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___________________________________
Audio Engineering Society
Convention Paper
Presented at the 115th Convention
2003 October 10–13 New York, New York
This convention paper has been reproduced from the author's advance manuscript, without editing, corrections, or consideration
by the Review Board. The AES takes no responsibility for the contents. Additional papers may be obtained by sending request
and remittance to Audio Engineering Society, 60 East 42nd Street, New York, New York 10165-2520, USA; also see www.aes.org.
All rights reserved. Reproduction of this paper, or any portion thereof, is not permitted without direct permission from the
Journal of the Audio Engineering Society.
___________________________________
Loudspeakers’ Electric Models for Study of the
Efforts in Audio Power Amplifiers
Rosalfonso Bortoni1 and Homero Sette Silva2
1Studio R Electronics, São Paulo, São Paulo, 04615-004, Brazil, www.studior.com.br
rosalfonso@terra.com.br
2Selenium Loudspeakers, Nova Santa Rita, Rio Grande do Sul, 92480-000, Brazil, www.selenium.com.br
homero@selenium.com.br
ABSTRACT
This work presents electric equivalent circuits for loudspeakers installed on infinite baffles and enclosures, as closed
box, bass-reflex, 4th and 6th orders band-pass enclosures, using two way and three way passive crossovers. The
impedance curves were derived from MATLAB® simulations. The impedance curves, along with module and phase,
are presented for each one of the cited models above. The transfer functions are also presented, besides the
necessary considerations to get the results from the loudspeakers specifications, dimensions and box tuning.
Examples of the efforts caused in the output stages of audio power amplifiers are presented and commented.
0. CLOSSARY
g
EVoltage source
g
ZOutput impedance of the voltage source
s
FLoudspeaker resonance frequency
as
VLoudspeaker equivalent volume
ts
QLoudspeaker total merit factor
es
QLoudspeaker electrical merit factor
ms
QLoudspeaker mechanical merit factor
E
RVoice coil electrical resistance
ed
RVoice coil nonlinear electrical resistance
e
LVoice coil inductance
ms
RLoudspeaker mechanical resistance
ms
MLoudspeaker mechanical mass
ms
CLoudspeaker mechanical compliance
lBForce factor
d
SEffective cone area
e
ZLoudspeaker electrical impedance
ms
ZLoudspeaker mechanical impedance
es
Zms
Z reflected to the electrical side
a
ZAcoustical impedance
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ma
Za
Z reflected to the mechanical side
ea
Za
Z reflected to the electrical side
b
VBox volume
tc
QClosed Box total merit factor
b
FBox tuning frequency
L
QBox leakage merit factor
b
ZBox acoustical impedance
vc
ZTotal electric impedance at voice coil
terminals
ab
RBox acoustical absorption loss resistance
ab
CBox acoustical compliance
c
ωClosed Box angular resonance frequency
c
QClosed Box merit factor
al
RVented Box leakage loss resistance
ap
MPort (duct) acoustical mass
b
ωVented Box angular resonance frequency
sComplex frequency,
ω
=js
ω
Angular frequency, fπ=
ω
2
fFrequency
1. INTRODUCTION
Audio power amplifiers are used in the most different
and diverse types of applications. In the real world,
the audio power amplifier must be able to properly
drive complex loads, and not only purely resistive
ones, commonly used to evaluate thermal
capabilities. Loudspeakers systems are extremely
complex loads. Complex circuits have been
considered and used as a realistic load in the tests of
audio power amplifiers [1-4]. With the advent of
computational tools new forms of analysis became
available (CAD). One of these is SPICE, the state of
the art in circuit simulation. Now power amplifiers
can be tested in the virtual domain, a less expensive
and less time consuming task.
Recently, it was presented a novel method for the
design of audio power amplifiers output stages
operating in class A, B, AB, G and H, considering
complex loads, where the average and instantaneous
temperatures of transistors junctions were calculated,
among others parameters, through the use of a
computational tool (MATLAB®). For doing this,
mathematical models had been developed taking into
account voltages, currents, dissipated powers and
temperatures, both averages and instantaneous, all
over the output stage. It was showed to be possible to
design power output stages, specifying the classes of
operation, under a complex load (loudspeaker) [5].
