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

Figure 1 A Simple PCB Transmission Line

Gate G1 connects a high speed digital signal to the input of the transmission line.

The signal travels along the transmission line and after some time arrives at the input of gate G2.

The resistance RL is the load (terminating) resistance of the transmission line.

Z0 is the characteristic impedance of the transmission line.

We shall examine how the signal travels along the transmission line in some detail.

Figure 2 The Signal Rise Time

Figure 2 The Signal Rise Time

We shall assume the signal has an amplitude of V volts and a rise time of tr seconds.

The signal travels down the transmission line as an electromagnetic wave.

We shall call A, B the wave front.

We have assumed a linear rise time, in practice this will not be the case.

For a high speed digital signal the rise time will be small, less than a billionth of a second.

At time t= 0, the signal is applied to the transmission line, point A.

The signal starts to travel down the transmission line.

After time tr, point B, all the wave front is now inside the transmission line.

The wave front now travels down the line towards gate G2.

Figure 3 The Situation on the Line at an Instant of Time

Figure 3 The Siutaion on the Line at an Instant of Time

The point A on the wave front has travelled a distance XA.

The point B on the wave front has travelled a distance XB.

The voltage at XA = 0

The voltage at XB = V

The wave front is spread-out over the region XA-XB.

We shall call XA-XB is the spatial extent of the wave front.

ux is the velocity of the wave front as it travels along the line.

In front of XA, the signal has not yet arrived, there is no voltage in this region of the line.

Behind XB, the signal has a value of V.

Within the spatial extent there is a current flowing through the dielectric, from the top conductor of the line to the bottom conductor.

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

Figure 4 Inside the Wave Front Spacial Extent

The voltage at A=0, the voltage at B=V.

The spatial extent of the wave front is XSE= XA-XB

The voltage gradient in the wave front is V/XSE

The current gradient is I/XSE

The voltage at x, inside the wave front is xV/XSE

The current at x is xI/XSE

There is magnetic field within the spatial extent.

The impedance at any distance x within the spatial extent is-

(xV/XSE)/x(I/XSE)= V/I= Z0, which is constant.

The characteristic impedance does not depend on the length of the line.

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

Figure 5 A Fast Digital Signal

The frequency of the signal is 2GHz.

The periodic time of the signal is 1/2GHz= 0.5ns, that is half a billionth of a second.

If the signal travels down a PCB transmission line, with a velocity ux, its spatial extent is uxTp

 

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

Figure 6 Voltage and Current Spatial Distribution on a Transmission Line

The spatial extent of the signal is less than the length of the line.

The signal pulse travels down the line with velocity ux

Before point A the line voltage is zero and so is the line current.

The voltage across the load is zero.

Between A and A1 the voltage varies between 0 and 3V.

Between A1 and B1 the voltage is 3V

Between B1 and B the voltage varies between 0 and 3V.

Between B and C the voltage is zero and so is the current.

The current is zero on both sides of the spatial extent, the current in the load resistance =0.

Current flows in a loop as shown- the loop is completed by the displacement current flowing in the regions A1 to A and B to B1.

Current always flows in loops.