CN1630452A - A fluorescent lamp filament preheating startup apparatus based on frequency conversion technique and design method thereof - Google Patents

Abstract

This invention refers to a frequency change technology based fluorescent lamp filament preheating activator and design method thereof, which contains lamp tube and semi bridge driving circuit, LC inductance capacitance resonant circuit set between semi bridge circuit, a transformer its primary serial connected with LC inductance capacitance resonant circuit and two secondary respectively connected with filament in two ends of lamp tube, a control switch for controlling transformer, electronic rectifier control IC its output end connected with semi bridge driving circuit to generate a control signal controlling switch on and off. Said method contains (1), converting circuit into equivalent circuit diagram, (2), setting parameter for equivalent circuit diagram. Said invention changes the work frequency of fluorescent lamp in preheating and normal work period, the switch and transformer provide adaptive preheating current in preheat period and make short circuit connection in normal work to reduce filament current and intensify preheat effect and prolong filament service life.

Description

A kind of Filament of fluorescent lamp pipeline start up by preheating device and method for designing thereof based on converter technique

Technical field

The present invention relates to a kind of electron rectifier circuit, relate in particular to a kind of Filament of fluorescent lamp pipeline start up by preheating device and method for designing thereof in the electron rectifier circuit that is applicable to the independent-excited half-bridge driven based on converter technique.

Background technology

It is that first build-up of luminance preheating starts luminous then that fluorescent lamp triggers startup.But in the prior art, fluorescent lamp trigger to start and not to bear glow discharge owing to filament reaches the thermionic emission state usually, thereby causes the serious sputter of cathode emission material, make filament on every side tube wall turn black in early days, reduced the life-span of fluorescent lamp.

In order to improve the life-span of fluorescent lamp, people have improved the preheating technology of fluorescent lamp, because the fluorescent lamp warm of prior art, thereby still influence life-span with filament of lighting of fluorescent lamp, therefore not have to solve the problem of lamp longevity reduction at all.

Summary of the invention

The object of the present invention is to provide a kind of Filament of fluorescent lamp pipeline start up by preheating device and method for designing thereof based on converter technique, the pipeline start up by preheating that its adopts converter technique to realize utilizes the frequency that changes series resonant tank and the circuit working point is changed reach pipeline start up by preheating.

The object of the present invention is achieved like this:

A kind of Filament of fluorescent lamp pipeline start up by preheating device based on converter technique comprises: fluorescent tube, and the half-bridge drive circuit of driving fluorescent tube is characterized in also comprising:

One LC inductance capacitance resonant tank, this LC inductance capacitance resonant tank is arranged between the half-bridge drive circuit of fluorescent tube;

Transformer, the elementary of this transformer is connected in the LC inductance capacitance resonant tank, two in transformer secondary respectively with the parallel connection of lamp tube ends filament;

One control switch S1, this control switch S1 is used for the work of control transformer;

One electron rectifier control integrated circuit, the output of electron rectifier control integrated circuit is connected with half-bridge drive circuit; The electron rectifier control integrated circuit also will produce a control signal, the closed and unlatching of control switch S1.

In above-mentioned Filament of fluorescent lamp pipeline start up by preheating device based on converter technique, wherein, described LC inductance capacitance resonant tank is by two capacitor C 1 and C2, and the inductance L that connects between two capacitor C 1 and the C2 forms, and inductance L is connected with fluorescent tube one end with the tie-point of capacitor C 2; Described primary is connected with the end in addition of capacitor C 2.

In the above-mentioned Filament of fluorescent lamp pipeline start up by preheating device based on converter technique, wherein, described control switch S1 is a transistor circuit.

In the above-mentioned Filament of fluorescent lamp pipeline start up by preheating device based on converter technique, wherein, described control switch S1 is made of silicon-controlled device.

