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Transconductance Power Amplifier Systems for Current-Driven Loudspeakers

Authors:

Abstract

Moving-coil loudspeakers generally provide a substantial improvement in linearity when current driven, together with the elimination of voice-coil heating effects. Consequently there is a need to investigate low-distortion power amplifier topologies suitable for this purpose. After considering established current feedback approaches, a novel method using a common-base isolation stage is outlined and extended to show a prototype amplifier circuit in detail. In addition, the elements of a two-way active current-driven system are described, with low-frequency velocity feedback control derived from a sensing coil. The coupling error between this coil and the main driving coil is nulled by electronic compensation.
PAPERS
TransconductancePowerAmplifier Systems
for Current-DrivenLoudspeakers*
P.G. L. MILLS
Tannoy Limited, Coatbridge,Strathclyde ML5 4TF, UK
AND
M. O, J. HAWKSFORD
University of Essex, Wivenhoe Park,Colchester, Essex, C04 3SQ, UK
Moving-coil loudspeakers generally provide a substantial improvement in linearity
when current driven, together with the elimination of voice-coil heating effects. Con-
sequently there is a need to investigate low-distortion power amplifier topologies suitable
for this purpose. After considering established current feedback approaches, a novel
method using a common-base isolation stage is outlined and extended to show a prototype
amplifier circuit in detail. In addition, the elements of a two-way active current-driven
system are described, with low-frequency velocity feedback control derived from a
sensing coil. The coupling error between this coil and the main driving, coil is nulled
by electronic compensation.
0INTRODUCTION At higher frequencies, nonlinearity occurs as the coil
inductance is modulated by movement in the magnetic
The moving-coil drive unit can readily be shown to circuit and by other effects such as magnetic hysteresis
benefit in terms of linearity when controlled by a current [4]. Measurements under current drive have shown, in
source rather than the more conventional voltage source, comparison with voltage drive, a high-frequency dis-
Throughout this paper we will term this mode of op- tortion reduction of typically 20-30 dB for a bass-
eration current drive, whereby the amplifier source midrange drive unit.
impedance can, to all intents and purposes, be consid- These performance advantages arise from the coil
ered infinite compared to the drive unit impedance, resistance and inductance being totally eliminated from
Of the drive unit error mechanisms that can be the system transfer function. The force on the cone is
countered by current drive, the voice-coil resistance proportional to the voice-coil current, not the applied
is of particular interest. As a result of self-heating in voltage. Analysis also shows a reduced dependence on
excess of 200°C, the increase in coil resistance leads nonlinearity within the force factor and mechanical
to sensitivity loss (often referred to as power com- impedance of the drive unit.
pression [1], [2]), -loss in electrical damping of the Thus as a result of the performance gains that can
fundamental resonance, and crossover filter misalign- be demonstrated using current drive, there arises the
ment. In their paper Hsu et al. [3] concluded that a need to investigate suitable power amplifier topologies
satisfactory method of compensating for the effect had to make the best of the technique. This paper therefore
yet to be found, aimsto review someof the earlier publishedworkon
transconductance amplifier design, while presenting
new topologies and detailed circuitry of a two-way
* Manuscript received 1988 July 6. This paper expands active prototype system. In addition, due to the loss
on some areas covered by the authors in "Distortion Reduction
in Moving-Coil Loudspeaker Systems Using Current-Drive of voice-coil damping under current drive, control cir-
Technology," volume 37, number 3 (1989 March). cuitry for restoring damping by means of motional
J. Audio Eng. Soc., Vol. 37,No. 10, 1989 October 809
MILLSANDHAWKSFORD PAPERS
feedback applied to the bass-midrange drive unit is in conjunction with a floating sensing resistor in order
described, along with the low-level crossover circuitry to maintain current feedback.
of the prototype system. Another technique used in implementing transcon-
ductance amplifiers involves the combination of supply
I POWER AMPLIFIER TOPOLOGIES FOR current sensing around a follower, together with current
CURRENT DRIVE mirrors feeding the load [9]. The arrangement is shown
in Fig. 2, where Rf is a dummy load and the transcon-
1.1 Review of Transconductance Amplifier ductance is again defined by Eq. (1). Operation of the
Techniques circuitistypicallyinclassAB.
A transconductance power amplifier requires a high While suitable for low output currents (<50 mA
output impedance that is linear and frequency inde- peak), the approach is difficult to extend to the levels
pendent. It must also possess the attributes of a con- required for driving a loudspeaker (typically 5 A peak
ventional voltage power amplifier such as high linearity, or more) due to the linearity of the mirrors and also
wide bandwidth, freedom from slewing-induced errors, power loss in Rf. Although the mirrors could be arranged
and insensitivity to load variations (be they linear or to provide current gain and could be partially linearized
nonlinear), by error-correctiontechniques [10], the techniqueis
The most commonly used technique to obtain a high not felt to offer a particularly practical solution.
output impedance is to apply current feedback around
a conventional power amplifier by means of a sensing 1.2 Methods Using a Common-Base Isolation
resistor in the loudspeaker earth return [5], [6], as il- Stage
lustrated in Fig. 1. The transconductance gm is defined The approach devised to overcome the limitations
cited as being inherent to existing topologies is illus-
1 trated in basicformby Fig. 3. The notableaspectof
gm = R_ ' (1) this strategy is the open-loop grounded base stage, which
isolates the load ZL from the main amplifier Atwhile
The method has also been used in high-current in- providing a naturally high output impedance without
dustrial applications. There are two main disadvantages the use of overall current feedback. In addition a cascade
with such a system. First, the open-loop gain of the configuration is formed in conjunction with the output
amplifier is frequency dependent as a result of the am- devices in the main amplifier At. Resistor Rf defines
plifier's dominant pole, and this is reflected in the output the transconductance, driven from amplifier At, a voltage
impedance. Second, the loudspeaker impedance, which source, which may operate with low values of supply
is both frequency dependent and nonlinear, tends to voltage + Vsl to reduce power dissipation. The loud-
modulate the transconductance of the amplifier. The speaker is referenced to ground and isolated from any
fact that the load is not ground referenced may be con- feedback loop used to linearize the amplifier At. A1-
sidered inconvenient in some applications, though a successful prototype based on this scheme
A refinement of the basic technique was described has been constructed, with amplifier At running in class
in Lewis [7]. The circuit was symmetrical in nature, A and with a class AB outputstage, it is to some extent
using two current-sensing resistors, with a ground ref- an uneconomical solution due to the need for two pairs
erenced load fed from MOSFET output devices. Good of floating power supplies.
linearity was indicated at 10-W average power into a
5-g load. However due to class A operation, the design
would be inefficient at the power levels necessary for l 'vcc
a moving-coil drive unit (between 50 and 100 W typ- current }
ically). Caremustbe takento minimizeoutputoffset mirror
currentwiththisscheme. __J t
Afurther ground-referenced current feedback scheme [
was described in Nedungadi [8], but this required the PI_ Ip Ip
complexity of a differential voltage-to-current converter
_11 voltage _12 _13
Io !_ 2 3
Via
o
_- N _IN IN
ZL
--I [.
f mirror
- i-Vcc
Fig. 1. Basic current-feedback-derived transconductance
amplifier. Fig.2. Voltage-currentconverter.AfterRaoandHaslett[9].
