by Jeffrey H. Johnson [Braun AG Frankfurt, W. Germany]
The story is told of the English child during the war who, on learning
of an impending bread shortage, remarked that this wouldn't bother him as
he always ate toast. Something of the same outlook has all too often been
evident in the attitude toward the amplifierloudspeaker interface. We measure
amplifiers with welldefined resistive loads, but we listen with loudspeakers,
and loudspeakers present anything but a constant, wellbehaved load to the
amplifier. This can lead to a number of problems, and it is becoming widely
recognized that an amplifier which "works just fine" on the test
bench may not perform so well in actual operation. To see what some of the
effects of nonideal loads on amplifiers are is the purpose of this article.
The Loudspeaker
Loudspeaker manufacturers specify a nominal or "rated" impedance
for their products, usually 4 or 8 ohms. This specification is not without
value, but we shouldn't forget that the impedance of a loudspeaker actually
exhibits considerable variation with frequency. Partly this is determined
by the designer's choice of crossover network parameters, etc., but it is
also to some extent inherent in the physical principles of operation of
the loudspeaker mechanism itself.
Figure 1 shows the measured impedance of a typical threeway air suspension
system rated at 4 ohms.
Now, at first glance, it might seem that these impedance variations would
be very undesirable from the standpoint of the power available from the
amplifier. Since an amplifier is very nearly a constantvoltage source,
the power output is inversely proportional to load impedance; the higher
the impedance, the smaller the available power. For example, if the unit
shown in Fig. 1 is driven at 6.32 Vor 10 W into the rated
4 ohm impedancea power meter would show that the actual power would vary
from about 11 W to about 1 W, depending on frequency. This might seem highly
undesirable, but in fact it is not. Loudspeakers are designed for flat frequency
response with a constant drive voltage, not constant power. There is no
problem here, except that amplifier meters labeled in watts are meaningless.
(For a further discussion, see refs. 1, 2, 3.) The problems caused by impedance
variations come from a different direction, namely from the fact that an
impedance which varies with frequency exhibits a reactive, as well as a
resistive, component. A reactance is nondissipative; it can only store
energy, not put it to use. Such stored energy is unavailable for conversion
into acoustical energy. What's worse, this stored energy must go somewhere,
and that somewhere is back into the amplifier, where it can cause trouble.
Before we look at what some of these troubles are, we need to take a moment
to clarify some terminology. Impedance is a complex quantity; that is, it
has two dimensions, not just one. We can express this by saying that it
has a real (or resistive) part and an imaginary (or reactive) part, and
write this as Z = R ± jX where R is resistance and X is reactance. A very
useful alternative expression is to ive the magnitude (or modulus) of the
impedance: Z = _/ (R^2 + X^2) . The other dimension is then expressed
as a phase angle:
L Z = tan 1 (X/R).
What we usually offhandedly call "impedance" is actually only
the magnitude of the impedance: to be completely accurate we should also
give the phase angle. The impedance in Fig. 1 is thus both
curves taken together. Habitually speaking of the magnitude only makes it
easy to overlook the reactive component.
SmallSignal Effects
Reactive loading can affect both the largesignal and the smallsignal
performance of an amplifier. The smallsignal effects have to do chiefly
with the feedback stability and the dynamic response of the amplifier.
An amplifier can be modeled by a forward gain path Avon with an internal
impedance Zo, enclosed in a feedback loop giving a closedloop overall gain
of Avon (Fig. 2) (Zo here should not be confused with the
output impedance of the complete amplifier, which is Zo divided by the loop
gain.) For stability the phase shift at unity loop gain must not exceed
180°, and for satisfactory dynamic (transient) response, some phase margin
is necessary, limiting the loop phase shift to 120° or perhaps 135°. In
terms of the familiar Bode plot, Fig. 3a, this means that
the curve of the forward gain must intersect the curve of the closedloop
gain with a slope not much greater than 6 dB/octave, and all higher breakpoints
must lie some distance above this frequency.