The proposal of the present work is to give electric
models for loudspeakers installed on baffles and
enclosures as close box, bass-reflex, 4th and 6th orders
band-pass, with passive crossovers of two and three
ways, of 1st and 2nd orders, where the impedance
curves were derived using MATLAB®, for any
loudspeakers, enclosure dimensions and tuning. The
necessary data must be supplied by the designer and
got from the manufacturers of the loudspeakers ( s
F,
as
V,ts
Q, etc.), and the enclosures characteristics
(b
F,b
V,L
Q, etc.). The impedance curves, along
with module and phase are presented, besides the
necessary considerations to get the results from the
loudspeakers and enclosures specifications. Examples
of the efforts caused in the output stages of audio
power amplifiers are presented and commented.
2. SPEAKERS
The equivalent circuits used in this work,
representing the driver installed in infinite baffle,
closed and tuned boxes, and 4th and 6th orders band
pass enclosures, will be derived from the equivalent
electro mechanical circuit depicted in Figure 1.
Figure 1. Electro mechanical and acoustical circuit of a driver excited
by a voltage source, loaded by a generic acoustical impedance, a
Z.
In this Figure the voltage source, g
E, and the output
impedance, g
Z, are the equivalents to the power
amplifier. The components E
R,ed
Rand e
L
correspond to the electric part of the loudspeaker, and
the components ms
R,ms
Mand ms
C correspond to
the mechanical part of the loudspeaker; while a
Z is
the acoustical impedance. Simplifying the above
circuit by grouping variables of the same physical
domain we get the one depicted in Figure 2.
Figure 2. Simplified version of circuit showed in Figure 1.
eedEe LsRRZ ⋅++= (1)
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r
X
red KR ω⋅= ;)1( −
ω⋅= l
X
le KL (2)
ms
msmsms Cs
MsRZ ⋅
+⋅+= 1(3)
Where llrr XKXK ,,, correspond to the non-linear
parameters derived after Wright from the driver
impedance curve [6].
Moving the acoustical impedance ( a
Z) to the
mechanical side, we get the circuit depicted in Figure
3.
Figure 3. Electro mechanical circuit equivalent to the one in Figure 2.
2
dama SZZ ⋅= ,(4)
d
Sis the loudspeaker effective diaphragm area. Now
moving the mechanical impedances ma
Zand ms
Zto
the electrical side, leads to the circuit in Figure 4 [7-
11].
Figure 4. Electrical equivalent circuit of Figure 3.
() ()
2
22
da
ma
ea SZ
B
Z
B
Z
⋅
== ll
(5)
and
()
ms
es Z
B
Z
2
l
=.(6)
lBis the force factor, representing the magnetic
density flux (
B
) trough the gap times the effective
wire length ( l) inside the gap. Then, the load present
to amplifier output will correspond to Equation (7).
eaes
evc
ZZ
ZZ 11
1
+
+= ,(7)
vc
Zis the electrical equivalent impedance at the
moving coil terminals, valid to any driver and all
arbitrary acoustical loads (cabinets) .
2.1. Infinity Baffle
To the infinity baffle the acoustical load is the air
impedance radiation, small enough if compared to the
other impedances, to be neglected. In this case, the
resulting electrical impedance at voice coil terminals
will be given by equation (8).
es
evc
Z
ZZ 1
1
+= .(8)
2.2. Closed Box
In the case of a closed box, the acoustical load to the
driver may be represented by a resistance ab
R (due
to internal absorption losses), in series with a
compliance ab
C (representing the air trapped inside
the box), according to Figure 5.
Figure 5. Closed box equivalent circuit.
Then the acoustical impedance will be given by (9)
s
RC
s
RZZ abab
abba
⋅
+
⋅==
1
,(9)
while the reflected acoustical impedance to the
electrical side will correspond to (10).
(
)
2
2
db
ebea SZ
B
ZZ
⋅
== l.(10)
Taking (9) and (10) into (7), we get (11)
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ebes
evc
ZZ
ZZ 11
1
+
+= ,(11)
Equivalent to (12)
ec
evc
Z
ZZ 1
1
+= ,(12)
where
()
2
2
dac
ebesec SZ
B
ZZZ
⋅
=+= l,(13)
s
Q
ss
CS
Zcc
c
msd
ac
1
12
2
2
+
⋅ω
+
ω
⋅
⋅
α+
=,(14)
α+⋅⋅π=α+⋅ω=ω 121 ssc F(15)
b
as
V
V
=α .(16)
2.3. Vented Box
In a bass reflex enclosure, the acoustical load
presented to the driver corresponds to a
resistance al
R (representing the leakage losses), in
parallel with a compliance ab
C (the air trapped
inside the box), in parallel with an inertance ap
M
(modeling the air in the port). See Figure 6.
