Lighting apparatus
8 claims: 7 independent, 1 dependent
- 1I claim as my invention:1. Lighting apparatus including a short-arc lamp of the xenon high-pressure type having a pair of electrodes between which an arc is fired, polyphase transformer means including variable reactance means connected in voltage-absorbing relationship with said transformer means, said reactance means including core means of the adjustable air-gap type, rectifier means of the silicon type connected to said transformer means for deriving direct-current output from said transformer means, and means connecting said rectifier means in direct-current power-supply relationship with said electrodes so that said output supplies a short arc between said electrodes, means connected to the reactance means for causing adjustment of the air gap to cause the voltagecurrent characteristic of said output to be correlated to the voltage-current characteristic of said lamp as the pressure in said lamp increases during the warm-up interval after said arc is first fired, so that said arc continues to burn from the instant when it is fired until after the final steady-state pressure is reached.
- 2Lighting apparatus including a short-arc lamp of the xenon high-pressure type having a pair of electrodes between which an arc is fired, polyphase transformer means including variable reactance means connected in voltageabsorbing relationship with said transformer means, said reactance means including core means of the adjustable air-gap type, rectifier means of the silicon type connected to said transformer means for deriving direct-current output from said transformer means, means connecting said rectifier means in direct-current power-supply relationship with said electrodes, high-frequency, high-voltage stabilizer means connected to said connecting means for firing said short arc between said electrodes, said output supplying said short arc between said electrodes, and means connected to said rectifier means and to said stabilizer means for suppressing flow of high-frequency current from said stabilizer to said rectifier means, means connected to the reactance means for causing adjustment of the air gap to cause the voltage-current characteristic of said output to be correlated to the voltage-current characteristic of said lamp as the pressure in said lamp increases during the warm-up interval after said arc is first fired, so that said arc continues to burn from the instant when it is fired until after the final steady state pressure is reached.
- 3Lighting apparatus including a short-arc lamp of the xenon high-pressure type having a pair of electrodes between which an arc is fired, polyphase transformer means including reactance means connected in voltageabsorbing relationship with said transformer means, said reactance means including core means of the air-gap type, and means connected to said core for varying the length of the air-gap thereof continuously to vary said reactance continuously, rectifier means of the silicon type connected to said transformer means for deriving direct-current output from said transformer means, and means connecting said rectifier means in direct-current power-supply relationship with said electrodes so that said output supplies a short arc between said electrodes, said varying means permitting the setting of said reactance to match the voltage-current characteristic of said output of the voltage-current characteristic of said lamp as the pressure in said lamp increases during the warm-up interval aftersaid arc is first fired, so that said arc continues to burn from the instant when it is fired until after the final steady state pressure is reached.
- 4Lighting apparatus including a short-arc lamp of the xenon high-pressure type having a pair of electrodes between which an arc is fired, polyphase transformer means including variable reactance means connected in voltage-absorbing relationship with said transformer means, said reactance means including core means of the adjustable air-gap type, rectifier means of the silicon type connected to said transformer means for deriving directcurrent output from said transformer means, means connecting said rectifier means in direct-current powersupply relationship with said electrodes, high-frequency, high-voltage stabilizer means connected to said connecting means for firing said short arc between said electrdes, and means connected to· said stabilizer means and responsive to the current conducted by said lamp for interrupting the operation of said stabilizer means when said current reaches a predetermined magnitude, means connected to said reactance means for causing adjustment of the air gap to cause the voltage-current characteristic of said output to be correlated to the voltage-current characteristic of said lamp, as the pressure in said lamp increases during the warm-up interval after said arc is first 3,249,809 fired, so that said arc continues to burn from the instant when it is fired until after the final steady state pressure is reached.
- 6Lighting apparatus including a short-arc lamp having a pair of electrodes between which an arc is fired, said electrodes being in a gaseous medium having a predetermined pressure in the absence of an arc, the pressure of said medium increasing during a warm-up interval after said arc is fired, until it reaches a substantially higher pressure than said predetermined pressure, the said apparatus including, polyphase transformer means, adjustable voltage-absorbing means connected in voltage-absorbing relationship with said transformer means, rectifier means connected to said transformer means for deriving direct-current output from said transformer means, means connecting said rectifier means in direct-current powersupply relationship with said electrodes, high-frequency, high-voltage stabilizer means connected to said connecting means for firing said short arc between said electrodes, and means connected to said stabilizer means and responsive to the current conducted by said lamp for interrupting the operation of said stabilizer means when said current is at a predetermined magnitude at which there is an established arc between said electrodes, means connected to said voltage-absorbing means for causing adjustment of said voltage-absorbing means to cause the voltage-current characteristic of said output to be correlated to the voltage-current characteristic of said lamp, as the pressure in said lamp increases during the warm-up interval after said arc is first fired, so that said arc continues to burn from the instant when it is fired until after the final steady state pressure is reached.