810 J, Audio Eng. Soc., Vol. 37, No. 10, 1989 October
PAPERS AMPLIFIERSFORCURRENT-DRIVENLOUDSPEAKERS
A more viable alternative is the revised topology rations [11], described how transformer-derived feed-
illustrated by Fig. 4. This circuit takes the form of a back could be used to generate transconductance and
current amplifier of current gain current gain functions, as shown in Fig. 5. In Fig. 5(a)
resistor Rf is still necessasry in order to define the stage
Rx transconductance.
ct - Rf (2) Although no research has been directed in this area
and the approach is only conceptual in nature, it may
The first-stage power supply + Vst is ground ref- be worth further investigation, given a wide-bandwidth
erenced, unlike the previous case, meaning that several transformer design.
power amplifiers within an active system may share a
common supply, thus reducing complexity and cost. 2PROTOTYPE AMPLIFIER SYSTEM
Like the previous scheme, the current flowing in the
transconductance defining resistor Rf is that which flows 2.1 General Overview
in the load ZL, except for any base current lost to ground The two-way active loudspeaker system constructed
in the common-base stage. The fact that the amplifier to validate the basic approach proposed for high output
Aiis referenced to the input of the common-base stage impedance power amplifier design was based on the
and not to ground tends to decouple it from any distortion Celestion SL600 loudspeaker. In this section the current
appearing at the emitters of the common-base stage, gain power amplifier is considered in detail along with
This topology forms the basis of the prototype system, the necessary transconductance preamplifier, while Sec.
the detailed circuitry of which is described in Sec. 2. 3 considers the associated motional feedback control
On a practical note, it is important to provide adequate circuitry, which is required for the bass-midrange drive
current gain in the common-base stage in order to pre- unit.
vent nonlinear current loss to ground, which introduces Throughout the design, the underlying philosophy
distortion, has been to use symmetrical direct-coupledcircuitry
to give good transfer function linearity without recourse
1.3 Alternative Approaches to high levels of overall negative feedback [12], [13].
All of the circuits described so far rely on a current- DC stability is taken care of by servo amplifiers (feed-
sensing resistor to define the overall system transcon- back integrators).
ductance. Even when this resistor is of a low value
(about 1 FZ), it still tends to dissipate an appreciable 2.2 Transconductance Preamplifier
amount of power. This element would at first seem to Fig. 6 shows a two-stage design, the basic topology
be fundamental to the design of a transconductance of which has often been used with overall feedback as
amplifier, but it is interesting to note the possibilities
of transformer-derived feedback in perhaps reducing o
suchlosses. · .R_
Nordholt, in his classification of feedback configu- lVin
1
Vino
Iout 1
g ictrcodencporamierusn
grounded-baseoutputstage, c _ : _ 1
Iin ' out
1
--_[J,JZL
)lVs_ j. Vsz - - -
[ our n 1
_IVs_ Vsz Iin
(b)
Fig. 5. Transformer-derived feedback systems. After Nordholt
Fig. 4. Alternative configuration for current gain. [11]. (a) Transconductance stage. (b) Current gain stage.
J.AudioEng. Soc.,Vol.37, No. 10,1989 October811
MILLSANDHAWKSFORD PAPERS
I
a voltage gain stage [14]. It is operated here open loop nulling output. These are only required for low-fre-
to provide a high output impedance and consequently quency use, and their function is described in Sec. 3
must be capable of good linearity, when considering the velocity feedback control cir-
Transistor pairs Q3/Q4 and Qs/Q6 form cascodes to cuitry.
increase high-frequency linearity and give a high output
impedance. Bias arrangements for the cascode are 2.3 Current Gain PowerAmplifier
somewhat unusual in that resistors R14and R15are not The current gain power amplifier, which accepts the
returned to the supply rails, but are connected to the output of the transconductance preamplifier, is based
emitters of the common-emitter part of the cascode, on the structure shown in Fig. 4. For the purpose of
thus avoiding nonlinearity from base current loss in description, it is split into three sections: input amplifier,
the common-base devices [15]. This reduces high-fre- power follower, and common-base output stage. Both
quency distortion by typically a factor of 10 at 20 kHz input amplifier and follower are represented by the gain
over the conventional bias method, block Aiin this simplified representation.
Operational amplifier ICl with associated passive We consider first the input amplifier, Fig. 7. This is
components forms a current-sensing differential servo essentially the same topology as the transconductance
amplifier to null any output offset current due to im- preamplifier, but with a few refinements. Input stage
balances in the main circuit and has no effect on per- biasing is'performed with current sources based around
formance within the audio band. This configuration of transistors Q] and Q2, instead of resistive biasing. This
servo amplifier, to the authors' knowledge, has not is a result of the need to provide immunity to the greater
been seen before in the literature, level of supply rail contamination caused by class AB
At frequencies within the passband of the amplifier, operation of the power follower stage. The output from
the transconductance gm may be approximated by the the transconductance preamplifier is fed to the emitters
expression of the input devices Q3and Q4, which thus operate in
common-base mode. The first and second stages of the
lout R6 amplifier are coupled together by current mirror pairs
gmVin Rl](R8/2 + Ri0) (3) Qs/Q8 and Qo/QI2 to reduce loading effects and inter-
action between the two stages. These mirrors are them-
With the component values shown, gm _ 4 mS. selves linearized by local error feedback correction
In addition to the main input and output, an auxiliary consisting of transistor pairs Q6/Q7 and Qlo/Q ]1. This
velocity feedback input is provided along with an error- approach has been previously documented [10], al-
i i O +V'== /_'v
¢q, C_
q._? i 3_3 35ol
_L _L
0a
6clt_.
q,
0£1/
_Our,'.*' { t.f
_1_00.Ag4,°t.tKt£,_ Or'_LY/)
_-q----}_l. i C ],t o ro_6-to &,oEr_
Tii_ _mP_tft_
V.. t?tT_
r4a,,oi_eu'r
6fo_
Or
lOz6wg_.