Figure 6. Equivalent circuit of a bass reflex enclosure.
The acoustical impedance will be given by (17)
1
2
2
+
⋅ω
+
ω
⋅==
Lb
b
apba
Q
ss
s
MZZ ,
(17)
where
msdb
ap CS
s
M
⋅⋅ω
=22 (18)
and
abap
bCM ⋅
=ω 1.(19)
The electrical impedance at the voice coil terminals
will be given by (11), taking (10)and(17) into
account.
2.4. 4th Order Band Pass
The 4ª order band pass enclosure has one sealed
chamber and a tuned one. The equivalent circuit is
showed in Figure 7. The leakage losses between the
two chambers where not taken into account in this
work.
Figure 7. Acoustical equivalent circuit of a 4ª order band pass
enclosure.
Then,
21 bba ZZZ += ,(20)
s
RC
s
RZ abab
abb11
11
1
⋅
+
⋅= (21)
1
22
22
2
22
+
⋅ω
+
ω
⋅=
Lb
b
apb
Q
ss
s
MZ .
(22)
The electrical impedance at the voice coil terminals
will be given by (23),
21
111
1
ebebes
evc
ZZZ
ZZ
++
+= ,(23)
where 1eb
Z and 2eb
Zwill be given by (10). All
considerations made to the closed box and the bass
reflex enclosure will also apply, noting that
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1
1
b
as
V
V
=α and
2
2
b
as
V
V
=α .(24)
2.5. 6th Order Band Pass
In the 6ª order band pass enclosure both chambers are
tuned and the acoustical equivalent circuit is depicted
in Figure 8, and the same considerations to the 4ª
order band pass enclosure will also apply here.
Figure 8. Acoustical equivalent circuit of a 4ª order band pass
enclosure.
The acoustical impedance will be given by (20),
where
1
11
21
2
11
+
⋅ω
+
ω
⋅=
Lb
b
apb
Q
ss
s
MZ
(25)
and 2b
Zis obtained from (22).
The electrical impedance at the voice coil terminals
will be given by (23), and 1eb
Z and 2eb
Zare
calculated from (10) taking (20), (24) and (25) into
account.
3. CROSSOVERS
The passive crossover networks used in this work can
be seen in Figures 9 to 14, with the high pass, low
pass and band pass sections, from orders 1st to 2nd,
respectively.
To build a two way or three way crossover network,
1st or 2nd order, just pick up the appropriate sections
connecting them in parallel. For instance, a three way
2nd order crossover can be built paralleling the
circuits from Figures 12, 13and14; in the case of a
two way 1ª order crossover do the same with circuits
from Figures 9and10.
The impedances HIGH
Z,LOW
Zand MID
Z are
representing the loads of each one of the high pass,
low pass and band pass sections.
Figure 9. High Pass section, 1st order.
1
1
1
Cs
ZZ HIGHH⋅
+= (26)
Figure 10. Low Pass section, 1st order.
11 LsZZ LOWL⋅+= (27)
Figure 11. Band Pass section, 1st order.
s
LCL
Zs
s
LZ
MID
M222
2
21
1
⋅
+
⋅
+
⋅= (28)
Figure 12. High Pass section, 2nd order.
3
2
333
2
2
1
L
Zs
s
LCZC
s
s
ZZ
HIGH
HIGH
HIGHH⋅
+
⋅
+
⋅
+
⋅= (29)
Figure 13. Low Pass section, 2nd order.
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444
444
2
21
1
LCL
Zs
LCZC
s
s
ZZ
LOW
LOW
LOWL
⋅
+
⋅
⋅
+
⋅
+
⋅= (30)
Figure 14. Band Pass section, 2nd order.