The feedback voltage is taken from the junction of Zo and the load, point
X in Fig. 2. Zo, which may be comparable to the load impedance
depending on the circuit configuration, forms a voltage divider for the
feedback in conjunction with the load impedance. Suppose now that the load
is inductive, so that its impedance increases with frequency. Unless Zo
is quite small, this means that the feedback voltage will also increase.
With luck, this can provide a degree of lead compensation, but more often
the result is that the loop bandwidth is extended so that higher frequency
poles begin to contribute to instability, as depicted in Fig. 3b.
Alternately, a capacitive load will tend to roll off the feedback with increasing
frequency, and so the slope of the forward gain curve is increased and instability
results (Fig. 3c). As if this were not enough, in many
circuits Zo is not constant but rather increases at higher frequencies due
to hfe falloff in the output transistors, etc. Zo will thus have an inductive
component, and should the load be capacitive, a secondorder LC filter will
be formed for the feedback signal, contributing an additional 12 dB/octave
rolloff. This leads to oscillation. Often a fairly small capacitance (10
nF to 0.1 µF) will be more troublesome than a large capacitance, since the
latter may spread the poles farther apart and give a less rapid rolloff.
The cure for these woes is the addition of load isolation or stabilizing
networks to the amplifier output. The simple RC network in Fig. 4a
loads down the amplifier at high frequencies, avoiding the situation of Fig. 3b
with inductive loads (which are typical of movingcoil loudspeakers), and
with the rise in Avon which some configurations exhibit without load. A
more thoroughgoing method is the use of the LCR network. A series inductor
with rising impedance at higher frequencies is added to prevent capacitive
loads from loading down the amplifier too much. The preferred form of this
network, Fig. 4b, can be made to effect a smooth transfer
of the amplifier from the external load to the resistor R at a suitable
frequency above the audio range (Ref. 4). Load isolation networks are sometimes
accused of ringing, but with proper design this is not so; most of the ringing
is attributable to reduced feedback phase margin in the amplifier.
The smallsignal effects are manifested mostly at frequencies well above
the audio range. The nature of the loudspeaker load is consequently quite
important in this region also. Loudspeaker impedance is usually measured
only to 20 kHz, but for some time now one manufacturer has been measuring
all new designs out to 1 MHz after it had been discovered that an unexpected
impedance dip around 200 kHz had been causing problems with a certain amplifier.
LargeSignal Effects
The major difficulties arising from reactive loading are associated with
the largesignal area. Unlike the smallsignal case, where the amplifier
as a whole is involved, the large signal effects are confined almost entirely
to the output stage.
One of the most important effects of reactive loading is its influence
on the power dissipation in the output devices of an amplifier. Probably
the best way to see how this happens is to examine the load line, which
is a plot of VcE and lc for a specified load.
If the load is resistive, the load line will consist of straight line segments
as in Fig. 5b (here, and in what follows, an ideal classB
circuit is assumed). The line 12 represents all values of VcE and lc during
the "on" halfcycle, and the line 13 shows that lc = 0 during
the "off" halfcycle. The slope of the line 12 is determined
by the load; if the solid line represents 4 ohms, for instance, the dashed
line would show 8 ohms.
An important property of the load line graph is that it also implicitly
shows the power dissipation of pr in the output device, since it relates
VCE to lc and pT = VCEle. During the "off" halfcycle, pT is obviously
zero. During the "on" half cycle, piis small when the output voltage
Vo is near zero (point 1 in Fig. 5b). As the output voltage
begins to increase, current flows into the load and lc increases. At first
pT increases, but since VcE decreases as Vo increases, pT begins to fall,
and when the crest of Vo is reached (point 2 in Fig. 5b)
pT is again very small. The overall dissipation is thus comparatively small,
and the operating conditions of the output device are quite favorable.
The situation is much different if the load is reactive. In a resistance,
current and voltage are in phase; but in a reactance, the current and voltage
are displaced from one another by the amount of the phase angle, and the
minima and maxima of the current and voltage waveforms no longer coincide.
