Monday, November 21, 2005

Tubes Rule!

Big, hot, heavy, expensive, fragile.

I'm not talking about Larry Ellison's ego; rather I 'm referring to vacuum electron tubes (or thermionic valves to our former colonial masters across the pond). To understand vacuum tubes, one has to go back to another egocentric US industrialist, Thomas Edison, who in 1883 observed that a current flowed between the filament of an incandescent lamp and a plate in the vacuum near it when the plate was connected to the positive end of the filament, but not when the plate was connected to the negative side. In 1899, J. J. Thomson showed that this Edison Effect was due to a stream of negatively-charged particles, electrons, that could be guided by electric and magnetic fields. Fleming patented the diode in 1904 and in 1907, Lee de Forest patented the triode (which he called the Audion; the term "triode" was not used until much later, after it threatened to become a trade name). For more than a half century, these devices (among other things) were the preferred choice for amplifying music.

Physically tubes are completely different from the modern choice for music amplification transistors. From an electron's eye view, a tube's vacuum still contains a lot of air molecules. At least 100, 000, 000, 000 air molecules per cubic inch have been left inside this "vacuum." Still that’s good enough for musicians, as the electron has few obstacles on its way from the cathode to the anode mainly other electrons repelling it in a space-charge of electrons that surrounds the cathode (the emitting electrode in the tube).

The speed of the electron depends on anode voltage (the anode is at the receiving end of the electron stream in a tube) . The electron travels with a speed between 5940 km./sec. at 100 Volts to closely 60 000 km./sec. at 10 000 Volts - the higher the voltage the higher the speed. The distances between anode and cathode in a tube are typically 1-1.5 centimeter in length. Electrons take around 0.000000000166 second to travel this distance. At higher voltages this speed reaches relativistic proportions of around 20% that of light. The mass of the electrons increase, and the distance to the plate decreases due to a relativistic effect called Lorentz contraction.

Compare this to transistors (and integrated circuits too, which are just really really small transistors and other circuit components prewired and ready to go). These look entirely different to an electron's eye. They are made from a different substance than the imperfect vacuum of a tube - silicon or metal-oxide to be exact. The electron travels differently too - more like a football player looking for empty spaces and bumping in the other team players (electrons or 'holes' in the solid state where no electrons exist). There are a lot more "solid state" obstacles on the way to the "anode - collector" than in a vacuum tube. Electrons can't progress more than a few kilometers/second (of course solid state devices are a lot smaller than tubes, even where they don't benefit from Lorentz contraction).

Most transistors are current regulated devices - the base also draws current (compared to a tube which is voltage regulated – MOSFET transistors though are voltage regulated, which is why they are used in solid state amplifiers so often) . That changes the input voltage, increasing distortions significantly, giving relatively low dynamic and higher distortions. But other than that, they are a lot more flexible from a design standpoint than tubes. They can be high power, they can be really really small. They don't inherently draw much power nor create much heat. For the electronics engineer, that's a lots better than the strange and esoteric things happening inside tubes.


An electron starts it's journey through the tube when the heater heats up to about 800 degrees centigrade, emitting a lot of electrons all at different energies. These all try leaving the heated cathode, but low energy ones don't get far, forming a negative space charge cloud around the cathode, dense enough that if no electrons are removed by attraction to the anode it throws back any electron to the cathode. The shape of this space charge is defined by the potential minimum, initial electron velocity distribution and other complex stuff. ­


External circuit components (including bass strings, pickups, and speaker magnets and coils) can make tube behavior even more complex (as if we didn’t already have enough on our minds). As an electron moves from the cathode to anode, it creates a time-variable electric field which changes as the electrons travel from the cathode to the anode. The field is generated by the electrical charge distributions from power supplies connected to the electrodes. These power supplies, with passive elements like resistors, inductances, and capacitors, make the external circuit which is affected as an electron moves in vacuum between the electrodes. One way to control this is to add massive power supplies.


The character of a tube amplifier changes over time as the electron gets nearer the anode (see picture) and in general is too complex for closed form mathematical solutions, so one has to physically measure tube performance to figure out what is going on. The implications for tube modeling are a big, hairy mathematical mess (don’t try this at home).

When the anode is made positive, some of the electrons are attracted out of the space-charge cloud, and a thermionic current results. The amount of this current is given by I = A V3/2, where V is the voltage from anode to cathode. This is called the Langmuir-Child law. It describes how the electric field surrounding the anode controls the current (the number of electrons traveling from cathode to anode). The cathode emits electrons copiously. So much that there are always enough electrons available to satisfy Langmuir-Child. At a sufficiently high anode voltage, the current will saturate – a condition where all the emitted electrons are sucked into the anode. It is at the saturation 'tipping point' that all of the interesting 'tubey' modulation of the music occurs.

To make things even more complex, near saturation the so-called Schottky effect causes the current density to rise and creates 'shot noise.' There are also small periodical deviations from linear response at high voltage, due to reflection of electrons near the anode. This reflection occurs when the electron from inside the crystal comes near the surface and again at the border with the vacuum.

On a bass guitar at volume, current can saturate on the attack of almost every note. So tubes can constantly be making significant modifications to attack and decay tone because of current saturation. Even faced with a sudden input overload, tubes produce pleasant "soft" clipping instead of the painfully unpleasant clip of an overloaded transistor. Tubes in general take physical torture better than transistors; the military likes them because they will even work after absorbing the radiation fallout and EMP of a nuclear blast. Consider this: if you'd been prescient enough to have purchased a tube amp, you'd be able to hook up your Fender and groove even after North Korea drops the bomb.

For almost a century, vacuum tubes have been the best choice for consumer and professional audio equipment designers and musicians. The sentiments "tubes sound natural", "tubes warm up your tone", "tubes sound soft and mild" are often expressed by professional musicians. Much of the musical magic we've come to expect from tube amplifiers arises from the complex physics surrounding current saturation at the anode. I, for one, think it may be sometime yet before this magic can be copied in a solid state device.

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