Design of CCFL Backlight Inverters with Frame & Bar Cores Summary Portable devices, such as notebook computers and personal digital assistants are developed rapidly nowadays, which places an increasing demand on display technology. The LCD with cold cathode fluorescent back lighting satisfies the requirements on display performance, size and efficiency. The backlight inverter plays a crucial role in supplying the power to the lamps of these flat-panel displays. The frame and bar ferrite cores, described in this brochure, are especially designed to build the slender, low profile transformers required for these inverters. A worked out design example is given, as well as data sheets of the standard range of 4 sizes frame and bare cores in 3C90 and 3C91, including the dedicated SMD coil formers. Contents page 1. Introduction 2. Design example 2.1. General 2.2. Choice of capacitance values on the secondary side 2.3. Transformer design 2.3.1. Circuit analysis 2.3.2. Transfer function 2.4. Core losses 2.5. Winding design 2.6. Copper losses 2.7. Losses, efficiency and temperature rise of the transformer 3 4 4 4 5 5 6 7 7 8 8 Appendix A Derivation of the transfer function of the resonant tank 9 Appendix B Determination of currents and voltages in the resonant tank 11 Appendix C Product range and materials 14 Fig.1 Exploded view of a Frame and Bar core assembly with wired bobbin 2 Ferroxcube 1. Introduction Portable devices, such as notebook computers and personal digital assistants (PDA) are developed rapidly nowadays, which places an increasing demand on display technology. Notebooks use very powerful and thus energy consuming processors; the processor consumes up to 60% while the backlight inverter needs only 10 to 20% of the battery power. The tasks of a PDA are less and so are the requirements of its processor. In PDAs almost 95% of the total battery power is needed for backlighting. This requires a very efficient backlight inverter, even more than in notebooks in order to increase the battery run-time. Cold cathode fluorescent lamps (CCFL) are used for backlighting of the LCD and satisfy the requirements on display performance, size and efficiency. A sinusoidal voltage across and current through the lamp is preferred to minimize EMI and maximize the lamp efficiency. While the displays get thinner, there is a tendency to restrict the space reserved for the backlight inverter to a very limited volume. Both height and width of the inverter are critical parameters. The transformer is usually the largest and highest component on the board. To avoid high voltage breakdown, the coil former must be quite long to provide enough distance between beginning and end of the secondary winding. Also it should have multiple sections to keep the winding capacitance within reasonable limits. Optimization of the magnetics for maximum throughput power under these conditions leads to very long and narrow core designs in which traditional core shapes like E or EFD are not always suitable anymore. Any deformation or shifting of the long core legs will cause variations in inductance of the transformer due to misalignment of the narrow mating faces. This makes it difficult to achieve a repeatable production of transformers or inductors. To avoid this problem, the magnetic circuit can be constructed with a closed ferrite frame and flat bar. In this way deformation does not play a major role anymore and mating faces have a larger surface area. Mounting of the transformer has become easy while inductance values are more repeatable. The frame and bar cores (including dedicated SMD coil formers) are standard available in 4 sizes and made of the low loss power ferrites 3C90 and 3C91. Other sizes are available on request. The 9 mm wide Frame cores can drive a lamp of approximately 3-4 W, the 10 mm wide core is suitable for 4-5 W lamps and the 12 mm wide type does 5-6 W. They are intended for use in Notebook PCs. In larger LCD monitors, 6-8 W is required for usually 2 or more backlighting lamps. The 15 mm