- 7Lighting apparatus including a short-arc lamp having a pair of electrodes between which an arc is fired, said electrodes being in a gaseous medium having a predetermined pressure in the absence of an arc, the pressure of said medium increasing during a warm-up interval after said arc is fired, until it reaches a substantially higher pressure than said predetermined-pressure, the said apparatus including, adjustable power-supply means having a predetermined output, means connecting said powersupply means in power-supply relationship with said electrodes, high-frequency, high-voltage stabilizer means connected to said connecting means for firing said short arc 8 between said electrodes, and means connected to said stabilizer means and responsive to the current conducted by said lamp for interrupting the operation of said stabilizer means when said current is at a predetermined magnitude at which there is an established arc between said electrodes, means connected to said power-supply means for causing adjustment of said power-supply means to cause the voltage-current characteristic of said output to be correlated to the voltage-current characteristic of said lamp, as the pressure in said lamp increases during the warm-up interval after said arc is first fired, so that said arc continues to burn from the instant when it is fired until after the final steady state pressure is reached.
- 8Apparatus for producing an arc between electrodes including a transformer having secondary winding means, variable reactance-winding means in circuit with said secondary winding means, rectifier means connected to said secondary winding means in rectifying relationship with the output of said secondary winding means, means connecting said rectifier means in D.C. arc power-supply relationship with said electrodes, a stabilizer connected to said electrodes, means connected to said stabilizer for energizing said stabilizer effectuating the firing of an arc between said electrodes when said electrodes are connected to said rectifier means as aforesaid, and means connected to said reactance-winding means and responsive to the arc current conducted by said reactance winding means for interrupting the energization of said stabilizer when an arc has been established between said electrodes. References Cited by the Examiner UNITED STATES PATENTS 1,076,884 10/1913 Hayden_____________313—29 1,154,852 9/1915 Fortescue____________321—12 1,977,193 10/1934 Logan_____________315—291 1,995,129 3/1935 Newill_____________315—281 2,265,930 12/1941 Scott_________ 315—282 2,429,162 10/1947 Keiser et al._________315—282 2,750,536 6/1956 Gomonet___________315—281 2,757,318 7/1956 Noel et al___________315—205 2,800,571 7/1957 Glenn et al.________219—131 2,892,126 6/1959 Popa____:__________315—205 2,923,858 2/1960 Trautner___________315—203 2,965,805 12/1960 Steinert_________315—281 X JOHN W. HUCKERT, Primary Examiner. DAVID J. GALVIN, Examiner. L. ZALMAN, Assistant Examiner.
Independent claims7
73 paragraphs in 12 sections, as filed
May 3, 1966
Filed Nov. 1, 1962
E F. STEINERT
LIGHTING APPARATUS
3,249,809
Sheets-Sheet 1
POWER SUPPLY
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LOWER
May 3, 1966 e. f. steinert 3,249,809
LIGHTING APPARATUS Filed Nov. 1, 1962 4 Sheets-Sheet 2
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May 3, 1966
3,249,809
E. F. STEINERT
LIGHTING APPARATUS
Sheets-Sheet 3
Filed Nov. 1, 1962
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May 3, 1966
E F. STEINERT
3,249,809
LIGHTING APPARATUS
Filed Nov. 1, 1962
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KVA INPUT
KW INPUT
KW OUTPUT o -----1-----1-----1----j-----u.—1-----1-----1——I-----1-----I-----1-----L
40 60 80 100 120 140
CURRENT OUTPUT- AMPERES
United States Patent Office
3,249,809
Patented May 3, 1966
3,249,809
LIGHTING APPARATUS
Emil F. Steinert, Williamsville, N.Y., assignor to Westinghouse Electric Corporation, East Pittsburgh, Pa., a corporation of Pennsylvania
Filed Nov. 1, 1962, Ser. No. 234,814
Claims. (Cl. 315—291)
This invention relates to the lighting art and has particular relationship to lighting apparatus in which high intensity light is produced. In its specific aspects this invention concerns itself with lighting apparatus in which the light is emitted by high pressure xenon and mercuryxenon lamps and the like. Lamps of this type are described in a paper by Wolfgang E. Thouret and George W. Gerunz presented before the National Technical Conference of the Illuminating Engineering Society on Septemper 13 through 17, 1954. This paper refers to other literature describing the xenon and mercury-xenon high pressure lamps. These lamps will be referred to herein as lamps or lighting units of the xenon type.
