How an Output Transformer Causes Distortion

In Two Parts - Part 1
Audio, February, 1957, Vol. 41, No. 2 (Successor to RADIO, Est. 1917).
Norman H. Crowhurst

The operation of audio transformers has long been surrounded with an aura of mystery. This article distinguishes the different forms of distortion an output transformer can produce, and gives some simple measurement methods.

  The use of audio transformers has long been depreciated on the grounds that they cause distortion. In fact the output transformer seems to be almost the sole survivor of the species and many attempts have been made to do without even this. A few amplifiers have been designed to dispense with the output transformer, apparently in the belief that the output transformer is the principal remaining cause of distortion.

   Careful analysis will usually show that the tubes introduce more distortion than the output transformer would have and that that a well-designed amplifier using the conventional output transformer can achieve a much lower order of distortion than is possible without one.

   A few simple facts about transformers seem to get overlooked: when the tube curvature causes distortion it distorts all frequencies; but the distortion a transformer causes due to nonlinearity of its magnetizing current is concentrated at the low-frequency end. The worst transformer made will not distort the middle frequencies and the way it distorts at both lower and higher frequencies is one of the things we shall clarify in this article.

   But, surely, someone will say, a transformer can cause distortion at middle frequencies? "I remember replacing a transformer, and the replacement would not give so much power without distortion as the original did." Doesn't this prove that the transformer distorts at the middle frequency? To understand the cause of this experience, let's consider the effect of transformer efficiency on amplifier performance.

The Importance of Efficiency

   Amplifiers are rated to give a certain maximum output, determined by the performance of the output tubes. However, the output power is always measured on the secondary side of the output transformer, as shown at Fig. 1.

Fig. 1. Usual method of measuring output power consists of calculating the watts dissipated in a load resistor connected to the secondary of the output transformer. While this is the available power output, the output tubes actually deliver a little more than this.

   A good output transformer is probably about 95 per cent efficient. This means that, if the amplifier gives 50 watts output, measured on the secondary side of the transformer, there must be nearly 53 watts output delivered to the primary side from the output tubes. The output tubes are having to give nearly 53 watts output for us to measure a good 50 watts.

   This is a little difficult to verify by actual measurements. The simplest step towards is to remove the secondary resistance load and apply a plate-to-plate load on the primary, as at Fig. 2. If the secondary load was 16 ohms and the transformer refers this back to be, say, 6000 ohms plate-to-plate resistance, then a 6000 ohm resistor, of at least 50 watts dissipation, should beconnected across the primary. The power is now delivered by the output tubes directly to the load, without passing through the output transformer, and can now be measured in the 6000-ohm resistor.

Fig. 2. Connecting a suitable load resistor on the primary of the output transformer to measure power avoids some of the loss in the output transformer, but the tubes still have to supply the core loss.

   But all of the losses in the output transformer have not been removed by transferring the load from the secondary to the primary. The transformer core loss is still present. If, of the 3 watts lost in the transformer, 1 watt is due to core losses and 2 watts to losses in the winding resistances, we shall only measure 52 watts in the load connected to the primary, because the odd 1 watt will still be lost in the core.

   This discussion is based on a transformer having an efficiency of 95 per cent. A 50-watt output transformer with an efficiency of 95 per cent, and a really good frequency response from 20 to 20,000 cps, is going to be fairly large and expensive. A 5 per cent power loss is only 0.2 db, so some will argue that we can accept a transformer of 90 per cent efficiency, which still represents a loss of less than 0.5 db, in order to achieve better quality in terms of frequency response, at a size and cost that is more reasonable. Fro, some aspects the second transformer could be regarded as a better quality job than the first, but . . .

   Supposing we have made a substitution of a 90 per cent efficiency transformer into an amplifier that originally used a 95 per cent transformer: the tubes will still be capable of giving the same output - slightly less than 53 watts, which, with a 95 per cent efficient transformer will deliver 50 watts on the secondary; but with with a 90 per cent efficient transformer, the same tubes will only deliver a little over 47 watts on the secondary.

   At first glance, this may not seem to be a very serious loss. If you make the measurement at 47 watts on the secondary, you may correctly assess its true value. But unfortunately, output tubes to give 50 watts quickly run into distortion when they are pushed to a higher level. The distortion characteristic is similar to that shown at Fig. 3: the distortion at the 53 watts required to give 50 watts from a 95 per cent efficient transformer may by only 0.5 per cent; but to get the almost 56 watts needed for a 90 per cent efficient transformer, the distortion may rise to 2.5 per cent, or even more. So, if the measurement is made only at the 50 watt level measured on the secondary, the impression can easily be obtained that the second output transformer is considerably increasing the distortion, as compared with the first one.