wide core set is designed for this power level. lamp inverter Fig.2 Example of Notebook computer with LCD backlighting 3 Ferroxcube 2. Design example 2.1 General The backlight inverter described in this application note is based upon the principle of the Royer oscillator. As this oscillator is very basic with hardly no protections, nowadays most inverters make use of dedicated control ICs and a resonant tank to provide the high voltage transformer with a regulated sinusoidal voltage. The schematic diagram is shown in figure 3. Monitoring the voltage across Rcur gives information about the lamp current but it also detects fault conditions like broken lamps. Another basic feature of the IC is a dim function. The basic operation of the backlight inverter is as follows: the DC input voltage is inverted into an alternating square wave voltage by the control IC and the two mosfets and applied to the resonant tank. The key component inside the tank is the transformer, which generates in combination with the ballast capacitor Cs and the lamp’s parasitic capacitance Cp. the sinusoidal ignition and burn voltage for the lamp. The ignition voltage is the minimum voltage required to ignite the CCFL. CCFLs require two to three times the operating voltage to ignite and this is generally dependent on length and thickness of the lamp. The exact ignition voltage is dependent on the age of the lamp and it’s ambient temperature. CCFL suppliers specify a worst case ignition voltage at the lamp’s end of life and this value must be used in the design of the high voltage transformer. In the next sections a complete design example of a backlight inverter for a 14” notebook + Vin C Vsec Cs Control IC - 1 Cp N Rlamp Rcur Fig.3 Schematic diagram of the backlight inverter is worked out. This screen size requires a 220 mm long CCFL. The electrical properties of this CCFL are: Ignition voltage of 1400 Vrms Lamp voltage and current in burning state: 600 V and 5 mA ( = 120 kΩ lamp resistance) 4 Ferroxcube 2.2. Choice of capacitance values on the secondary side Each CCFL has parasitic capacitances to its surroundings. Nominal values for 14” lamps are 10..20 pF in burning state. In this example is chosen for 15 pF. The parasitic capacitance Cp needs to be determined for each lamp. As the parasitic capacitances become more dominant at higher frequencies, normally the operating frequency of most backlight inverters is between 50 and 150 kHz, while the burn frequency is close to 50 kHz. After a value has been determined for Cp, the value for the ballast capacitor Cs can also be chosen. A normal value for Cs to start with is 47 pF. As the optimization can easily be made by simulation, in practice some additional bench measurements have to be done to achieve a satisfied design. 2.3. Transformer design 2.3.1. Circuit analysis A typical input voltage for backlight inverters for notebooks is 12 V. The control IC in combination with the mosfets inverts this voltage into a square wave voltage between 12 V and ground, present at the left side of DC-blocking capacitor C. Due to this capacitor, an alternating square wave voltage between +6 V and -6 V is present at the primary winding of the transformer. As capacitor C only has to block the DC-component of the input voltage, it’s value can be high and as a consequence the component can be ignored in the calculation of the transfer function of the resonant tank. Using the Fourier series, it can be proved that the first harmonic of the square wave can be written as: inductance, but also the input voltage Vin to the secondary side. This leads to the circuit shown in figure 5. L Vsec Cs 2 (1 - k ) + sec L prim ( k - k2 ) L prim . L sec L prim 2 = L sec(1 - k ) Cp Rlamp Fig. 5. Simplified schematic diagram With this circuit the transfer function of the resonant tank will be determined. The input voltage Vin present at the primary side, transferred to the secondary side becomes: Vs = N L s1 + L m 2 = L Vs L s1 L m L = Ls 2 + Lm L s1 + L m N Vin = k N Vin 5 L Vsec Vs  