If such a load line is plotted, the resulting curve is not a straight line
but becomes elliptical. As the phase angle increases, the ellipse becomes
broader (Fig. 6). A comparison of these elliptical load
lines to the resistive case yields some unwelcome facts. Consider the point
of zero V0, where VCE = V. For a resistive load, pT is zero (point 1 in Fig. 5b),
but for a reactive load there is a significant flow of lc at this point,
and hence considerable dissipation. Or take the "off" halfcycle;
here again there is a substantial flow of lc in the reactive case compared
to zero for a resistance. This is particularly undesirable, since the combination
of high VcE and high lc can initiate secondary breakdown, resulting in a
catastrophic destruction of the output transistors.
Additional insight can be gained if the curve of the maximum permissible
dissipationthe "safe operating area" (SOA) curveis added to
the diagram. This is done in Fig. 7.
The resistive load line (a) remains comfortably within the SOA. But a reactive
load of the same impedance magnitude (b) fills and even somewhat exceeds
the SOA. Reactive load lines in general use the available territory less
efficiently; they bulge out just about where the SOA curve dips inward.
It is a little difficult to get a quantitative picture from the load line
diagram, so in Fig. 8 the dissipation pT has been plotted
over one complete cycle, normalized to a peak output of 1 W (or 1 VA). The
dissipation is seen to increase substantially as the load phase angle increases.
With a purely reactive load (90°) the maximum pT is over five times as great
as for a resistive (0°) load. Integrating or averaging pT over time gives
the average dissipation pT, which determines the heat sink requirements
of the amplifier. This is shown in Fig. 9, with a resistive
load taken as unity. Here again there is a significant, if not quite so
dramatic, increase in dissipation as the load becomes more and more reactive.
It is now time to introduce a complicating factor. So far, operation at
full output has been assumed, but in fact the dissipation is a function
of output level. We can include this factor by introducing a "drive
factor" k, which varies from 0 to 1 (or 0 to 100 percent). Note that
k is in terms of voltage, not power. The dissipation as a function of k
is shown in Fig. 10. For a resistive load, the greatest
dissipation occurs at k = 63 percent output (40 percent of maximum power
output). As the load becomes increasingly reactive, the dissipation increases,
and the decline in dissipation near full output also disappears.
Fig. 1Impedance of a typical loudspeaker system.
Fig. 2Model of a power amplifier.
Fig. 3Bode plots for (a) resistive load, (b) inductive
load, and (c) capacitive load.
Fig. 4Load isolation networks, (a) RC and (b) LCR.
It should by now be abundantly clear that operating an amplifier into a
pure resistive load is far kinder, far less demanding, than is operation
into a reactive load like a loudspeaker. And these relationships apply,
let it be added, regardless of whether the output devices used are tubes,
transistors, or FETs. To put it another way, an amplifier which is to operate
without difficulty into highly reactive loads must be more conservatively
designed than would be expected on the basis of purely resistive loading.
It must also be borne in mind that the efficiency of realworld amplifiers
is less than the ideal case assumed in this discussion.
And speaking of realworld situations, it ought to be noted that this discussion
has tacitly assumed sinusoidal signals. For a variety of reasons, such signals
have great usefulness in analysis, but they don't correspond very closely
to either speech or music. Since the energy content of pro gram material
is generally less than a sine wave of equal peak amplitude, the dissipation
will in many cases be less than the curves we have seen would suggest. Unfortunately,
it is simply not possible to say how much. There are random signals which
can model program material quite well, it is true; but strictly speaking
impedance is defined only in the frequency domain, and the only signals
which would not involve treating a band of frequencies are the exponential
and the sinusoid. And once we have to look at a band of frequencies, the
precise nature of the load (its impedance versus frequency) would have to
be specified, making a general solution impossible.
A Special Case
Before we leave the subject of output stage dissipation, there is an interesting
special case that ought to be considered. So far we have allowed the phase
angle to vary while holding the magnitude of the impedance constant. A different
picture emerges if, instead, we require only that the real part of the impedance
remain constant. This is equivalent to saying that the magnitude of Z is
allowed to increase as we increase the phase angle, and is shown by the
dashdot line in Fig. 11. The dissipation in this case
is shown also in Fig. 11.