A kind of Filament of fluorescent lamp pipeline start up by preheating Design of device method of making above-mentioned based on converter technique is characterized in may further comprise the steps:

1) circuit diagram is deformed into equivalent circuit diagram, at the fluorescent tube warm-up phase, switch S 1 disconnects, the frequency of A point input signal Vin is set to a high frequency fpre away from LC resonant tank 3 resonance points, at this moment, the voltage Vlamp that A is ordered is very low, and equivalent electric circuit is equivalent to the fluorescent tube open circuit;

2) parameter of equivalent electric circuit is set:

R ₂, R ₃Be the equivalent resistance of filament, R ₂=R ₃(1)

R ₁The filament resistance that is transformer secondary output is coupled to elementary equiva lent impedance,

$R_1={\left(\frac{M}{N}\right)}^2{R}_2={\left(\frac{M}{N}\right)}^2{R}_3----\left(2\right)$

M, N are the primary and the secondary number of turns,

U ₁Be the voltage on the primary,

U ₁=I _C2R ₁, (I _C2Be the electric current on the C2) (3)

I _C2Be C in the resonant tank ₂On electric current, ${\mathrm{<figure-callout\; id="2"\; label="I\; C"\; filenames="A20031010939000112.png"\; state="\{\{state\}\}">I</figure-callout>}}_C=\frac{V_{\mathrm{in}}}{\left|\mathrm{j\&omega;L}\right|+\frac{1}{\left|\mathrm{j\&omega;}{\mathrm{<figure-callout\; id="1"\; label="C"\; filenames="A20031010939000112.png,A20031010939000121.png"\; state="\{\{state\}\}">C</figure-callout>}}_1\right|}+\frac{1}{\left|\mathrm{j\&omega;}{\mathrm{<figure-callout\; id="2"\; label="C"\; filenames="A20031010939000112.png"\; state="\{\{state\}\}">C</figure-callout>}}_2\right|}+{\mathrm{<figure-callout\; id="1"\; label="R"\; filenames="A20031010939000112.png,A20031010939000121.png"\; state="\{\{state\}\}">R</figure-callout>}}_1},\mathrm{\&omega;}=2\mathrm{\&pi;f},$

At warm-up phase, f=f _Pre, because fpre is the high frequency away from resonance point, so ω=2 π f _PreIt is very big, $\frac{1}{\left|\mathrm{j\&omega;}{\mathrm{<figure-callout\; id="1"\; label="C"\; filenames="A20031010939000112.png,A20031010939000121.png"\; state="\{\{state\}\}">C</figure-callout>}}_1\right|},\frac{1}{\left|\mathrm{j\&omega;}{\mathrm{<figure-callout\; id="2"\; label="C"\; filenames="A20031010939000112.png"\; state="\{\{state\}\}">C</figure-callout>}}_2\right|},{\mathrm{<figure-callout\; id="1"\; label="R"\; filenames="A20031010939000112.png,A20031010939000121.png"\; state="\{\{state\}\}">R</figure-callout>}}_1$ Very little, the impedance of resonant tank is based on induction reactance, promptly

$\left|\mathrm{j\&omega;L}\right|>>\frac{1}{\left|\mathrm{j\&omega;}{\mathrm{<figure-callout\; id="1"\; label="C"\; filenames="A20031010939000112.png,A20031010939000121.png"\; state="\{\{state\}\}">C</figure-callout>}}_1\right|}+\frac{1}{\left|\mathrm{j\&omega;}{\mathrm{<figure-callout\; id="2"\; label="C"\; filenames="A20031010939000112.png"\; state="\{\{state\}\}">C</figure-callout>}}_2\right|}+{\mathrm{<figure-callout\; id="1"\; label="R"\; filenames="A20031010939000112.png,A20031010939000121.png"\; state="\{\{state\}\}">R</figure-callout>}}_1,$

So have ${\mathrm{<figure-callout\; id="2"\; label="I\; C"\; filenames="A20031010939000112.png"\; state="\{\{state\}\}">I</figure-callout>}}_C\&ap;\frac{V_{\mathrm{in}}}{\left|\mathrm{j\&omega;L}\right|},\mathrm{\&omega;}=2\mathrm{\&pi;}{f}_{\mathrm{pre}}----\left(4\right)$

