Variable Amplifier Impedance
Rod Elliott (ESP)
Introduction
Is this a project or an article? Since you may have arrived here from
either index, you might be a little confused. This is fine, as it has
elements of both, but lacks the in-depth analysis of other articles, and
also lacks the application of a final design that is common to my
projects. This is for the experimenter. No further work will be done to
refine formulae or produce "magic" spreadsheets to allow you to
determine the impedance that is best for a speaker / enclosure
combination or anything else. Readers' contributions are of course
welcome, and I would be interested to hear about any massive
improvements that were made to systems using these techniques. (Or minor
improvements, for that matter.)
The idea of being able to vary the output impedance of a power
amplifier has been around for a long time. I have used these techniques
for over 30 years in various designs, and much as I would like to be
able to claim otherwise, I was by no means the first.
The technique has been used to drive spring reverb units, and
various other transducers where current drive is preferable to voltage
drive. The latter is what we all strive for with power amplifiers - a
perfect (ideal) voltage amplifier has zero ohms output impedance, and
the amplitude does not change as the load varies. Loudspeakers are very
non-linear loads, and the impedance will change at different frequencies
for all sorts of reasons.
So voltage drive maintains a constant voltage across the load,
while a current drive circuit will produce exactly the same current into
the load - in both cases regardless of impedance. In reality neither
approach is ideal ...
- Voltage drive will produce greater power into the load as the
impedance falls, since the load voltage remains constant, and a lower
impedance means more current and thus more power.
- Current drive has exactly the opposite effect, so when the load
impedance rises, a greater voltage is needed to maintain the same
current. So with the same current but a greater voltage there is again
more power, but now it is with higher impedances rather than lower.
Most loudspeaker systems are optimised for voltage drive, however in
many cases "optimised" is overly optimistic, since they are just
assembled and the builder hopes for the best. A tweak here, an
attenuator there, and a Zobel network somewhere else rounds off the
process and yet another "world's best" loudspeaker system is born.
Not so much a real project as a field day for experimenters, this
article describes the methods you can use to tailor an amplifier to a
specific driver. Much is empirical (i.e. design by experiment, trial and
error), and although formulae are possible, the load presented by a
typical loudspeaker is very complex and leaves big holes in the final
result if the maths are allowed to take over. Having said that, good
results can be obtained by either method (theoretical or practical), so
here goes ...
Description
Figure 1 shows two amplifiers (shown as opamps), with (a) being
conventional voltage drive, and (b) is current drive. The output
impedances are in the order of zero ohms and infinite ohms in each case
(this IS a theoretical discussion at the moment!). The gain will appear
to be exactly the same for each into an 8 ohm resistive load, but will
change based on load
for the current amp. We shall see that this is not really the case -
some power is lost in the series feedback resistor. The voltage amp has
the same gain regardless of load.
Figure 1 - Voltage and Current Amplifiers
The feedback is applied differently to achieve the desired result, as
can be seen, although the difference is not at all subtle at first
glance, as you look more closely you will see that it really is a simple
rearrangement of feedback resistances. With the 8 ohm load, both amps
have a gain of 11, but the series feedback in (B) actually means that
the gain to the load is 10. With 1V AC signal applied, the voltage amp
will develop 15.125W (11V at 8 ohms) into the load. The current amp will
develop 12.5W (10V at 8 ohms) into the load, with 1.25W dissipated as
heat in R1. This will remain constant for all load impedances.
Where things get interesting is when the load impedance changes.
Should the load increase to 16 ohms (such as at resonance), the voltage
amp will produce the same voltage, so power is halved. The current amp
will provide the same current, so power into the load is increased
fourfold to 50W, with the same 0.125W lost in the series feedback
resistor. This of course assumes that the power supply voltage is high
enough to allow the amp to do this without clipping.
Likewise, with a dip in impedance to 4 ohms, the voltage amp will
provide double the power (30.25W - again assuming the supply can now
provide the necessary current), but the current amp will only produce
6.25W under the same conditions.
Which of these approaches is correct? For resistive loads it does
not matter - both will perform identically except for the slightly
lower gain of the current amp (this is easily compensated for). With
loudspeaker loads, neither is ideal. Power to the load will vary widely
depending on the impedance, which in turn depends upon frequency. The
voltage amp will create a dip in response at each frequency where the
impedance rises (and a rise wherever there is a lower impedance), and
the current amp will do exactly the opposite.
It is worth pointing out that the current drive system shown above should never
be used in practice. The open loop gain is effectively infinite, and
it will be prone to pick up radio and other interference. While the
technique is still perfectly valid, it can only work properly with
instrumentation systems where everything is anclosed in the one case.
For audio, use the following method ...
