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| APPLICATION NOTE Design of HF wideband power transformers ECO6907 w w w t a .D S a e h U t4 e .c m o w w w .D a aS t ee h 4U t om .c Philips Semiconductors Design of HF wideband power transformers CONTENTS 1 2 3 3.1 3.2 4 4.1 4.2 5 5.1 5.2 6 6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.8 6.8.1 6.8.2 7 7.1 7.2 8 INTRODUCTION TRANSFORMER SPECIFICATION INFLUENCE OF THE CORE ON PERFORMANCE Primary Inductance Core Losses INFLUENCE OF THE TRANSMISSION LINE ON PERFORMANCE Resistive Loss and Power Handling Mismatch loss COMPENSATION TECHNIQUES Compensation at Low Frequencies Compensation at High Frequencies TRANSFORMER CONFIGURATION Phase Reversing Transformer Balanced to Unbalanced Transformer Symmetrical 1 : 4 Impedance Transformer Asymmetrical 1 : 4 Impedance Transformer Symmetrical 9 : 1 Impedance Transformer Asymmetrical 1 : 9 Impedance Transformer Single-ended Hybrid Push-pull Hybrid Impedance Step-up Type Impedance Step-Down Type PRACTICAL EXAMPLES 12.5 Balanced to 50 Unbalanced Transformer 50 Unbalanced to 5.55 Balanced Transformer REFERENCES Application Note ECO6907 1998 Mar 23 2 Philips Semiconductors Design of HF wideband power transformers 1 INTRODUCTION Application Note ECO6907 Transmission line power transformers can be used to perform a variety of functions, among which are phase reversal, balanced to unbalanced coupling, impedance transformation and hybrid functions. Such transformers find many applications in wide-band power amplifiers for both s.s.b. transmitters in the h.f. region and f.m. transmitters in the lower v.h.f. region. The properties of a practical h.f. power transformer are discussed here and their effect on transformer performance is analysed. Since losses must be kept low, in practice the transformer will use a ferrite core. Further, we have limited the discussion to cores without an air-gap since these have a low stray magnetic field, a high permeability, and can cover the power range (up to 80 W) dealt with here. Data (dimensions, permeability values etc.) on all core types can be found in our Data Handbook "Soft Ferrites", MA01. A glance through the Handbook will show the wide range of materials, dimensions and types from which the designer may choose. It must be remembered, of course, that when cores constructed in two parts (pot-cores and cross-cores, for example) are used, the type without an air-gap must be selected. Throughout we have aimed at giving practical solutions to the problems posed by material and design limitations. In particular, compensating techniques for extending the frequency range of a number of transformer configurations are discussed. To give an idea of some application possibilities, practical examples in several transformer configurations have been worked, using transformer cores from our range of ferrites. 2 TRANSFORMER SPECIFICATION The transformer design considerations dealt with in this publication are: * Maximum power level to be handled * Frequency range * Input and output impedance * Allowable reflection and resistive losses. How a transformer can meet the above considerations for a particular application is analysed in the following three sections. The first two sections deal with the influence of the core and transmission line respectively on transformer performance, and the third with mismatch compensation techniques. 3 3.1 INFLUENCE OF THE CORE ON PERFORMANCE Primary Inductance This inductance determines the amount of reflection at the low frequency end of the band. It can be calculated using the formula: L = orn2 A/l in which: L = inductance in H o = 4 10-7 (rationalised M.K.S. units) r = relative permeability A = average ferrite cross section in m2 l = average length of the lines of force in m n = number of turns between the input connections. 