{21 { l: =
8ct't_
O 3X3 3Jo; C,_C;I
u'...... rtr/_ '?0,,"}]t°°rl
.._.rr ( f.co-[/cc ff'v
AM_l.atit.._ o_Lr_
[
t_j. r'_. : I_, LKA_PCtftE_
_'lff HF AN_CIItI_I_
Fig. 6. Transconductance preamplifier.
812 J. Audio Eng. Soc., Vol. 37, No. 10,1989 October
s
PAPERS AMPLIFIERSFORCURRENT-DRIVENLOUDSPEAKERS
though in this case some current gain has been intro- Qi6 and Q17. Further linearization is achieved by current
duced into the mirrors to enable correct quiescent op- mirror transistors Q25 and Q26, which form a negative
erating conditions to be established in the first and feedback loop, thus reducing the source impedance
second gain stages, seen by output Darlingtons Q3o and Q31.
The outputs from the cascode pairs Q8/Q13 and Q12/Moving now to Fig. 9, which shows the output com-
Q14are displaced _+4 V about ground by green LEDs mon-base stage, the preceding follower drives current
D1-D4, in order to bias the next stage. Resistor R28 through resistor Q67, which in conjunction with R2
and capacitor C3 are included to define the open-loop (Fig. 7) sets the midband current gain of the complete
gain characteristics of the amplifier, to ensure that sta- amplifier to around 800. Inductor L2 serves to reduce
bility is maintained under closed-loop conditions, the high-frequency current gain of the amplifier to ensure
Fig. 8 shows the next section, which is a follower stability. The current in R67 flows into the common-
with extensive error-correction circuitry and is essen- base output stage, consisting of Darlingtons Q32 and
tially similar to a previously published topology [16], Q33, along with driver devices Q36 and Q37, the bases
but with improvements to biasing arrangements. It is of which are referenced to ground. Except for any cur-
worth briefly reviewing the principle of operation, rent loss to ground, such as through the bases of these
Transistor pairs Qi6/Qi8 and QiT/Q19 form a Dar- devices and through the biasing current sources (Q34,
lington follower, preventing loading of the previous Q35), the current in R67 flOWS through the load via
stage and driving the Darlington output devices Q30 floating power supplies _+Vcc2.
and Q3]- Transistors Q28 and Q29 form Vbemultipliers In order to establish a low-output offset current for
to bias the output Darlingtons, but are also configured the amplifier (typically less than + 2 mA), a servo based
as error amplifiers, which together with Q22 and Q23 around ICl and referenced to the input of the common-
form the main error feedback loop, delivering a cor- base stage, is used to feed a dc compensation current
rection current through resistors R38and R7s in response back to the input of the amplifier.
to any nonlinearity in the output devices Q30 and Q31. To prevent switch-on and switch-off transients from
R48 is included as an adjustment to achieve the best reaching the load, relay RL1 is included, controlled by
distortion null. a time-delay circuit on startup and almost instanta-
In order to linearize Q]8 and Q19, which have to neously dropping out on power down. The control cir-
drive the output Darlingtons, additional error correction cuitry to perform this function is not shown.
in the form of feedforward is applied with the aid of The power amplifier together with the transcon-
Q20 and Q21, in combination with the input transistors ductance preamplifier was evaluated in terms of standard
1)$ /_q. Oot
_2£v(_-vcte)
_, c,R,, ,%jtr_?TT ....
?v
cfIn
c&gf_ Rt+
_tsu _'r 3Yo_06 _ ¢2_
Rr O, g2_.2#2
25,'_toa'f _*l.?.Sllol_.s'
MPSu_'5'
%/t:::
61t_'
t t
Rt _.7oa 2>2
R_oD3
lgo_t_:.s
_s
_2_ 2_ x
Q_
Cat_l o!
[72'lO011 69Cto
lOoO
I-2_'v ¢- v,, _)
_I t._oos
Fig. 7. Prototype amplifier, input stage.
J. AudioEng.Soc.,Vol. 37, No. 10,1989 October 813
MILLSANDHAWKSFORD PAPERS
measurements and found to be comparable with a typical 3 VELOCITY FEEDBACK CONTROL SYSTEM
high-performance conventional amplifier. The results
are as follows: 3.1 Outline Approach
In order to compensate for the loss in electric damping
of the bass-midrange unit caused by the high amplifier
Ratedpoweroutput output impedance, velocity feedback was used to restore
(8-_ resistive load) 75W average
Totalharmonicdistortion damping [5], [6]. While many forms of sensing ar-
at ratedpower rangement have been described ([17]-[23], for ex-
20Hz -79 dB ample), themethod adoptedhere is attractiveforreasons
1kHz - 86dB
20kHz -68 dB of mechanical simplicity and cost effectiveness. The
Intermodulationdistortion technique used is to wind a sensing coil over the main
(19 and 20 kHz at equal levels voice coil of the drive unit. The output voltage of the
atratedpower) -86 dB
Humandnoise(remaximum sensing coil will ideally be defined by
output) -90dB
Small-signal bandwidth, -3 dB 0.1 Hz to 50 kHz Vs = (B1)sU(4)
Output impedance*
20Hz 4.1M_
1kHz 106 k_ where (B/)s is the sensing coil Bl product, N/A, and u
20 kHz 11.4 kf_ is the cone velcity, m/s.
* From computer simulation, due to the difficulty in Unfortunately an error is induced in the sensing coil
performing these measurements, by transformer action from the main driving coil. In
the previously documented work induced errors were
It is interesting to note that the distortion measure- overcome by neutralizing coils or by an altogether more
ments may only easily be made indirectly by converting elaborate mechanical arrangement to physically isolate
the output current to a voltage, by means of a resistive the driving and sensing coils. With the approach con-
load bank. The measurements as shown will thus reflect sidered here, a procedure of electronic compensation
any nonlinearity in the load. has been chosen in order to avoid expensive tooling
The protective features, consisting of output fuses costs for a specialized drive unit.
and relay contact, should not introduce any degradation The physical arrangement of the assembly is shown
in performance, as they are in series with a high source in Fig. 10. It should be noted that in this case, the
impedance, which is not the case with a conventional sensing coil follows roughly the same BI profile as the
power amplifier, main driving coil, so the action of velocity feedback
O f'2_v
ct2¢ _/oon(*v"O
9tAS = =
I_'OR 2IR
Qt_ Q2_'mPSus'g
2Sc'l_'O_' j
_1_ -- _)._0HTIIOI$
mPsaof
Q2o Qlz8cto7R,,._ R_o
R3V 370.q
F_o_o/aA_Jt_Ct_'t.t. ]Rcf
3_OR Cu In tqjft /fOR J82oR
too4
_Rlui.._$T_r_.E R$2fitO_TPt_T'TO
_._Ol{Cotw_ot46AS_
tooR C,vuc_) Lt (,.'-_o_
Ctlfa R_.o :}_0._
_j QI'/
£a0,,4o/!O 3_o_8c2/t e
(IIF_l& MeS.o$'
If;OR _20R 2_SZ i i
IOoo
,C_.7 *7°,_TTo_2_.v(_Vccl_
(_/*)
Fig. 8. Prototypeamplifier, follower stage.