Mixed Mode Feedback
By applying a mixture of both forms of feedback, it is possible to
define the output impedance at any value between the two extremes. To
emulate a valve amp for example, an output impedance of about 4 to 6
ohms is needed, assuming an 8 ohm load (this is the assumed nominal load
impedance for all examples cited).
Figure 2 shows the arrangement used, and with the values shown
the output impedance is a bit under 4 ohms. We could simply use a 4 ohm
resistor in the amp's output, but this will waste much of the amplifier
power, which will be dissipated in the resistor instead of the load. The
same power output is available from a current amp as a voltage amp
(give or take a fraction of a dB to account for the series feedback
resistor).
Figure 2 - A Four Ohm Output Impedance Amplifier
As can be seen, there is minimal additional complexity to achieve
this result, and in my experience the final exact impedance is not
overly critical, given the "real world" variations of a typical
loudspeaker.
The no-load voltage is 18.8V with an input of 1V, and this drops
to 12.8 at 8 ohms, and 9.7V with a 4 ohm load. These voltages are
measured across the load, ignoring the voltage drop of the series
feedback resistor.
From this, we can calculate the exact output impedance from ...
| I L = VL / RL |
(where I L=load current, VL=load Voltage and RL=load resistance) |
| Zo = (Vu - VL) / I L |
(where Zo=output impedance, Vu=unloaded voltage, VL=loaded voltage) |
| |
| I L = 12.8 / 8 = 1.6 |
| Zout = (18.8 - 12.8) / 1.6 | = 6 / 1.6 = 3.75 ohms |
An approximate formula (provided by a reader) is shown below. According to this formula, Zout
is 3.77 ohms. This is not entirely in agreement with the result I
obtained above, nor with a simulation, but it will be more than
acceptable for the normal range of desired impedances.
| Zout = R3 * ( R1 + R2 ) / R2 |
(where R1, R2 and R3 are in the locations shown in Figure 2) |
So we have created an amp with an output impedance of 3.75 ohms, with
very little loss (just over 0.5W is lost in the 0.2 ohms series
feedback resistor with 20W output into 8 ohms). To see if this is
useful, we will now have a look at what happens when the load impedance
doubles or halves.
With a 16 ohm load, the power into the load falls to 14.6W, or
about 1.37 dB. Contrast this with the conventional low impedance amp
whose power will fall by 3dB (i.e. half).
When the impedance is reduced to 4 ohms, the output power is now
23.5W (an increase of 0.7dB), while a conventional amp would be
producing 40W - an increase of 3dB.
Somewhere, there is a magical impedance that will give almost the
same power into any load from double to half the nominal, give or take a
dB or so. I am not about to test all possibilities, but having
experimented with the concept for many years I am quite convinced that
there are practical benefits to the use of modified current drive, where
the impedance is defined. The exact impedance will depend to a very
large degree on just what you are trying to achieve.
Further Applications
It has been suggested that loudspeaker intermodulation distortion is
dramatically reduced by using a high impedance source (but by whom I
cannot recall - I do know that one site I looked at was Russian, and a
reader sent me a translation many months ago). I have experimented with
this idea to some extent, but have been unable to prove that this is the
case - at least with the drivers I tried it with.
This does not mean that the claim is false, but I am unable to
think of any valid reason that could account for such driver behaviour.
It is interesting anyway, and some of you might like to carry out a few
experiments of your own. I would be most interested to hear about your
results should you decide to test this theory - preferably more
thoroughly than I did.
By adjusting the impedance of an amplifier, the total Q (Qts) of a
loudspeaker can also be altered, so driver behaviour in a given sized
box can be changed. This can be used to adapt an otherwise unsuitable
loudspeaker to a speaker enclosure, but does have limitations in terms
of the overall variation that can be achieved.
More variation can be achieved by virtue of the fact that it is
now possible to either retain or increase the power delivered to a
loudspeaker at resonance, so that the ultimate -3dB frequency may be
lowered from that theoretically claimed for a loudspeaker / enclosure
combination. Care is needed, since too much additional power will make
the speaker boomy,
and usually additional internal damping is needed to compensate for the
minimal damping factor provided by the amplifier. With the amplifier
output impedance set at 4 ohms, damping factor into an 8 ohm load is 2 -
a far cry from the figures of several hundred typically quoted. These
(of course) fail to take into consideration the resistance of the
speaker leads, and loudspeakers themselves are usually compromised by
the crossover network, so the damping factor is not always as useful as
it might seem.
The results of using modified impedance can be very satisfying,
allowing a useful extension of the bottom end. My own speakers are
driven from a 2 ohm amplifier impedance, and there is no boominess or
other unpleasantness, but a worthwhile improvement in bass response is
quite noticeable.
