### The speed of computers is limited by the speed of light

Computers are working at higher and higher speeds, is there a limit to how fast they can go?

Computers, like all electronic products, use electromagnetic signals, which travel at the speed of light.

Light is an electromagnetic phenomena and it travels through space at a speed of 300 million metres per second.

The Earths circumference is about 40,000Km, that is 40 million metres.

A burst of light could travel around the Earth about 7.5 times in a second.

The speed of light limits how fast computers can go.

Light, which is an electromagnetic wave, slows down when it passes through material objects.

Light travels slower in water, glass and any physical material.

Computers use digital logic elements such as NAND gates, Flip flops and Complex Integrated Circuits mounted on printed circuit boards (PCBs).

The speed at which electrical signals travel on a printed circuit board is about half the speed of light, 150 million metres/second.

The time it takes a signal to travel 15cms on a PCB is about 1 billionth of a second, that is 1 nanosecond.

A computer using a clock speed of 1GHz (Gigahertz) ticks at a rate if 1 billion times a second- the time between ticks is 1 nanosecond.

This is the time it takes a signal to travel 15cms on a PCB.

It is getting more difficult to design and manufacture computers that go faster and faster- the speed of light is a limiting factor.

What follows is for NERDS and assumes some understanding of electronics.

Many electronic engineers are educated using circuit theory, which cannot be applied directly to high speed circuits.

Many of the ideas below do not used traditional, conventional, circuit theory. Figure 1 A Simple PCB Transmission Line

We shall examine how the signal travels along the transmission line in some detail. Figure 2 The Signal Rise Time Figure 3 The Situation on the Line at an Instant of Time

The current flowing through the dielectric is called a displacement current. It is a real current and it is due to the displacement of charge in the dielectric.

The current flowing in the transmission line conductors is called a conduction current and it is due to the flow of charge carriers, electrons, in the metal.

The value of the conduction current = the value of the displacement current.

#### Important- the displacement current controls the value of the conduction current.

We have assumed the metal conductors of the line are perfect, there is no volt drop along them.

The transmission line tracks do not affect the value of the current.

Behind the wave front-

the signal is a direct signal, the current in the conductors is constant and the voltage between them is constant.

there is a constant electrostatic field between the conductors

there is a constant magnetic field surrounding each conductor. Figure 4 Inside the Wave Front Spacial Extent

The time it takes for signals to travel, that is propagate, along PCB tracks must be taken into account for high speed systems.

When the spatial extent of the wave front is less than, or about the same as the PCB tracks, transmission line design techniques must be used.

Transmission lines must be terminated with a resistor that has a value equal to the characteristic impedance of the line to avoid signal reflections.

So RL=Z0 in figure 1, to avoid reflections.

Signal reflections degrade signals, they are a form of interference that may cause electronic gates and memory circuits to not work as intended.

Consider a digital signal of frequency 2Ghz, shown in figure 5. Figure 5 A Fast Digital Signal

If the velocity of propagation on then line is half the speed of light, ux=150 million metres/second.

The spatial extent is 150,000,000*0.5/1000,000,000=0.075m=7.5cms

If we image the signal is applied to a transmission line 12cms long, a single pulse will all be propagating down the line before any of it has reached the end.

We shall assume the Z0 for the line is 50ohms and the Signal Voltage V= 3V, so the current entering the line is 3/50=60mA. Figure 6 Voltage and Current Spatial Distribution on a Transmission Line