Therefore, fpre during preheating, L, certain, I _C2Substantially constant;

U ₂, U ₃Be respectively the induced voltage of two secondary winding of transformer,

${\mathrm{<figure-callout\; id="2"\; label="U"\; filenames="A20031010939000112.png"\; state="\{\{state\}\}">U</figure-callout>}}_2={\mathrm{<figure-callout\; id="3"\; label="U"\; filenames="A20031010939000112.png,A20031010939000131.png"\; state="\{\{state\}\}">U</figure-callout>}}_3=\frac{N}{M}{U}_1----\left(5\right)$

Get from (1)～(5) formula, the preheat curent that flows through filament is:

The present invention, a kind of Filament of fluorescent lamp pipeline start up by preheating device and method for designing thereof based on converter technique owing to adopted above-mentioned technical scheme, make it compared with prior art, have following advantage and good effect:

1. the present invention passes through to change the operating frequency of fluorescent lamp in preheating and normal work stage, thereby has realized pipeline start up by preheating;

2. switch of the present invention and transformer are supplied with the suitable preheat curent of filament at warm-up phase, strengthened pre-heat effect, after finishing, the fluorescent tube preheating enters normal work stage, the frequency of A point input signal Vin changes to the frequency f work of close resonance point from fpre, light tube electric voltage Vlamp is raise rapidly, fluorescent tube punctures to be lighted, so the fluorescent tube pre-heat effect is good;

3. the present invention is behind fluorescent lamp starting, and the lamp tube ends filament has reduced heater current respectively by short circuit, has guaranteed the life-span of filament.

4. the present invention utilizes control signal of the direct output of electron rectifier control integrated circuit to come control switch S1, makes the electron rectifier circuit simple and practical thus.

Description of drawings

By following to the present invention a kind of based on converter technique Filament of fluorescent lamp pipeline start up by preheating device and an embodiment of method for designing in conjunction with the description of its accompanying drawing, can further understand purpose of the present invention, specific structural features and advantage.Wherein, accompanying drawing is:

Fig. 1 be in lamp tube ends voltage and the inductance capacitance loop signal frequency concern schematic diagram;

Fig. 2 is the electrical schematic diagram of a kind of Filament of fluorescent lamp pipeline start up by preheating device based on converter technique of the present invention;

Fig. 3 is the equivalent circuit diagram during the fluorescent tube preheating in Fig. 2 circuit;

Fig. 4 be in Fig. 3 circuit during the fluorescent tube preheating in lamp tube ends voltage and the inductance capacitance loop signal frequency concern schematic diagram;

Fig. 5 is the equivalent circuit diagram after the fluorescent tube preheating finishes in Fig. 2 circuit;

Fig. 6 is the schematic diagram that concerns that the fluorescent tube preheating finishes signal frequency in back fluorescent tube both end voltage and the inductance capacitance loop in Fig. 5 circuit;

Fig. 7 is the equivalent circuit diagram behind the lamp tube starting in Fig. 2 circuit.

Embodiment

The fluorescent lamp pipeline start up by preheating is meant that the lamp electrode is heated to the temperature back light ability triggered as normal startup (it just is the thermionic emission state that the temperature of electronics emission must be higher than 700 ℃) of electronics emission.Therefore, for the electronic rectifier of fluorescent lamp of pipeline start up by preheating mode, adopt control cathode electric current or two kinds of forms of control cathode voltage pipeline start up by preheating usually.But no matter be the startup of adopting any mode, all must satisfy following requirement:

1. before negative electrode reached the electronics emission state, the open circuit voltage at lamp two ends should be enough low, fluorescent tube not conducting substantially this moment, and cathode fluorescent tube can cold shock not be sent out and filament is suffered damage;

2. after negative electrode was reaching emission state, open circuit voltage should be enough high, and lamp is started rapidly;

3. in the cathode preheat stage, warm must be fully.If preheating is insufficient, certainly will causes cold shock to be sent out and influence life-span of filament;

4. after fluorescent lamp starting was finished, what the pressure drop on the filament should be enough was little, guaranteed that filament can not influence the life-span because of overcurrent.

