Maximum frequency of electrical pulses through wire?

[Matt Jacques]

We have Pentiums ranging in the mid three gigahertz range, they're not too efficient, but how do the electronics generate the clock pulses at such a high frequency? What I am asking is, what is the maximum frequency of pulses through an electrical wire? And How would someone say, produce a frequency of, say, a terahertz, or a petahertz in a wire?

 

[Janitor]

"Self inductance" is what you are asking about.

Even a straight wire has inductance, and it causes problems for circuit designers at high enough frequencies. I have seen various approximations to the high-frequency limit of self inductance. One such is:

L=0.002 l [ln(2 l/r) - 3/4]

for the inductance L in microHenries, where l is the length of the wire in cm and r is the radius of the wire in cm. (Careful: don't read "l" as "one" in the formula.)

 

[Janus]

Just to expand a little on what Janitor said.

Self inductance is generally caused by the magnetic field generated by the wire. In AC this field is always building, collapsing, reversing polarity, building etc. as the current switches back and forth in direction. The changing field reacts with the electrons in the wire opposing the current flow. This opposition is called inductive reactance, and acts somewhat like resistance(it is even measured in ohms). Inductive reactance directly increases with frequency and the inductance of the conductor by the formula:

$$X_{L}= 6.28fL$$

Thus double the frequency for any given conductor and you cut the currrent flow in half.

There is also capacitive reactance which decreases with frequency. this can also cause problems at high frequencies by bleeding current off. (the air gap between an conductor and ground can actually behave like a capacitor, shorting the current ot ground.

 

[Averagesupernova]

3 Ghz is not that fast in the general scheme of things. Transmission lines can carry signals much higher than that. a lot of the time though, microwave signals are carried long distances on something called waveguide which is the alternate to transmission lines. Think about this also: X-rays, gamma rays, visible light, all are part of the electromagnetic spectrum. They may not be carried on wires in the conventional manner, but they are still used and exploited by humans.

 

[Matt Jacques]

Yes, I know they are all part of the electromagnetic spretrum, but it is paramount I know whether wires can handle such frequency.

 

[Averagesupernova]

Individual 'wires' don't really handle the frequencies when they get that high. A transmission line would instead.

 

[wimms]

Interesting, we can put question not about parasitics or transmission lines, but about borderline between medium being conductive vs transparent/opaque.
I can't imagine radio waves of visible light frequency to be still conducted by _copper_, waveguides or not. So some sort of limit of frequency seems to be there. Though its very high and obviously together with attacking higher frequencies, new materials will be used.
Problem with very high frequencies is that space around wires becomes better conductor than wires themselves. Copper starts working better as insulator rather than conductor (waveguides?).

As to generating any frequency, all you need is positive feedback with specific phase shift, so that delayed signal adds up with itself, causing resonant oscillation. Parasitics definitely limits the frequency, as does speed of semiconductors.

Without any real qualification to state so, having only some electronics background, I'd guess that Terahertz maybe, petahertz no way for traditional copper based chip technologies. And there's no need either, all-optical computing is coming anyway.

 

[Ivan Seeking]

As an absolute upper limit, understanding of course that other factors mentioned might make this limit impossible, I would think that we might approximate something by looking at the atomic spacing in copper wire. I don't know how to calculate the proper wave function and such for a valence electron in copper [I think did once for about a week], but the average signal velocity is about 1/2 C. Doesn't this loosely imply a maximum frequency of transmission on the order of C/a; where a is the average distance between copper atoms?

 

[russ_watters]

Averagesupernova, you may be confusing electricity (electrons moving in wires) with electromagnetic radiation (microwaves, light, etc.). Different issues.

 

[NateTG]

We have Pentiums ranging in the mid three gigahertz range, they're not too efficient, but how do the electronics generate the clock pulses at such a high frequency? What I am asking is, what is the maximum frequency of pulses through an electrical wire? And How would someone say, produce a frequency of, say, a terahertz, or a petahertz in a wire?

I'm not an EE or EECS type, so I can't give you really good answers, but I know the following:

All wires act as inductors or capacitors depending on the length. As a result, certain lengths of wire will not conduct at particular frequencies. Although there are problems with short pulse propagation, the limiting factor on CPU's is typically transistor switching time, and not the maximum frequency that the wire can cary.

Typically computers work on detecting transitions. One of the things that happens is that as it propagates down a wire a sharp transition becomes less sharp, and at modern CPU speeds they can probably no longer be modeled with a simple step.

For typical applications, the preferred method for generating signals at a particular frequency is a piezoelectric crystal. In practice it's relatively easy to build circuits that will generate rapidly occilating signals, but those circuits are usually extremely sensitive. For example, hooking the output of a not gate into the the input of the not gate is liable to generate a high frequency signal - but the particular frequency depends on temperature, supply voltage, and probably ambient capacitence.

 

[Averagesupernova]

Averagesupernova, you may be confusing electricity (electrons moving in wires) with electromagnetic radiation (microwaves, light, etc.). Different issues.

No, I am well aware of the differences. I am simply gave an example of how power is transmitted within a confined area without the use of conventional wires.

