# Maximum frequency of electrical pulses through wire?

1. Mar 27, 2004

### 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?

2. Mar 27, 2004

### Janitor

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.)

3. Mar 27, 2004

### Janus

Staff Emeritus
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.

Last edited: Mar 27, 2004
4. Mar 27, 2004

### Averagesupernova

3 Ghz is not that fast in the general scheme of things. Transmission lines can carry signals much higher than that. Alot 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.

5. Mar 27, 2004

### 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.

6. Mar 27, 2004

### Averagesupernova

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

7. Mar 30, 2004

### 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.

8. Mar 31, 2004

### Ivan Seeking

Staff Emeritus
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?

9. Mar 31, 2004

### Staff: Mentor

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

10. Mar 31, 2004

### NateTG

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.

11. Mar 31, 2004

### Averagesupernova

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.

12. Mar 31, 2004

### 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

13. Mar 31, 2004

### chroot

Staff Emeritus
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

14. Mar 31, 2004

### chroot

Staff Emeritus
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

15. Apr 3, 2004

### 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???

16. Apr 3, 2004

### Averagesupernova

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.

17. Apr 3, 2004

### 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......

18. Apr 5, 2004

### wimms

It isn't rectangular shape of the signal that makes it digital, but 2 thresholds that are detected as binary high vs low. Infact 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.

19. Apr 8, 2004

### 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

20. Apr 9, 2004

### 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 thats 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.