For this reason, the pipeline start up by preheating that the present invention adopts converter technique to realize is to utilize the frequency that changes series resonant tank and the circuit working point is changed reach the purpose of pipeline start up by preheating.

See also shown in Figure 1, Fig. 1 be in fluorescent lamp tube 1 both end voltage Vlamp and the LC loop signal frequency concern schematic diagram.Among Fig. 1, Fc is the resonance point of LC inductance capacitance resonant tank, $F_c=\frac{1}{2\mathrm{\&pi;}\sqrt{\mathrm{LC}}}.$

When the fluorescent lamp preheating, the operating frequency of setting LC inductance capacitance resonant tank is fpre, and as the point of the B among Fig. 1, at this moment, 1 both end voltage Vlamp is very low for fluorescent tube, and fluorescent tube is in preheat mode and can light.

When the fluorescent lamp operate as normal, the operating frequency of resonant tank changes to fwork by fpre, and promptly the point of the B from Fig. 1 moves on to the A point.This moment, lamp tube ends voltage Vlamp raise rapidly, and fluorescent tube is breakdown to be lighted.

See also shown in Figure 2ly, Fig. 2 is the electrical schematic diagram of a kind of Filament of fluorescent lamp pipeline start up by preheating device based on converter technique of the present invention.The present invention, Filament of fluorescent lamp pipeline start up by preheating device based on converter technique, comprise: the half-bridge drive circuit 2 of fluorescent tube 1 and driving fluorescent tube 1, also comprise: a LC inductance capacitance resonant tank 3, this LC inductance capacitance resonant tank 3 is arranged between fluorescent tube 1 and the half-bridge drive circuit 2, wherein inductance L is connected with fluorescent tube 1, capacitor C 1 and the mid point A place that is connected half-bridge drive circuit 2 after inductance L is connected in series; One transformer 4, is the number of turns of this transformer 4 than being M: N, the elementary (filter capacitor that passes through of transformer 4?) capacitor C 2 is connected in the LC inductance capacitance resonant tank 3,4 two in transformer secondary respectively with the parallel connection of lamp tube ends filament; One control switch S1, this control switch S1 is used for the work of control transformer 4; One electron rectifier control integrated circuit 5, the output of this electron rectifier control integrated circuit 5 are connected with half-bridge drive circuit 2 control switch S1 respectively.

Work and the control principle of Fig. 2 are that the effect of transformer 3 is preheat curents that filament is provided when fluorescent tube 1 preheating, turn-offs heater current during operate as normal; The effect of electron rectifier control integrated circuit 5 and half-bridge drive circuit 2 is to produce a variable-frequency pulse signal Vin at half-bridge mid point A point, is operated in different working points to drive LC resonant tank 3; Simultaneously, electron rectifier control integrated circuit 5 also will produce a control signal, the closed and unlatching of control switch S1.

It is as follows to make above-mentioned a kind of Filament of fluorescent lamp pipeline start up by preheating Design of device method based on converter technique.

Please in conjunction with Fig. 2 referring to shown in Fig. 3,4, Fig. 3 is the equivalent circuit diagram during the fluorescent tube preheating in Fig. 2 circuit, Fig. 4 be in Fig. 3 circuit in the lamp tube ends voltage Vlamp during the fluorescent tube preheating and the LC loop signal frequency concern schematic diagram.The elementary of transformer 3 among Fig. 3 is connected in the LC resonant tank 3 by capacitor C 2, two of transformer 3 secondary respectively with fluorescent tube 1 two ends filament parallel connection, its effect is the preheat curent that filament is provided when fluorescent tube 1 preheating, turn-offs heater current during operate as normal.

