Design of a Resonant Power Source to Drive HPS Lamps
CHRISTIAN BRANAS REY Christian
Design of a Resonant Power Source to Drive HPS Lamps
Christian Brañas, Francisco J. Azcondo, Salvador Bracho
Dept. of Electronic Technology, System Engineering and Automation
University of Cantabria
Ave. de los Castros (s/n) 39005. Santander, SPAIN
{branasc, azcondof, brachos}@unican.es
Acknowledgement
The Spanish Ministry of Science and Technology supports this research under the project reference
DPI 2001-1047.
Keywords
Electronic ballasts, Resonant power converters, Soft switching.
Abstract
The aim of this paper is to define a new criterion for the design of resonant inverters applied to the
control of high-pressure sodium (HPS) lamps, which is extended to metal halide (MH) lamps. Once
the effect of the ageing on the lamp is determined, the analysis is focused on the selection of the most
suitable value of the LCsCp resonant network in order to achieve a good repeatability of the circuit
performance. The study is based on the analysis of the lamp power sensitivity regarding tolerance of
circuit components. The proposed design is validated with experimental results and a statistical
simulation by the Monte Carlo method.
Introduction
Nowadays, electronic ballasts for fluorescent lamps are gaining market share. However, since
production cost is one of the most important issues in the success of a new product, the still high cost
of electronic ballasts for HPS lamps limits their wide application [1]. The high voltage needed to
achieve the lamp ignition, the lamp ageing and the acoustic resonance phenomenon increase the
complexity and design effort. This paper is focused on the design of high-frequency resonant-inverterbased electronic ballasts that lead to circuit simplifications. The lamp ignition is achieved using the
large voltage gain, presented by the inverter, as the switching frequency approaches the unloaded
resonant frequency, avoiding the use of an auxiliary circuit.
In steady state, the ballast must ensure that the power supplied to the lamp, Plamp, is maintained
within the operational area defined by the trapezoidal diagram [2] of the lamp. The design sequence
proposed in this paper minimises the Plamp variation, for an open loop operation at a constant switching
frequency. Practical prototypes easily achieve a maximum Plamp deviation lower than 20% throughout
the lamp lifetime. This characteristic simplifies the design, since no additional feedback control circuit
is needed to stabilise Plamp. Additional constraints to the design sequence are introduced when
considering the tolerance of the inductance and capacitor of the resonant tank. The analysis of
sensitivities allows the definition of limits to the component tolerances to guarantee that a large
enough number of circuits meet the quality specification.
Since the acoustic spectrum shifts to lower values of frequency as the lamp size increases then, for
medium to high power HPS lamps, it is possible to set the switching frequency above the highest
frequency of acoustic arc resonance, ensuring an operation free of arc instabilities. In [3] the acoustic
resonant phenomenon is measured in MH lamps, showing that for lamps over 100W at frequencies
higher than 50kHz the instabilities seem to be damped.
EPE 2003 - Toulouse
ISBN : 90-75815-07-7
P.1
Design of a Resonant Power Source to Drive HPS Lamps
CHRISTIAN BRANAS REY Christian
Output Power Sensitivity of the LCsCp Resonant Inverter
The class D LCsCp inverter is shown in Fig. 1. Some considerations have been assumed in order to
make the circuit analysis easier. First, the circuit analysis is based on the fundamental approximation,
i.e. taking into account only the first harmonic of the square voltage vAB. Also, the capacitor CZ is
neglected during the circuit analysis. This capacitor is short-circuited during most of the switching
cycle, thus its effect on the input impedance of the resonant circuit can be assumed to be negligible.
Cp
Cp
M1
+
Vdc
+
v1
-
L
Cs
Rlamp
A
M2
+
v2
+
L
+
B
vlamp
ii
CZ
-
A
Cs
-
ii
B
ilamp
Zi
(a)
-
vlamp
vAB1
ilamp
Rlamp
+
(b)
Fig. 1 (a): Class D LCsCp resonant inverter and (b) simplified circuit for analysis purposes.
The LCsCp resonant circuit is correctly described by the following parallel parameters:
Table I
Parallel Resonant
Frequency
1
ωp =
LC p
Characteristic
Impedance
Z p =ωpL =
Parallel Quality
Factor
Rlamp
Qp =
Zp
1
ω pC p
According to these assumptions, the module Zi, and phase φi, of the input impedance of the
resonant circuit is calculated with (1) and (2).
2
Cp 
C