A lamp of the xenon type includes a pair of electrodes sealed in an envelope in which there is gas or vapor which may be xenon and mercury vapor produced by a droplet of mercury or xenon and krypton. The pressure of the gas with the lamp unenergized is approximately one atmosphere. The electrodes are spaced about four millimeters and in operation a relatively high power short arc is produced between the electrodes in the gas. Typically the lamps may be rated 2.5 to 7.5 kilowatts. The arc emits intense light in the visible part of the spectrum. By reason of the heat developed by the arc the gas is heated and its pressure increases to about 10 atmospheres or more. The warm-up time is of the order of 5 minutes. As the pressure of the gas increases, the voltage necessary to maintain the arc increases and the current decreases.
To fire the lamp a high frequency potential of about 30,000 or 40,000 volts is required. Once the arc is fired it may be maintained burning by a direct-current or lowfrequency alternating-current supply capable of delivering about 75 to 100 volts.
Lamps of the xenon type may be used where high intensity illumination is required. A typical such use is in the lighting of the extensions of the runways and the runways of airports. But recently such lamps have been used in solar simulators for simulating solar radiation in the testing of the skins of missiles and the like to determine the capability of skin material to withstand solar radiation. In solar simulators it is necessary that the light source have a precise demanded spectrum and a number of lamps of the xenon type requiring different energization are usually combined.
This invention contemplates complete lighting apparatus including the lamp of xenon type and its power supply. In solar simulators where a number of different lamps of different ratings and types are used it is necessary that the supply be capable of supplying power over the demanded wide range and it is a specific object of this invention to provide apparatus including such a power supply.
In accordance with the teachings of the prior art lighting apparatus both with static and with motor-generator power supplies have been provided but have proved unsatisfactory. In the use of a static power supply it is necessary to include ballast between the output terminals of the power supply and the arc load and for this purpose a ballast has been interposed. An important disadvantage in the use of a ballast resistor is the large power loss which results from the energy absorbed by the resistor. For example in the case of a 2½ kilowatt lamp the arc during steady state operation conducts 49 amperes and the voltage drop across the arc is 51 volts. Under such circumstances the resistor must absorb approximately 64 volts in a situation in which the lamp is supplied from a 115 volt supply. The loss in the resistor is then the product 5 of 64 volts and 49 amperes or 3136 watts. This loss is higher than the energy developed by the lighting arc. In addition, where the ballast is a resistor the voltage-ampere characteristic curve is relatively flat. As a result fluctuations in load voltage produce substantial fluctuations in IQ load current reducing the life of the lamp which is relatively high cost item (in excess of $500). In addition in the use of the ballast resistor apparatus the lamp requires an excessively long time to reach steady state.
A motor generator power supply includes a direct-cur15 rent magnetic field. . Such apparatus has a relatively high time constant and responds slowly to changes in the load. The lamps are then subjected to surges which materially shorten their life. In addition, the characteristic of a motor-generator power supply changes materially with 20 temperature. As the resistance of the shunt-field winding changes the output voltage and current are affected. The change in the output voltage and current may be as high as 10 or 15 percent. These changes affect the operation of the lamp and tend to shorten its life.
It is accordingly an object of this invention to provide lighting apparatus which shall not suffer from the above described disadvantages.
Another object of this invention is to provide lighting apparatus for producing highly intense light with a xenon<sup>30</sup> type lamp in the use of which the losses encountered in resistor-ballast supplies and the variations encountered in the use of resistor ballast supplies and motor-generator sets shall be avoided.