 

[Njorl]

I've seen coaxial cables and striplines handle over 90 GHz. Things are very sensitive at these frequencies though. Touch a cable even lightly and you can change the signal passing through it.

I've found that up to 20 GHz, things are not too bad. I doubt PC's will get that fast though. I think parallellism will be the way to increase computer power. Once increasing parallellism is more cost effective than increasing clockspeed, electro-optic components will start replacing electronics. Optics are great for parallel processing.

Njorl

 

[chroot]

You're essentially talking about the point where you have to stop thinking about electrical signals as electrons moving through wires and begin thinking about them as electromagnetic fields propagating through space.

The speed at which a signal can propagate through a wire actually has little to do with the wire itself -- it is mostly determined by the permittivity and permeability of the dielectric material surrounding the wire, since it impedes the creation of the magnetic field that needs to surround the wire as current flows. As you reach higher and higher frequencies, the wire's surroundings become much more important than the wire itself. Eventually you begin using waveguides, which are no longer wires but cavities -- the signal actually passes through vacuum (or air) in the form of electromagnetic waves.

- Warren

 

[chroot]

NateTG:

Crystals are actually limited to about 200MHz for mechanical reasons. They become extremely small and hard to manufacture to good tolerance. Also, if you drop a 200MHz XO only a few inches, you'll shatter it. Some companies have had good success using a low-frequency crystal and filtering it to get only its high-order harmonics, though.

Generally, for high frequencies, a phase-locked loop is used.

- Warren

 

[flexifirm]

Remember one thing

Whoever said that transmission lines can handle higher frequencies than 3Ghz so it wasn't a big deal... remember one thing...


3Ghz is the frequency of the pulse wavetrain produced within the Penitum 4... these are not sine waves... but have considerable higher order harmonics that produce a quasi-rectangular waveform...

The critical constituent frequencies might extent well past the 30Ghz point (comparable to EHF radio band).

Now isn't the PENTIUM AMAZING?

 

[Averagesupernova]

Whoever said that transmission lines can handle higher frequencies than 3Ghz so it wasn't a big deal... remember one thing...


3Ghz is the frequency of the pulse wavetrain produced within the Penitum 4... these are not sine waves... but have considerable higher order harmonics that produce a quasi-rectangular waveform...

The critical constituent frequencies might extent well past the 30Ghz point (comparable to EHF radio band).

Now isn't the PENTIUM AMAZING?

Transmission lines typically get lossier as the frequency increases. So your point about square waves doesn't completely hold water. You will eventually see the square edges of a waveform rounded of as the length of coax forms a low pass filter.

 

[flexifirm]

Yes but..

Yes, there can never be a true square wave (digital) signal in any type of medium.. because that would require an infinite bandwidth...

The digital pulses in high speed circuits have rounded edges, but they still have a "rectangularish" shape... like a rectangular waveform with softened edges... so a 3Ghz clock in modern computer systems should have sine/cosine components higher than 3Ghz. I don't think the digital clock in computers is a pure sine wave...

 

[wimms]

It isn't rectangular shape of the signal that makes it digital, but 2 thresholds that are detected as binary high vs low. In fact shape of signals in cpus has long ago stopped being even remotely like square wave. Its only convenient to think of them that way.
If you think of 3GHz clock, then its probably closest to pure sine wave you could find inside cpu...

In terms of required frequency response inside cpu, you'd need to think in terms of signal bandwidth imposed onto carrier. To have 3GHz digital signal changing fast enough to transmit 3GHz random data, you'd need twice as much bandwidth, not much more. These signals are far from rectangular, but it doesn't stop cpus from considering them digital and making sense of them.

 

[flexifirm]

hmmm

Yeap... that's what i was saying in my message

I don't think high speed clocks are closer to sine waves than rectangular... i would suspect there are a couple harmonics at the very least.. i work on systems with 160 Mhz clocks.. and there are harmonics

 

[wimms]

160MHz is looong way to go to 3GHz, and this isn't irrelevant. 3GHz is limit we are trying to push, and constraint is power and consistency. Any higher harmonics that's useless for actual processing is just wasted energy and only adds trouble with oscillations at RF. Its potentially causing false switching and is thus avoided as much as possible.
Think of phase modulated sine wave carrier. Sure there are harmonics, but not that many to imagine square wave shape. Thats what I've understood.

 

[jdavel]

Doesn't this loosely imply a maximum frequency of transmission on the order of C/a; where a is the average distance between copper atoms?

Perhaps. But since a is about an angstrom, and c is about 10^18A/s, it's a pretty safe bet that something else will limit PC speed before that pesky interatomic spacing does!

