High-Q Tank Circuit for Ultra-High Frequencies
September 1939 QST

When I see that mechanical drawing of an oscillator tank circuit, the cross-section of a screw-on type automotive oil filter comes to mind. Ham radio operators who build their own equipment have never shied away from tackling leading-edge, technically challenging projects. Indeed, many Amateurs have pioneered radio circuit, antenna, and propagation concepts that were later adopted by military and commercial concerns. One of the first examples was the relegation of hitherto believed to be unimportant shortwave frequency bands for amateur radio use. Quite unexpectedly, Hams quickly took up the challenge and exploited the unique long range communications capabilities possible due to atmospheric channeling and reflection phenomena. This 1939 QST magazine article features coaxial resonant cavities used to construct high-Q oscillators. While the title says "Ultra-High Frequencies," the highest frequency mentioned is for 1¼ meters, that is around 240 MHz, which according to today's spectrum assignments doesn't quite reach into the 300 MHz to 3 GHz realm where UHF officially resides. The 1¼ meter through 5 meter bands are within VHF.

High-Q Tank Circuit for Ultra-High Frequencies

Designing U.H.F. Oscillators of High Stability

By Arnold Peterson*

The author covers the basic requirements for the construction of stable u.h.f. oscillators, discloses the shortcomings of ordinary tank circuits, describes a different type circuit - really a "tank" - especially designed for use with oscillators. The new tank is admittedly more difficult to build, but the amateur who is handy with tools will not find those difficulties insuperable. If you pretend to have even a casual interest in the ultra-high frequencies you'll have to give this article a careful reading.

The new regulations, which extend the requirements of frequency stability to the 5- meter band, are prompting those amateurs who prefer to use the simplest possible equipment to explore the possibilities of bands located still higher up in the frequency spectrum. Fortunately, a sufficient background in the technique for the 2 1/2- and 1 1/4-meter bands has been developed by the early workers in the field so that new arrivals can construct satisfactory apparatus for communication.

Recently some oscillators for these higher frequency bands were designed by the author in accordance with the results of an investigation of oscillator frequency stability at the ultra-high frequencies. This investigation was conducted as a part of a cooperative research program of the General Radio Company and the Massachusetts Institute of Technology. The oscillators include two for the 1 1/4-meter band, one for 2 1/2 meters, and one for 5 meters. These particular ones have been built for Mr. Henry S. Shaw, W1FGA, and since Mr. Shaw has found them useful for his amateur work, other amateurs may obtain worthwhile information from a description of them. However, because the mechanical details make difficult the construction of these transmitters by the average amateur, this article is not intended to be a how-to-build-it one, but rather a discussion of the reasons for certain particulars of the design with the thought that those working at 2 1/2 and 1 1/4 meters may receive some helpful ideas.

Oscillator Requirements

In the amateur's search for suitable ultra-high-frequency generators, more and more power seems to be the principal end in view. This goal is a natural one, but higher power is not the only means to more reliable communication. In particular, as many amateurs realize, the use of generators of high-frequency stability will make that power more effective. This consideration may seem to be out of place, since many are going to the higher frequencies to dodge the frequency stability requirement; but a little reflection will show that it is advantageous for the amateur to strive for reasonable frequency stability. For normal transmission with amplitude-modulated signals, any accompanying spurious frequency modulation seems to have harmful effects only. For instance, the usual modulated oscillators for operation at these frequencies have such broad signals that even the moderate selectivity provided by a single good tuned circuit in the receiver can introduce noticeable distortion by not passing all of the frequency-modulated signal. Further, the relative signal-to-noise ratio that can be obtained with the use of simple amplitude modulation decreases as the band width required for the reception of the signal increases. Finally, the ease with which the superheterodyne method of reception, with all its attendant advantages, can be applied is directly dependent on the frequency stability of the signal sources. Thus when these bands become more crowded, the stable signals will be more and more appreciated, particularly because of the smaller interference they will cause. At any rate one can see that any gain in frequency stability that can be made is to be desired, especially if this improvement does not involve a noticeable sacrifice in output.