A further object of this invention is to provide lighting <sup>3o</sup> apparatus including a light source of the xenon type and a power supply which shall have a relatively low time constant and in the use of which sudden changes in the load shall not produce excessive surges which would tend to damage the light source.
<sup>4</sup> ' This invention arises from an understanding of the characteristic of the short arc from which the light is derived and from the realization that a power supply including voltage absorbing reactance can be adapted to the characteristic.
It has been discovered that in the operation of the lighting apparatus according to this invention it is most essential that the power supply characteristic be closely matched to the characteristic of the lamp during the warm<sub>5</sub>θ up interval. In a typical situation involving a 2½ kilowatt lamp of the xenon type this warm-up interval consumes about 5 minutes and during this interval the arc voltage across the short arc increases from approximately 15 volts to approximately 51 volts while the current decreases <sub>5</sub>g from about 75 amperes to about 49 amperes. The lamp reaches the 51 volt and 49 ampere current in about 5 minutes and during this five minutes it is essential that the power supply match the characteristic.
In accordance' with this invention lighting apparatus in00 eluding a lamp of the xenon type is provided in which the power supply is of the three phase rectifier type including substantially linear air core reactance for absorbing the voltage drop. Specifically, this apparatus includes a polyphase transformer in which the reactance is interposed. 65 A rectifier of the silicon-diode type is connected in directcurrent power deriving relationship with the output of the secondary of this transformer. The electrodes of the lamp are connected across the output of the power supply. Specifically, the power supply may be similar to a Westing70 house WS supply (see Steinert 2,965,805 and Steinert et al. 2,957,118).
One of the important features of this supply is that the
3,249,809 ώ
reactance is of the movable-core type in which the magnitude of the reactance is varied by varying the air gap of the core. The output and volt-current characteristic of this supply may be varied over a wide range by varying the air-gap length of the core. The variable reactance, does not tend to saturate at higher currents because of the air-gap and is substantially linear within the operating range. Distortion is thus minimized and the current ripple is of very small magnitude. The volt-ampere characteristic of the lamp during the warm-up interval and the arc in the lamp burns steadily during this interval and is stable thereafter. The ohmic resistance of the reactance and also of the transformer is relatively small so that the ohmic loss by reason of the voltage absorbed by the reactance is negligible. The variation in output as the temperature of this power supply changes is relatively small. But to the extent that there is a tendency for the resistance to increase with temperature this tendency is substantially compensated by the negative characteristic of the silicon-diode rectifier.
The power supply has a low time constant and responds to sudden load changes in a very short time interval so that the surges which tend to damage the light source are not present. In accordance with the specific aspects of this invention capacitance is interposed between the power supply and the stabilizer to prevent the high voltage from the stabilizer from damaging the silicon diodes of the rectifier.
The lamps of the xenon type which are available typically operate at 2½ kilowatts, 5 kilowatts and 7½ kilowatts. In a typical situation where the lamp is of the 2½ or 5 kilowatt rating and the gas in the lamp is either xenon or mercury-xenon the power supply has an opencircuit voltage of 105 volts and a load circuit voltage of 70 and a current rating of 125 amperes.
The novel features considered characteristic of this invention are described generally above. For a better understanding of this invention both as to its organization and as to its methods of operation together with additional objects and advantages thereof reference is made to the following description of a specific embodiment taken in connection with the accompanying drawings, in which:
FIGURE 1 is a schematic showing a preferred embodiment of this invention;
FIG. 2 is a view in perspective of a transformer-reactor unit which constitutes an important feature of the POWER SUPPLY in lighting apparatus in accordance with this invention;
FIG. 3 is a view in section of the unit shown in FIG. 2;
FIG. 4 is a graph showing the changes in current and voltage of a typical light source of the xenon type used in the practice of this invention during the warm-up period;
FIG. 5 is a graph showing the characteristic of the same lamp during the warm-up period;
FIG. 6 is a graph showing volt-ampere characteristics of the POWER SUPPLY; and •FIG. 7 is a graph showing the performance of the apparatus according to this invention.
The apparatus in accordance with this invention includes a LAMP and a POWER SUPPLY. The LAMP is of the xenon type and has electrodes El and E2.
