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Negative Feedback In=20 Amplifiers

Including a discussion about phase-shift errors and = output=20 stage and transformer design

Original=20 Title:
Basic Design = Requirements:=20 Alternative Specifications

Condensed from preface in a Wireless World booklet = circa=20 >=3D1949, '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=20 useful range of shellac pressings has been extended from the limited 50 = =E2=80=93 8,000=20 c/s which, with certain notable exceptions, has been standard from 1930 = until=20 the present, to a range of some 20 =E2=80=93 15,000 c/s. This has been = accompanied by an=20 overall reduction in distortion and the absence of peaks, and by the = recording=20 of a larger volume range [he means dynamic range], which combine to make = possible a standard of reproduction not previously attainable from disc=20 recordings. The resumption of the television service, with its = first-class sound=20 quality, and the possibly extension of u.h.f. high-quality = transmissions,=20 increase the available sources of high-quality sound.

Full = utilization of=20 these recordings and transmissions demands reproducing equipment with a = standard=20 of performance higher than that which has served in the past. Extension = of the=20 frequency range, involving the presence of large-amplitude, = low-frequency=20 signals, gives greater likelihood of intermodulation distortion in the=20 reproducing system, whilst the enhanced treble response makes this type = of=20 distortion more readily detectable and undesirable. The purpose of the = amplifier=20 is to produce an exact replica of the electrical input voltage waveform = at a=20 power level suitable for the operation of the loudspeaker.

The=20 requirements of such an amplifier may be listed as:=20

1. Negligible non-linear distortion up to the maximum rated output = (this=20 includes production of undesired harmonic frequencies and the = intermodulation=20 of component frequencies of the sound wave). This requires that the = dynamic=20 output/input characteristic be linear within close limits up to the = maximum=20 output at all frequencies within the audible range.

2. 2.a. Linear frequency response within the audible spectrum of = [here he=20 quotes 10 =E2=80=93 20,000 c/s, but 10 Hz is much too low for nearly = all practical=20 purposes].

2.b. Constant power handling capacity for negligible non-linear = distortion=20 at any frequency within the audible spectrum.

2.b.1. This requirement is less stringent at the high frequency = end of the=20 spectrum but should the maximum power output/frequency response at = either end=20 of the spectrum (but especially, at the low frequency end) be = substantially=20 less than that at medium frequencies, filters must be arranged to = reduce=20 the level of these frequencies before they reach the = amplifier, as=20 otherwise severe intermodulation will occur. This is especially = noticeable=20 with organ music where pedal notes of the order of 10 =E2=80=93 20 c/s = cause bad=20 distortion, even though they may be inaudible in the output. [Assuming = the=20 recording medium and its playback system is able, in its turn, to = produce such=20 frequencies.]

3. Negligible phase shift within the audible range. = Although the=20 phase relationship between the component frequencies of a complex = steady-state=20 sound does not appear to affect the audible quality of the sound, the = same is=20 not true of transients, the quality of which may be profoundly altered = by=20 disturbance of the phase relationship between component = frequencies.

3.a. The reduction of phase shift in amplifiers operating with = negative=20 feedback is of prime importance, as instability will result = should a=20 phase shift of 180=C2=B0 occur at a frequency where the vector = gain of the=20 amplifier and feedback network [combined] is greater than = unity.=20 [That is, the negative feedback actually becomes positive = feedback=20 due to a phase shift of 180=C2=B0 at a particular frequency and the = overall gain=20 is greater than X1, whereupon the amplifier effectively goes into=20 oscillation at that frequency. Note this cannot occur in amplifiers = without=20 negative feedback.]

3.b. "It is possible for steady-state signal across the output = load to=20 rise, say, positively when the input signal is rising negatively. = This is=20 sometimes, though inaccurately, regarded as 180=C2=B0 phase shift. = In reality it=20 is signal inversion such as derived from negative feedback... Real = phase=20 shift results from a reactive network of some kind in the amplifier" = [in our=20 case, the output transformer is prime suspect]... "A steady-state = sinusoid=20 at the output will either rise or fall in sympathy with the input = when there=20 is zero phase shift at the particular test frequency. If the output = signal=20 at that frequency is given a zero-degree phase datum, then any = departure=20 from this condition [when the reactive network is added] constitutes = phase=20 shift. It is tantamount to the output rising some time after = or some=20 time before the input signal rises." [However] "If the phase = shift=20 changes non-linearly with frequency then some frequencies of a = complex music=20 signal will arrive at the loudspeaker after or before others, = altering the=20 output waveform, and this is called phase or group delay distortion, = where=20 time refers to the time of a complex signal cycle (phase = shift that=20 is proportional to frequency is not phase distortion)." = =E2=80=93 Gordon=20 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=20 effective gain due to current and voltage cut-off in any stages, the = utmost=20 care in the design of iron-cored components, and the reduction of such = components to a minimum.