To illustrate a method that can be used to achieve good oscillator frequency stability, the basic construction of the tank circuit¹ used here will be described, and the reasons for the design adopted will be discussed.

Basic Tank Circuit

The basic type of tank circuit used in the oscillators to be described here is shown in section in Fig. 1. This tank circuit is cylindrically symmetrical about the center-line axis and consists of a large outer cylinder (A), capped at both ends, with a slightly smaller inner cylinder (B) supported coaxially from one of these ends by means of a central rod (C) and a connecting disc (D) from the rod to the inner cylinder. Although in appearance it does not resemble the usual tuned circuits, nevertheless, schematically it is nothing more than an inductance and condenser connected in parallel. The capacitance is practically that formed between the larger outer cylinder (A) and the smaller inner one (B) and the inductance is practically that resulting from the flux surrounding the central rod (C).

Since the radial flow of current in the connecting discs (D and E) contributes no appreciable inductance, the values of inductance and capacitance for structures of this type can be calculated rather accurately by the standard coaxial line formulas:

where l_L = effective length of inductance (cm.)

b_L = inside diam. of outside tube (B) of inductance

a_L = outside diam. of central rod (C) of inductance

l_c = effective length of capacitance (cm.)

b_c = inside diam. of outside tube (A)

a_c = outside diam. of inside tube (B)

(If any dimension of the tank circuit exceeds about one-twentieth of the wavelength, these formulas can not be applied.) The capacitance from the lower disc (D) to the end cap (F) can usually be estimated with sufficient accuracy from the ordinary parallel-plate capacitance formulas² and then added to the capacitance of the cylindrical condenser. These formulas and a consideration of the capacitance loading of the oscillator tube will furnish the information needed in the design for operation at a given frequency.

Design Considerations

The fundamental reason for the use of a structure of this type is to obtain a tuned circuit that has low losses and whose elements are relatively fixed by reason of excellent mechanical stability. However, the mere use of this structure is not sufficient to ensure that a stable oscillator will result. For this purpose one must arrange that the energizing vacuum tube be connected to the tank circuit in such a manner that variations in the tube's characteristics have as small an effect as possible on the frequency of oscillation. A consideration of the factors that produce instability in oscillators will show how this arrangement can be achieved.

At the ultra-high frequencies probably the most important of the factors that produce frequency modulation when the oscillator is amplitude-modulated is the variation of the effective interelectrode capacitances with electrode voltage. In order to reduce the effect of this variation to the smallest value practical, one has recourse to the standard amateur practice of using a hi-Q (high capacity) tank circuit for the oscillator. An equivalent procedure is the use of a low-loss tank circuit and coupling so loosely to it that changes in the tube will not affect the resonant frequency too seriously. This procedure must be followed when resonant lines are used for the tank circuit if one desires to take full advantage of the low losses of these circuits for obtaining frequency stability. A similar method should be used for low-capacity low-loss circuits of all types. However, by using a hi-Q tank circuit, one obtains the advantage of a smaller physical size, and, at the same time, parasitic oscillations are usually not so troublesome when it is possible to connect directly across the main elements of the tuned circuit as opposed to coupling loosely to the stabilizing circuit.

But an attempt to use a hi-Q circuit for the oscillator quickly leads to considerable difficulties in producing oscillations at these high frequencies. Generally this difficulty is a result of using components of standard construction, which often have relatively high losses. That these losses are more detrimental for hi-Q circuits than for low-C circuits can be seen by the following line of reasoning. The developed impedance of the tank circuit at the operating frequency must be high enough to prevent the tank circuit from loading up the vacuum tube beyond the point at which oscillations can be maintained. For a given loss in the circuit the larger the capacitance used, the smaller is this developed impedance. Then to develop a high impedance with a hi-Q circuit one must have a low-loss circuit.