Negative Impedance
Again, this has been about for many years, but I have only found one
driver type that seems to obtain any improvement from its use - horn
loaded compression drivers. All cone speakers (including horn loaded)
sound worse with negative impedance, but you might have some weird
driver that can benefit from a negative impedance amp.
As the name suggests, when a negative impedance amp is loaded,
the output voltage rises. The greater the load, the more output is
applied. This is very risky, and negative impedance amplifiers can
easily oscillate when connected to a reactive load such as a
loudspeaker. Indeed, negative impedance oscillators have been with us
for many years in RF (and other) work, and there are quite a few
electronic components that exhibit negative impedance. So, not new, but
interesting.
Figure 3 shows how the circuit is rearranged to accomplish this
most bizarre of ideas. By simply substituting the "real" earth
connection for the junction of load and series feedback resistor, the
voltage developed across the resistor now increases the gain by adding
to the input signal voltage.
Figure 3 - A Negative Impedance Amplifier
This circuit with the values as shown will provide an open circuit
load with 11V (as with a conventional amplifier as shown above), but
when the load is applied the voltage increases as the load resistance is
reduced. With the values shown, the load voltage will increase from 11V
to 14.7V with an 8 ohm load, rising to 22V with a 4 ohm load. A quick
calculation using the formulae above will show that the output impedance
is about -2 ohms.
The negative impedance amp is by its very nature unstable - the
output voltage will continue to rise as the load is reduced, until at
some point positive feedback exceeds negative feedback and the circuit
will oscillate. Another undesirable side-effect is that distortion is
increased, because negative feedback (which reduces distortion) is being
counteracted by positive feedback. Again, this is a non-linear
function, and the results are unpredictable at best. Reactive
loudspeaker loads can cause a negative impedance amp to oscillate,
either at the frequency between the loudspeaker's resonance and box
resonance (where impedance falls), or at some other frequency determined
by crossover components. Such oscillation can damage speakers (and
ears!), so care is needed to ensure that this cannot happen. Low values
of negative impedance (not less than -4 ohms) are strongly recommended.
I have found that only relatively small amounts of negative
impedance are useful in practice. For example, one could use negative
impedance to remove the resistance of the speaker cable and crossover
components, although the results will not be as good as expected, and
probably far worse. Even with a negative impedance of about 1 ohm, most
speakers will show signs of "displeasure", and amplifier distortion will
be increased - usually by an amount that is disproportionate to the
feedback factor.
Conclusions
This "project" is not really a project at all (which is why it has
also been included in the articles index), but more of a starting point
for experimenters. The circuits shown will all work with "real"
amplifiers, but great care and considerable testing are needed to ensure
that the results you actually obtain are providing a real benefit.
It is too easy to make a change such as shown here, and fully
believe that the result is an improvement, where in reality (as
eventually discovered after extensive listening and comparison) the
opposite is true. While negative impedance may be found useful for horn
compression drivers, it is unlikely (in my experience) to provide any
benefit at all to cone loudspeakers.
Positive impedance can produce an improvement in bass response,
but the cost can be high - boomy, over-accentuated bass at resonance,
usually accompanied by a loss of bass "speed" and definition. There will
be more freedom for the speaker cone to waffle about after the signal
has gone ("overhang"), and it is rare that a speaker driven by a higher
than normal impedance will perform well without additional damping in
the enclosure.
There is no doubt that at output impedances in the order of 4 to 6
ohms your amp will sound more like a valve amp (but without the
distortion), but it is up to you to decide if this is what you really
want to do. The technique works well for guitar amps, as it allows the
speaker to add its own colouration to the sound, which adds to the
overall combination of distortion and other effects to produce pleasing
results. For Hi-Fi the case is less clear, and experimentation is the
only way you will ever find out for sure.
Interestingly, some lunatics from the Tymphany Corporation in the
US have decided that they are entitled to a patent on the general ideas
shown here. Despite the copyright notice below that specifically
prohibits commercial use, and without asking permission or thinking
rationally, Tymphany has used this article as a reference in the patent,
and the US Patents Office granted it! Well apart from the fact that the idea is common knowledge, their idea is quite obviously not appropriate for a patent - everything
they claim has been done before. They do rabbit on about using DSP to
tailor the amp behaviour depending on frequency, but so what? Others
have done the same things long ago, although without the DSP in most
cases.
That the patent would fall like a house of cards in a court of
law is quite obvious. I for one cannot believe the gall and audacity of
anyone to obtain a patent based on material that fully describes the
patent in prior art and/or websites. In typical patent verbiage, they
basically claim that the patent is for a mixed-mode amplifier (as shown
in Figure 2). If you want to read the patent (so that it may be violated
in full and without fear of recrimination) I have a copy right here. Enjoy 
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Post By：2010-9-12 11:19:36 [只看该作者]