Please in conjunction with Fig. 3 referring to shown in Figure 4, the course of work of circuit shown in Figure 3 is:

At warm-up phase, switch S 1 disconnects, and the frequency of A point input signal Vin is set to a high frequency fpre (see figure 4) away from LC resonant tank 3 resonance points; At this moment, the voltage Vlamp that A is ordered is very low, and fluorescent tube is equivalent to open circuit, is equivalent to the equivalent circuit diagram of Fig. 5 this moment.

Please in conjunction with Fig. 2 referring to shown in Figure 5, Fig. 5 is the equivalent circuit diagram of the equivalent circuit diagram after the fluorescent tube preheating finishes in Fig. 2 circuit.Among Fig. 5:

R ₂, R ₃Be the equivalent resistance of filament, R ₂=R ₃(1)

R1 is that the filament resistance of transformer secondary output is coupled to elementary equiva lent impedance,

${\mathrm{<figure-callout\; id="1"\; label="R"\; filenames="A20031010939000112.png,A20031010939000121.png"\; state="\{\{state\}\}">R</figure-callout>}}_1={\left(\frac{M}{N}\right)}^2{\mathrm{<figure-callout\; id="2"\; label="R"\; filenames="A20031010939000112.png"\; state="\{\{state\}\}">R</figure-callout>}}_2={\left(\frac{M}{N}\right)}^2{R}_3----\left(2\right)$

U ₁Be the voltage on the primary,

U ₁=I _C2R ₁, (I _C2Be C ₂On electric current) (3)

I _C2Be C in the resonant tank ₂On electric current, ${\mathrm{<figure-callout\; id="2"\; label="I\; C"\; filenames="A20031010939000112.png"\; state="\{\{state\}\}">I</figure-callout>}}_C=\frac{V_{\mathrm{in}}}{\left|\mathrm{j\&omega;L}\right|+\frac{1}{\left|\mathrm{j\&omega;}{\mathrm{<figure-callout\; id="1"\; label="C"\; filenames="A20031010939000112.png,A20031010939000121.png"\; state="\{\{state\}\}">C</figure-callout>}}_1\right|}+\frac{1}{\left|\mathrm{j\&omega;}{\mathrm{<figure-callout\; id="2"\; label="C"\; filenames="A20031010939000112.png"\; state="\{\{state\}\}">C</figure-callout>}}_2\right|}+{\mathrm{<figure-callout\; id="1"\; label="R"\; filenames="A20031010939000112.png,A20031010939000121.png"\; state="\{\{state\}\}">R</figure-callout>}}_1},\mathrm{\&omega;}=2\mathrm{\&pi;f},$

At warm-up phase, f=f _Pre, because fpre is the high frequency away from resonance point, so ω=2 π f _PreIt is very big, $\frac{1}{\left|\mathrm{j\&omega;}{\mathrm{<figure-callout\; id="1"\; label="C"\; filenames="A20031010939000112.png,A20031010939000121.png"\; state="\{\{state\}\}">C</figure-callout>}}_1\right|},\frac{1}{\left|\mathrm{j\&omega;}{\mathrm{<figure-callout\; id="2"\; label="C"\; filenames="A20031010939000112.png"\; state="\{\{state\}\}">C</figure-callout>}}_2\right|},{\mathrm{<figure-callout\; id="1"\; label="R"\; filenames="A20031010939000112.png,A20031010939000121.png"\; state="\{\{state\}\}">R</figure-callout>}}_1$ Very little, the impedance of resonant tank is based on induction reactance, promptly