Changes in effective gain during=20 'low-frequency' transients occur in amplifiers with output stages of = the=20 self-[cathode]-biased Class AB type, causing serious distortion which = is not=20 revealed by steady-state measurements. The transient causes the = current in the=20 output stage to rise, and this is followed, at a rate determined by = the time=20 constant of the biasing network, by a rise in bias voltage which = alters the=20 effective gain of the amplifier [output valve(s)].

5. Low output resistance. This is concerned with the attainment of = good=20 frequency and transient response from the loudspeaker system by = ensuring that=20 it has adequate electrical damping. Maximum damping will be achieved = when the=20 voice coil is effectively short-circuited, hence the output resistance = of the=20 amplifier should be much lower than the coil impedance.

6. Adequate power reserve. The realistic reproduction of = orchestral music=20 in an average room requires peak power capabilities of the order of 15 = =E2=80=93 20=20 Watts when the electro-acoustic transducer is a baffle-loaded = moving-coil=20 loudspeaker system of normal efficiency [however, speaker magnets are = much=20 more powerful these days!]. The use of horn-loaded loudspeakers may = reduce=20 this requirement to the region of 10 Watts.

The Output Stage
An output of the order of 15 = =E2=80=93 20 Watts may=20 be obtained in one of three ways, namely, push-pull triodes, = push-pull=20 triodes with negative feedback, or push-pull tetrodes with = negative=20 feedback. The salient features of these methods are of = interest.

Push-pull triode valves without negative feedback form the = mainstay of=20 present-day high-fidelity equipment. A stage of this type has a = number of=20 disadvantages. With reasonable efficiency in the power stage such = an=20 arrangement cannot be made to introduce non-linearity to an extent = less=20 than that represented by about 2 =E2=80=93 3 per cent harmonic = distortion. The=20 output/input characteristic of such a stage is a gradual curve = (Fig. 1(a)=20 below). With this type of characteristic distortion will be = introduced at=20 all signal levels and intermodulation of the component signal = frequencies=20 will occur at all levels. The intermodulation with such a = characteristic=20 is very considerable and is responsible for the harshness and = 'mushiness'=20 which characterizes amplifiers of this type. In addition, further=20 non-linearity and considerable intermodulation will be = introduced by=20 the output transformer core.

If the load impedance is = chosen to=20 give maximum output [then] the load impedance/output resistance = ratio of=20 the amplifier will be about 2, which is insufficient for good = loudspeaker=20 damping.

It is difficult to produce an adequate frequency = response=20 characteristic in a multi-stage amplifier of this type as = the=20 effect of multiple valve capacitances and the output = transformer=20 primary and leakage inductances becomes serious at the ends of the = a.f.=20 spectrum.

Bandwidth Limiting Filters
(para. = 2.b.1.=20 above) The well-respected Marantz 8B push-pull amplifier uses a = double=20 differentiator at the input to roll off the bass by =E2=80=933 dB = @ 30 Hz, and =E2=80=938=20 dB @ 10 Hz. Note also the inclusion of a capacitor adding = to the=20 grid to plate capacitance to limit gain in the upper frequency = band,=20 working in conjunction with a 33k grid=20 resistor.

Valve capacitances =E2=80=93 = "Suppose a=20 triode amplifies 25 times. An input voltage change of 1 volt will then = cause an=20 anode voltage change of 25 Volts, which means that the signal charges = the=20 anode-grid capacitance not to 1 Volt but to 25 Volts. Seen at the grid, = the=20 capacitance is therefore not just the anode-grid capacitance, but this=20 capacitance multiplied by the amplification of the stage. If our = valve is=20 half a double triode ECC83, where Ca-g is 1.6pF, this capacitance acts = as if it=20 was 25 x 1.6 =3D 40pF + strays.