Voltage Vs is not the real secondary voltage, but the voltage present 4 at the magnetizing inductance Lm V1 = Vsq sin( 2πft )  π transferred to the secondary side of the ideal transformer. The factor in which Vsq represents the amplitude of the square wave voltage k, known as the couple factor, is a figure describing how much flux of 6V. The rms-value Vin of the generated by the primary winding sinusoidal voltage V1 is equal to 1/ √2 • V1 = 5.4 V and will be applied is catched up by the secondary. Or in other words: the magnetizing to the resonant tank. In order to (or mutual) inductance Lm is equal calculate the inductance values and to Lprimk, the primary leakage to analyze the resonant tank, first inductance is Lprim(1-k) and the a simple model is introduced. The secondary leakage inductance is non-ideal transformer can be split up into a magnetizing inductance Lm, Lsec(1-k). The ratio between the secondary inductance and primary the leakage inductances at primary to the square of (Ls1) and secondary side (Ls2) and it’s inductance is equal 2 = L /L the turns ratio: N sec prim. As turns ratio N, see figure 4. the primary and secondary windings Ls1 Ls2 Vsec Cs are adjacent to each other in the coil Vin former, the couple factor is normally Cp 1 Lm N Rlamp between 0.4 and 0.7. In this design example, a couple factor of 0.6 has been chosen. Fig. 4. Schematic diagram of the resonant Inductance L, which is the series tank connection of Ls2 and the parallel This diagram can further be value of the primary inductances simplified by transferring all primary transferred to the secondary side, components like the primary can be described as: leakage inductance, the magnetizing Ferroxcube  The series equivalent value C of the parasitic capacitance Cp and the ballast capacitor Cs is 11.37pF, see also section 2.2. Before ignition, the lamp resistance is several megohms and therefore figure 5 can even be more simplified to the schematic diagram of figure 6. C Figure 6. Simplified schematic diagram before ignition. The resonant frequency f0 of these reactive components at the secondary side is: f0 = 1 2π  LC Choosing a resonant frequency of 55kHz, the value for L can be calculated and is 736mH. The couple factor of 0.6 gives a secondary inductance Lsec of 1.15H, see formula . Table 1 shows the components and parameters which have been determined so far: Cs 47pF Cp 15pF k 0.6 Vin 5.4V L 736mH Lsec 1.15H f0 55kHz Table 1. Determined circuit values. After ignition the lamp voltage drops to 600 V and the current stabilizes at 5 mA. Most backlight inverters operate V lamp at the right side of the resonance H ( j ω) = peak in the so-called inductive area Vs  (the resonant tank is acting more 1 V lamp inductive as capacitive) to obtain = G ( j ω) = Cp jω L 1 2 a safe switching behaviour for the + + V sec 1 − ω L Cp + Cs R lamp j ω R lamp C s mosfets. 1 The primary number of turns Nprim = Cp then is Nsec/N = 2145/289 = 7.4. 1 A complete derivation of this 1+ + This figure is rounded to 7 and as a Cs j ω R lamp C s transfer function, including the  consequence the secondary number determination of Vs and operating of turns reduces to 7 × 289 = 2023 frequencies can be found in appendix To ignite a 220 mm lamp for a 14” and the maximum flux density during A. Resistance Rlamp follows from the notebook, a worst case lamp voltage ignition increases up to 350 mT lamp properties (600 V/5 mA) in of about 1400 Vrms is needed. With (formula ). With the secondary burning state. As the lamp resistance equation , the secondary ignition inductance L and knowing that sec before ignition is very high, the voltage Vsec-ign is 1847 V. N2 = Lsec/Lprim, the primary “not ignited” transfer function can The “not ignited” curve will inductance is 13.8 µH. be obtained by omitting the two reach a lamp voltage of 1400 V Having this value, the core imaginary parts in formula . at a frequency of 67.5 kHz (as parameters of the FRM27/3.8/9 core As Vs is 935 V (see appendix A) the determined in appendix A), see set and the