Coupling Effects on Interconnects, Guided Waves on Interconnects, Radiation & Interference, Electromagnetic Compatibility, Power/Ground-Noise, Testing & Interconnects, Optical Interconnects