The solid curve represents the worstcase dissipation, obtained by letting
k be whatever value gives the greatest dissipation. The result is interesting;
the dissipation with any arbitrary reactive load under these conditions
never exceeds the value of dissipation observed for a resistive load.
In fact, for highly reactive loads (over about 51°), it actually is less.
We saw earlier that for reactive loads, the dissipation was greatest for
k = 1, and this condition is shown by the dotted line. Here again the worstcase
resistive load dissipation under these conditions would never be greater
than it would be for a resistive load equal in value to the minimum real
part of any complex load. The significance of this will be discussed later,
for it forms the basis for a rationalized loudspeaker impedance rating.
Fig. 5Load line graph.
Fig. 6Load lines for several load phase angles.
Fig. 7Load line graph with transistor SOA curve, (a) resistive
load and (b) reactive load.
Fig. 8Instantaneous collector power dissipation over
1 cycle of output waveform.
Fig. 9Average collector power dissipation as a function
of load phase angle.
Fig. 10Average dissipation as a function of drive for
several load phase angles.
Fig. 11Average dissipation as a function of load phase
angle for constant real part of load impedance.
Fig. 12Protection circuit characteristics, (a) threshold
curve, (b) with shorted output, and (c) with capacitive load.
The Protection Problem
Another important set of largesignal problems springs, somewhat ironically,
from what ought to be a good idea, output transistor protection circuits.
The kind of circuit which causes problems seeks to clamp 1 to some value
which is a function of the VCE at that instant. Such a circuit, whose threshold
characteristics are shown in Fig. 12a, permits the SOA
to be nearly fully utilized. A short on the output is clamped as in Fig. 12b,
and a purely capacitive load is prevented from exceeding safe limits as
in Fig. 12c.
Things are altogether different if the load happens to be inductive. Should
the protection circuit be activated in this case, an annoying and potentially
dangerous very loud popping sound results. These are the notorious "flyback
impulses" illustrated in Fig. 13. The impulses are
usually short (tens of microseconds) but of considerable amplitude. Since
they contain large amounts of highfrequency energy, damage to tweeters
is not unknown. These impulses can occur under seemingly unobjectionable
conditions, for example when the magnitude of the load impedance is fairly
high and hence the amplifier is only lightly loaded. All that is required
is that the load be inductive (i.e., the impedance is increasing with frequency)
and that it activate the protection circuit at some point.
Such flyback impulses come neither from the load nor from the amplifier
alone, but rather from the combination of the two. The ultimate culprit
is the negative slope of the protection circuit threshold. When the current
flow into the load is stopped by the clamping action of the protection circuit,
the tendency of the inductive load to produce a reversepolarity voltage
forces the protection circuit into even greater limiting. Suppose the output
were positivegoing at some point, and so VcE were decreasing. If now the
current into the load is clamped, the sense of the resulting load voltage
will be negativegoing. This implies an increase in V that in turn reduces
the current clamping level to a smaller current. A regenerative situation
exists, and the end result is that the output voltage of the amplifier tends
to slam into the clipping region with the opposite polarity. If one such
event does not dissipate the energy stored in the load, several pulses may
follow one another in rapid succession.
A number of solutions to this problem have been advanced. The basic idea
is to avoid having a negativeslope threshold at signal frequencies. One
approach places large capacitors in the protection circuit to slow it down
("delayed limiting"), avoiding a regenerative situation. Another
method is to use pure current limiting. A glance at the SOA curves shows
that this places heavy demands on the output transistors, even when the
current limit is made a slowly varying function of signal level. For this
reason, paralleled heavyduty output transistors must be used. The ultimate
expression of this line of attack is to use a great many, very rugged transistors
in the output stage so that protection circuits can be eliminated entirely.
(Tube amplifiers, of course, fall naturally into this category, since tubes
can withstand very large shortterm overloads.) And finally there is the "solution" of
simply making the protection threshold larger, but leaving the output stage
as is, on the assumption (or hope) that the overloads encountered in "normal
use" will be small enough not to destroy the poorlyprotected transistors.