"When the signal passes from one = stage with=20 an output resistance greater than zero to the next stage with an input=20 capacitance greater than zero, this forms a low-pass filter with a = cut-off=20 frequency, above which the signal will decrease by 6 dB per octave. But = we must=20 realise that such a filter not only affects amplitude of the signal. = It=20 introduces a phase shift too." [Therefore, there should not be too = many high=20 gain triode stages.] "An amplifier with many stages can show = considerable=20 frequency-dependent phase shift, making global NFB very difficult, and = this may=20 perhaps account for the sometimes bad reputation of this type of = feedback. If we=20 look at the most classic of all amplifiers, the Williamson, we see a = four stage=20 amplifier with drivers. To keep this amplifier stable, Williamson had to = specify=20 his output transformer to meet extremely stringent demands and even = then, his=20 amplifier was only just stable." =E2=80=93 Claus Byrith =

Fig. 1. Output/input characteristics (a) = without=20 feedback (b) with negative feedback.

The application of negative feedback to push-pull triodes = results in=20 the more or less complete solution of the disadvantages outlined = above.=20 Feedback should be applied over the whole amplifier, from = the=20 output transformer secondary to the initial [input] stage as this = method=20 corrects distortion introduced by the output transformer = and makes=20 no additional demands upon the output capabilities of any stage of = the=20 amplifier.

The functions of negative feedback are:=20

7.a. To improve the linearity of the amplifier, and output=20 transformer.

7.b. To improve the frequency response of the = amplifier and=20 output transformer.

7.c. To reduce the phase shift in the amplifier and = output=20 transformer within the audible frequency range.=20

7.d. To improve the low-frequency characteristics of the output = transformer, particularly defects due to the non-linear relation = between=20 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=20 amplifier and supply voltage changes, and of any spurious effects. =

A=20 [output] stage of this type is capable of fulfilling the highest = fidelity=20 requirements. The output/input characteristics is of the type shown in = Fig. 1(b)=20 and is virtually straight up to maximum output, when it curves sharply = with the=20 onset of [forward] grid current in the output valves. Non-linear = distortion can=20 be reduced to a degree represented by less than 0.1% harmonic = distortion, with=20 no audible intermodulation. The frequency response of the whole = amplifier from=20 input to output transformer secondary can be made linear, and the power = handling=20 capacity constant over a range considerably wider than that required for = sound=20 reproduction.

The output resistance, upon which the loudspeaker = usually=20 depends for most of the damping required, can be reduced to a small = fraction of=20 the speech coil impedance. A ratio of load impedance/output resistance=20 (sometimes known as 'damping factor') of 20 =E2=80=93 30 is easily = obtained.

'Kinkless' or 'beam' output tetrodes used with negative feedback can, = with care,=20 be made to give a performance midway between that of triodes with = and=20 without negative feedback. The advantages to be gained from the use of = tetrodes=20 are increased power efficiency and lower grid drive voltage.

It = must be=20 emphasised that the characteristics of the stage are dependent solely = upon the=20 character and amount of the negative feedback used. The feedback must = remain=20 effective at all frequencies within the a.f. spectrum under all = operating=20 conditions, if the quality is not to degenerate to the level usually = associated=20 with tetrodes without feedback. Great care must be taken with the design = and=20 operation of the amplifier to achieve this, and troubles such as = parasitic=20 oscillation and instability are liable to be = encountered.

When=20 equipment has to be operated from low-voltage power supplies a tetrode = stage=20 with negative feedback is the only choice, but where power supplies are = not=20 restricted, triodes are preferable because of ease of operation and = certainty=20 of results.

It appears [therefore] that the design of an = amplifier=20 for highest possible fidelity should centre around a push-pull triode = output=20 stage, and should incorporate negative feedback.

The most = suitable types=20 of valve for this service are the PX25 and the KT66. Of these the = KT66 is=20 to be preferred, since it is a more modern indirectly-heated type with a = 6.3=20 Volts heater, and will simplify the heater supply problem. = Triode-connected, the=20 KT66 has characteristics almost identical with those of the = PX25.

Using a supply voltage of some 440 Volts a power output of 15 = Watts=20 per pair may be expected.

The Output Transformer =
This=20 is probably the most critical component. If incorrectly designed it is = capable=20 of producing distortion which is often mistakenly attributed to the = electronic=20 part of the amplifier. Distortion producible directly or indirectly by = the=20 output transformer may be listed as follows:=20

8.a. Frequency distortion due to low winding inductance, high = leakage=20 reactance and resonance phenomena.