814 J. Audio Eng. Soc., Vol. 37, No. 10, 1989 October
PAPERS AMPLIFIERSFORCURRENT-DRIVENLOUDSPEAKERS
does not improve linearity above that already afforded ·
by the current drive.
If a longer sensing coil could be accommodated (or
indeed a very short coil that remained well within the
magnet gap), a further reduction in distortion would
be possible.
3.2 Coupling Error Compensation
In order to investigate the nature of the transformer
coupling error, Fig. 11 shows the error magnitude with
respect to frequency for the coil assembly at equilibrium
and also at both extremes of travel. For this measurement
the driving coil was powered from the prototype trans-
conductance amplifier system. The level of error is Fig. 10. Sensing-coil assembly.
seen to be frequency dependent, rising initially at a
rate of approximately 4.6 dB/octave. This unusual
characteristic is considered to be a function of pole- AmpLitude-27
piece coupling with the magnetic circuit, but a full _Bv
A - coil fuHyin (toward · _._
analysis of the mechanisms at work has not been un- ._qnet) . ___
.......... ]B - coltin centre position ] _/_
dertaken. In addition, some positional dependence of c- coilfullyout(owoy / /
the errormagnitudeis also apparent.At 100Hz[he
couplederroris around 15 dB belowthevoltageap- :..f_omj__..
pearing on the driving coil, thus illustrating the need
06
for an effective compensation system. /o;v
To implement the compensator, it is necessary to
derivea signalproportionalto the currentin the driving A : :.......... : :
coil and to subjectthissignalto thesamefrequency
dependence as the error mechanism itself in order to
null the error from the sensing coil output. The variation -_7
START: 20 HZ 8W: 2.5 HZ STOP: 1 020 HZ
in error level with displacement (typically + 3 dB) has Frequency
not been accounted for. Fig. 11.Measuredtransformercouplingerror.
t{_3
3f try_t.¢,'4P$ct_'_'
,u,,,,
eog_,rL_ g?+ ['tr_v
I(+v.o
i,vtu rF'n'o_0tl_( Ntg_t,i
roc.oo_act? il. t(ir_.,,_,t,
t?_&$j_ 036RI-lc _')
t
--oTo--
a -- gzfa'_ R_4; 180_
( £E_.) _[f Qdo_ 037
t_uto
/
Pr/-er _$S
t
PtPSuor_
o -.Z_v(-V.Q
Fig. 9. Prototype amplifier, common-base stage. Protection relay contacts RL_ are shown with amplifier shut down.
d. Audio Eng. Soc., Vol. 37,No. 10, 1989 October 815
MILLSANDHAWKSFORD PAPERS
Fig. 12 illustrates the general approach to synthesis of the transconductance preamplifier (Fig. 6). Thus the
of the frequency-dependent element of the compensator, input to the compensator is proportional to the drive
A number of first-order sections are combined, with unit current. This differential signal is converted to
pole-zero locations set to produce a slope approxi- single-ended format before the 4.6-dB/octave weighting
mating that desired. The general circuit configuration is applied by the circuitry based around ICld. R22 pro-
to give this response is shown in Fig. 13 for an nth- vides an adjustment to enable the best error null to be
order compensator. The transfer function of this circuit obtained with a static motor coil assembly connected
is written to thevelocityfeedbackinput.
In order to maintain stability of the closed-loop sys-
_( _ rem, a second-orderlow-passfilter at500Hz isincluded
Vout _ jtoRC_ _ (5)
Vin r=0 1 + jtoRrCr/' in the feedback control loop. This also has the benefit
of reducing any residual transformer coupling error at
A software optimization routine was used to select high frequencies, where the compensator is no longer
component values in order to match the 4.6-dB/octave as effective due to the changing slope of the error.
slope required. For a 6th-order compensator, the corn- Finally the output of the controller is summed with the
puter-predicted frequency response is shown in Fig. main signal at the velocity feedback input of the trans-
14, which also lists the nearest preferred value corn- conductance preamplifier, with R27 (Fig. 15) providing
ponent values chosen. The result is deemed more than an adjustment of the low-frequency Qalignment.
adequate for our purposes, bearing in mind that some To illustrate the performance of the velocity feedback
positional dependence of the coupling error is present, control system, a number of frequency and time domain
together with a gradual deviation from the idealized measurements were obtained. First, Fig. 16(a) shows
4.6-dB/octave response with increasing frequency.
Amplitude
3.3 Complete ControlSystem (,ogscote) re®mstope._.-
We continue by consideringthe complete velocity .._
feedback control system shown in Fig. 15. The sensing
coil (source impedance 28 _) is connected to a high
input impedance buffer stage IC2a via an attenuator .-
network to avoid overload. IC2b forms a summing am-
plifier in order to subtract the signal derived from the
coupling error compensator, z_ Pi z2P2 Z) P3 Z_. Pt, Frequency
The compensator input is differential, accepting the (tog_co_e)
voltage across the serve current-sensing resistor R18 Fig. 12. Basis for synthesis of coupling error compensator.
[o Ro
II
[1 R1 R
II _ __
Vinl oE2 R2 I_
II _ _ lVo_t
; ' i
I
-- i Cn Rn
i II rn-- --
Fig.13. General configuration for nth-order compensator.
Amptitude (dB) Phase (degrees) c_ponentvalues (npv):
lB, ;.................. i ................ i ................. 7................ :tBS,
% = 330kn
i i ,m,"'y ' .....
Ra = 5.1 kO
Rs :39 n
i i i,/; : c0 .....
-15,,.......................................................................,,.j _, c, ,so._
c2
c3 68 nP//ll.? nF
c5 39 nF
iii i .............................................
40, :...............:.................'............... '................'-180,
16, 47,287 223,81 1,g5741<5,1{
Frequency {Hz)
Fig. 14. Computer-predicted response of compensator.