 + k − p
Q p2  1 − k 2 +

C s 
kC s


Zi = Z p ⋅
2
1 + k 2Q p

φ i = Tan −1  k −

(
C p  1 + k 2Q p

kC s 
Qp
2




2
,
(1)
) − Q k  ,
p
(2)


where k is the normalised switching frequency, k=ω/ωp. The resonant frequency of the loaded LCsCp
network dependent on the parallel quality factor is expressed in (3)
kr =


C
1 + p − 1  +
2 

Cs Q p 

2


4C p
C
1 + p − 1  +
2 
2

C
Q
Q
s
p
pCs


2
.
(3)
As is well known, at any switching frequency above resonance (k >kr), the transistors of the
inverter section turn on at zero-voltage (ZVS). The ZVS mode at turn-on is preferred because fast
recovery diodes are not needed [4], even when there are switching losses during the turn-off transition,
which are reduced by CZ. Making Qp→• in (3), the unloaded resonant frequency is obtained as
k r ( off ) = 1 +
Cp
.
(4)
Cs
The input current to the resonant circuit is obtained from (5).
2Vdc
⋅
Iˆi =
π ⋅Zp
EPE 2003 - Toulouse
1 + k 2Q p
Cp

Q p2 1 − k 2 +
Cs

(5)
2
2
C
 
 +  k − p
kC
s
 
ISBN : 90-75815-07-7



2
P.2
Design of a Resonant Power Source to Drive HPS Lamps
CHRISTIAN BRANAS REY Christian
The maximum value of input current to the resonant circuit is the maximum current stress of
transistor M1 and M2. On the other hand, the power supplied to the lamp, Plamp, is given by (6)
Plamp =
2V dc2
π Zp
2
⋅
.
Qp
2
Cp  
C

 +k − p
Q p2 1 − k 2 +
 
C
kC
s 
s






(6)
2
Using (6) and making use of the sensitivity definition, given in (7), it is possible to obtain the
sensitivity of Plamp regarding the different circuit elements.
S xP
x= x o
=
∂P ( x ) xo
⋅
∂x P ( xo )
(7)
Sensitivity of Plamp vs. Rlamp
The lamp equivalent resistance, Rlamp, is the most variable element in a ballast circuit, increasing to
up to 200% of the nominal value of a new lamp throughout the lamp lifetime. For this reason, the
analysis of the Plamp sensitivity regarding Rlamp is of interest. It is calculated with (8), which is
represented in fig.2.
P
lamp
S R lamp
Cp

Q p2 1 − k 2 +
Cs

=−
C

p
Q p2 1 − k 2 +
Cs

2
C
 
 −k − p
 
kC s
 
2
C
 
 +k − p
 
kC s
 




2




2
(8)
P
lamp
S Rlamp
1
Qp=0.2
0.5
Qp=0.5
0
∆S
-0.5
Qp=1.5
-1
0
0.2
0.4
0.6
0.8
1
1.2
1.4
k
Fig. 2: Sensitivity of Plamp regarding Rlamp for three values of quality factor Qp and Cp/Cs=0.1.
The lamp ageing leads to an increment of Qp, which produces the sensitivity variation indicated in
fig.2. The values of Qp that make the sensitivity of Plamp regarding Rlamp equal to zero are relevant:
Cp 


Q PM = ±  k −

kC
s 

C 

1 − k 2 + p  .

C s 

(9)
At Qp=QPM, the maximum value of Plamp is reached, and it has no dependence on Rlamp,
PM = ±
Vdc2
.
(10)
C p 
C 

 1 − k 2 + p 
π 2 Z p  k −


kC s 
C s 

In order to achieve a straightforward implementation of the soft start-up sequence [5], only the
frequency range k<kr(off) is of interest. From (10), note that for k≠kr(off), the Plamp vs. Qp curves have a
maximum value. This feature may allow us to maintain the power supplied to the lamp within the
operation area defined by the trapezoidal diagram during the whole lamp life. Accordingly, the curve
Plamp vs. Qp for the proposed LCsCp inverter is designed to meet the characteristic depicted in Fig.3.
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P.3
Design of a Resonant Power Source to Drive HPS Lamps
CHRISTIAN BRANAS REY Christian
Plamp(W)
Point of Maximum Power
Operation
Area
Plamp(Max)
PM
∆Plamp
Plamp(N)
Lamp at the
end of its life
time
New
Lamp
Ballast
Curve
Plamp(Min)
Qp(Min) Qp(N)
QPM
Qp(Max)
Qp
Fig. 3: Proposed ballast curve.
The aim of the design is to achieve that the maximum deviation of Plamp, regarding the lamp ageing,
fulfils the trapezoid limit. The power increment due to the ageing process, ∆Plamp (see Fig.3), is
normalised in (11) with the nominal power supplied to the new lamp, Plamp(N), and the resulting
parameter is defined as the power regulation index. For the proposed ballast curve, this index defines
the amplitude of the maximum power deviation and thus how much the inverter approximates to a
power source. The power regulation index is calculated as follows:
2
∆Plamp
Plamp ( N )
=
PM − Plamp ( N )
Plamp ( N )
Cp 
C


