Cathode bias
In order for a vacuum tube
Vacuum tube
In electronics, a vacuum tube, electron tube , or thermionic valve , reduced to simply "tube" or "valve" in everyday parlance, is a device that relies on the flow of electric current through a vacuum...

 (or valve) to operate in a fairly linear region of its characteristic curve, the grid element must be maintained at a bias voltage more negative than the cathode
A cathode is an electrode through which electric current flows out of a polarized electrical device. Mnemonic: CCD .Cathode polarity is not always negative...

. One method for accomplishing this is "cathode bias."

Early techniques

Early experimenters and manufacturers used a battery to provide this bias. This battery, called the "C" or bias battery provided voltage
Voltage, otherwise known as electrical potential difference or electric tension is the difference in electric potential between two points — or the difference in electric potential energy per unit charge between two points...

 but almost never was called upon to deliver current. Thus, such batteries lasted nearly as long in service as they would have on a shelf. In 1985, The Department of Engineering and Technology at Cuesta College
Cuesta College
Cuesta College is a public community college located in San Luis Obispo County near the Central Coast of California. It currently offers 76 Associate's degree programs and 96 certificate programs...

 in San Luis Obispo, California
San Luis Obispo, California
San Luis Obispo is a city in California, located roughly midway between San Francisco and Los Angeles on the Central Coast. Founded in 1772 by Spanish Fr. Junipero Serra, San Luis Obispo is one of California’s oldest communities...

 was presented with a "C" battery date stamped 1927. Department Chairman W.E. English and Instructor W.T. Hanley conducted experiments which demonstrated that the battery still performed satisfactorily in its originally intended role more than 50 years after its manufacture.

Battery bias, however, is not self adjusting, and does not accommodate differences between a new tube and one that has aged, differences between various tubes of the same type, or substitutions that may be made in tube type by repair technicians. Cathode bias automatically accounts for all these possibilities. It is inherent in the technique that the bias level is set by the operation of each individual tube.

Establishing cathode bias

To establish cathode bias, a resistor
A linear resistor is a linear, passive two-terminal electrical component that implements electrical resistance as a circuit element.The current through a resistor is in direct proportion to the voltage across the resistor's terminals. Thus, the ratio of the voltage applied across a resistor's...

 is placed between the emitting element, or cathode and the negative return of the "B" or HT supply. Current drawn through this resistor by tube conduction places the cathode slightly more positive than the negative return. The grid input is returned directly to the negative supply, causing it to be negative with respect to the cathode. Thus, changes in tube conduction are automatically compensated by changes in bias.

This scheme inherently introduces dynamic, even harmonic distortion. As the input signal becomes more positive, cathode current increases, increasing bias and reducing gain. As the input signal becomes more negative, cathode current decreases, decreasing bias and increasing gain. The result is a plate signal with positive excursions greater than the negative input and negative excursions smaller than the positive input. It must be borne in mind that the input and output signals are ideally exactly out of phase. Since cathode bias is normally employed at audio or very low radio frequencies, issues such as transit time and interelectrode capacitance may be disregarded and the ideal assumed.

Overcoming problems

To overcome this problem, the bias resistor is typically shunted by a capacitor. In general, the capacitor value is selected such that the time constant of the capacitor and bias resistor is an order of magnitude greater than the period of the lowest frequency to be amplified. The capacitor thus acts as a dynamic battery, and makes the bias constant through input signal swings.

In some designs, the degeneratve feedback inherent in cathode bias may be desirable. In this case, two carefully designed successive stages may be employed, such that the distortion introduced by the first stage is exactly cancelled by that introduced in the second. This technique is not recommended, as the design considerations become very complex. Other degenerative feedback techniques are easier to design, and should be used.

An exception to the general rule may be made in the case of "push-pull", or balanced circuits. A pair of tubes, driven by identical signals 180 degrees out of phase, may share a common unbypassed cathode resistor. Slight differences in tube conduction are then dynamically balanced by bias variations that tend to reduce distortion. This technique is useful in the input circuits of balanced line receivers or push-pull power output circuits.


Cathode bias is also used to achieve phase inversion
Phase inversion
Phase inversion means the swapping of the two poles of an alternating current source. A phase inversion is neither a time shift nor a phase shift, but simply a swap of plus and minus....

. In a more simple circuit, which has less than unity gain, the cathode and plate resistors are made equal. In accordance with Kirchoff's law
Kirchhoff's circuit laws
Kirchhoff's circuit laws are two equalities that deal with the conservation of charge and energy in electrical circuits, and were first described in 1845 by Gustav Kirchhoff...

, the current through both resistors will be equal, thus the voltage across them will also be equal. As the plate becomes more negative, the cathode will become more positive, and conversely. The resulting signals are capacitively coupled to any succeeding stages, providing a pair of signals 180° out of phase.

The other technique is to use a pair of amplifier tubes with a common cathode resistor. In this case, the input tube is operated as a standard common cathode amplifier, while its twin is operated in common grid mode. The input signal is amplified by the input tube in the normal fashion. An unbypassed cathode resistor, common to both tubes, couples the signal to the cathode of the second amplifier, which is operated in "Grounded grid" mode, with the grid resistor bypassed by a capacitor which maintains a constant grid voltage. The pair of tubes produce outputs exactly out of phase, but the gain of the grounded grid amplifier is slightly higher, requiring that their plate resistances be different in order to maintain balance.

Mathematically, the gain of the phase inverting stage is given by the product of the amplification factor and the load impedance divided by the sum of the plate resistance and the load impedance. The gain of the in phase stage is given by the product of (one plus the amplification factor) and the load impedance divided by the sum of the plate resistance and the load impedance. In order for the gains to be equal, it is customary to use different values of plate resistance. For example, in such a phase inverting circuit using a 12AX7, the inverting stage would have a plate resistor of 100KΩ
The ohm is the SI unit of electrical resistance, named after German physicist Georg Simon Ohm.- Definition :The ohm is defined as a resistance between two points of a conductor when a constant potential difference of 1 volt, applied to these points, produces in the conductor a current of 1 ampere,...

 while the in phase stage would use a resistor of 82 KΩ. Mathematically, it works out pretty close.

Another problem is a slight reduction in gain. The cathode, or bias resistor appears in series with the plate, or load resistor. The bias voltage must be subtracted from the total "B" or HT voltage in gain calculations. In most circuits, this problem is easily overcome by selecting a load impedance at least two orders of magnitude greater than the bias resistance. For example, a 1K bias resistor will have virtually no effect if the load impedance is at least 100K. These values were, in fact, used by Leo Fender in many of his guitar amplifier designs. Refer to "The Tube Amp Book" by Gerald Weber, schematic section.

Sources for further information

Perhaps the best discussion of cathode bias, in terms of clarity and simplicity, is to be found in one of the many editions of The RCA Receiving Tube Manual, in the applications section. This manual was published in many forms and editions for over 40 years, but has long since been out of print. Edition RC-17, released around 1971 is likely to be the most available. Information in this article is based on that edition.

Excellent discussions of cathode bias may also be found in Basic Electronics, by Bernard Grob, published in no fewer than eight editions over the years (with continued revisions after his death) by McGraw Hill. U.S. Air Force Manuals 52-8 and 101-8 also cover this subject, although they have long been out of print. Copies may still be available from the U.S. Government Printing Office. The problem is that the technology is getting old fast, and nobody writes much about it any more.[edit: The technology maybe old, but many guitar players and HiFi audiophiles will never give them up. To that end, this is the best site that I know of for more tube amp info. ]
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