Projection engineering (Sept 1929-Nov 1930)

Page 22 Projection Engineering, October, 1929 Considerations in the Design of AudioFrequency Apparatus Output and High-Ratio Transformers By C. H. W. Nason PART I THE logical trend in radio development is always toward the ideal in theoretically disassociated units. The design of an audio-frequency amplifier, save for specific services where narrow fre-_ quency bands are to be employed, is therefore undertaken with the view that the input and load circuits with their attendant apparatus fulfill the requirements of the ideal. For accurate reproduction of speech and music, an amplifier should have a response essentially flat from 0 to 15,000 cycles or higher.1 Practical limitations render this impossible, however, and a response from 50 to 7,000 cycles may be taken as ideal with present needs in mind. If this ideal is to be obtained, it is essential that the "reproduction factor" or "per cent turn ratio" of the individual transformer be not less than 95 per cent as this deviation from the normal is magnified with the number of stages employed with the number acting as a geometrical factor. That is; if we have a reproduction factor of 80 per cent in each stage for a given frequency, when amplified through five stages of like character, the reproduction factor for that frequency will be .806 = .328, or 32.8 per cent. Thus a factor of distortion quite tolerable in the single stage will be impossible of use in a multi-stage amplifier. Besides this distortion of the frequency characteristic, there is also a "harmonic distortion" due to the loading of the core which will be taken up under the problem of "core material" in the second article of this series. The purpose of this article is to present the necessary data on the design of audio-frequency apparatus in a theoretical treatment, to be followed by a series of practical design problems in which the design of several representative transformers, together with the considerations to be employed in the design of the complete amplifier, 1 See Fletcher — "Speech and Hearing"D. Van Nostrand Co. Representative load circuits with low-ratio transformers. will be undertaken. To this end considerable data on available core materials and standard core laminations has been collected and put into a form suitable for design reference. There are two major types of transformers classified according to design methods. High-ratio transformers, where the capacitance of the secondary circuit and the leakage inductances are of a considerable magnitude ; and lowratio transformers, where the load in the secondary circuit may be of appreciable nature and may vary with frequency, but where the primary inductance and the turns ratio are the main factors in design. In designing a transformer with a pre-determined response curve, the equations for "per cent turn ratio" resolve themselves into two distinct series. The equations employed at the low frequencies (from the lowest desired frequency up to about one-third of the range from the low-frequency end to the high-frequency resonant point) are along a separate line of attack from those involved in the calculations over the high frequency range. Output Transformers The low-ratio transformers may be considered to include "tube-to-load," "tube-to-line," "line-to-line" and other types involving a secondary to primary ratio not much greater than 1 :1, where the capacitance and leakage resonance are not consequent. p— WAAAAAAA/Rp R2: 9— ^/WWWVW| R3 I e i i i L1 FIG. 3 FIG.4 Fig. 3. Redrawn primary circuit and Fig. 4, an equivalent circuit. At a low frequency ( Fig. 1 ) Ei = Rti2 + w Li it But R is small as compared with w Li and may be neglected, ("j" is the vector operator denoting the fact that "i" lags ninety degrees behind the impressed voltage. This is an imaginary quantity with an arithmetic value V-l, and must be cleared according to standard algebraic practice before any numeric value may be assigned to the solution of an equation, w denotes the "angular velocity" and has a value of 2 t f . The eddy current and hysteresis losses of the core material have not been delineated in the figure and will be neglected. For all practical purposes we may write : If "A" is the turns ratio of the transformer E2 = A Ei and the current in the secondary circuit is i2 = — — u. A The primary circuit may be redrawn as in Fig. 3 and the transferred load resistance takes the form R2 = Rz The ratio Ei/E will be equivalent to the relationship between Zi (the impedance of Li and R2 paralleled) and Zo (the impedance of the entire circuit looking from E). The relation E2 17 = A is constant and the value of the "reproduction factor" will be dependent upon Ei Zi e =~z7 In order to obtain the "per cent turn ratio" at a low frequency, it is necessary to calculate Zi/Z0 at that frequency and at some mid-range fre