$\left|\mathrm{j\&omega;L}\right|>>\frac{1}{\left|\mathrm{j\&omega;}{\mathrm{<figure-callout\; id="1"\; label="C"\; filenames="A20031010939000112.png,A20031010939000121.png"\; state="\{\{state\}\}">C</figure-callout>}}_1\right|}+\frac{1}{\left|\mathrm{j\&omega;}{\mathrm{<figure-callout\; id="2"\; label="C"\; filenames="A20031010939000112.png"\; state="\{\{state\}\}">C</figure-callout>}}_2\right|}+{\mathrm{<figure-callout\; id="1"\; label="R"\; filenames="A20031010939000112.png,A20031010939000121.png"\; state="\{\{state\}\}">R</figure-callout>}}_1,$

So have ${\mathrm{<figure-callout\; id="2"\; label="I\; C"\; filenames="A20031010939000112.png"\; state="\{\{state\}\}">I</figure-callout>}}_C\&ap;\frac{V_{\mathrm{in}}}{\left|\mathrm{j\&omega;L}\right|},\mathrm{\&omega;}=2\mathrm{\&pi;}{f}_{\mathrm{pre}}----\left(4\right)$

Therefore, fpre during preheating, L, certain, IC2 is constant substantially.

U ₂, U ₃Be respectively the induced voltage of two secondary winding of transformer,

${\mathrm{<figure-callout\; id="2"\; label="U"\; filenames="A20031010939000112.png"\; state="\{\{state\}\}">U</figure-callout>}}_2={\mathrm{<figure-callout\; id="3"\; label="U"\; filenames="A20031010939000112.png,A20031010939000131.png"\; state="\{\{state\}\}">U</figure-callout>}}_3=\frac{N}{M}{U}_1----\left(5\right)$

Get from (1)～(5) formula, the preheat curent that flows through filament is:

From Fig. 5 and above-mentioned relation formula as can be seen, when preheating, two secondary winding of transformer are equivalent to two voltage sources, provide preheat curent to filament; And the size that the filament pre-heating electric current is provided can be by the primary and secondary ratio of winding (M: N) change (seeing equation (6)) of conversion transformer under the certain condition of pre-heat frequency.

Please in conjunction with Fig. 5 referring to shown in Figure 6, Fig. 6 is the schematic diagram that concerns that the fluorescent tube preheating finishes signal frequency in back fluorescent tube both end voltage and the inductance capacitance loop in Fig. 5 circuit.Enter normal work stage after preheating finishes, the frequency of A point input signal Vin changes to the frequency f work of close resonance point from fpre; At this moment, fluorescent tube 1 voltage Vlamp raises rapidly, fluorescent tube 1 is punctured light, and the fluorescent tube after lighting is equivalent to be connected in parallel on the resistance on the C2, is equivalent to the equivalent circuit diagram of Fig. 7 this moment.

Please in conjunction with Fig. 2 referring to shown in Figure 7, Fig. 7 is the equivalent circuit diagram behind the lamp tube starting in Fig. 2 circuit.Among Fig. 7, after fluorescent lamp 1 operate as normal, because switch S 1 closure, transformer 3 is elementary by short circuit, U ₁=0, so 3 two secondary induced voltage U of transformer ₂=U ₃=0, be equivalent to fluorescent tube 1 two ends filament respectively by short circuit, at this moment, heater current I _Filament=0.

In sum, the present invention a kind of Filament of fluorescent lamp pipeline start up by preheating device and method for designing thereof based on converter technique by changing the operating frequency of fluorescent lamp in preheating and normal work stage, have realized pipeline start up by preheating; Simultaneously,, strengthened pre-heat effect, when operate as normal, then made the filament short circuit, reduced heater current, guaranteed the life-span of filament because switch and transformer are supplied with the suitable preheat curent of filament at warm-up phase; Pre-heat effect of the present invention is obvious, and the electron rectifier circuit that high-power senior executive presses fluorescent lamp that especially suits to be applied to is therefore very practical.