 

[thetieman]

i agree with most of what's already been mentioned. but, talking about a processor or any kind of device that uses multiple connections, this isn't just the possible bandwidth of one connection. we're talkin about multiple connections and the nature and bandwidth of each of those connections. if one wire has say a max bandwidth of one gh and we have just 4 wires then it would seem sensible to think that each wire can handle one gh of data transfer and together they should carry 4 gh. concerning light based electronics, they have their own limitations in use. to make an almost completely light based computer. one would pretty much have to make all the components integrated to see a significant difference. it would be like a redesign of the cpu all over again. we could call it the COC... lol. the Computer On a Chip. which in that case, it would be more sensible to use an electro/light hybrid technology. light based concepts and electronic based concepts both have their strengths and limitations. i also think there's a huge limitation in bandwidth depending on the nature of how the signals are transferred. one can have sync, ground, and two info lines and achieve one overall bandwidth while someone else can achieve nearly twice that by using all 4 lines to transfer info. while 2 wires can only transfer one possible band of info in either direction, 3 can transfer 3. this depends on combinations and permutations. another thing to think about, binary isn't not analog. if it was possible to have a pure on/off or up/down signal then whatever is carrying that signal would have infinite bandwidth like mentioned earlier. this means that all binary signals are essentially analog signals that are only being read at certain points in time as either being above one voltage or below another. i love thinkin about this stuff


----------------
Now playing: Rob Zombie - Living Dead Girl
via FoxyTunes

 

[sophiecentaur]

If you can see a digital signal that looks like square waves then the system could almost certainly be handling a much higher data rate. 'Real' digital signals in comms sytems, handling optimal data rates are 'rounded' (low pass filtered) and there is significant inter symbol interference. They are sampled at a suitable point where the ISI is minimal (the 'eye'), the wave shapes being tailored by the filtering. Internal signals on a complicated processor board can't all be so optimally shaped but, for many GHz working, the impedances of amplifiers, receivers and connecting lines will be really critical - not to mention the lengths / delays, which need to be tightly matched. About 4ns delay per metre of transmission line delay means that you require line accuracies of only a couple of cm even at 3GHz to get the timing right. That implies some ingenuity to lay out a 32bit wide bus so that all the bits arrive at the same time after going round corners.
I'm gobsmacked by what you can find in a box in your living room these days! And I'm not talking chocolates.

 

[thetieman]

lol. i agree with your "living room boxes" comment. i love finding strange little things and what not. though I'm not familiar with most of your terms, i did get that you were talkin about timing. demolition experts use long coils of wire to delay when certain explosives are set off when blowing up a building or what ever.

 

[sophiecentaur]

For a significant delay, by explosives standards, the coil would be there as an inductive element rather than a simple 'transmission line delay', I think. A delay of 1ms ( the sort of time that I would imagine would be significant in an explosion chain) you would need about 200km of line. A delay of a few ms is much easier to achieve with the inductance of a single coil of wire.

Look at this link
http://en.wikipedia.org/wiki/Eye_pattern"
to see what I meant about 'real' digital signals and the problems of symbols interfering with each other. No 'boxcar 'waveforms with square edges here.
Think of reducing the spacing between typed characters (to get more on the page); if you cram them up very close or even overlap them, you can read some sense but you can go too far and the text is unreadable.

 

[thetieman]

interesting. I've thought about this but i just didn't know what it was called. it's like organizing multiple signals to run on a single line. i can see the obvious timing and interference complications involved too.

 

[sophiecentaur]

Digital comms is all about maximising the data rate down a given channel. Having seen the eye patterns, you will appreciate that the noise and external interference levels will further affect the size of the eye. When the eye is closed for a significant proportion of time, the channel is not usable. Reducing the data rate will open the eye again - it's a matter of compromise between Power, noise and data rate.
If you try to watch Sky TV in heavy rain, you will notice it drops out (freezes) significantly more than with clear sky, with some installations. That's just on the margin of the eye being open enough or not.

 

[Starkid]

If copper wires on computer boards can support 3Ghz freq(clock) then why do we need waveguides in microwave antennas? can't we use copper as conductor for microwave signal??...is vice-versa true??

 

[sophiecentaur]

There isn't anything fundamental about this - it down to engineering practicalities.
You can't use just any old wires to carry 3GHz around computer boards. The signals are carried on accurately printed 'microstrip' transmission line. It can be either a single line over an Earth plane (the back of the board) or a pair of lines on either side of a board. This is a 'fairly recent' invention, made possible by good printing methods and the availability of very low loss substrate (board) material. The 'brown stuff' just doesn't work! The signals don't travel very far on such transmission lines whereas a waveguide can carry signals for hundreds of metres. Coax cable used to be limited to a few hundred MHz of operation but now, with similar high quality dielectric, can also be used over significant distances for signals of tens of GHz.
Waveguide is a real pain to use and, where you can get away without it, coax or stripline is preferred. I remember a design of flat plate receiving antenna, based on many small dipoles, printed on a board, with a branched system of microstrip feeds to each of the elements. It worked fine for a small area of board but you couldn't make a really large antenna array because the signal never got to the dipoles due to loss in the long microstrip feeds.

 

[Airbag79]

If copper wires on computer boards can support 3Ghz freq(clock) then why do we need waveguides in microwave antennas? can't we use copper as conductor for microwave signal??...is vice-versa true??

The skin effect, signal integrity, bandwidth, impedance matching, transmission loss, and maximum power transfer to name a few.