 + k − p
Q p2 ( N ) 1 − k 2 +


C
kC
s 
s


=±
C p 
Cp 

2
 1 − k +
Q p
2 k −
kC s 
C s 





2
−1
.
(11)
The value of Qp(N) is calculated to adjust the initial Vlamp. Eq. (12) calculates Qp(N) as a function of
the normalised switching frequency, k.
Cp

Q p ( N ) =  k −
kC
s





 2V
dc

 π 2V
lamp

2
2
 
 − 1 − k 2 + C p 
 
C s 

(12)
Working with (12), (11) and (10), expression (13) is obtained, where the resulting value of k
defines the on-steady-state switching frequency, kωp.
C   2Vdc

1 − k 2 + p  = 

C s   π 2Vlamp



Π


(13)
where Π becomes a design parameter calculated from the power regulation index ∆Plamp/Plamp(N).
2
Π=
 ∆Plamp 
2 ∆Plamp

 +
 Plamp ( N ) 
Plamp ( N ) .
1


−
2
 ∆Plamp

2
+ 1
 Plamp ( N )



(14)
Sensitivity of Plamp vs. L
In the circuit under study, for the frequency range of interest k<kr(off), the highest sensitivity
corresponds to the inductance variation [5].
P
S Llamp
Cp   2 Cp

 − 2 k −
2 k 2 Q p2  1 − k 2 +
C s  
Cs

=
2
2
Cp  
C 

 + k − p 
Q p2  1 − k 2 +
C s  
kC s 





(15)
Expression (15) is depicted in the graph of fig.4.
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ISBN : 90-75815-07-7
P.4
Design of a Resonant Power Source to Drive HPS Lamps
CHRISTIAN BRANAS REY Christian
P
S L lamp
1
0
-1
∆S
Qp=1.5
Qp=0.5
-2
Qp=0.2
-3
0
0.2
0.4
0.6
0.8
1
1.2
1.4
k
Fig. 4: Sensitivity of Plamp regarding L for three values of quality factor Qp and Cp/Cs=0.1.
From fig. 4, the highest values of sensitivity of Plamp regarding L takes place for k>kr(off). Note that
for k<kr(off), the sensitivity is greatly reduce as Qp increases. Thus, the worst case of sensitivity takes
place at the beginning of the lamp lifetime. Therefore, to achieve a good yield in industrial production
using a circuit without a feedback control loop, the sensitivity of the design with regard to the
inductance tolerance must be incorporated as a design input parameter.
Load range and power balance
Due to the effect of the high variability of the HPS lamp upon Plamp and the switching mode, the
load range of the inverter should be defined in the first step of the design process. The maximum value
allowed for Rlamp is defined by Qp(Max) (see fig. 3). A larger value of Rlamp will lead to the loss of the
ZVS mode. Qp(Max), is
Q p ( Max ) =
1
k
 2 Cp
k −

Cs





C

1 − k 2 + p

Cs

.



(16)
Thus, the load range, where the ZVS mode is maintained, is calculated according to:
∆Q p
Q p( N )
 2V
dc
= 
 π 2Vlamp


 1− Π2


(

)

  2V
dc
1 − 
  π 2Vlamp

 
Π  Π − 1 .
 
 
(17)
Finally, working with (16), (12) and (6), the condition such that Plamp is equal at the end and
beginning of the lamp lifetime is obtained:
 2V
dc

 π 2V
lamp

(
)
 1+ 1− 4 1− Π 2 Π 2
.
=

2Π

(18)
Expression (17) and (18) are depicted in fig. 5.
3
∆Q p
2.5
Qp( N )
2
1.5
2Vdc
π 2Vlamp
1
0.5
0
0
0.05
0.1
0.15
0.2
0.25
∆Plamp/Plamp(N)
Fig. 5: Load range and voltage ratio as a function of the power regulation index
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P.5
Design of a Resonant Power Source to Drive HPS Lamps
CHRISTIAN BRANAS REY Christian
Figure 7 shows the relationship between the load range and the supply to lamp voltage ratio. The
load range increases with the voltage ratio. Higher voltage ratio increases the initial phase of the input
impedance, φi, of the resonant circuit as can be deduced from (19).
  2V

dc
  π 2Vlamp
φ i = Tan −1  


 − Π






1− Π2  .

