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Last Modified: 5 Jun 2012


Including a discussion about phase-shift errors and output stage and transformer design


Original Title:
Basic Design Requirements: Alternative Specifications


Condensed from preface in a Wireless World booklet circa >=1949, 'excessive waffle' excluded! Author unknown


R
ecent improvements in the field of commercial sound recording have made practicable the reproduction of a wider range of frequencies than hitherto. The useful range of shellac pressings has been extended from the limited 50 – 8,000 c/s which, with certain notable exceptions, has been standard from 1930 until the present, to a range of some 20 – 15,000 c/s. This has been accompanied by an overall reduction in distortion and the absence of peaks, and by the recording of a larger volume range [he means dynamic range], which combine to make possible a standard of reproduction not previously attainable from disc recordings. The resumption of the television service, with its first-class sound quality, and the possibly extension of u.h.f. high-quality transmissions, increase the available sources of high-quality sound.

Full utilization of these recordings and transmissions demands reproducing equipment with a standard of performance higher than that which has served in the past. Extension of the frequency range, involving the presence of large-amplitude, low-frequency signals, gives greater likelihood of intermodulation distortion in the reproducing system, whilst the enhanced treble response makes this type of distortion more readily detectable and undesirable. The purpose of the amplifier is to produce an exact replica of the electrical input voltage waveform at a power level suitable for the operation of the loudspeaker.

The requirements of such an amplifier may be listed as:

1. Negligible non-linear distortion up to the maximum rated output (this includes production of undesired harmonic frequencies and the intermodulation of component frequencies of the sound wave). This requires that the dynamic output/input characteristic be linear within close limits up to the maximum output at all frequencies within the audible range.

2. 2.a. Linear frequency response within the audible spectrum of [here he quotes 10 – 20,000 c/s, but 10 Hz is much too low for nearly all practical purposes].

2.b. Constant power handling capacity for negligible non-linear distortion at any frequency within the audible spectrum.

2.b.1. This requirement is less stringent at the high frequency end of the spectrum but should the maximum power output/frequency response at either end of the spectrum (but especially, at the low frequency end) be substantially less than that at medium frequencies, filters must be arranged to reduce the level of these frequencies before they reach the amplifier, as otherwise severe intermodulation will occur. This is especially noticeable with organ music where pedal notes of the order of 10 – 20 c/s cause bad distortion, even though they may be inaudible in the output. [Assuming the recording medium and its playback system is able, in its turn, to produce such frequencies.]

3. Negligible phase shift within the audible range. Although the phase relationship between the component frequencies of a complex steady-state sound does not appear to affect the audible quality of the sound, the same is not true of transients, the quality of which may be profoundly altered by disturbance of the phase relationship between component frequencies.

3.a. The reduction of phase shift in amplifiers operating with negative feedback is of prime importance, as instability will result should a phase shift of 180° occur at a frequency where the vector gain of the amplifier and feedback network [combined] is greater than unity. [That is, the negative feedback actually becomes positive feedback due to a phase shift of 180° at a particular frequency and the overall gain is greater than X1, whereupon the amplifier effectively goes into oscillation at that frequency. Note this cannot occur in amplifiers without negative feedback.]

3.b. "It is possible for steady-state signal across the output load to rise, say, positively when the input signal is rising negatively. This is sometimes, though inaccurately, regarded as 180° phase shift. In reality it is signal inversion such as derived from negative feedback... Real phase shift results from a reactive network of some kind in the amplifier" [in our case, the output transformer is prime suspect]... "A steady-state sinusoid at the output will either rise or fall in sympathy with the input when there is zero phase shift at the particular test frequency. If the output signal at that frequency is given a zero-degree phase datum, then any departure from this condition [when the reactive network is added] constitutes phase shift. It is tantamount to the output rising some time after or some time before the input signal rises." [However] "If the phase shift changes non-linearly with frequency then some frequencies of a complex music signal will arrive at the loudspeaker after or before others, altering the output waveform, and this is called phase or group delay distortion, where time refers to the time of a complex signal cycle (phase shift that is proportional to frequency is not phase distortion)." – Gordon J. King, Audio Equipment Tests, 1979.