1998 Mar 23 3 Philips Semiconductors Design of HF wideband power transformers Application Note ECO6907 In a simple example, like the phase reversing transformer, this relation holds. Other cases may require a transformation (see Section 7.1). If degrading of performance at the high end of the band is to be avoided, the value of L must not be higher than really necessary. A good practical value is: L = 4R/min in which: R = midband input resistance in min = 2 times the minimum frequency in Hz. Where requirements are severe the compensation technique described in Section 5.1 may be used. 3.2 Core Losses The losses caused by the core material will be represented here as a resistance (Rp) in parallel with the input. This resistance depends on: * The sort of ferrite material * The frequency * The quantity L/r * The maximum flux density Bmax. In the small signal case (Bmax 0), Rp can be calculated with the aid of curves of the type shown in Fig.1(1). In these curves a comparison is made between different core materials based on equal core dimensions and equal number of turns. It can be seen that 4C4 and 4C6 are the best materials for frequencies above approximately 2.5 MHz. In the high v.h.f. region IZ2 ferroxplana shows interesting properties as can be seen from the same figure. The power handling capability of a transformer is closely dependent on the behaviour of Rp as a function of Bmax. For the section of the B-H curve with which we are dealing, Bmax can be calculated using the formula: Bmax = Vmax/ x A x n in which: Bmax = maximum flux density in T(2) = 2 times frequency in Hz A = ferrite cross section in m2 n = number of turns Vmax = maximum value of voltage across n turns in V. (1) The curves of Figs 1 to 7 have been drawn from measurements on single samples of the ferrite materials. Thus the average curves may differ somewhat from those shown. (2) The letter T stands for Tesla, the unit of magnetic flux density in the SI unit system. The following relationship holds: 1T = 1 Wb/m2 = 1 Vsec/m2 = 10000 gauss. 1998 Mar 23 4 Philips Semiconductors Design of HF wideband power transformers Application Note ECO6907 1012 handbook, full pagewidth rRp L (sec-1) 4C4 1Z2 MGL235 1011 4C6 4B1 4A4 3H1 1010 1 10 102 f (MHz) 103 Fig.1 Curves of rRp/L plotted against frequency for our various ferrites. The curves have been plotted for small signal conditions (Bmax 0). In Figs 2 to 7 the quantity rRp/L is given for different ferrite materials as a function of the product Bmax x with the frequency as a parameter. The product Bmax x has been chosen because, for most transformers, its value remains constant for changing frequency. From Figs 2 to 7 it can be seen that Rp decreases as Bmax increases, especially at lower frequencies. This forms the primary limit on the power handling capability of these transformers. If 4C4 material (Fig.5) is used in the h.f. region, the Bmax x product must not be higher than approx. 2 x 104 T.Hz. Combining this with the choice of L according to the second equation in Section 3.1, we find that the power loss caused by the core material will be no more than 1%. At frequencies of 30 MHz and higher it seems that higher Bmax x products, perhaps up to 105 T.Hz, can be used. For IZ2 ferroxplana this has already been confirmed by measurements at 165 MHz. A very conservative choice of the Bmax value must also be avoided because this leads to a greater length of the transmission line and consequently more loss at the high end of the band. 4 4.1 INFLUENCE OF THE TRANSMISSION LINE ON PERFORMANCE Resistive Loss and Power Handling The power loss in the transmission line depends on: * The type of line * The frequency * The length. Data on power loss in some 50 coaxial cables is given in Fig.8. This power loss and the allowable maximum cable temperature restrict the power handling of the cable. The maximum power which can be transmitted depends on the type of cable and the frequency; data is given in Fig.9. 