(19)
The phase displacement between vAB and ii implies a penalty in terms of reactive energy in the
resonant circuit. Fig. 6 shows the power balance at the input of the resonant tank.
v AB
V dc/2
ii
Îi
φi
P lamp
PA
t
Pr
Îi
V dc/2
I
III
II
IV
Fig.6: Power balance of the resonant inverter for ZVS mode.
In figure 6, Pr is the power that returns to the Vdc supply from the resonant circuit. On the other
hand, PA is the power drawn by the resonant circuit from Vdc. Considering a resonant circuit free of
losses, the power supplied to the lamp can be calculated as Plamp=PA-Pr. The expressions are given
below,
PA =
Vdc Iˆi [1 + Cosφ i ] ,
2π
(20)
Pr =
Vdc Iˆi [Cosφ i − 1] ,
2π
(21)
Plamp =
Vdc Iˆi Cos φ i
π
(22)
.
The power transfer index, T, defined as the initial Plamp to PA ratio is,
T=
Plamp
PA
=
2Cosφi .
1 + Cosφi
(23)
Expression (23) is depicted in figure 7 as a function of the power regulation index ∆Plamp/Plamp.
T
1
0.95
0.9
0.85
0.8
0.75
0.7
0
0.05
0.1
0.15
0.2
∆Plamp/Plamp(N)
0.25
0.3
Fig. 7: Power transfer index as a function of the power regulation index
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P.6
Design of a Resonant Power Source to Drive HPS Lamps
CHRISTIAN BRANAS REY Christian
Using (23) and fig.7, it is possible to evaluate the amount of reactive energy in the resonant tank at
the beginning of the lamp lifetime. The selection of the exact supply to lamp voltage ratio, as is
derived from (18) and (23) implies that Cosφi=1 for Qp(Max) i.e. at the end of the lamp lifetime. We call
this situation quasi-optimum mode [6], given that the amount of reactive energy in the resonant tank is
just enough to assure ZVS until the end of the lamp lifetime.
Design for manufacturing
In section II, it was commented that the inductance is the element with highest value of sensitivity
regarding Plamp. In order to find a design criterion to minimise the Plamp sensitivity regarding L, it is of
interest to rewrite expression (15) as a function of the input design parameters.
P
S L lamp
2
   2V
 
dc
 1− 
   π 2Vlamp
 
Π 
 
 
 π 2V
lamp

 2Vdc

 