8.b. Distortion due to the phase shift produced when negative = feedback=20 is applied across the transformer. This usually takes the form of=20 parasitic oscillation due to phase shift produced in the = high=20 frequency region by a high leakage reactance.

8.c. Intermodulation and harmonic distortion caused by = overloading at=20 low frequencies when the primary inductance is insufficient. This = is=20 primarily due to a reduction in the effective load impedance below the = safe=20 limit, resulting in a very reactive load at low frequencies. This may = cause=20 the valves to be driven beyond cut-off since the load ellipse will = tend to=20 become circular.

8.d. Harmonic and intermodulation distortion produced by the = non-linear=20 relation between flux and magnetizing force in the core material. This = distortion is always present, but will be greatly aggravated if = the=20 flux density in the core exceeds the safe limit.

8.e. Harmonic distortion introduced by excessive resistance in the = primary=20 winding.

The design of a practical transformer has to be a = compromise=20 between these conflicting requirements.

[This is the interesting = part] At=20 a low frequency =C6=92_b, such that the reactance of the = output transformer=20 primary is equal to the resistance formed by the load resistance and the = valve=20 AC impedances in parallel, the output voltage will be 3 dB below that at = medium=20 frequencies. At a frequency 3=C6=92_b the response will = be well=20 maintained, the transformer reactance producing only 20=C2=B0 phase = angle. Similarly=20 at the high frequency end the response will be 3 dB down at a frequency=20 =C6=92_t such that the leakage reactance is equal to the = sum of the=20 load and valve AC resistances. Again at a frequency =C6=92_t/3 = the response=20 will be well maintained.

[Here again a frequency response flat = down to 10=20 Hz at the bottom end is mentioned, which is quite rediculous for all = practical=20 everyday purposes, so I substituted a value of 30 Hz]

If then the = required frequency range is 30 =E2=80=93 20,000 c/s, = =C6=92_b may be taken as=20 10 c/s [30 Hz / 3] and =C6=92_t as 60 kc/s [20 x 3 =3D 60 = kHz]. A=20 transformer which is only 3 dB down at frequencies as widely spaced as = this=20 would be difficult to design for some conditions of operation, and where = this is=20 so the upper limit may be reduced, as the energy content = of sound=20 at these frequencies is not usually high. The limiting factor = will be the=20 necessity of achieving stability when feedback is applied across = the=20 transformer, i.e., that the [closed] loop gain should be less than unity = at=20 frequencies where the phase shift reaches 180=C2=B0.

To = illustrate the=20 procedure, consider the specification for an output transformer coupling = two=20 push-pull KT66 valves [wired as triodes!] to a 15 Ohms load.=20

Primary load impedance =3D 10,000=CE=A9

Turns ratio =3D =E2=88=9A

10,000=20 / 15

=3D 25.8:1

Effective AC = resistance of valves =3D=20 2,500=CE=A9
[NB this is the internal anode = impedance (Ri) of=20 KT66 wired as triode, as 1.25 kilohms, x 2 (because there are two of = them).=20 However from the KT66 data sheet an actual figure of 1.3 kilohms is = specified=20 for triode mode and where HT =3D 440V, but we'll let this pass for the=20 moment.]

Low-Frequency Response =E2=80=93

Parallel load and valve resistance =3D	2,500 x 10,000	=3D 2,000=CE=A9
2,500=20 + 10,000

For = =C6=92_b =3D 10 Hz, response=20 should be 3 dB down.

[At this point a = =CF=89 calculation=20 creeps in, the result of which is used to get the required = incremental=20 inductance. This is lower-case Greek omega ('curly w'), representing = 2 x pi,=20 which is then multiplied by the frequency, as used with inductor=20 calculations]

Where =C6=92_b =3D 10 Hz, = =CF=89_b =3D 63=20 (approx.)

Therefore primary incremental inductance L = =3D=20	2,000	=3D 31 Henries.
63=20

High-Frequency Response =E2=80=93: Sum of load and AC resistances =3D 10,000 + 2,500 =3D = 12,500=CE=A9

At=20 =C6=92_t =3D 60 kHz (=CF=89_t =3D = 376,000) response should be=20 3 dB down.

Therefore leakage reactance =3D	12,500	=3D 33 mH.
376=20

This then is the specification for the = transformer.