Fig. 3. Typical distortion characteristic of amplifier, plotted in terms of the power given by the tubes, to illustrate how use of transformers of differing efficiency can change the distortion at rated maximum output quite drastically, because the tubes also have to supply the transformer losses.

   Unfortunately also, many people place considerable stress on getting the full value of wattage stated, within the rated distortion limit. If the output is stated to be 50 watts at 0.5 per cent distortion, than an amplifier is cinsidered to be seriously lacking if it only delivers 48 watts with 0.5 per cent distortion, and runs up to 2 or 3 per cent distortion when the output is pushed to 50 watts. This viewpoint can be seriously detrimental to an assessment of transformer quality, when the only deficiency in the transformer is that it is slightly less efficient: it introduces a loss of 0.5 db, or mayby even less, instead of the original 0.2 db.

Low-Frequency Distortion

   At the low-frequency end of the response, an output transformer causes distortion due to saturation of the core, which causes a nonlinear magnetizing current. This at one time was always true. But in recent years, with modern magnetic materials, and with some methods of operating tubes, the statement needs modifying, as we shall see. First let us see how we measure the low-frequency waveform of the transformer itself, and what kind of results we get.

Transformer Waveforms

   In Fig. 4, (A) shows the arrangement for measuring the magnetizing current in a simple transformer by means of an oscilloscope pattern. Resistor R should be chosen so its voltage drop is a small fraction of that across the transformer winding, so the voltage of the winding is also close to sinusoidal. As full line voltage will probably be not enough to produce saturation in the promary of an output transformer the secondary winding should be used for the test, leaving the primary oper-circuited and taking care not to get too near the open ends, which will produce a prohibitively large a.c. voltage.

   It is important to take care which way round the Variac is connected to the line and also to see that the ground side of the scope does not return to the line ground, because, in these measurements, the scope ground is returned to a floating point between the resistor R and one side of the transformer winding. So take care to avoid having more than one ground point and also avoid metal-to-metal contact between the scope case and other grounded chassis.

Fig. 4. Circuit arrangements for producing the oscilloscope traces: (A) the arrangement for the trace of (A) in Fig. 5; (B) connections for setting 90-deg. phase shift, by adjusting to get circle of (B) in Fig. 5; (C) connections to use with 90-deg. phase shift to give hysteresis loop at (C) in Fig. 5; (D) circuit with switching so that each display can be presented in quick sequence.

   The type of trace that the arrangement of (A) Fig. 4 gives when the core begins to go into saturation is shown at (A) in Fig. 5. The voltage applied to the vertical plates is approximately sinusoidal while the horizontal voltage follows the magnetizing current waveform, shown separately against a conventional time base at (D) in Fig. 5.

Fig. 5. Traces associated with core analysis: (A) magnetizing current horizontal with voltage vertical, using nearly sinusoidal voltage waveform; (B) circular pattern to check for 90-deg. phase shift in voltage display; (C) hysteresis loop obtained by 90-deg. shift on vertical plates; (D) waveforms displayed by normal time base, corresponding to the patterns of (A) and (C). Magnetic flux is shown dotted, because this cannot be displayed directly.

   With a little adaptation, the circuit can be made to display the well-known hysteresis loop for the transformer core. The necessary changes are illustrated at (B) and (C) in Fig. 4. When a sinusoidal voltage is used the magnetic flux in the core is also sinusoidal, but displaced 90 deg. from the voltage it induces. So, by introducing a 90 deg. phase shift in the vertical deflection, we can produce a hysteresis loop.

   First we have to set up the 90-deg. phase shift. To do this, the components shown at (B) in Fig. 4 are added and the 0.25-megohm variable resistor and the scope gain controls are adjusted to obtain the circular trace of Fig. 5. Then without altering the setting of the 0.25-meg. resistor, change the circuit to the arrangement of C in Fig. 4, when the hysteresis loop shown at (C) in Fig. 5 will be displayed.

   This setting will give the hysteresis loop at 60 cps, and its behavior at different levels can be observed by turning the Variac up and down. However, to arrange the setup so that this procedure can be repeated at different frequencies, the switching arrangement of (D) in Fig. 1 can be included, which provides for making the connections shown at (A), (B) and (C) of Fig. 4 in quick succession. The Variac should then by fed from a high-power amplifier that deliver the necassary voltage without waveform distortion at the frequencies required.