()
()
656
656
65
65
65
6565
6565
65
6565
55656
6
23
234
2
1
1
LLC
Z
G
LLC
LL
F
LL
ZLL
E
LLCC
D
ZLLCC
LL
C
LLCC
LCLLC
B
ZC
A
GsFsEs
DCsBsAsS
ZZ
MID
MID
MID
MID
MIDM
⋅⋅
=
⋅⋅
+
=
⋅
⋅+
=
⋅⋅⋅
=
⋅⋅⋅⋅
+
=
⋅⋅⋅
⋅++⋅
=
⋅
=
⋅+⋅+⋅
+⋅+⋅+⋅+
⋅=
(31)
4. IMPEDANCES SIMULATIONS
To exemplify, the curves of impedance (magnitude
and phase) for the equivalents circuits shown in
Sections 2 and 3 had been generated, using the
drivers of the Appendix.
4.1. Infinite Baffle
In the case of infinite baffle, the curves of
impedances are gotten directly from the data of the
manufacturer (Appendix). See Figures 15 and 16.
4.2. Closed Box
The closed box for the Driver A has an internal
volume of 200 liters ( lVb200=) and 2=
c
Q
(Figure 17). The closed box for Driver B has an
internal volume of 18 liters ( lVb18=) and 2=
c
Q
(Figure 18).
4.3. Vented Box
The vented Box tuned to Driver A has an internal
volume of 200 liters ( lVb200=), tuned to 35 Hz
(HzFb35=) and 7=
L
Q (Figure 19). The box
tuned to Driver B has an internal volume of 50 liters
(lVb50=), tuned to 130 Hz ( HzFb130=) and
7=
L
Q (Figure 20).
4.4. 4th order Band Pass
The 4th order Band Pass enclosure, optimized to
Driver A has a 200 liters closed chamber
(lVb200
1=) and another, with 100 liters
(lVb100
2=), tuned to 60 Hz ( HzFb60
2=),
2=
c
Qand 7=
L
Q (Figure 21). The 4th order Band
Pass enclosure, optimized to Driver B has an 18 liters
closed chamber ( lVb18
1=) and another, with 50
liters ( lVb50
2=), tuned to 130 Hz ( HzFb130
2=),
2=
c
Q and 7=
L
Q (Figure 22).
4.5. 6th order Band Pass
The 6th order Band Pass enclosure, optimized to
Driver A has a 200 liters ( lVb200
1=) tuned to 40
Hz ( HzFb80
1=) and another chamber with 100
liters ( lVb100
2=), tuned to 80 Hz ( HzFb80
2=),
and 7=
L
Q (Figure 23). The 6th order Band Pass
enclosure, optimized to Driver B has a 100 liters
(lVb100
1=) tuned to 90 Hz ( HzFb90
1=) and
another chamber with 50 liters ( lVb100
2=), tuned
to 130 Hz ( HzFb130
2=), and 7=
L
Q (Figure 24).
4.6. 1st Order Two Way Crossover
The cut-off frequency in this case is 5 kHz and the
high pass and low pass sections are depicted,
respectively, in Figures 9 and 10. The components
values in the low pass section are FC µ= 98.3
1and
HL µ= 7.254
1. To the highs we supposed the use of
a driver with HzFs500,1=,20.0=
ts
Q,22.0=
es
Q
and Ω= 8
E
R. The low frequencies are reproduced
with the tuned box of Figure 20 (impedance curve).
See Figure 25.
4.7. 1st Order Three Way Crossover
The cut-off frequencies in this case are 500 Hz (low),
and 5 kHz (high). The high pass, low pass and band
pass sections are showed in Figures 9, 10 and 11,
respectively, and the parts values are FC µ= 98.3
1,
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mHL55.2
1=,FC µ= 8.43
2 and HL µ= 7.231
2.
To the high frequency reproduction we used the same
driver of item 4.6. In the band pass section we have
the closed box of Figure 18 (impedance curve). In the
low end we have the tuned box of Figure 19
(impedance curve). See Figure 26.
4.8. 2nd Order Two Way Crossover
The cut-off frequency in this case is 5 kHz. The high
pass and low pass sections are depicted in Figures 12
and 13, respectively, and the parts values are
FCC µ== 99.1
43 and HLL µ== 3.509
43 .The
same loads from the item 4.6 are also used here. See
Figure 27.
4.9. 2nd Order Three Way Crossover
The cut-off frequencies in this case are 500 Hz (low),
and 5 kHz (high). The high pass, low pass and band
pass sections are showed in Figures 12, 13 and 14,
respectively, and the parts values are FC µ= 99.1
3,
HL µ= 3.512
3,FC µ= 8.19
4,mHLL 12.5
54 == ,
FC µ= 6.25
5,FC µ= 79.1
6and HL µ= 5.423
6.