Confusion=20 arises about specifying the inductance for a transformer, since = the=20 apparent inductance varies greatly with the method of measurement. = The=20 inductance is a function of the excitation, the variation being of = the=20 form shown in Fig. 2. The exact shape of the curve is dependent on = the=20 magnetization characteristic for the core material.

The = maximum=20 inductance, corresponding to point C, occurs when the core = material is=20 nearing saturation and is commonly 4 =E2=80=93 6 times the 'low = excitation' or=20 'incremental' value at A, which corresponds to operation near the = origin=20 of the magnetization curve. In a correctly designed output = transformer the=20 primary inductance corresponding to the voltage swing at maximum = output at=20 50 c/s will lie in the region of B.

In specifying the = component,=20 the important value is the incremental inductance = corresponding to=20 point A, since this value determines the frequency response at low = outputs.

Fig. 2. Variation of inductance with AC = excitation.=20

The above procedure as applied to VT1041, 'Super 20-30W Output = Transformer',=20 with 8=CE=A9 secondary and using same output stage goes as=20 follows:

Primary load impedance =3D 6,600=CE=A9

Turns ratio =3D =E2=88=9A

6,600=20 / 8

=3D 28:1 (approx.)

Effective AC resistance of valves (in series) =3D = 2,600=CE=A9 (from=20 data sheet)
Low-Frequency Response =E2=80=93

Parallel load and valve resistance =3D	2,600 x 6,600	=3D 1,865=CE=A9
2,600=20 + 6,600

If = =C6=92_b =3D 10 Hz,=20 =CF=89_b =3D 63 (approx.)

Therefore primary incremental inductance L = =3D=20	1,865	=3D 29 Henries.
63=20

This is not as daft as it seems, because = according to=20 the data sheet two KT66's in triode push-pull are supposed to take a 2.5 = kilohms=20 (Ra-a) load for a supply of 250V, and 4 kilohms for a supply of 440V. So = 6.6=20 kilohms should be a doddle!

Fig. 3. Circuit Arrangements.

Phase Shift
Which was defined earlier, mentioned again = here=20 to add "that the introduction of more than one transformer into = the=20 feedback path is likely to give rise to trouble from instability. = As it is=20 desirable to apply feedback over the output transformer the rest = of the=20 amplifier should be R-C coupled."

Capacitors in = series in=20 the signal path will add a phase lag at the low-frequency end = =E2=80=93 albeit=20 reducing the signal level at the same time =E2=80=93 whereas shunt = capacitances in=20 parallel with the signal path add phase lag at the = high-frequency=20 end. This includes grid to anode capacitance of triodes (in = particular)=20 which is multiplied by the gain of the stage, as mentioned = earlier.=20

Since it is good engineering practice to make your first = stage=20 that with the highest gain in the system, it makes sense that it = should be=20 a pentode, which has a small grid capacitance which in turn is not = greatly=20 affected by the anode, if at all, since it is shielded by the = screen and=20 suppressor grids, and therefore remains a more or less = consistently small=20 value at all frequencies. Wiring the thing as a triode immediately = loses=20 this advantage.

Also avoid using capacitors in the closed-loop (includes the = NFB)=20 signal path whose dielectric absorption is variable with = frequency. This=20 means that all ceramic =E2=80=93 especially the high K types = =E2=80=93 and mica types,=20 which are the worst offenders, are out for a start. You stand a = much=20 better chance with polystyrene, polypropylene and/or polycarbonate = types,=20 similarly electrolytics, having a higher K, with benefit from = being=20 shunted by polystyrene or polypropylene. Also avoid types whose=20 construction adds an undesirable amount of inductance.

In = Wireless=20 World's reprint of the 1949 article for the Williamson amplifier, = there is=20 an almost plaintive comment to the effect that it was high time = that=20 loudspeaker design caught up with the capabilities of 'modern = amplifiers'.=20 A loudspeaker is not a purely resistive load, but can be very = reactive.=20 While you are trying to roll off the high-frequency end to offset = some=20 spurious or parasitic oscillation at some point, it is not helped = by voice=20 coil inductance raising the loudspeaker input impedance as the = frequency=20 increases. This has the effect of raising the amplifier gain to = greater=20 than unity at the point where the instability occurs, exactly what = you are=20 trying to avoid! Therefore impedance correcting Zobel networks for = the=20 speaker driver(s) are essential in order to present as constant as = possible a load impedance to the amplifier output at all = frequencies,=20 especially at the top end.

