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Harmonic Distortion
Audio response may be good according to Figs. 109, 110, 111, and 113, but at the same time the output may be badly distorted because of changes in load impedance or phase angle.
This possibility is considered here for the case in which the load impedance is twice the source impedance. The phase angle of the equivalent circuits of Figs. 107 (a) and (e) is found by taking the angle whose tangent is the ratio of imaginary to real components of the total circuit impedance in each case.
This angle is plotted in Figs. 114 and 115 for the low and highfrequency ranges, respectively, with the same abscissas as in Figs. 108 and 110.
It is the angle between the voltage E_{1} and the current entering the equivalent circuits of Figs. 107(c) and (e) and therefore represents the angle between ac grid voltage and plate current. Positive angle indicates lagging plate current. The phase angle exhibited by a transformer over the range considered in Figs. 114 and 115 does not exceed 30°, whereas for the most favorable curve in Fig. 115 (B = 1.0) it does not exceed 15°. To study the effect of phase angle alone upon distortion, the light load of 8,800 ohms is plotted upon the plate characteristics of triode type 851 in Fig. 116. The result is a sine wave of plate voltage. If the phase angle between grid voltage and plate current waves is then arbitrarily made 30°, as in Table XII, the elliptical load curve obtains.
Table XII. 851 Triode Operation with 8,800Ohm 30° Phase Angle Load
The wave of plate voltage is plotted for both zero and 30° phase angle in Fig. 117.
These wave forms indicate that the phase angle encountered in audio transformers does not of itself introduce much distortion in a lightly loaded triode. The influence of load impedance on distortion will be considered next. In Fig. 107(c) the load impedance, to the right of the dotted line, is
Hence
Equation 66 is plotted in Fig. 118.
It shows the change in load Z from its medianfrequency value R_{2}, as the frequency is lowered. Abscissas are X_{N}/R_{2} instead of X_{N}/R_{1} as in Fig. 108. For the higher audio frequencies, the load impedance at the right of the dotted line in Fig. 107(e) is
If we let X_{c}/R_{2} = D at frequency f_{r}, then, at any frequency f, X_{c}/R_{2} = Df_{r}/f. If this substitution is made in equation 67 and also if X_{L}/X_{c} = f^{2}f_{r}^{2},
Equation 67a is plotted in Fig. 119 for several values of D. The impedance varies widely from its medianfrequency value, especially at lower values of D.
From Figs. 118 and 119 it is possible to compare the change in impedance with the frequency response curves in Figs. 108 and 110. When this comparison is made it should be remembered that B = 2D for the triode conditions assumed here. If the amplifier response is allowed to fall off 1.0 db at the lowest frequency, the corresponding value of X_{N}/R_{1}. from Fig. 108 is 1.3. This means that X_{N}/R_{2} is 0.65. The corresponding load impedance in Fig. 118 is only 0.55 of its medianfrequency value. Likewise, for 0.5db droop of the frequency characteristic, the load impedance falls to 0.7R_{2}, whereas for a good load impedance of 0.9R_{2} the frequency characteristic can fall off only 0.1 db. It is thus evident that load impedance may vary widely even with comparatively flat frequency characteristics.
It might be thought that, since 0.75f_{r} is the upper frequency limit, the harmonics resulting from the low value of load impedance would not be amplified, and no harm would be done. But at the frequency 0.375f_{r}, whose second harmonic would be amplified, the load impedance is only 0.69R_{2}. Between 0.375f_{r} and 0.75f_{r} (over half of the amplifier frequency range) the load impedance gradually drops from 0.69R_{2} to 0.327R_{2}. Thus distortion is large over a wide frequency range. It would be much better to design the transformer so that B = 2.0; the change in impedance is much less, and the rise in response is slight. To ascertain how much distortion these low load impedances produce, a series of loads was plotted in Fig. 116 on 851 plate characteristics: 100, 70, and 50 per cent of the class A UPO value of twice the plate resistance (3,100, 2,200, and 1,550 ohms, respectively). The distortion is tabulated below for 54 volts grid swing.
The plate voltage amplitude decrease with low impedance loads means that the combination of tube and transformer has a characteristic which droops instead of remaining flat as indicated by the curve B = 1.0 in Fig. 110. This droop modifies the upper ends of the curves of Fig. 110. Although these curves were intended specifically for vacuum tubes, they were derived on the basis of a constant sinusoidal voltage in the source. Figure 119 demonstrates one important fact: For vacuum tubes operating into loads of twice the tube plate resistance, it is better to design transformers so that B = 2 or more. Then the output voltage and distortion are less affected by impedance variations at high frequencies. The actual frequency characteristics for triodes lie somewhere between the curves of Fig. 110 and the corresponding curves of Fig. 119. Designing transformers for B ≥ 2.0 means keeping the effective capacitance lower, but the leakage inductance may be proportionately greater than for transformers having B = 1.0. Variations of load impedance at high frequency shown in Fig. 119 are for stepup transformers. Similar variations for stepdown transformers may be found from equation 68.
Equation 68 is plotted in Fig. 120.
Impedance rises to peaks in the vicinity of f_{r}, in contrast to the valleys in Fig. 119. For the same variation of impedance, the frequency range is greater for stepdown transformers, especially with values of D = 0.5 and 0.7. Besides the harmonic distortion caused by variations in load impedance, at low frequencies additional distortion is caused by nonlinear magnetizing current. If a transformer is connected to a 60cycle supply line, the noload current contains large harmonics, but the voltage wave form remains sinusoidal because the line impedance is low. But if distorted magnetizing current is drawn from an amplifier tube, the plate resistance is high enough to produce a distorted voltage wave form across the transformer primary winding, caused mainly by the third harmonic. If the harmonic current amplitude I_{H} in the magnetizing current is found by connecting the transformer across a lowimpedance source, the amplitude of harmonic voltage appearing in the output with a higherimpedance source is
where E_{h} = harmonic voltage amplitude If flux density is below the knee of the saturation curve, and if X_{N} = 3R_{2} at the lowest operating frequency, the harmonic amplitude is less than 5 per cent. An air gap in the core reduces this figure. Table XIII gives typical harmonic currents for silicon steel.
Table XIII. Typical SiliconSteel Magnetizing Current Harmonic Components with Zero Impedance Source
Output voltage distortion may be analyzed to find harmonic content by the usual Fourier method. Several simplifications have been devised to reduce the labor and increase accuracy.^{(2)} In general, if the recommended tube load impedances are maintained, harmonic percentages will be as given in the tube manuals. If other load impedances obtain at some frequencies, to predict the harmonic output requires harmonic analysis.


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