primary number of turns, relation between the lamp voltage figure 7. the effective permeability of the core and frequency can be made and is With the ignition voltage, the can be determined: shown in figure 7 secondary number of turns can be . L prim l e determined: 2.3.2.Transfer function The transfer function of the resonant tank in figure 5 can be described with: the lamp is sufficient to ignite the lamp. The transfer function between the real secondary voltage Vsec and the lamp voltage (see fig. 5) can easily be derived and is equal to: µe = Vlamp V Not ignited [V] Burning state 3000 N 2500 2000 1500 1000 500 0 45 50 55 60 65 70 Frequency [kHz] Fig. 7. Lamp voltage as function of frequency With formula , the turns ratio N can be determined and is 289. Before ignition, the operating frequency of the inverter starts at a frequency higher than the resonant frequency of the tank and is decreasing until the voltage across sec = sec − ign 2 2 π f B sat A e 2 µ 0 Nprim A e  in which µ0 represents the permeability of free space (= 4π ·10-7 H/m). The application temperature for backlight inverters in notebooks and This formula returns a value for µe of 1342. This leads to a small air PDAs is normally around 40 to 50 °C. For these temperatures 3C91 gap, which is necessary to tune the primary inductance and keep it’s is the best material to use, because it has it's minimum loss value around value within a specified tolerance. 60 °C. Having a reasonable value for the maximum flux density in a 3C91 core of 330 mT (by assuming a worst case transformer temperature of 60 °C) and the minimum effective core area of the FRM27/3.8/9 core set of 8.7 mm2, the formula returns 2145 turns for the secondary winding.  6 Ferroxcube 2.4. Core losses 2.5. Winding design In burning state, the operating frequency of the backlight inverter is controlled by the IC and is 54 kHz (see appendix A). According formula , the secondary voltage in burning condition is equal to 851 V. This leads to a flux density in burning state of 202 mT, which is significant lower than during ignition. The core volume Ve of the FRM27/3.8/9 core set is 504 mm3. (see appendix C) The core loss density can be calculated with the following fit formula: Lprim 13.8 µH Lsec 1.15 H Nprim 7 Nsec 2023 N 289 µe 1342 le 52.1 mm Ae 8.7 mm2 In order to complete the design, one has to calculate the wire thickness for both primary and secondary side and the total copper loss. Essential data for the electrical design are: the winding area and the average turn length. The data for the FRM27/3.8/9 SMD bobbin are: • • Winding area Aw (primary): 1.75 mm2 and Aw (secondary): 5 slots of 1.7 mm2, Average turn length lavg: 18.5 mm The total length ltot of a wire can be calculated and is equal to the Pcore = Cm Ct f B Table 3. Calculated values for the product of the number of turns of transformer properties. the primary or secondary winding with frequency in Hz and flux density and the average turn length lavg. in T. The maximum cross section A of The fit parameters for 3C90 and the primary wire (including it’s Ignition state Burning state insulation) is 1.75 mm2 divided by 7 3C91 are shown in table 2: turns and is equal to 0.25 mm2. Vlamp 1400 V 600 V From IEC wire tables, a wire having 3C90 3C91 an overall cross section less than Ilamp 0 5 mA 0.25 mm2 is chosen. In this case the Cm 3.2 x 10-3 3.5 x 10-3 wire diameter will be 0.45 mm and Rlamp 120 kΩ ∞ it’s copper cross section is 0.159 Ct 1 0.61 mm2. 