Fig. 13Flyback impulses with inductive load.
The Practical Conclusion
We have seen some of the effects that reactive loads can have on amplifiers,
and we have noted some of the problems that can occur. The question remains,
what can be done about them? The smallsignal problems can be avoided by
sound design and thorough verification of an amplifier's stability before
the design is released for production. Amplifiers from reputable manufacturers
are usually free of problems.
Largesignal behavior is another matter. It would be easy to say that any
amplifier should be able to cope with highly reactive loads. But here we
come up against economic limitations. Power sells, and to remain competitive,
the temptation is very great to design the amplifier for very high power
into a resistive load at the expense of adequate and costly "elbow
room" for operation into reactive loads.
One possible solution would be for prospective purchasers to become more
aware that the usual power rating per se is only a part of the story. The
test reports in the several hifi magazines could be of real service here
by including reactive load measurements. Heavy capacitive loading has often
been used, but inductive loading seems conspicuously absent. A reasonable
approach would seem to be to use a set of loads at each rated impedance
and at several frequencies. These could be 1) a real load R equal to the
magnitude of the rated impedance Zr ; 2) an inductive load ZILI = 2Zr Z
+60°, and 3) a capacitive load Z(c) = 2Zr L, 60°. (In other words, R + j0
and R ± j 3X where R and X equal Zr at the frequency of measurement. Proposals
of this kind have appeared in the literature (Refs. 2, 5). Another very
worthwhile endeavor would be a clarification of the rather nebulously defined "rated
impedance" applied to loudspeakers. The most logical approach would
be to specify the minimum value of the real part of the loudspeaker impedance,
as suggested by Pramanik (Ref. 6). We have seen that the amplifier dissipation
with reactive loading will not exceed the dissipation observed with the
minimum real part of the impedance. Accordingly, such a specification represents
a useful and meaningful measure of the loading produced by the loudspeaker
on the amplifier.
Since this specification would not in itself alert a prospective user to
possible protection circuit problems in the case of a highly reactive loudspeaker,
there would continue to be a need for impedance data, in reviews if not
in spec sheets.
Such data should include the angle as well as the magnitude of the impedance,
or, as in Audio, the real and imaginary parts.
These proposals are suggested as possible ways to avoid or at least minimize
some of the problems we have seen in connection with the amplifierloudspeaker
interface. It is hoped that in the discussion, some light was shed on the
origin and nature of the problems as well as on some of the possible solutions.
The ultimate resolution of these problems depends, however, on the user.
Those who use amplifiers must become aware that presently used specifications
do not tell the whole story, and be ready to insist on complete specifications.
And perhaps we should also be content with an amplifier that appears a little
less powerful on paper, but which makes music come alive through a loudspeaker
and does so reliably and without fuss.
Acknowledgements I would like to thank all those within the industry with
whom I have discussed these problems. For particularly interesting and illuminating
discussions I would like to thank Peter Walker of Acoustical Manufacturing
(Quad), S. K. Pramanik of Bang and Olufsen, and Gerry Margolis of JBL; and
for bringing to my attention the "delayed" protection circuit
I thank J. H. Michel of Gerätewerk Lahr (Thorens/EMT).
References
1G. J. King, HiFi News and Record Review, Dec. 1976, p. 87.
2J. H. Johnson, "Realistic Specifications of Amplifier Output," delivered
to AES 56th Convention, 1977; AES Preprint 1201.
3S. K. Pramanik, "Specifying the LoudspeakerAmplifier Interface," delivered
to AES 53rd Convention, 1976; AES Preprint.
4A. N. Thiele, "Load Stabilizing Networks for Audio Amplifiers," Journal
of the AES, 24:1 (1976), p. 20.
5P. J. Walker, Letter, Wireless World, 81:1480 (Dec. 1975), p. 568.
6S. K. Pramanik, Letter, HiFi News and Record Review, Mar. 1977, p. 83.
(Source: Audio magazine, Aug. 1977, )
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