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Negative Feedback In
Amplifiers
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

Recent 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
An output of the order of 15 – 20 Watts may
be obtained in one of three ways, namely, push-pull triodes, push-pull
triodes with negative feedback, or push-pull tetrodes with negative
feedback. The salient features of these methods are of interest.

Push-pull triode valves without negative feedback form the mainstay of
present-day high-fidelity equipment. A stage of this type has a number of
disadvantages. With reasonable efficiency in the power stage such an
arrangement cannot be made to introduce non-linearity to an extent less
than that represented by about 2 – 3 per cent harmonic distortion. The
output/input characteristic of such a stage is a gradual curve (Fig. 1(a)
below). With this type of characteristic distortion will be introduced at
all signal levels and intermodulation of the component signal frequencies
will occur at all levels. The intermodulation with such a characteristic
is very considerable and is responsible for the harshness and 'mushiness'
which characterizes amplifiers of this type. In addition, further
non-linearity and considerable intermodulation will be introduced by
the output transformer core.

If the load impedance is chosen to
give maximum output [then] the load impedance/output resistance ratio of
the amplifier will be about 2, which is insufficient for good loudspeaker
damping.

It is difficult to produce an adequate frequency response
characteristic in a multi-stage amplifier of this type as the
effect of multiple valve capacitances and the output transformer
primary and leakage inductances becomes serious at the ends of the a.f.
spectrum.

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

Fig. 1. Output/input characteristics (a) without
feedback (b) with negative feedback.

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 ƒb, 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 3ƒb 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
ƒt such that the leakage reactance is equal to the sum of the
load and valve AC resistances. Again at a frequency ƒt/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, ƒb may be taken as
10 c/s [30 Hz / 3] and ƒt 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 ƒb = 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 ƒb = 10 Hz, ωb = 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
ƒt = 60 kHz (ωt = 376,000) response should be
3 dB down.

Therefore leakage reactance =

12,500

= 33 mH.

376

This then is the specification for the transformer.

Confusion
arises about specifying the inductance for a transformer, since the
apparent inductance varies greatly with the method of measurement. The
inductance is a function of the excitation, the variation being of the
form shown in Fig. 2. The exact shape of the curve is dependent on the
magnetization characteristic for the core material.

The maximum
inductance, corresponding to point C, occurs when the core material is
nearing saturation and is commonly 4 – 6 times the 'low excitation' or
'incremental' value at A, which corresponds to operation near the origin
of the magnetization curve. In a correctly designed output transformer the
primary inductance corresponding to the voltage swing at maximum output at
50 c/s will lie in the region of B.

In specifying the component,
the important value is the incremental inductance corresponding to
point A, since this value determines the frequency response at low
outputs.

Fig. 2. Variation of inductance with AC excitation.

The above procedure as applied to VT1041, '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 ƒb = 10 Hz,
ωb = 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!

Fig. 3. Circuit Arrangements.

Phase Shift
Which was defined earlier, mentioned again here
to add "that the introduction of more than one transformer into the
feedback path is likely to give rise to trouble from instability. As it is
desirable to apply feedback over the output transformer the rest of the
amplifier should be R-C coupled."

Capacitors in series in
the signal path will add a phase lag at the low-frequency end – albeit
reducing the signal level at the same time – whereas shunt capacitances in
parallel with the signal path add phase lag at the high-frequency
end. This includes grid to anode capacitance of triodes (in particular)
which is multiplied by the gain of the stage, as mentioned earlier.

Since it is good engineering practice to make your first stage
that with the highest gain in the system, it makes sense that it should be
a pentode, which has a small grid capacitance which in turn is not greatly
affected by the anode, if at all, since it is shielded by the screen and
suppressor grids, and therefore remains a more or less consistently small
value at all frequencies. Wiring the thing as a triode immediately loses
this advantage.

Also avoid using capacitors in the closed-loop (includes the NFB)
signal path whose dielectric absorption is variable with frequency. This
means that all ceramic – especially the high K types – and mica types,
which are the worst offenders, are out for a start. You stand a much
better chance with polystyrene, polypropylene and/or polycarbonate types,
similarly electrolytics, having a higher K, with benefit from being
shunted by polystyrene or polypropylene. Also avoid types whose
construction adds an undesirable amount of inductance.

In Wireless
World's reprint of the 1949 article for the Williamson amplifier, there is
an almost plaintive comment to the effect that it was high time that
loudspeaker design caught up with the capabilities of 'modern amplifiers'.
A loudspeaker is not a purely resistive load, but can be very reactive.
While you are trying to roll off the high-frequency end to offset some
spurious or parasitic oscillation at some point, it is not helped by voice
coil inductance raising the loudspeaker input impedance as the frequency
increases. This has the effect of raising the amplifier gain to greater
than unity at the point where the instability occurs, exactly what you are
trying to avoid! Therefore impedance correcting Zobel networks for the
speaker driver(s) are essential in order to present as constant as
possible a load impedance to the amplifier output at all frequencies,
especially at the top end.

Fig. 4. 'Paraphase' circuit combines phase splitter and
push-pull driver with gain.

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.

An Explanation Of Leakage Reactance

Leakage
reactance, or leakage inductance, is most simply described as that property of
an electrical transformer that causes each of the mutally-coupled transformer
windings to appear to have some extra self-inductance added in series with
itself. The flux set up by the primary winding does not completely cut the
secondary winding; there will always be a small measure of flux that
misses the secondary winding, and therefore, is not affected by any load placed
across the secondary. Not surprisingly, this is called the leakage flux,
which does not link with all the turns and is due to imperfect coupling
of the windings. It's like the primary and secondary each have an extra small
coil added in series, as in jx1 and jx2 in the equivalent electrical model shown
below...

The leakage flux alternately stores and discharges
magnetic energy with each electrical cycle and thus effectively acts as an
inductor in series with each of both the primary and secondary circuits, and
they are carrying the same current as the remainder of the winding. Because
these 'extra small coils' are not coupled to each other, the energy thus stored
has nowhere to go. This becomes significant at high frequencies, if not for the
magnitude of the reactance, which may manifest itself as voltage spikes and
similarly spurious oscillations, then for the phase shift it causes.

One
good way of addressing this problem is to add a 'snubber' network, or a Zobel
network, across each half of the primary (assuming it's push-pull) to
absorb this energy. This is simply a resistor and a capacitor in series
which, together with the leakage inductance, form a lossy tuned circuit where
the energy flows between the capacitor and the leakage inductance. The energy
that was stored in the leakage inductance is then dissipated in the resistor. A
good starting point is 470Ω  for the resistor, while the capacitor
value may begin at 1,000pF, going up to as much as 10 – 22nF, as necessary.
However arriving at precise values requires a pulse or square-wave test signal
and an oscilloscope to observe the effect on the output waveform. Too much will
load the output valves and reduce the bandwidth of the
amplifier.