1847 V 851 V Vsec The secondary winding of 2023 x 1.46 1.4 turns is split up over the 5 sections Vs 935 V 935 V and four sections will have 404 turns, while one slot will contain 407 turns. y 2.75 2.5 f 67.5 kHz 54 kHz For the secondary side the cross Table 2. Fit parameters for 3C90 and 3C91. section of the wire is 0.0042 mm2, so Bmax 350 mT 202 mT a wire diameter of 0.050mm can be Using formula , the specified used with a copper cross section of Pcore 450 mW 83 mW core loss density for 3C91 at a flux 0.00196 mm2. density of 202 mT, a frequency of Table 4. Calculated values for the ignition The resistance of a winding can be 54 kHz and a transformer and burning state. determined by the following formula: temperature inside the application of 60 °C is equal to 165 mW/cm3. n l av g From this, it follows that the core  R = ρ⋅ Cu A loss is 165 mW/cm3 x 0.504 cm3 = 83 mW. in which ρ represents the resistivity of copper (20·10-9 Ωm at 60°C transformer temperature) and n x y  Ve 504 mm3 7 Ferroxcube PCu can be calculated by : the number of turns of the primary or secondary winding. The copper resistances are shown in figure 8. The core losses, calculated in the previous section are represented by Rcore. 2 PC u = I R Cu  with I is the input current of 2.08 A or secondary current of 5.86 mA (both found in appendix B). The primary copper loss equals 70.5 mW. The total secondary loss is about 13 mW. The total copper losses then are about 84 mW. 2.6. Copper losses In order to calculate the copper losses inside the transformer, first the currents through the resonant tank of figure 8 have to be determined. From figure 8 it is obvious that the input current of the transformer (flowing through Ls1) is not simply the secondary current multiplied by the turns ratio. Resistor Rcore (representing the core losses), but especially magnetizing inductance Lm has a significant contribution to the input current. The input current is the scalar sum of the currents through Lm, Rcore and the primary winding of the ideal transformer. In appendix B a detailed analysis of calculating the currents is given for both primary and secondary side. The copper loss 2.7. Losses, efficiency and temperature rise of the transformer The total losses of the transformer are the sum of the core- and copper losses and are less than 167 mW. As the total losses of the backlight inverter are also dependent on the capacitors, mosfets and control IC used, it is obvious that for a high efficiency of the complete design low loss components have to be used. With the lamp properties in burning state (600 V/ 5mA), the efficiency of the transformer becomes 3 W/3.167 W = 94.7 %. Primary side Secondary side The thermal resistance Rth which has been determined emperically for the wound Frame & Bar combinations can be described by: R th = 1 19 . V e  The effective volume (Ve) has to be inserted in units of cm3 which returns Rth as °C/mW. In thermal equilibrium the total losses in a transformer (Ptot) can be related to the temperature rise (∆T) by the following relation: Ptot = ∆T R th  As the total losses are equal to 167 mW, the temperature rise of the transformer is 12.4 °C. Assuming an ambient temperature of 50 °C, it will result in an operating temperature of 62 °C for the core set. If higher ambient temperatures are required, 3C90 (having minimum losses around 100 °C) can be a good alternative. Pcore 83 mW Wire size 0.45 mm Wire size 0.050 mm PCu 84 mW Wires/slot 7 Wires/slot 404 x 4 + 407 Ptot 167 mW 382 Ω η 94.7 % ∆T 12.4 °C RCu1 RCu2 16.3 mΩ Table 5. Wire sizes, number of wires per slot and resistances. Ls1 RCu1 Ls2 RCu2 Table 6. Total losses, efficiency and temperature rise of the transformer. Cs Vin Lm RCore 1 Cp N Rlamp Fig. 8. Schematic diagram of the resonant tank including loss components. 8 Ferroxcube Appendix A Derivation of the transfer function of the resonant tank L Vsec Cs Vlamp Vs Cp Rlamp Fig. A.1. Schematic diagram of the resonant tank. To determine the transfer function H(jω)=Vlamp/Vs of the schematic diagram shown in figure A.1., first the impedance of the lamp (including it’s parasitic capacitance Cp) is derived: R lamp ⋅ Z lamp ( j ω) = R lamp + 1 jω C p 1 = R lamp 1 + j ω R lamp C p jω C p [A.1] By considering the series reactance of L and ballast capacitor Cs as Zs(jω): Z s ( j ω) = j ω L + 1 jω C s [A.2] the transfer function H(jω) can be written as: R lamp H ( j ω) = Z lamp ( j ω) Z lamp ( j ω) + Z s ( j ω) 1 + j ω R lamp C p = R lamp + jω L + 1 + j ω R lamp C p 1 jω C s [A.3] Multiplying both nominator and denominator with (1 + jω RlampCp) leads