The POWER SUPPLY includes a transformer reactor unit TR having primary windings Pl, P2 and P3 and secondary-reactor windings SRI, SR2, and SR3. The primary windings Pl, P2, P3 are wound on the legs LI, L2 and L3, of a fixed-reluctance transformer core CF held by strips 6. The secondary-reactor windings SRI, SR2, SR3 are wound partly on the legs LI, L2, L3 of the transformer core CF and partly on the leg L6-LS3 and the other two legs of a variable-reluctance reactor core CV. The secondary-reactor windings SRI, SR2 and SR3 each has a number of turns Tl, T2, T3, respectively, both on the leg L6-LS3 and the other two legs of the variable reluctance core CV and on the legs LI, L2, L3 of the fixed core CF and a number of turns TV1, TV2 and TV3 respectively only on the leg L6-LS3 and the other two legs. The turns TV1, TV2, TV3 constitute reactor turns the reactance of which is variable by varying the reluctance of core CV.
The P0WER4SUPPLY also includes the coil or winding CAD. This coil CAD is replaceably suspended from a mounting clip in bracket 1’1 about leg LS of core CV in inductive relationship with the coil. The current induced in coil CAD depends on the current flowing through, and the voltage absorbed by, the secondary-reactor windings SRI, SR2, SR3.
The primaries Pl, P2 and P3 are connected in delta, and are supplied from conductors Wl, W2 and W3 which may, in turn, be connected to the buses VI, V2, V3 of a commercial supply typically of 460 volts 60 cycles, through the contacts Ma, Mb, Me of a contactor M. Power factor correcting capacitors 6C, 7C, 8C are connected across conductors Wl, W2, W3. The coils of inverse-time relays ICR and 2CR are interposed in the primary delta and one or more thermal elements in the secondary-reactor SR (see Patent 3,125,703, granted March 17, 1964 to Rebuffoni-Steinert). The secondary-reactor windings SRI, SR2 and SR3 of secondary SR are preferably connected in a delta network although other connections are within the scope of the invention.
The apparatus also includes a main rectifier RX consisting of rectifier units 56α through 56/. The units 56a through 56/ are silicon diodes connected in a rectifying bridge network to the apices of the delta including the secondary-reactor windings SRI, SR2 and SR3. The rectifier has direct-current output conductors SL1 and SL2.
The conductors SL1 and SL2 are connected to the electrodes El and E2 of the LAMP through the secondary 2TS of the output transformer 2T of a stabilizer ST. The primary 2TP is energized from ST through the break contact 5CRa of relay 5CR. The coil of 5CR is energized from winding CAD when the current through the secondary windings SRI, SR2, SR3 reaches a magnitude corresponding to an established arc. To prevent the stabilization current which may be supplied at a voltage of 30,000 or 40,000 volts from damaging the diodes 56α through 56/ of the rectifier RX capacitor 2C shunts the rectifier RX. The coil of M is adapted to be energized from the secondary ITS of the transformer IT, the primary 1TP of which is connected to conductor V2 and V3. The coil M is adapted to be connected across the secondary ITS through the normally-closed contacts MTa of a circuit breaker MT and the start switch SW of the apparatus. The coil of circuit-breaker MT is adapted to be connected across secondary ITS through front contacts ICRa or 2CRa of the inverse-time relays or contact TGa of the thermal element TG and through the start switch SW. On the occurrence of excess current in one or more of the windings Pl, P2, P3 of the primary P or of overheating in the transformer one of the contacts ICRa, 2CRa or TGa is closed energizing the coil at and opening the contact MT to de-energize the apparatus.
The movable legs L4, L5, L6 of the variable reluctance core CV are continuously movable over their range of adjustment by a motor MO which is connected to the bar 12. The motor is of the single-phase split-phase type and is supplied from a portion of the primary 1PT. The direction in which the motor rotates is controlled by relays 3CR and 4CR, the coils of which may be selectively connected to the secondary ITS through a selector switch SW1. The relay 3CR is energized to raise the movable arms L4, L5 and L6 and the relay 4CR is energized to lower these arms. The contacts 3CRa and 3CR6 and 4CRa and 4CRZ> are interposed between the windings of the motor MO and the secondary 1TP so tbat the motor is rotated in the proper direction.