816 J.AudioEng.Soc.,Vol.37,No.10,1989October
PAPERS AMPLIFIERSFORCURRENT-DRIVENLOUDSPEAKERS
lC,((O.'- - O * _'_c /_'_'
C........ CS)c_c_
·w4"v O_Q R_Jk$Rt J_$_12ZOn _o,_.{JOirICl C_) tOOn Cl_'
Ce./)_On _.201_ '[_ 00V
c/_Ctz
r,o~ --0[]--1 *,,'* _,},g___[
TRR_5. _ 1_'?-tCtj ,ir
cJr &_n
$1t._
,,_ *--[] _,-,-[-._ Oo/,,-.
,t I_ YRA_$co_auc ?_t_cE
Fig,15. Velocity feedback control system.
AmpLitude AmpLitude
-tS -15 ,
dBvd_v
dB dB
/OlV /OlV
-55 -55
START: 20 Hz 8w: 2.5 HZ STOP: I020 Hz START: 20 HZ BH: 2,5 HZ STOP: 1 020 Hz
X: 62.5 HZ Y:-15.43 dBvFrequency X: 62.5 HZ Y:-15.49 OBv Frequency
(a) (b)
Amplifude
-: 5 /_%
\
/\
/'/
/OlV I
%
......
START: 20 m_ _W: _ 5 HZ STOP: _.020 HZ
×: 625 _7 'f: 15.69 dBv Frequency
(c)
Fig. 16. Velocity feedback control signal. (a) Sensing-coil output voltage. (b) Addition of compensator. (c) Addition of
compensator and low-pass filter.
J. AudioEng. Soc.,Vol. 37, No. 10, 1989 October 817
MILLSANDHAWKSFORD PAPERS
the output of the sensing coil, corresponding to velocity, Amptitude
20
with frequency. Thepeak at 62.5 Hz correspondsto .....
thedriveunit-enclosure fundamentalresonance,while
the risinghigh-frequencyoutputis due to thecoupling
error betweendrive and sensingcoils. Fig. 16(b)shows ,2,t
the addition of the coupling error compensator, giving ....
a much reduced spurious high-frequency output. The
further addition of the second-order low-pass filter at
500 Hz gives the response of Fig. 16(c), which is close -2°
to an idealizedvelocity function, s.........._............ T_me
Steady-statesine-wavemeasurementsof the acoustic (a)
output suggest a worthwhile improvement in linearity Amplitude
of the bass-midrange drive unit compared to voltage
drive. Thefollowing acousticdistortion measurements
ata drivecurrentof 1 Apeakareillustrative:
Voltage Current
Drive Drive*
J
(dB) (dB) ....
Total harmonic distortion
at100Hzrefundamental -34.1 -43.3 ·
Totalharmonicdistortion s_A_,:-2°,_7_..............
Time
at 3 kHz re fundamental -28.4 -55.0 (b)
· Under closed-loop conditions.
Amplitude
The effectiveness of the coupling error compensator v2°_tIi ii i .,
and filter is confirmed by the fact that no increase in I_
harmonic distortion is measurable up to 3 kHz and
beyond (that is, over the full operating range of the _ ;iiii-- i _ ___
drive unit)when the feedbackloop is closed.The actual 'j;}[ ....
increase in distortion level present on the unfiltered
and uncompensated velocity signal, compared to the
· : .:
drive unit acoustic output, ranges from 11 to 23 dB as
-no
frequency is increased from 500 Hz to 3 kHz. _............... _im_.......
The ability to vary the system Qwith the velocity (c)
feedback control circuit is shown by means of near-
field acoustic step response measurements. Fig. 17(a) Amptifude2o
volt
is without the velocity feedback operational, showing
]
aQofaround2.5, which is the natural mechanical Q(t i ' iiiii iiiiii · ·iiii
of the drive unit. Fig. 17(b)-(e)shows compensated iiiiiiiiii ii iiiiii
Qalignments of 1.5, 1.0, 0.7, and 0.5, respectively. _o,_
A value of Q= 0.7 preserves the low-frequency char- ": : : : :
acteristicsof the unmodifiedloudspeakerundervoltage
drive
-a0
START:187.5ps STOP:38t-88m
Time
4LOW-LEVELCROSSOVER (d)
To complete the two-way prototype system, a second- Amplitude
orderlow-level high- and low-passcrossoverwas in- 47t
cluded to integrate the drive units together, with a nom-
inal crossover point of 3 kHz.
The crossover is implemented by passive RC ele-
ments, the time constants of which are individually _;'_
adjustabletogivetheflattestfrequencyresponse,with : : i
bufferamplifiersbetween stages, to avoid loadinget- i
fects.Thecompletesystemis showninmodularform .....
by Fig. 18. After the input level control, amplifier A1_;_.....................
Time
provides a low-impedance drive to the first low- and (e)
high-pass filters, which are buffered by amplifiers A2
Fig. 17. Measured step responses of bass-midrange drive
and A3 before the second set of filter sections. A4 and unit. (a) Q= 2.5 (no feedback). (b) Q= 1.5. (c) Q= 1.0.
A5 are the transconductance preamplifiers previously (d) Q= 0.7. (e) Q= 0.5.
818 J. Audio Eng. Soc., Vol. 37,No. 10, 1989 October
PAPERS AMPLIFIERS FOR CURRENT-DRIVEN LOUDSPEAKERS
described, which drive the high- and low-frequency room measured frequency response curve of Fig. 20,
power amplifiers, respectively, with the measurement microphone 1 m on axis. The
The circuit topology of buffer amplifiers Al, A2, and uneven high-frequency response is a function of the
A3(Fig. 19) is similar to the transconductance pream- tweeter characteristics, with the resonant peak near 19
plifier, but with the addition of an output follower and kHz being due to the first bending mode resonance of
overall negative feedback to provide a low output the copper dome. There is no discernible frequency
impedance. Certain gain and frequency response de- response deviation in moving from voltage drive to
fining components are specific to individual amplifier current drive with this device,due to its high level of
stagesas indicated, intrinsic damping.
The performance of the system is shown by the in- While the low-frequency drive unit benefits sub-
............. ........: ¢>
c1J_j i, ¢_ J 10ut
33_ 7 3_(Hr)
!l 2_2
Vin
ct
J_'"
I
set input
[eve[
Al-inputbuffer 1_ i
A2-HF buffer _/_ _k 'j_ 'L_Jk'_ _,o2_
LL ' - - ;;ofo LFpower
A/C HF ] tronsconducfance preamps. _ lout amptifier
Ab-LF " (LP)i
....Z: Z '
Itot1i'-
, , ,_=-j j ( ovelocity
ii i
............ .J L ............ J iF/Binpuf
plug -in crossover
board
Fig. i 8. Block diagram of low-level crossover.