Fig. 4. 'Paraphase' circuit combines phase = splitter and=20 push-pull driver with = gain.

It is=20 pointless adding a Zobel network to the output of the amplifier itself = without=20 knowing the voice coil inductance to start with, and so component values = for it=20 that are chosen arbitrarily are no good. You could use something called = a=20 'system impedance correction network', comprising of a resistor, = capacitor and=20 inductor in series, but to derive this you will still need to plot the=20 loudspeaker impedance against frequency, and that system will only work = with=20 that particular loudspeaker.

Alternative = Circuits
Although=20 the amplifier may contain push-pull stages it is desirable that the = input and=20 output should be 'single-ended' and have a common earth terminal. Three = circuit=20 arrangements suggest themselves.

The block diagram of Fig. 3(a) = shows the=20 simplest. The output valves are preceded by a phase splitter which is = driven by=20 the first stage. This arrangement is advantageous in that the phase = shift in the=20 amplifier can easily be reduced to a low value as it contains the = minimum=20 number of stages. However, it has a number of disadvantages which = render it=20 unsuitable. The input voltage required by the phase splitter is rather = more than=20 can be obtained from the first stage for a reasonable distortion with = the=20 available HT voltage, and in addition the phase splitter is operating at = an=20 unduly high level. The gain of the circuit is low even if a = pentode is=20 used in the first stage, and where a low-impedance loudspeaker is used,=20 insufficient feedback voltage will be available.

The addition of = a=20 push-pull driver stage to the previous arrangement, as in Fig. 3(b), = provides a=20 solution to most of the difficulties. Each stage then works well within = its=20 capabilities. The increased phase shift due to the extra stage has not = been=20 found unduly troublesome provided that suitable precautions are = taken.

The functions of phase splitter and push-pull driver stage may be = combined in a=20 self-balancing 'paraphase' circuit giving the arrangement of Fig. 3(c). = The grid=20 of one drive valve is fed directly from the first stage, the other being = fed=20 from a balanced resistance network between the anodes of the driver = valves as=20 shown in Fig. 4. [The second valve therefore functions as a unity gain=20 inverter.] This arrangement forms a good alternative to the preceding = one where=20 it is desirable to use the minimum number of valves.

An Explanation Of Leakage = Reactance

Leakage=20 reactance, or leakage inductance, is most simply described as that = property of=20 an electrical transformer that causes each of the mutally-coupled = transformer=20 windings to appear to have some extra self-inductance added in series = with=20 itself. The flux set up by the primary winding does not completely cut = the=20 secondary winding; there will always be a small measure of flux = that=20 misses the secondary winding, and therefore, is not affected by any load = placed=20 across the secondary. Not surprisingly, this is called the leakage = flux,=20 which does not link with all the turns and is due to imperfect = coupling=20 of the windings. It's like the primary and secondary each have an extra = small=20 coil added in series, as in jx1 and jx2 in the equivalent electrical = model shown=20 below...

The leakage flux alternately stores and = discharges=20 magnetic energy with each electrical cycle and thus effectively acts as = an=20 inductor in series with each of both the primary and secondary circuits, = and=20 they are carrying the same current as the remainder of the winding. = Because=20 these 'extra small coils' are not coupled to each other, the energy thus = stored=20 has nowhere to go. This becomes significant at high frequencies, if not = for the=20 magnitude of the reactance, which may manifest itself as voltage spikes = and=20 similarly spurious oscillations, then for the phase shift it causes. =

One=20 good way of addressing this problem is to add a 'snubber' network, or a = Zobel=20 network, across each half of the primary (assuming it's push-pull) to=20 absorb this energy. This is simply a resistor and a capacitor in = series=20 which, together with the leakage inductance, form a lossy tuned circuit = where=20 the energy flows between the capacitor and the leakage inductance. The = energy=20 that was stored in the leakage inductance is then dissipated in the = resistor. A=20 good starting point is 470=CE=A9 for the resistor, while the = capacitor=20 value may begin at 1,000pF, going up to as much as 10 =E2=80=93 22nF, as = necessary.=20 However arriving at precise values requires a pulse or square-wave test = signal=20 and an oscilloscope to observe the effect on the output waveform. Too = much will=20 load the output valves and reduce the bandwidth of the=20 amplifier.

=20