Claims (5)

1. Filament of fluorescent lamp pipeline start up by preheating device based on converter technique comprises: fluorescent tube (1), drive the half-bridge drive circuit (2) of fluorescent tube (1), and it is characterized in that also comprising:

One LC inductance capacitance resonant tank (3), this LC inductance capacitance resonant tank (3) are arranged between the half-bridge drive circuit (2) of fluorescent tube (1);

Transformer (4), the elementary of this transformer (4) is connected in the LC inductance capacitance resonant tank (3), (4) two in transformer secondary respectively with the parallel connection of lamp tube ends filament;

One control switch S1, this control switch S1 is used for the work of control transformer (4);

One electron rectifier control integrated circuit (5), the output of electron rectifier control integrated circuit (5) is connected with half-bridge drive circuit (2); Electron rectifier control integrated circuit (5) also will produce a control signal, the closed and unlatching of control switch S1.

2. the Filament of fluorescent lamp pipeline start up by preheating device based on converter technique as claimed in claim 1, it is characterized in that: described LC inductance capacitance resonant tank (3) is by two capacitor C 1 and C2, and the inductance L that connects between two capacitor C 1 and the C2 forms, and inductance L is connected with fluorescent tube (1) one end with the tie-point of capacitor C 2; Described transformer (4) is elementary to be connected with the end in addition of capacitor C 2.

3. the Filament of fluorescent lamp pipeline start up by preheating device based on converter technique as claimed in claim 1, it is characterized in that: described control switch S1 is a transistor circuit.

4. the Filament of fluorescent lamp pipeline start up by preheating device based on converter technique as claimed in claim 1, it is characterized in that: described control switch S1 is made of silicon-controlled device.

5. make above-mentioned Filament of fluorescent lamp pipeline start up by preheating Design of device method for one kind, it is characterized in that may further comprise the steps based on converter technique:

1) circuit diagram is deformed into equivalent circuit diagram, at the fluorescent tube warm-up phase, switch S 1 disconnects, the frequency of A point input signal Vin is set to a high frequency fpre away from LC resonant tank 3 resonance points, at this moment, the voltage Vlamp that A is ordered is very low, and equivalent electric circuit is equivalent to the fluorescent tube open circuit;

2) parameter of equivalent electric circuit is set:

R ₂, R ₃Be the equivalent resistance of filament, R ₂=R ₃(1)

R ₁The filament resistance that is transformer secondary output is coupled to elementary equiva lent impedance,

$R_1={\left(\frac{M}{N}\right)}^2{R}_2={\left(\frac{M}{N}\right)}^2{R}_3---\left(2\right)$

M, N are the primary and the secondary number of turns,

U ₁Be the voltage on the primary,

U ₁=I _C2R ₁, (I _C2Be the electric current on the C2) (3)

I _C2Be C in the resonant tank ₂On electric current, $L_{C2}=\frac{V_{\mathrm{in}}}{\left|\mathrm{j\&omega;L}\right|+\frac{1}{\left|\mathrm{j\&omega;}{C}_1\right|}+\frac{1}{\left|\mathrm{j\&omega;}{C}_2\right|}+R_1},\mathrm{\&omega;}=2\mathrm{\&pi;f},$

At warm-up phase, f=f _Pre, because f _PreBe high frequency, so ω=2 π f away from resonance point _PreIt is very big,

Very little, the impedance of resonant tank is based on induction reactance, promptly

$\left|\mathrm{j\&omega;L}\right|>>\frac{1}{\left|\mathrm{j\&omega;}{C}_1\right|}+\frac{1}{\left|j{\mathrm{\&omega;C}}_2\right|}+R_1,$

So have $I_{C2}\&ap;\frac{V_{\mathrm{in}}}{\left|\mathrm{j\&omega;L}\right|},\mathrm{\&omega;}=2\mathrm{\&pi;}{f}_{\mathrm{pre}}---\left(4\right)$

Therefore, fpre during preheating, L, certain, I _C2Substantially constant;

U ₂, U ₃Be respectively the induced voltage of two secondary winding of transformer,

$U_2=U_3=\frac{N}{M}{U}_1---\left(5\right)$

Get from (1)～(5) formula, the preheat curent that flows through filament is:

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