Ii: I °+*'
_. ,Rtl 22o_'_ n
21e_ _s'O_
OC_l
CS
O,option C1,C2J R1 R17
8ctgrt
Q*
8c.,,_.I A1 lp _7k omit
I
er c_ [ o._ ,..A2 0'l.u 100k 2k2
Z'rx*r A3 lp Jl00k 2k2+2ktrimmer
_2 $9R
,%
input _J i ._gl_' =_,-_s l ._,9output
m C._ --
_Ot7 JCf C&
4_-0-t ).-o , I 2_o.. looo
Fig. !9.Boffer amplifiers forcrossovernetwork.
J. AudioEng. Soc., Vol. 37, No.10, 1989 October819
MILLSANDHAWKSFORD PAPERS
stantially from current drive, the improvements in lin- the drive unit when equalized by velocity feedback to
earity to the tweeter are more modest, largely as a give the same Qat fundamental resonance as in the
result of a more linear magnetic circuit and lower cone voltage-driven case (Q--_0.7). Under these conditions,
displacements. A distortion improvement of typically also with a 3-kHz crossover point, the current waveform
3-7 dB is afforded. However, benefits in terms of the is seen to be similar to the voltage-driven case,while
elimination of thermally induced errors are still ap- the voltage waveform shows peaks due to the voice-
parent, coilinductance(Fig. 23). Theinstantaneousimpedance
modulus is similar to that under voltage drive, but
5DYNAMIC CURRENT AND VOLTAGE DEMAND slightly lower at 4.05 f_.
The main significance of these results is that while
Under certain signal conditions, drive units and the power amplifier is similarly stressed under both
loudspeaker systems have, under voltage drive, been voltage and current drive, allowance must be made for
shown to exhibit an instantaneous impedance modulus sufficient headroom in the power amplifier for the volt-
lower than might initially be suggested from the steady- age peak resulting from the coil inductance. The problem
state impedance characteristics, thus stressing the power is worsened by voice-coil heating. The effect of a tem-
amplifier in terms of current delivery [24]-[28]. In perature rise of 200°C (meaning that the coil resistance
this section we consider the implications of this work increases to 13 _ using copper) is shown by the wave-
inrelation to current drive, forms of Fig. 24. While the current waveform is iden-
As an example, the bass-midrange unit and enclosure tical to that at normal temperature, as expected, the
combination is considered. The equivalent electrical voltage waveform is increased in magnitude in order
model is shown in Fig. 21. Under voltage drive, a to keep the current constant. The negative-going ex-
pulse is applied to the drive unit, the duration of which cursion is seen to be 1.7 times greater. Although the
is set to excite the large negative-going current excursion performance of the drive unit is unaffected by the in-
shown in Fig. 22. The voltage signal has been second-
VoltagetV)
order low-pass filtered at 3 kHz to represent realistic _0. .....................................................................t0.
operatingconditions. Atthepoint ofmaximum negative- ii-_'"_ t
going current, the instantaneous impedance modulus is 0.................................................. 0.
4.15 f_, lower than the steady-state minimum of 7 f_.
Under current drive it is only realistic to consider
-_0, :................ ................. ·................ ................. '-t0.
0. 0._02_ e,005 0.0875 0.0_
Time(s)
Amplitude(a)
-s,,,
dBv
'' ' 'Current (A)
2, Z................ _.................. :.................. : ................. :2,
-1/ -1
-L:............. '.............. '................ '................ '-2.
-85 0. 0,0025 0.005 0.0075 0,01
Time(s)
START: 50 HZ BN: 50 HZ STOP: 20 050 HZ
Frequency (b)
Fig. 22. Bass-midrange unit: dynamic current demand under
Fig. 20. Measured frequency response of complete system, voltage drive.
Le 1.05mil ReT^
Rx 25a
AMPLIFIER 30OFFT 35.
0
,_ of 20%
Fig. 21. Electrical model of bass-midrange drive unit and enclosure combination. Lc--Voice-coil inductance; Rx--losses
due to pole piece coupling; Re--Voice-coil resistance; Cme--capacitance due tomoving mass; Rmc--resistance due to
mechanical losses; Lms--inductance due to suspension compliance; Leah--inductance due to volume of air in cabinet.
820 J. AudioEng. Soc.,Vol.37,No.10, 1989 October
MILLSANDHAWKSFORD PAPERS
Feedback Circuits for Loudspeakers," presented at the Feedback with Loudspeakers," Philips Tech.Rev., vol.
73rd Convention of the Audio Engineering Society, J. 29, pp. 148-157 (1968).
Audio Eng.Soc.(Abstracts), vol. 31, p. 364 (1983 [19] D. de Greif and J. Vandewege, "Acceleration
MAY), preprint 1964. Feedback Loudspeaker," Wireless World, pp. 32-36
[6] R. A. Greiner and T. M. Sims, Jr., "Loudspeaker (1981 Sept.).
Distortion Reduction," J.Audio Eng.Soc., vol. 32, [20] G. J. Adams, "Adaptive Control of Loudspeaker
pp. 956-963 (1984 Dec.). Frequency Response at Low Frequencies," presented
[7] K. Lewis, "Transconductance Amplifiers," at the 73rd Convention of the Audio Engineering So-
Electron.Wireless World, pp. 580-582 (1987 June). ciety, J.Audio Eng.Soc.(Abstracts), vol. 31, p. 364
[8] A. Nedungadi, "High Current Class AB Converter (1983 May), preprint 1983.
Technique," Electron.Lett., vol. 16, pp. 418-419 [21] E. de Boer, "Theory of Motional Feedback,"
(1980 May). IRE Trans.Audio, pp. 15-21 (1961 Jan./Feb.).
[9] M. K. N. Rao and J. W. Haslett, "Class AB [22] A. F. Sykes, "Damping Electrically Operated
Voltage-Current Converter," Electron.Lett., vol. 14, Vibration Devices," UK patent 272622 (1926 Mar.).
pp. 762-764 (1978Nov.). [23] R. L. Tanner, "Improving Loudspeaker Re-
[lO] M. J. Hawksford, "Low-Distortion Program- sponse with Motional Feedback," Electronics, pp. 142
mable Gain Cell Using Current-Steering Cascode To- ff. (1951 Mar.).
pology," J.Audio Eng.Soc., vol. 30, pp. 795-799 [24] P. G. L. Mills and M. J. Hawksford, "Transient
(1982 Nov.). Analysis: A Design Tool in Loudspeaker Systems En-
[11] E. H. Nordholt, Design of High-Performance gineering," presented at the 80th Convention of the
Negative-Feedback Amplifiers (Elsevier, Amsterdam, Audio Engineering Society, J.Audio Eng.Soc.(Ab-
1983). stracts), vol. 34, p. 386 (1986 May), preprint 2338.