Π − 1  +  2Vdc

   π 2Vlamp



Π − 1 = C p

Cs

(24)
Expression (24) is represented in fig.8.
Cp/Cs
1
0.8
0.015
0.6
0.4
0.03
0.05
0.07
0.2 0.1
0.15
-2
-1.8 -1.6 -1.4 -1.2
-1
-0.8 -0.6
P
S Llamp
Fig. 8:
Capacitor ratio Cp/Cs as a function of the sensitivity of Plamp regarding L and ∆Plamp/Plamp as
parameter.
Using (24), this paper suggests calculating Cp/Cs in accordance with the value of sensitivity of Plamp
that ensures high design repeatability with the available inductance tolerance ∆L/L. The proposed
design sequence is as follows:
1) The steady state electrical data for a new 250W HPS lamp at high frequency were experimentally
obtained: Plamp=250W, Vlamp=100Vrms, Ilamp=2.5Arms and Rlamp=40Ω . A value of power regulation
index of ∆Plamp/Plamp =0.16 results in Π=0.496.
2) For Π=0.496, using expression (18), the voltage ratio is 1.517, then Vdc=337V for quasi-optimum
operation. Also, using (17), the load range is ∆Qp/Qp(N)=2.05, which means that the inverter
accepts an increment of 200% in Rlamp. This load range is high enough to ensure the ZVS mode
during the whole lamp lifetime.
3) The Plamp sensitivity with regard to ∆L/L was fixed at –1.4, considering a worst case of tolerance
for the inductance of ∆L/L=±15%. From (24), the capacitor ratio is calculated: Cp/Cs=0.01.
4) The input current is Îi=3.59A. The phase of the input impedance to the resonant circuit is
calculated from (19), φi=49.6º. This value of phase results in an initial power transfer index of
T=0.78, which indicates that almost 80% of the apparent power is transferred to the lamp.
5) From expression (13), k is obtained: k=0.506.
6) From (12), the parallel quality factor for nominal conditions is calculated Qp(N)=0.37.
7) Knowing Qp(N), the characteristic impedance Zp is: Zp=Rlamp/Qp(N)=108.3Ω .
8) The switching frequency is fixed above the highest value of arc acoustic resonance.
kωp=2π(150kHz), so ωp=2π(296.4kHz).
9) Finally, from table I, the reactive components are: L=Zp/ωp=58µH, Cp=1/ωpZp=4.95nF and
Cs=495nF.
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ISBN : 90-75815-07-7
P.7
Design of a Resonant Power Source to Drive HPS Lamps
CHRISTIAN BRANAS REY Christian
The ballast curve of the designed LCsCp resonant inverter is shown in fig. 9. This curve was
obtained using the parametric sweep together with the performance analysis of pSpice. From the
simulation results, the maximum lamp power is PM=291.5W, which is reached for a value of lamp
equivalent resistance of RPM=71Ω.
Plamp
300W
290W
(71Ω,291.5W)
280W
270W
260W
(126.0Ω,254.7W)
(40.6Ω,250.313W)
250W
240W
40Ω
50Ω
60Ω
70Ω
80Ω
90Ω
MAXr(avg(-i(rlamp)*v(rlamp:2)), 150us, 200us)
100Ω 110Ω 120Ω 130Ω
Rlamp
Fig. 9: Simulated ballast curve.
The design repeatability was evaluated using the Monte Carlo simulation. The Monte Carlo method
was applied making use of the electrical simulator pSpice [7][8] to analyse the effect of the L, Cs and
Cp tolerances in the circuit performance. The normal distribution was assumed for all values. A value
of ±15% of tolerance was chosen for the inductance L and ±5% (J) for Cs and Cp. Figure 10 shows the
histogram obtained for Plamp in the designed prototype after 400 cycles of Monte Carlo.
P
c
t
10
o
f
S
a
m
p
l
e
s
5
0
160
n samples
n divisions
mean
180
=
=
=
200
400
30
249.417
220
240
260
MAXr(avg(i(rlamp)*i(rlamp)*40),
sigma
minimum
10th %ile
=
=
=
17.8911
192.909
227.941
160us,
280
200us)
median
90th %ile
maximum
300
=
=
=
320
340
247.846
274.429
308.719
Fig. 10: Plamp histogram considering a tolerance in the value of L equal to 15% and 5% for Cs and Cp.
In order to evaluate the result, the upper and lower specification limits (USL and LSL) were
established according to the trapezoidal diagram for 250W HPS lamps. In this case, LSL=180W and
USL=290W. The parameters of the resulting distribution are µ=249.41W and σ=17.89W. According
to these values, a quality level equal to 3σ is expected, which means a very low defect rate [9].
Experimental results
A practical implementation of the class D LCsCp inverter was carried out according to the proposed
design sequence. The selected MOSFET transistor was the low-charge, fast-switching IRF840LC with
the IR2111 circuit as driver. The practical values used in the experimental prototype were Vdc=340V,
L=55µH, Cs=470nF and Cp=4.7nF.
Fig.11 shows the experimental waveforms of the instantaneous lamp voltage, power and current for
a new 250W LUCALOX lamp manufactured by General Electric, as well as for a more than 10,000hour old lamp of the same type. The ageing was estimated considering a voltage rate increment of 2V
per 1000 operation hours.
EPE 2003 - Toulouse
ISBN : 90-75815-07-7
P.8