4. Good transient response. In addition to low phase and frequency distortion, other essential factors are the elimination of changes in effective gain due to current and voltage cut-off in any stages, the utmost care in the design of iron-cored components, and the reduction of such components to a minimum.

Changes in effective gain during 'low-frequency' transients occur in amplifiers with output stages of the self-[cathode]-biased Class AB type, causing serious distortion which is not revealed by steady-state measurements. The transient causes the current in the output stage to rise, and this is followed, at a rate determined by the time constant of the biasing network, by a rise in bias voltage which alters the effective gain of the amplifier [output valve(s)].

5. Low output resistance. This is concerned with the attainment of good frequency and transient response from the loudspeaker system by ensuring that it has adequate electrical damping. Maximum damping will be achieved when the voice coil is effectively short-circuited, hence the output resistance of the amplifier should be much lower than the coil impedance.

6. Adequate power reserve. The realistic reproduction of orchestral music in an average room requires peak power capabilities of the order of 15 – 20 Watts when the electro-acoustic transducer is a baffle-loaded moving-coil loudspeaker system of normal efficiency [however, speaker magnets are much more powerful these days!]. The use of horn-loaded loudspeakers may reduce this requirement to the region of 10 Watts.

The Output Stage

Bandwidth Limiting Filters
(para. 2.b.1. above) The well-respected Marantz 8B push-pull amplifier uses a double differentiator at the input to roll off the bass by –3 dB @ 30 Hz, and –8 dB @ 10 Hz. Note also the inclusion of a capacitor adding to the grid to plate capacitance to limit gain in the upper frequency band, working in conjunction with a 33k grid resistor.

Valve capacitances – "Suppose a triode amplifies 25 times. An input voltage change of 1 volt will then cause an anode voltage change of 25 Volts, which means that the signal charges the anode-grid capacitance not to 1 Volt but to 25 Volts. Seen at the grid, the capacitance is therefore not just the anode-grid capacitance, but this capacitance multiplied by the amplification of the stage. If our valve is half a double triode ECC83, where Ca-g is 1.6pF, this capacitance acts as if it was 25 x 1.6 = 40pF + strays.

"When the signal passes from one stage with an output resistance greater than zero to the next stage with an input capacitance greater than zero, this forms a low-pass filter with a cut-off frequency, above which the signal will decrease by 6 dB per octave. But we must realise that such a filter not only affects amplitude of the signal. It introduces a phase shift too." [Therefore, there should not be too many high gain triode stages.] "An amplifier with many stages can show considerable frequency-dependent phase shift, making global NFB very difficult, and this may perhaps account for the sometimes bad reputation of this type of feedback. If we look at the most classic of all amplifiers, the Williamson, we see a four stage amplifier with drivers. To keep this amplifier stable, Williamson had to specify his output transformer to meet extremely stringent demands and even then, his amplifier was only just stable." – Claus Byrith


The application of negative feedback to push-pull triodes results in the more or less complete solution of the disadvantages outlined above. Feedback should be applied over the whole amplifier, from the output transformer secondary to the initial [input] stage as this method corrects distortion introduced by the output transformer and makes no additional demands upon the output capabilities of any stage of the amplifier.

The functions of negative feedback are:

7.a. To improve the linearity of the amplifier, and output transformer.

7.b. To improve the frequency response of the amplifier and output transformer.

7.c. To reduce the phase shift in the amplifier and output transformer within the audible frequency range.

7.d. To improve the low-frequency characteristics of the output transformer, particularly defects due to the non-linear relation between flux and magnetizing force.

7.e. To reduce the output resistance of the amplifier.

7.f. To reduce the effect of random changes of the parameters of the amplifier and supply voltage changes, and of any spurious effects.

A [output] stage of this type is capable of fulfilling the highest fidelity requirements. The output/input characteristics is of the type shown in Fig. 1(b) and is virtually straight up to maximum output, when it curves sharply with the onset of [forward] grid current in the output valves. Non-linear distortion can be reduced to a degree represented by less than 0.1% harmonic distortion, with no audible intermodulation. The frequency response of the whole amplifier from input to output transformer secondary can be made linear, and the power handling capacity constant over a range considerably wider than that required for sound reproduction.