[12] J. J. Davidson, "A Low-Noise Transistorized [25] I. Martikainen, A. Varla, andM. Otala, "Input
Tape Playback Amplifier," J.Audio Eng.Soc., vol. Current Requirements of High-Quality Loudspeaker
13, pp. 2-16 (1965 Jan.). Systems," presented at the 73rd Convention ofthe Audio
[13] J. L. Linsley Hood, "Symmetry in Audio Am- Engineering Society, J.Audio Eng.Soc.(Abstracts),
plifier Circuitry,"Electron.Wireless World, pp. 31- vol. 31, p. 364 (1983 May), preprint 1987.
34 (1985Jan.). [26] M. Otala and P. Huttunen, "Peak Current Re-
[14] R. N. Marsh, "A Passively Equalised Phono quirement of Commercial Loudspeaker Systems," J.
Pre-amplifier,"Audio Amateur, no. 3, pp. 18 (1980). Audio Eng.Soc., vol. 35, pp. 455-462 (1987 June).
[15] M. Hawksford, "Reduction of Transistor Slope [27] D. Preis, "Peak Transient Current and Power
Impedance Dependent Distortion in Large-Signal Am- into a Complex Impedance," presented at the 80th
plifiers," J.Audio Eng.Soc., vol. 36, pp. 213-222 Convention of the Audio Engineering Society, J.Audio
(1988 Apr.). Eng.Soc.(Abstracts), vol. 34, p. 386 (1986 May),
[16] M. J. Hawksford, "Power Amplifier Output- preprint 2337.
Stage Design Incorporating Error-Feedback Correction [28] J. Vanderkooy and S. P. Lipshitz, "Computing
with Current-Dumping Enhancement," presented at the Peak Currents into Loudspeakers," presented at the
74th Convention of the Audio Engineering Society, J. 81st Convention of the Audio Engineering Society, J.
Audio Eng.Soc.(Abstracts), vol. 31, p. 960 (1983 AudioEng.Soc.(Abstracts), vol. 34, pp. 1036-1037
Dec.), preprint1993. (1986Dec.), preprint2411.
[17] P. G. A. H. Voight, "Improvements in or Re-
lating to Thermionic Amplifying Circuits for Teleph-
ony,'' UK patent 231972 (1924 Jan.). Biographies for Drs. Mills and Hawksford were published
[18] J. A. Klaassen and S. H. de Koning, "Motional in the March issue.
822 J. Audio Eng. Soc.,Vol. 37, No. 10, 1989 October
... A variety of different techniques have been proposed included current feedback [7,81], velocity feedback [53] and acceleration feedback [12,37]. There were also techniques which used both current and velocity feedback [32,68]. Of course, the main difficulty with most of these approaches is the need for a suitable sensor to provide the feedback signal. ...
... Of course, the main difficulty with most of these approaches is the need for a suitable sensor to provide the feedback signal. Various ways of sensing coil displacement [11,31], velocity [68], or acceleration exist today. Adding a sensor to the loudspeaker is not always trivial [35,68], and may render the assembly of a smaller drive unit rather complex and result in a lower efficiency due to the added mass. ...
... Various ways of sensing coil displacement [11,31], velocity [68], or acceleration exist today. Adding a sensor to the loudspeaker is not always trivial [35,68], and may render the assembly of a smaller drive unit rather complex and result in a lower efficiency due to the added mass. Another more recent technique involves feed forward. ...
Thesis
Full-text available
The aim of this thesis is to provide simplified hardware and software solutions to the problem of real time loudspeaker linearisation. Most of the existing methods require the use of external sensors, use complex nonlinear models, or attempt to optimise all the nonlinear parameters of the feed forward model. From an industrial standpoint simplicity is attractive, so the main thematic of this work is to propose a linearisation framework that is as simple as possible while still being competitive with other methods.In order to make the algorithm as simple as possible, most of the nonlinear parameters are provided a priori through the use of simulations and data sheets. Only the nonlinear function used to represent the loudspeaker suspension is optimised in real time to adapt the parameters to the sample drive unit. The algorithm is run on a low latency controller, and the control signal applied to the loudspeaker system via a transconductance power amplifier system. Both the controller and the power amplifier system were designed, built and validated by the author during this thesis.The control system is simulated and the effects of ADC resolution, model error, and mechanical damping on the compensation are analysed. Measurement results show that the control system is capable of reducing both harmonic and intermodulation distortions in the cone acceleration by up to 25 dB between 10 Hz and 1000 Hz. The control system also enables the control of the linear frequency response of the loudspeaker system, removing the peaking present at the loudspeaker resonance frequency or providing a more broad band modification of the frequency response.
... The exact topology of the power ampli er is not covered in this discussion. but follows from previously presented work [13]. ...
... Excitar a etapa de saída com corrente faz com que a etapa de saída deixe de ser um seguidor de tensão para ser fonte de corrente também. Pode parecer mais natural conectar um alto-falante eletrodinâmico a uma fonte de corrente que a uma fonte de tensão [2], mas deve-se considerar que isso faz com que seja difícil manter a estabilidade do amplificador, pois o circuito equivalente do alto-falante passa a ter papel mais importante na malha de realimentação [11]. ...
Article
Full-text available
Os amplificadores de potência de áudio ocupam uma posição limítrofe entre a ciência e a arte, devido à sua aplicação e ao perfil muito exigente do usuário desses equipamentos. O objetivo deste trabalho é apresentar deficiências de projeto que reconhecidamente afetam a qualidade do sinal, especificamente na etapa excitadora, e apresentar uma nova abordagem para o projeto desta etapa. Ao final é apresentado um projeto como exemplo.
... Excitar a etapa de saída com corrente faz com que a etapa de saída deixe de ser um seguidor de tensão para ser fonte de corrente também. Pode parecer mais natural conectar um alto-falante eletrodinâmico a uma fonte de corrente que a uma fonte de tensão [2], mas deve-se considerar que isso faz com que seja difícil manter a estabilidade do amplificador, pois o circuito equivalente do alto-falante passa a ter papel mais importante na malha de realimentação [11]. ...
Article
Full-text available
The growing presence of power ramps, typically caused by the intermittency of renewable energy sources (RESs), may ultimately threaten the stability and reliability of the power grid. In the context of power smoothing algorithms such as Moving Average, Ramp Rate and First-Order Low-Pass Filter have been widely used in reference generation for Energy Storage Systems (ESSs). In this scenario, this paper analyzes typical metrics used for evaluating power smoothing techniques and comments on their limitations. Validation of this analysis is conducted using PV generation data sourced from the National Renewable Energy Laboratory (NREL). The results highlight the need to develop new metrics for a fairier comparison. Finally, this work also sets a concrete path for the evolution of said metrics.