The same loads from the item 4.7 are also used here.
See. Figure 28.
Figure 15. Infinite Baffle - Driver A.
3
Figure 16. Infinite Baffle - Driver B.
Figure 17. Closed Box - Driver A.
Figure 18. Closed Box - Driver B.
Figure 19. Vented Box - Driver A.
Figure 20. Vented Box - Driver B.
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Figure 21. 4th order Band Pass - Driver A.
Figure 22. 4th order Band Pass - Driver B.
Figure 23. 6th order Band Pass - Driver A.
Figure 24. 6th order Band Pass - Driver B.
Figure 25. 1st order Two Way Crossover.
Figure 26. 1st order Three Way Crossover .
Figure 27. 2nd order Two Way Crossover.
Figure 28. 2nd order Three Way Crossover.
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5. EFFORTS IN POWER AMPLIFIERS
To demonstrate the applicability of the electrical
equivalent models presented in items 2 and 3, one
generated the load lines, current x voltage
(CECVI ×), corresponding to a Class B power out
put stage , able to deliver 100 watts to a 8 ohms load
(Figures 29 to 43). The used loads correspond to the
impedance curves in Figures 15 to 28. To help
comparing the different efforts from complexes loads
as drivers and loudspeakers, to the power output
stage, one also presented the results from an 8 ohms
resistance, as in Figure 29. Figures 29 to 43 were
obtained from [5]. Comparing the graphics we can
see that a more complex load is more demanding to
the power amplifier. In the three way second order
passive crossover network (Figure 43), we have twice
the current in the power stage. The dissipated power
in all examples (Figures 30 to 43), also increased due
the power factor
ϕ
cos , where
ϕ
is the phase angle
between voltage and current in the load. The method
for dimensioning power stages shown in [5], together
with the electric models shown in this work, forms a
powerful tool for audio amplifiers designers.
Figure 29. 8 ohms (resistive) load.
Figure 30. Infinite Baffle load (Figure 15).
Figure 31. Infinite Baffle load (Figure 16).
Figure 32. Closed Box load (Figure 17).
Figure 33. Closed Box load (Figure 18).
Figure 34. Vented Box load (Figure 19).
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Figure 35. Vented Box load (Figure 20).
Figure 36. 4th order Band Pass load (Figure 21).
Figure 37. 4th order Band Pass load (Figure 22).
Figure 38. 6th order Band Pass load (Figure 23).
Figure 39. 6th order Band Pass load (Figure 24).
Figure 40. 1st order Two Way Crossover load (Figure 25).
Figure 41. 2nd order Two Way Crossover load (Figure 26).
Figure 42. 1st order Three Way Crossover load (Figure 27).
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Figure 43. 2nd order Three Way Crossover load (Figure 28).
6. DISCUSSIONS AND CONCLUSIONS
Electrical models (equivalent circuits) of drivers
installed in infinite baffle, closed box, bass reflex
enclosures, and 4th and 6th order band pass cabinets,
and two and three way passive crossovers networks
of 1st and 2nd orders, had been presented. Using the
parameters presented in manufacture’s data sheets,
and the equivalent circuits of the acoustical cabinets
along with the cross over networks, one got, from
simulation, the impedance curves corresponding to
each case. New box models are obtainable
introducing the new parts into the models discussed.
The efforts from the complex loads, to the power
amplifier output stages are shown in the current x
voltage graphics, so called load lines.
7. REFERENCES
[1] JOHNSON, Jeffrey H., “Power Amplifiers and
The Loudspeaker Load: Some Problems and a Few
Suggestions,” Audio, August, 1977.
[2] BENJAMIN, Eric, “Audio Power Amplifiers for
Loudspeaker Loads,” Journal of The Audio
Engineering Society, Vol. 42, No. 9, September,
1994.
[3] OTALA, Matti and HUTTUNEN, Pertti, “Peak
Current Requirement of Commercial Loudspeaker
Systems,” Journal of The Audio Engineering Society,
Vol. 35, No. 6, June, 1987.
[4] MARTIKAINEN, Ilpo and VARLA, Ari,
“About Loudspeaker System Impedance With
Transient Drive,” Audio Engineering Society 71st
Convention, Montreux, March 2-5, 1982.