To keep the overall losses of the tank circuit small, probably the best procedure is to design the tank circuit as an integral whole. If each component is constructed individually, the advantages gained by an efficient design of both the condenser and the inductance may be lost because of the manner in which the two are connected together. In the tank circuit of Fig. 1 the connections from the main capacitance to the inductance have been made an inherent part of the structure, and in that way the extra loss introduced can be made relatively small.

The fundamental attitude that is taken in designing these low reactance (hi-Q) circuits is the minimization of resistance and of inductance rather than the minimization of capacitance. In order to do this successfully one must have in mind the essential nature of inductance and the behavior of current flow when skin effect is complete. Fortunately a simplified account of this behavior is all that is necessary for obtaining qualitative design methods.

It is well known that at high frequencies the current tends to concentrate near the surface of conductors. In fact this tendency is so marked at the ultra-high frequencies for metallic conductors that for most practical purposes one can consider the current as flowing only in a very thin skin layer at the surface without any appreciable penetration of the current into the metal. This phenomenon is commonly known as skin effect.

The limited depth of current penetration implies that for the current in a conductor to go from one point to another it must travel on the surface only and cannot travel by way of the interior of the conductor. To illustrate what this means, consider current flow down the rotor of a variable condenser of normal construction. If contact is made to the shaft bearings, current may flow through this contact along the surface of the shaft until it comes to the first rotor plate. Here one normally considers that the main body of the conduction current travels through the plate while some of it flows as capacitive current to the first stator plate. However, if the plate is of reasonable thickness (say, greater than 0.001"), at the ultra-high frequencies the current will flow out radially at the surface of the rotor plate, pass over at the edge of the plate to the other side of the rotor plate, and then travel inward radially to the rotor shaft. In doing so of course a fraction of the cur-rent flows capacitively to the second stator plate, but the rest continues merrily on its way just skimming the surface. That is, it travels along the surface of the shaft, then expands outwardly along the surface of the plates across the edge and back in again and so on.

Thus at high frequencies the current does not take advantage of the total area of the conductor, and it also ignores paths that require penetration through the interior of the conductor. The corresponding effective resistance of the conductor is therefore enormously increased. These considerations indicate that the small-diameter condenser shaft in the preceding illustration produces a series of bottlenecks for current flow and suggest the disadvantages resulting from forcing the current to flow over paths of small surface area.

For the inductance of the tank circuit, one has the specific problem of designing for a particular value of inductance with the purpose of obtaining that value with the lowest losses possible. Fortunately certain relations that have been worked out for the realization of hi-Q inductances can be used here. The one that is of particular interest is that for an inductance formed by a circular rod and a surrounding tube connected to it at one end by a conducting disc. For this case the desirable relation of dimensions is that the outside tube should have a diameter of about 3 to 4 times the diameter of the center rod. Incidentally, a similar relation exists for simple single-loop inductances, in that the spacing of conductors (diameter of the loop) should be about 3 to 6 times the diameter of the conductor. However, for an open loop of this type where radiation is a serious factor the overall dimensions should be limited to less than about one-twentieth of a wavelength, while the coaxial inductance mentioned above is not so quickly limited. As one might expect, the Q of the coaxial inductance increases as the diameter of the tube and rod are increased, but too large a diameter leads to a system that can no longer be considered as a lumped inductance.

In considering a design for its inherent inductance one should remember that decreasing the spacing, decreasing the length, or increasing the cross-section of conductors will decrease the inductance. Thus, for those conductors that need to have very low inductance only short, heavy leads that are relatively close to the corresponding return conductor should be used.

* General Radio Co., 30 State St., Cambridge, Mass.

1 Peterson, Arnold, "An Ultra-High-Frequency Oscillator," General Radio Experimenter, XII, 5 (October 1947).

2 See for instance: The American Radio Relay League, The Radio Amateur's Handbook (15th ed.), p. 43.

Posted November 10, 2022
(updated from original post on 6/12/2016)