The coil of the raising relay 3CR is connected to the secondary ITS through a normally closed limit switch ILS which opens when the movable core reaches an
3,249,809 <sup>5</sup> uppermost position and the lowering core 4CR is similarly connected through the limit switch 2LS which opens when the core reaches a lowermost position. The switches ILS and 2LS are actuated by bar 12 which rides on shafts 14 and 16 and is guided by angles 38 secured to channel 7. The limit switches are positioned with reference to the core CV so that they operate to prevent damage to the LAMP.
In the use of the apparatus the movable legs L4, L5 and L6 of the variable-reluctance core CV are set by selectively operating relays 3CR and 4CR to correspond to the LAMP included in the apparatus. The switch SW is next· closed to apply a potential between the electrodes El and E2 and thereafter the stabilizer ST is energized to apply the firing high-frequency high voltage between the electrodes El and E2. The short arc is then fired and continues to burn. As the arc burns the voltage and the current change reaching a stable condition after about five minutes of warm-up.
The change in the voltage and the current during the warm-up period is shown graphically for a 2½ kilowatt LAMP in FIGURE 4. In this view voltage and current are plotted vertically in volts and amperes respectively and timed horizontally. It is seen that the voltage rises from a minimum magnitude of 15 volts to a plateau of about 51 volts while the current drops from a maximum magnitude of 75 amperes to a generally constant magnitude of about 49 amperes. The characteristic of the LAMP to which this variation corresponds is plotted in FIG. 5 in which the voltage across the short arc of the LAMP is plotted vertically in volts and the current through the arc is plotted horizontally in amperes.
Characteristics of the POWER SUPPLY are shown graphically in FIG. 6. These characteristics correspond to two remote settings of the variable-reluctance reactor CV. Specifically these settings may be with the movable core CV in its extreme positions. In the practice of this invention the characteristics may be changed continuously from the one corresponding to the curve on the right hand side to the one corresponding to the curve on the left hand side. By properly setting the variable-reluctance curve CV the reactors may be set to fit a characteristic of the selected lamp. To illustrate this feature of the apparatus the characteristic curve shown in FIGURE 5 is plotted in FIGURE 6. It is seen that for a proper setting of the variable-reluctance cores CV reasonably precise matching to the lamp characteristic may be achieved.
In. FIGURE 7 the performance of the apparatus according to this invention, with a 2½ kilowatt lamp is shown graphically. Kilowatts and kilovolt-amperes and efficiency and power in .percent are plotted vertically and the current conducted by the LAMP in amperes is plotted horizontally. The power factor and efficiency are derived from the kilovolt-ampere input and kilowatt input and output curves. It is seen that the power factor during steady state operation exceeds 70% and that the efficiency is very nearly 80%. The loss in prior art apparatus encountered in the ballast resistor is thus avoided.
While a preferred embodiment of this invention has been disclosed herein many modifications thereof -are possible. This invention then is not to be restricted except insofar as is necessitated by the spirit of the prior art.
Contents12
11 sheets
Sheet 1 Sheet 2 Sheet 3 Sheet 4 Sheet 5 Sheet 6 Sheet 7 Sheet 8 Sheet 9 Sheet 10 Sheet 11
Every citation, both ways
| Document | Relation | Office | Cited during |
|---|---|---|---|
| US3336681A | Cited by | United States of America | Search report |
| US3787751A | Cited by | United States of America | Search report |
| US1076884A | Cites | United States of America | Search report |
| US1154852A | Cites | United States of America | Search report |
| US1977193A | Cites | United States of America | Search report |
| US1995129A | Cites | United States of America | Search report |
| US2265930A | Cites | United States of America | Search report |
| US2429162A | Cites | United States of America | Search report |
| US2750536A | Cites | United States of America | Search report |
| US2757318A | Cites | United States of America | Search report |
| US2800571A | Cites | United States of America | Search report |
| US2892126A | Cites | United States of America | Search report |
| US2923858A | Cites | United States of America | Search report |
| US2965805A | Cites | United States of America | Search report |
2 priority claims, no other members on record
Priority claims2
| Document | Office | Kind | Date |
|---|---|---|---|
| 23481462 | United States of America | A | |
| US19620234814 | – | – | – |
Numbers
- Publication, DOCDB
- 3249809
- Publication, EPODOC
- US3249809
- Application
- 234814
- Application, DOCDB
- 23481462
- Application, EPODOC
- US19620234814
Titles
- English
- Lighting apparatus
Classification
- CPC, 1
- H05B41/231
- IPC, 1
- H05B41 231