... This system was used to apply negative impedance to the system to counteract the voice coil impedance increase with temperature. Similar studies have been carried out focusing on amplifier design [12] [13]. These projects have taken the knowledge of the thermal properties of the voice coil and have designed amplifier circuitry to that works to reduce the effects of voice coil heating. ...
Thesis
Full-text available
The modern day loudspeaker’s performance is limited by a number of factors. An important limiting factor is voice coil heating. Most loudspeakers are extremely inefficient. That is, of the input electrical power only a small fraction of that power is actually converted into acoustical power. The vast majority of this lost power is converted into heat in the voice coil. The heat generated can lead to a significant loss of performance and may eventually lead to the destruction of a loudspeaker. It is important to understand the causes and effects of voice coil temperature gain to allow for loudspeakers that are designed in anticipation of this problem. This paper will explore the principles behind loudspeaker behavior and the simulation of and experimentation on a loudspeaker under varying voice coil temperatures. This will help to understand exactly how the voice coil’s temperature affects the overall loudspeaker performance.
... In [5] the network is described as one in which "the zeros of one stage partially cancel the poles of the next stage." In [7] a similar network is described to realize an operational-amplifier circuit which exhibits a gain slope of +4.6 dB per octave over the audio band. The authors stated that the network component values were selected with the aid of a software optimization routine to match the desired slope. ...
Article
Two simple Zobel impedance compensation networks for the lossy voice-coil inductance of a loudspeaker driver are described. Design equations for the element values are given, and a numerical example is presented. The synthesis procedure can be extended to realize general RC networks which exhibit an impedance that decreases with frequency at a rate of -n dec/dec, where 0 < n < 1.
Article
The past 50 years have seen the demise of the vacuum tube, the development of the transistor, and the development of the integrated circuit. There has been an explosive development of analog and digital circuits and systems. These developments have had an incredible impact on the field of audio engineering, most of which has been chronicled in the Journal of the Audio Engineering Society. The papers on electronic technology that have been published in the last 50 years in the Journal are summarized.
Article
The electro dynamic loudspeaker is often referred to as the weakest link in the audio chain due to low efficiency and high distortion levels at low frequencies and high diaphragm excursion. Compensating for loudspeaker non-linearities using feedback or feedforward methods can improve the distortion and enable radical design changes in the loudspeaker which can lead to efficiency improvements. In combination this has motivated a revisit of the accelerometer based motional feedback technique. Experimental results on a 8 inch subwoofer show that the total harmonic distortion can be significantly reduced at low frequencies and large displacements.
Article
Current driven loudspeakers have previously been investigated but the literature is limited and the advantages and disadvantages are yet to be fully identified. This paper makes use of a non-linear loudspeaker model to analyse loudspeakers with distinct non-linear characteristics under voltage and current drive. A multi tone test signal is used in the evaluation of the driving schemes since it resembles audio signals to a higher degree than the signals used in total harmonic distortion and intermodulation distortion test methods. It is found that current drive is superior over voltage drive in a 5" woofer where a copper ring in the pole piece has not been implemented to compensate for eddy currents. However the drive method seems to be irrelevant for a 5" woofer where the compliance, force factor as well as the voice coil inductance has been optimized for linearity.
Article
In motional feedback the mechanical vibrations of the loudspeaker cone are the source of the feedback voltage. Feedback then improves the over-all response characteristic and reduces the total distortion. The theory of this method is presented here in a simplified, though enlightening, way. The treatment is based on an unorthodox theorem on impedance conversion by feedback.
Article
A high current class AB convertor technique offering both v.c.c.s. and c.c.c.s. capability is described. A simple realisation is proposed which provides peak output currents greater than 100 mA with low distortion and reduced supply drain over a useful frequency range.
  • R A Greiner
  • T M Sims
R. A. Greiner and T. M. Sims, Jr., "Loudspeaker (1981 Sept.).
A Passively Equalised Phono quirement of Commercial Loudspeaker Systems
  • R N Marsh
R. N. Marsh, "A Passively Equalised Phono quirement of Commercial Loudspeaker Systems," J.
Reduction of Transistor Slope [27] D. PreisPeak Transient Current and Power Impedance Dependent Distortion in Large-Signal Aminto a Complex Impedance," presented at the 80th plifiers
  • M Hawksford
M. Hawksford, "Reduction of Transistor Slope [27] D. Preis, "Peak Transient Current and Power Impedance Dependent Distortion in Large-Signal Aminto a Complex Impedance," presented at the 80th plifiers," J. Audio Eng. Soc., vol. 36, pp. 213-222 Convention of the Audio Engineering Society, J. Audio (1988 Apr.).
Improvements in or Relating to Thermionic Amplifying Circuits for Telephony
  • P G A H Voight
P. G. A. H. Voight, "Improvements in or Relating to Thermionic Amplifying Circuits for Telephony,'' UK patent 231972 (1924 Jan.). Biographies for Drs. Mills and Hawksford were published
A Low-Noise Transistorized [25] I. Martikainen, A. Varla, andM. Otala
  • J J Davidson
J. J. Davidson, "A Low-Noise Transistorized [25] I. Martikainen, A. Varla, andM. Otala, "Input Tape Playback Amplifier," J. Audio Eng. Soc., vol. Current Requirements of High-Quality Loudspeaker 13, pp. 2-16 (1965 Jan.).
presented at the Feedback with Loudspeakers
Feedback Circuits for Loudspeakers," presented at the Feedback with Loudspeakers," Philips Tech. Rev., vol. 73rd Convention of the Audio Engineering Society, J. 29, pp. 148-157 (1968).
Symmetry in Audio Am- Engineering SocietyAbstracts), plifier Circuitry
  • J L Linsley
  • Hood
J. L. Linsley Hood, "Symmetry in Audio Am- Engineering Society, J. Audio Eng. Soc. (Abstracts), plifier Circuitry," Electron. Wireless World, pp. 31- vol. 31, p. 364 (1983 May), preprint 1987. 34 (1985 Jan.).
Transconductance Amplifiers," at the 73rd Convention of the Audio Engineering So- Electron. Wireless World
  • K Lewis
K. Lewis, "Transconductance Amplifiers," at the 73rd Convention of the Audio Engineering So- Electron. Wireless World, pp. 580-582 (1987 June). ciety, J. Audio Eng. Soc. (Abstracts), vol. 31, p. 364