to: R lamp H ( j ω) = 2 R lamp + j ω L − ω R lamp L C p + 9 Ferroxcube 1 jω C s + R lamp C p Cs [A.4] Dividing by Rlamp leads to the transfer function used in this application note: V H ( j ω) = 1 lamp = V Cp jω L 1 2 s + + 1− ω L Cp + R lamp Cs j ω R lamp C s [A.5] In this stage of the design example, voltage Vs (which is determined by kNVin, see formula  in section 2.3.1.) has not been determined yet, because the turns ratio N is still unknown. But important to know is that Vs is frequency independent. The other parameters and component values of the tank are shown in table A.1. Ignition state Burning state Vlamp 1400 V Vlamp 600 V Rlamp ∞ Rlamp 120 kΩ L 0.736 H L 0.736 H Cs 47 pF Cs 47 pF Cp 15 pF Cp 15 pF Table A.1. Lamp voltage and component values in the resonant tank. In burning state Vs is equal to: Vs = V lamp H ( j ω) = V lamp (1 − ⋅ 2 ω L C p+ Cp 2 ) Cs 2 + ωL − R lamp 1 ω R lamp C s [A.6] In ignition state, the lamp resistance is infinite, and voltage Vs can be written as: Vs = V lamp H ( j ω) = V lamp ⋅ ( 1− ω 2 L Cp + Cp Cs ) [A.7] Normally the operating frequency in burning state is close to the minimum frequency of 50 kHz, see section 2.2. Choosing an operating frequency in burning state of 54 kHz, results with formula [A.6] in a voltage Vs of 935 V. With this voltage, the ignition frequency can be determined with formula [A.7] and equals 67.5 kHz. Vs 935 V fburn 54 kHz fign 67.5 kHz Table A.2. Voltage Vs and frequencies in burning and ignition state. 10 Ferroxcube Appendix B Determination of currents and voltages in the resonant tank Ls1 RCu1 Ls2 RCu2 Cs Vin Iin Isec Lm ILm RCore IR 1 N IPrim Cp ICp Rlamp Ilamp Figure B.1. Schematic diagram of the resonant tank including loss components. With the use of table B.1, which gives the lamp resistance and the reactances of the other components at the burning frequency of 54 kHz, the currents in the resonant tank of figure B.1. will be determined. Compared to the values of the other secondary components, copper resistance RCu2 (= 382 Ω ) is very small. The same holds for the reactance of the primary leakage inductance and RCu1 (= 16.3 mΩ ). Their contribution in calculating the currents is negligible and for this reason RCu1 and RCu2 will not be used in the determination of the primary and secondary current. Rlamp 120 kΩ XCp 196.5 kΩ XCs 62.7 kΩ XLs1=XLprim(1-k) 1.87 Ω XLs2=XLsec(1-k) 156.1 kΩ Table B.1. Resistance and reactances of the circuit at the burning frequency of 54 kHz. As the lamp voltage is 600 V in burning state, the current ICp through the parasitic capacitance Cp can be calculated and is equal to 600 V/196.5 kΩ = 3.05 mA. The total secondary current Isec delivered by the transformer is the scalar sum of this parasitic current and the current through Rlamp (5 mA) and equals 5.86 mA. Due to the influence of the capacitor Cp, current Isec will lead on the lamp current Ilamp with a phase angle which is equal to arccos(5/5.86) = 31.4°. Putting real values on the horizontal axis and imaginary values on the vertical axis, the relation between voltages and currents can be displayed in a vector diagram, see figure B.2. ICp Isec 3.05mA 5.86mA Ilamp 31.4˚ 5mA 600V Fig. B.2. The relation between the lamp voltage and –current. 11 Ferroxcube The secondary current is flowing through ballast capacitor Cs and secondary leakage inductance Ls2. As the reactance of the leakage inductance is greater than the reactance of Cs (see table B.1.), the equivalent reactance X (= XLs2 – XCs) of both components is 93.4 kΩ and is inductive. The voltage across the equivalent reactance X can be calculated with Isec·X and is 547 V, see also figure B.3. Because of the inductive behaviour of X, the voltage is 90° ahead on the secondary current. The voltage can be split up into a real and an imaginary part, see figure B.3. Due to the 90° phase angle between voltage X and the secondary current, the phase angle of 31.4° can also be found between the voltage of 547 V and the imaginary part of this voltage. The imaginary and