The output resistance, upon which the loudspeaker usually depends for most of the damping required, can be reduced to a small fraction of the speech coil impedance. A ratio of load impedance/output resistance (sometimes known as 'damping factor') of 20 – 30 is easily obtained.

'Kinkless' or 'beam' output tetrodes used with negative feedback can, with care, be made to give a performance midway between that of triodes with and without negative feedback. The advantages to be gained from the use of tetrodes are increased power efficiency and lower grid drive voltage.

It must be emphasised that the characteristics of the stage are dependent solely upon the character and amount of the negative feedback used. The feedback must remain effective at all frequencies within the a.f. spectrum under all operating conditions, if the quality is not to degenerate to the level usually associated with tetrodes without feedback. Great care must be taken with the design and operation of the amplifier to achieve this, and troubles such as parasitic oscillation and instability are liable to be encountered.

When equipment has to be operated from low-voltage power supplies a tetrode stage with negative feedback is the only choice, but where power supplies are not restricted, triodes are preferable because of ease of operation and certainty of results.

It appears [therefore] that the design of an amplifier for highest possible fidelity should centre around a push-pull triode output stage, and should incorporate negative feedback.

The most suitable types of valve for this service are the PX25 and the KT66. Of these the KT66 is to be preferred, since it is a more modern indirectly-heated type with a 6.3 Volts heater, and will simplify the heater supply problem. Triode-connected, the KT66 has characteristics almost identical with those of the PX25.

Using a supply voltage of some 440 Volts a power output of 15 Watts per pair may be expected.


The Output Transformer
This is probably the most critical component. If incorrectly designed it is capable of producing distortion which is often mistakenly attributed to the electronic part of the amplifier. Distortion producible directly or indirectly by the output transformer may be listed as follows:

8.a. Frequency distortion due to low winding inductance, high leakage reactance and resonance phenomena.

8.b. Distortion due to the phase shift produced when negative feedback is applied across the transformer. This usually takes the form of parasitic oscillation due to phase shift produced in the high frequency region by a high leakage reactance.

8.c. Intermodulation and harmonic distortion caused by overloading at low frequencies when the primary inductance is insufficient. This is primarily due to a reduction in the effective load impedance below the safe limit, resulting in a very reactive load at low frequencies. This may cause the valves to be driven beyond cut-off since the load ellipse will tend to become circular.

8.d. Harmonic and intermodulation distortion produced by the non-linear relation between flux and magnetizing force in the core material. This distortion is always present, but will be greatly aggravated if the flux density in the core exceeds the safe limit.

8.e. Harmonic distortion introduced by excessive resistance in the primary winding.

The design of a practical transformer has to be a compromise between these conflicting requirements.

[This is the interesting part] At a low frequency ƒ_b, such that the reactance of the output transformer primary is equal to the resistance formed by the load resistance and the valve AC impedances in parallel, the output voltage will be 3 dB below that at medium frequencies. At a frequency 3ƒ_b the response will be well maintained, the transformer reactance producing only 20° phase angle. Similarly at the high frequency end the response will be 3 dB down at a frequency ƒ_t such that the leakage reactance is equal to the sum of the load and valve AC resistances. Again at a frequency ƒ_t/3 the response will be well maintained.

[Here again a frequency response flat down to 10 Hz at the bottom end is mentioned, which is quite rediculous for all practical everyday purposes, so I substituted a value of 30 Hz]

If then the required frequency range is 30 – 20,000 c/s, ƒ_b may be taken as 10 c/s [30 Hz / 3] and ƒ_t as 60 kc/s [20 x 3 = 60 kHz]. A transformer which is only 3 dB down at frequencies as widely spaced as this would be difficult to design for some conditions of operation, and where this is so the upper limit may be reduced, as the energy content of sound at these frequencies is not usually high. The limiting factor will be the necessity of achieving stability when feedback is applied across the transformer, i.e., that the [closed] loop gain should be less than unity at frequencies where the phase shift reaches 180°.