   If you switch the scope back to regular time base, which means the horizontal input is then disconnected and the vertical is displayed against time, the wavefors shown at (D) in Fig. 5 can be obtained (except the magnetic flux waveform, because there is no means of measuring this). Although these waveforms can be displayed there is no simple means of identifying the relative phase. This is the advantage of using the loop kind of display shown in Fig. 5 at (A), (B), and (C).

Transformers in Tube Circuits

   All of these displays use at least an approximately sinusoidal voltage waveform. Distortion occurs because the voltege departs from the true sine wave. This happens because the distorted current waveform is drawn from the source resistance that produces a volt drop. In the arrangement of Fig. 4 we used the Variac and the low value of resistor R to maintain an approximate sinusoidal voltage by avoiding this voltage drop. But in practical amplifier circuits the plate resistance of the output tubes does not allow this condition.

Pentode Outputs

   A pentode is virtually a "current" source, so swinging to the other extreme for a moment, we could assume that the current is sinusoidal, as represented at (A) in Fig. 6. In this case the magnetic flux will be determined from the hysteresis loop and the voltage, in turn, is produced by the rate at which the flux varies at any instant. The waveforms produced are shown at (A) in Fig. 7. Current and voltage can of course be displayed on the scope, but the magnetic flux we can only deduce.

Fig. 6. Showing the quantities displayed in Fig. 7: (A) fed from a pentode, or high resistance source, the current is sinusoidal; (B) with a lower source resistance, neither the voltage or current is sinusoidal.

Fig. 7. Waveforms in different practical circuits: (A) with a pentode or high resistance source, the current is sinusoidal; (B) with a lower source resistance, these waveforms are typical.

   These waveforms apply approximately to a pentode output stage without feedback. When feedback is used, the voltage waveform gets fed back over the whole amplifier so as to "correct" the current waveform, which then is no longer sinusoidal.

Triode Outputs

   (B) in Fig. 6 shows how we can simulate the conditions for triode amplifiers. The input voltage, which is sinusoidal, can be regarded as the open-circuit voltage at the plate. This input voltage is that applied to the grid multiplied by the amplification factor of the tube. The source resistance corresponds with the tube plate resistance and because of the drop in this source resistance, due to the current drawn by the transformer winding, the terminal voltage will differ from the output voltage, as shown at (B) in Fig. 7.

   Notice that the terminal voltage comes much nearer to being in phase with the input voltage than the phase relationship between voltage and current at (A) in Fig. 7.

   From this brief discussion it becomes evident that the magnetizing current and terminal voltage of a transformer cannot both be sinusoidal. In practice both of them depart from a true sine wave in shape and a certain amount of distortion results.

Another Kind of Low-Frequency Distortion

   However, if the magnetizing current is a relatively small proportion of the total current in the transformer windings, the distortion may be a very small percentage. These curves were displayed with the transformer unloaded so that the magnetizing current is the only current in the windings. Had the transformer been terminated by the normal load resistance, the waveforms would probably have been indistinguishable from pure sine waves and distortion could only be detected by means of an analyzer.

   Magnetizing current is invariably related to effective primary inductance and the way a transformer distorts at low frequency depends upon the precise relationship between primary inductance and magnetizing current. Two numerical cases will illustrate this distinction.

   First, suppose that the magnetizing current is 10 per cent of the load current. This means that the reactance due to primary inductance would be ten times the primary load resistance. This would cause an attenuation of less than .05 db. But if this magnetizing current was running into saturation co the magnetizing current waveform is as shown at (B) in Fig. 7, containing 20 per cent harmonic, this magnetizing current, being 1/10th of the total load current, could produce 1/10th this amount od distortion in the output waveform, or 2 per cent.

   The second kind of distortion that can occur at low frequencies is not directly due to the waveform of the magnetizing current at all. The transformer may operate well within the saturation limit, but the inductance only represents a reactance of, say, twice that of the load resistance. This will result in about 1 db loss at this frequency and also will cause the load line on the tube characteristics to open out into an ellipse. In this case the distortion present will be due to the elliptical load line rather than to the nonlinearity of the transformer magnetizing current.

   Another variation of this condition occurs in amplifiers with large amounts of feedback. This produces a low effective source resistance, so the distortion component of magnetizing current does not appreciably distort voltage. With a damping factor of 30, a magnetizing current 25 per cent of load current, and containing 30 per cent of harmonic, will only cause 0.25 per cent distortion in the output. But the 25 per cent reactive magnetizing current may cause the tubes to clip, producing a much bigger distortion than this.

(to be concluded)

(Part 2)

The content of the article for electron tube enthusiasts was provided by Grzegorz 'gsmok' Makarewicz