real part can be calculated by 547 V·cos(31.4) = 467 V and 547 V·sin(31.4) = 285 V. The real part of the voltage across the series connection of X and the lamp impedance is 600 V - 285 V = 315 V. The secondary voltage Vsec-ideal of the ideal transformer is then √((315 V)2 + (467 V)2) = 563 V. The phase angle between voltage Vsec-ideal of 563 V and the 600 V lamp voltage is arcos (315/563) = 56°. And as a result the phase angle between the voltage of 563 V and the secondary current is 56° - 31.4° = 24.6° . Vsec-ideal 547V 547V 467V 563V X Isec 5.86mA 5.86mA 1 N 563V Zlamp 31.4˚ 600V 24.6˚ 31.4˚ 285V 315V 600V Fig. B.3. The relation between secondary voltages and –current. Voltage VLm on the primary side can be found by dividing Vsec-ideal by the turns ratio N of 289 and equals 1.95V. This voltage is put on the horizontal axis, because it is present across the “core loss” resistor Rcore, see figure B.4. The current through the primary of the "real" transformer (Iprim-ideal ) can be found by multiplying the secondary current of 5.86 mA·with the turns ratio and equals 1.7 A. The phase angle between voltage Vlm and current Iprim-ideal is still 24.6°, see figure B.4. Resistor Rcore, representing the core losses (table 3), is connected in parallel with the magnetizing inductance Lm. The current IR through Rcore is 83 mW / 1.95 V = 43 mA. Current Iprim-ideal of 1.7 A can be split up into a real part of 1.55 A and an imaginary part of 0.71 A, see figure B.4. Knowing that B = µH = µNI/le, the current through Lm can be determined. With the effective flux density B of 202 mT/ √2 = 143 mT in burning state, the current can be determined (see also table 3): I Lm = B le µ 0 µ e N prim and has a value of 0.63 A. 12 Ferroxcube [B.1] Ls1 VLm 1.95V Vin 0.043A 1.55A 1.95V Iin 24.6˚ Lm 0.63A RCore 1 N 1.7A 43mA Iprim-ideal 0.63A 0.71A 1.7A Fig. B.4. Voltages and currents at the primary side. The current through the primary leakage inductance, and thus the current Iin flowing into the transformer, is the scalar sum of the real part (43 mA + 1.55 A = 1.59 A) and the imaginary part (0.71 A + 0.63 A = 1.34 A) in figure B.4 and equals 2.08 A. The phase angle between the real part of 1.59 A and the input current of 2.08 A is arccos(1.59/2.08) = 40.1°, see also figure B.5. 2.98V 3.89V 5.4V 3.89V Ls1 2.08A 5.4V 34.4˚ 1.95V 2.51V Lm 1.95V RCore 1 N 4.46V 40.1˚ 2.08A Fig. B.5. Input voltage and -current. The voltage across the primary leakage inductance Ls1 is equal to 2.08 A·1.87 Ω = 3.89 V. This voltage is 90° ahead on the input current, the angle between this voltage and it’s real part is 90° - 40.1° = 49.9°. Again the voltages of the real and imaginary part can be calculated and are 2.51 V and 2.98 V respectively. The total real part of the input voltage Vin is the sum of 2.51 V and 1.95 V and is 4.46 V. Having the imaginary part of 2.98 V, input voltage Vin is equal to √(( 2.98 V)2 + (4.46 V)2) = 5.4 V. This is a known voltage, see section 2.3.1., because it was a parameter to start the design with. The phase angle between the input voltage and it’s real part is arccos(4.46/5.4) = 34.4° and the angle between the input voltage and current is 34.4° + 40.1° = 74.5°. In the table below, the currents necessary to calculate the copper losses can be found. Isec 5.86 mA Iin 2.08 A Table B.2. Secondary and input current of the resonant tank. 13 Ferroxcube Survey of the avaible Frame & Bar core range A B A C D C B E FRM 21/4/12 FRM 24/3.9/10 FRM 27/3.8/9 BAR 20/3/5.5 BAR 22/2/6 BAR 25/2.2/4 BAR 28/3.8/2.3 core factor Σ l/A(mm-1) 3.29 5.06 5.65 5.56 3.29 5.06 5.65 5.56 eff. volume 3 Ve (mm ) 655 312 370 504 655 312 370 504 eff. length le (mm) 46 40 45.8 52.1 46 40 45.8 50 eff. area 2 Ae (mm ) 14 7.9 8.1 9.7 14 7.9 8.1 9.0 min. area 2 Amin (mm ) 7.4 5.7 6 8.7 7.4 5.7 6 8.7 mass of core half (g) ≈ 2.1 ≈ 1.5 ≈ 1.3 ≈ 1.6 ≈ 1.5 ≈1 ≈ 1.2 ≈ 1.2 A 19.7 ± 0.3 21 ± 0.2 23.8 ± 0.3 26.7 ± 0.7 19.9 ± 0.3 21.8 ± 0.3 24.7 ± 0.3 28 ± 0.5 B 15.6 ± 0.3 16.2 ± 0.3 19.2 ± 0.3 19.7 ± 0.6 2.85 ± 0.05 1.8 ± 0.1 2.15 ± 0.05 3.8 ± 