To illustrate the procedure, consider the specification for an output transformer coupling two push-pull KT66 valves [wired as triodes!] to a 15 Ohms load.

Primary load impedance = 10,000Ω 

Turns ratio = √

10,000 / 15

= 25.8:1

Effective AC resistance of valves = 2,500Ω  
[NB this is the internal anode impedance (Ri) of KT66 wired as triode, as 1.25 kilohms, x 2 (because there are two of them). However from the KT66 data sheet an actual figure of 1.3 kilohms is specified for triode mode and where HT = 440V, but we'll let this pass for the moment.]

Low-Frequency Response –

Parallel load and valve resistance =	2,500 x 10,000	= 2,000Ω
	2,500 + 10,000

For ƒ_b = 10 Hz, response should be 3 dB down.

[At this point a ω calculation creeps in, the result of which is used to get the required incremental inductance. This is lower-case Greek omega ('curly w'), representing 2 x pi, which is then multiplied by the frequency, as used with inductor calculations]

Where ƒ_b = 10 Hz, ω_b = 63 (approx.)

Therefore primary incremental inductance L =	2,000	= 31 Henries.
	63

High-Frequency Response –

Sum of load and AC resistances = 10,000 + 2,500 = 12,500Ω 

At ƒ_t = 60 kHz (ω_t = 376,000) response should be 3 dB down.

Therefore leakage reactance =	12,500	= 33 mH.
	376

This then is the specification for the transformer.

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The above procedure as applied to Danbury Electronics DB1041, 'Super 20-30W Output Transformer', with 8Ω  secondary and using same output stage goes as follows:

Primary load impedance = 6,600Ω 

Turns ratio = √

6,600 / 8

= 28:1 (approx.)

Effective AC resistance of valves (in series) = 2,600Ω  (from data sheet)

Low-Frequency Response –

Parallel load and valve resistance =	2,600 x 6,600	= 1,865Ω
	2,600 + 6,600

If ƒ_b = 10 Hz, ω_b = 63 (approx.)

Therefore primary incremental inductance L =	1,865	= 29 Henries.
	63

This is not as daft as it seems, because according to the data sheet two KT66's in triode push-pull are supposed to take a 2.5 kilohms (Ra-a) load for a supply of 250V, and 4 kilohms for a supply of 440V. So 6.6 kilohms should be a doddle!



It is pointless adding a Zobel network to the output of the amplifier itself without knowing the voice coil inductance to start with, and so component values for it that are chosen arbitrarily are no good. You could use something called a 'system impedance correction network', comprising of a resistor, capacitor and inductor in series, but to derive this you will still need to plot the loudspeaker impedance against frequency, and that system will only work with that particular loudspeaker.


Alternative Circuits
Although the amplifier may contain push-pull stages it is desirable that the input and output should be 'single-ended' and have a common earth terminal. Three circuit arrangements suggest themselves.

The block diagram of Fig. 3(a) shows the simplest. The output valves are preceded by a phase splitter which is driven by the first stage. This arrangement is advantageous in that the phase shift in the amplifier can easily be reduced to a low value as it contains the minimum number of stages. However, it has a number of disadvantages which render it unsuitable. The input voltage required by the phase splitter is rather more than can be obtained from the first stage for a reasonable distortion with the available HT voltage, and in addition the phase splitter is operating at an unduly high level. The gain of the circuit is low even if a pentode is used in the first stage, and where a low-impedance loudspeaker is used, insufficient feedback voltage will be available.

The addition of a push-pull driver stage to the previous arrangement, as in Fig. 3(b), provides a solution to most of the difficulties. Each stage then works well within its capabilities. The increased phase shift due to the extra stage has not been found unduly troublesome provided that suitable precautions are taken.

The functions of phase splitter and push-pull driver stage may be combined in a self-balancing 'paraphase' circuit giving the arrangement of Fig. 3(c). The grid of one drive valve is fed directly from the first stage, the other being fed from a balanced resistance network between the anodes of the driver valves as shown in Fig. 4. [The second valve therefore functions as a unity gain inverter.] This arrangement forms a good alternative to the preceding one where it is desirable to use the minimum number of valves.

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