[5] BORTONI, Rosalfonso, FILHO, Sidnei Noceti
and SEARA, Rui. "On The Design and Efficiency of
Class A, B, AB, G and H Audio Power Amplifier
Output Stages". Journal of The Audio Engineering
Society, Vol. 50, No. 7/8, pp. 547-563, 2002
July/August.
[6] WRIGHT, J. R. "An Empirical Model for
Loudspeaker Motor Impedance". Journal of The
Audio Engineering Society, Vol. 38, No. 10, pp. 749-
754, 1990 October.
[7] THIELE, A. Neville. "Loudspeakers in Vented
Boxes: Parts I and II". Journal of The Audio
Engineering Society, Vol. 19, No. 5, pp. 382-392,
1971 May; and Vol. 19, No. 6, pp. 471-483, 1971
June.
[8] SMALL, Richard H. "Direct-Radiator
Loudspeaker System Analysis". Journal of The Audio
Engineering Society, Vol. 20, No. 5, pp. 383-395,
1972 June.
[9] SMALL, Richard H. "Closed-Box Loudspeaker
Systems – Part I: Analysis, and Part II: Synthesis".
Journal of The Audio Engineering Society, Vol. 20,
No. 10, pp. 798-808, 1972 December; and Vol. 21,
No. 1, pp. 11-18, 1973 January.
[10] SMALL, Richard H. "Vented-Box Loudspeaker
Systems – Part I: Small-Signal Analysis, Part II:
Large-Signal Analysis, Part III: Synthesis, and Part
IV: Appendices". Journal of The Audio Engineering
Society, Vol. 21, No. 5, pp. 363-372, 1973 June; Vol.
21, No. 6, pp. 438-444, 1973 July; Vol. 21, No. 7, pp.
549-554, 1973 September; and Vol. 21, No. 8, pp.
635-639, 1973 October.
[11] SILVA, Homero Sette, Analysis and Synthesis of
Loudspeakers & Enclosures by Thiele-Small Method
(in Portuguese), H. Sheldon Serviços de Marketing
Ltda., Rio de Janeiro, Brazil, 1996.
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8. APPENDIX
Driver A
Model: 18SW1P (18")
Manufacturer: Selenium
Thiele-Small Parameters
s
F…………...... 29 Hz
as
V…………...... 395 l
ts
Q…………...... 0.34
es
Q…………...... 0.35
ms
Q…………...... 10.93
0
η…………...... 2.03 %
d
S…………...... 0.1194 m2
d
V…………...... 1,134.3 cm3
max
X…………...... 9.3 mm
lim
X…………...... 25 mm
Additional Parameters
lB…………...... 20.7 Tm
E
R…………...... 5.5 Ω
ms
M…………...... 147.3 g
ms
C…………...... 198.6 µm/N
ms
R…………...... 2.5 kg/s
Non-linear Parameters
se FL @…………….. 10.694 mH
kHzLe1@ …………….. 2.152 mH
kHzLe20@…………….. 0.508 mH
sed FR @…………….. 0.77 Ω
kHzRed 1@ …………….. 8.88 Ω
kHzRed 20@…………….. 80.23 Ω
r
K…………….. 14.375 mΩ
r
X…………….. 0.735
l
K…………….. 145.290 mH
l
X…………….. 0.518
Driver B
Model: 10MB1P (10")
Manufacturer: Selenium
Thiele-Small Parameters
s
F…………...... 84.3 Hz
as
V…………...... 23 l
ts
Q…………...... 0.32
es
Q…………...... 0.33
ms
Q…………...... 17.39
0
η…………...... 3.20 %
d
S…………...... 0.0363 m2
d
V…………...... 72.6 cm3
max
X…………...... 2.0 mm
lim
X…………...... 7.0 mm
Additional Parameters
lB…………...... 16.7 Tm
E
R…………...... 5.97 Ω
ms
M…………...... 28.86 g
ms
C…………...... 123.5 µm/N
ms
R…………...... 0.88 kg/s
Non-linear Parameters
se FL @…………….. 2.047 mH
kHzLe1@ …………….. 0.830 mH
kHzLe20@…………….. 0.293 mH
sed FR @…………….. 0.22 Ω
kHzRed 1@ …………….. 2.15 Ω
kHzRed 20@…………….. 30.18 Ω
r
K…………….. 1.879 mΩ
r
X…………….. 0.826
l
K…………….. 24.172 mH
l
X…………….. 0.626