0.1 C 14.8 ± 0.3 11.8 ± 0.25 9.8 ± 0.2 9.0 ± 0.3 5.45 ± 0.15 5.5 ± 0.2 4.4 ± 0.2 2.3 ± 0.1 D 11.4 ± 0.25 8.9 ± 0.2 7.3 ± 0.2 6.5 ± 0.2 E 4.6 ± 0.1 4.0 ± 0.1 3.85 ± 0.1 3.8 ± 0.2 effective core parameters dimensions (mm) coil formers Summary : ♦ Narrow design ♦ Easy to assemble ♦ Large winding space to accommodate a high number of turns FRM 20/5/15 Core type CPHS mounting parts Cores with a design similar to Frame and Bar cores have been available from Philips under the name of H cores, since 1971. They were mainly applied as signal transformers in Telecom applications. The new Frame and Bar cores have been modified to a slim and elongated rectangular shape in order to meet the dimension requirements of a flat LCD panel. The elongated rectangular shape is also optimized to accommodate the large number of turns required to generate the high ignition voltage (1400 Vrms) for a backlight discharge lamp. Besides this, the Frame and Bar core is also easy to assemble into a transformer and has been adopted as a standard core for the LCD backlight inverter transformer. A backlight inverter is an electronic DC to AC circuit that drives a Cold Cathode Fluorescent Lamp (CCFL) for the backlighting of a notebook LCD display or LCD monitor . COV For full details of cores and bobbins see our Data Handbook or visit our web site at www.ferroxcube.com 14 Ferroxcube FRM20/5/15 FRM21/4/12 FRM24/3.9/10 FRM27/3.8/9 Matching cores BAR20/3/5.5 BAR22/2/6 BAR25/2.2/4 BAR28/3.8/2.3 core SETS for power applications Core type 3C90 500 400 370 350 3C91 600 470 440 420 500 ungapped core set. AL = 500 AL value (nH) measured at Bˆ ≤ 0.1 mT, f ≤ 10 kHz, T = 25°C AL tolerance: ± 25% C P H S - FRM20/15 - FRM20/5/15 - 3C90 coil former (bobbin) core type core size core material 8S - 10P number of pins or solder pads plastic material type: P- thermoplastic S- thermoset number of sections BAR20/3/5.5 - 3C90 core type core size core material mounting orientation: H- horizontal V- vertical associated core type mounting type: S- surface mount 15 Ferroxcube Material characteristics 3C90 SPECIFICATIONS SYMBOL CONDITIONS VALUE 25 °C; ≤10 kHz; 0.1 mT 100 °C; 25 kHz; 200 mT 25 °C; 10 kHz; 250 A/ m 100 °C; 10 kHz; 250 A/ m 100 °C; 25 kHz; 200 mT 100 °C; 100 kHz; 100 mT 100 °C; 100 kHz; 200 mT DC, 25 °C µi µa B PV ρ TC density UNIT 2300 ± 20% 5500 ± 25% ≥ 430 mT ≥ 340 mT ≤ 80 kW/m3 Properties measured on sintered, non ground ring cores of dimensions ∅25 x ∅15 x 10 mm which are not subjected to external stresses. 3C91 SPECIFICATIONS SYMBOL CONDITIONS µi µa B PV ≤ 80 ≈ 450 ≈5 ≥ 220 ≈ 4800 ρ TC density Ωm °C kg/m3 800 10 4 3C90 µ's , µ''s f B (kHz) (mT) 600 µ's 10 3 3C90 Pv (kW/m 3 ) 100 VALUE 25 °C; ≤10 kHz; 0.1 mT 100 °C; 25 kHz; 200 mT 25 °C; 10 kHz; 250 A/ m 100 °C; 10 kHz; 250 A/ m 60 °C; 100 kHz; 100 mT 60°C; 100 kHz; 200 mT UNIT 3000 ± 20% 5500 ± 25% ≥ 430 mT ≥ 330 mT ≤ 80 kW/m3 ≤ 80 DC, 25 °C ≈5 ≥ 220 ≈ 4800 Ωm °C kg/m3 10 4 3C91 µ's µ's , µ''s 200 10 3 µ''s µ''s 400 200 100 10 2 10 2 200 100 25 10 10 1 1 10 f (MHz) 10 2 0 Complex permeability as a function of frequency 500 40 80 T (o C) 10 10 1 120 Specific power loss for several frequency/ flux density combinations as a function of temperature. 1 3C90 10 f (MHz) 10 2 Complex permeability as a function of frequency 500 25oC 100oC B (mT) 100 200 0 25 oC 100 oC B (mT) 400 400 300 300 200 200 100 100 0 3C91 0 25 0 25 50 150 250 25 0 25 50 150 H (A/m) Typical B-H loops Typical B-H loops 20 0k Hz 100 5 kHz kHz 0 kHz f B (kHz) (mT) 600 100 10 4 3C91 T = 100 oC Pv (kW/m 3) 200 25 kHz 10 3 400 25 10 3 3C91 Pv (kW/m 3 ) 200 kH z kHz 3C90 T = 100 oC 100 800 10 4 Pv (kW/m 3) 250 H (A/m) 200 100 10 2 10 2 200 25 100 200 100 0 10 1 10 10 2 B (mT) 10 3 Specific power loss as a function of peak flux density with frequency as a parameter. 0 40 80 120 T (o C) Specific power loss for several frequency/ flux density combinations as a function of temperature. 16 Ferroxcube 10 1 10 10 2 B (mT) 10 3 Specific power loss as a function of peak flux density with frequency as a parameter.