Design of a Resonant Power Source to Drive HPS Lamps
CHRISTIAN BRANAS REY Christian
(b)
(a)
Fig. 11: Experimental waveforms measured in (a) new LUCALOX lamp and (b) old LUCALOX
lamp. In both cases: Upper trace:Vlamp, Middle Trace: Plamp, Bottom Trace: Ilamp.
For the new lamp, the measured Rlamp, is 39Ω. The measured lamp current crest factor is CF=1.33,
below the maximum value, 1.7, recommended by [2]. For the old lamp, the power rises up to
Plamp=288W, Rlamp being 67Ω. Note that for a variation of ∆Rlamp/Rlamp=72%, the measured increment
of Plamp over the nominal value was only ∆Plamp/Plamp=15%, in accordance with the standard. The
measured CF of the lamp current was CF=1.15.
Metal Halide Lamps
Since the design accepts a large variation of the load, its performance has also been verified with
MH lamps. The deviation foreseen in MH lamps is from 2V to 4V per 1000 hours of operation.
Considering 10,000 hours of operation, a Rlamp equal to 105Ω can be considered at the end of the lamp
lifetime, which is in the range covered by this design. Two types of MH lamps were tested with an
initial Rlamp=36Ω and 54Ω respectively. The experimental waveforms are shown in fig.12.
(b)
(a)
Fig. 12: Experimental waveforms: (a) measured in a new HQI-T-250W Osram lamp. (b) measured in a
new HSI-T-250W Sylvania lamp. Upper trace: Vlamp, Middle Trace: Plamp, Bottom Trace: Ilamp.
The Sylvania HSI-T-250W lamp operating at 150kHz, free of acoustic resonance, is shown in the
photograph of fig. 13.
Fig. 13: Arc at 150kHz.
EPE 2003 - Toulouse
ISBN : 90-75815-07-7
P.9
Design of a Resonant Power Source to Drive HPS Lamps
CHRISTIAN BRANAS REY Christian
Turn-off switching losses
The calculation of capacitor CZ is carried out assuming that its charging time is much shorter than
the switching cycle. Thus, the capacitor CZ can be obtained from (25),
tD ≥
Vdc C Z
,
Iˆi Sinφ i
(25)
where tD is the dead time of the driver signals of transistors M1 and M2. The driver IR2111, with a
typical value of 600ns, imposes the dead time. Taking a safe margin in order to prevent short-circuit of
Vdc through M1 and M2, a maximum time of charge for CZ of 100ns was assumed. Substituting in (25)
the value of Cz is obtained, CZ=800pF. Finally, the experimental value used for CZ was 470pF. The
waveforms obtained in transistor M1 are shown below.
(a)
(b)
Fig.14: (a) Transistor waveforms vds and ids. (b) Switching losses.
Conclusions
A study of the sensitivity of the power supplied to a HPS lamp by LCsCp inverters and a new design
sequence for this circuit has been presented. The most variable element in the ballast circuit is Rlamp.
The design sequence limits the expected variation of Plamp regarding Rlamp below the standard
restriction. The sensitivity analysis allows us to evaluate how critical the components of the design
are, showing that the inductance L is the element whose variation produces the highest deviation in
Plamp. The experimental results verify a low distortion of the lamp current, with CF<1.7. Furthermore,
the design evaluation by the Monte Carlo method, in this case, predicts a good yield for industrial
production of the circuit.
References
[1]- G. Trestman, "Minimizing Cost of HID Lamp Electronic Ballast", Proceedings of the 28th Ann. Conf. of the
IEEE Industrial Electronics Society (IECON'02), Vol.2, pp.1214-1218.
[2]- "High Pressure Sodium Vapour Lamps", European Standard EN60662, June 1990.
[3]- J. Oslen and W. Moskowitz, "Optical Measurement of Acoustic Resonance Frequencies in HID Lamps",
IEEE Industry Applications Society Conference, Oct. 1997.
[4]- Marian K. Kazimerczuck, Wojciech Szaraniec, “Electronic Ballast for Fluorescent Lamps”, IEEE
Transactions on Power Electronics, Vol. 8, No. 4, October 1993, pp. 386-395.
[5]- Ch. Brañas, F. Azcondo, S. Bracho, “Study of Output Power Variation due to Component Tolerances in
LCsCp Resonant Inverters Applied to HPS Lamp Control”, Proceedings of IECON'01, pp. 1021-1026.
[6]- Ch. Brañas, F.J. Azcondo, S. Bracho, “Contributions to the Design and Control of LCsCp resonant Inverters
to Drive High Power HPS Lamps”, IEEE Trans. on Ind. Elect., Vol. 47, No. 4, August 2000, pp. 796-808.
[7]- Yiyoung Sun, “Using pSpice to Determine Lamp Current Variation Due to Electronic Ballast Component
Tolerances”, IEEE Trans. on Industry Applications, Vol. 33, No. 1, pp. 252-256, January/February 1997.
[8]- HSPICE User's Manual H9001, Meta-Software Inc. 1990.
[9]- R.V. White, "Component Tolerance and Circuit performance: A case of study", Proceedings of the 8th Ann.
Appl. Power Elec. Conf. (APEC'93), pp.922-927.
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ISBN : 90-75815-07-7
P.10