1998 Mar 23 5 Philips Semiconductors Design of HF wideband power transformers 4.2 Mismatch loss Application Note ECO6907 Another kind of loss caused by the transmission line can occur if the characteristic impedance of this line is not the required value. This results in a mismatch being maximum at the high frequency end of the band. The amount of mismatch depends on: * The ratio between the length of the line and the wavelength on the line * The ratio between the required and the actual value of the characteristic resistance. 1012 handbook, full pagewidth rRp L (sec-1) MGL236 1011 1.6 MHz 5 MHz 15/28 MHz 1010 102 103 104 Bmax *f (T*Hz) 105 Fig.2 3H1 material. 1998 Mar 23 6 Philips Semiconductors Design of HF wideband power transformers Application Note ECO6907 1012 handbook, full pagewidth rRp L (sec-1) MGL237 1011 1.6 MHz 5 MHz 15 MHz 28 MHz 1010 102 103 104 Bmax *f (T*Hz) 105 Fig.3 4A4 material. 1012 handbook, full pagewidth rRp L (sec-1) MGL238 1011 4 MHz 10 MHz 15 MHz 28 MHz 1.6 MHz 1010 102 103 104 Bmax *f (T*Hz) 105 Fig.4 4B1 material. 1998 Mar 23 7 Philips Semiconductors Design of HF wideband power transformers Application Note ECO6907 1012 handbook, full pagewidth rRp L (sec-1) MGL239 15 MHz 5 MHz 28 MHz 1011 1.6 MHz 1010 102 103 104 Bmax *f (T*Hz) 105 Fig.5 4C4 material. 1012 handbook, full pagewidth rRp L (sec-1) MGL240 1011 1.6 MHz 1010 102 103 104 Bmax *f (T*Hz) 105 Fig.6 4C6 material. 1998 Mar 23 8 Philips Semiconductors Design of HF wideband power transformers Application Note ECO6907 1012 handbook, full pagewidth rRp L (sec-1) 165 MHz MGL241 1011 1010 103 104 105 Bmax *f (T*Hz) 106 Fig.7 1Z2 material. handbook, full pagewidth 1 MGL242 loss (dB/m) A 10-1 B C 10-2 1 10 102 f (MHz) 103 Fig.8 Curves of power loss plotted against frequency for three 50 coaxial cables. A: diameter = 1.7 mm. B: diameter = 2.8 mm. C: diameter = 5 mm. 1998 Mar 23 9 Philips Semiconductors Design of HF wideband power transformers Application Note ECO6907 103 handbook, full pagewidth power handling capability (W) B MGL243 102 A 10 1 10 102 f (MHz) 103 Fig.9 Curves of power handling capability plotted against frequency for two 50 coaxial cables. A: diameter = 2.8 mm. B: diameter = 5 mm. From transmission line theory the input impedance is given by: 1 + jrtanl Z in = R in x ---------------------------1 1 + j -- tanl r in which: Rin = midband input resistance r = ratio between the actual and the required characteristic resistance = 2/ = wavelength on the line (for 50 coaxial cables approx. 67-70% of wavelength in free space) l = length of the line. If the deviation of Zin from the required value is unacceptably large it is in many cases possible to make use of the compensation technique described in Section 5.2. 1998 Mar 23 10 Philips Semiconductors Design of HF wideband power transformers 5 5.1 COMPENSATION TECHNIQUES Compensation at Low Frequencies Application Note ECO6907 handbook, halfpage handbook, halfpage R R E R L E R MGL218 MGL219 Fig.10 Schematic diagram. Fig.11 Low frequency equivalent diagram. handbook, halfpage CL CL handbook, halfpage CL R L E R R R E MGL220 CL MGL221 Fig.12 Equivalent diagram with compensation. Fig.13 Schematic diagram with compensation. 1998 Mar 23 11 Philips Semiconductors Design of HF wideband power transformers Application Note ECO6907 Compensation will be illustrated by means of the phase reversing transformer. The schematic diagram is given in Fig.10 and the equivalent diagram for the low frequency end of the band is shown in Fig.11. For compensation we add two equal capacitors CL such that a high-pass T-filter section is formed (Fig.12). According to filter theory: C L = 2L R 2 The original diagram of Fig.10 is now transformed to the new one of Fig.13. If L is dimensioned according to eq.(2) the input impedance without compensation at the lowest frequency is R//(+ j4R). With compensation the input impedance is (.999R//+j264R), illustrating that the mismatch has been reduced to a negligible level. For some types of transformer, the capacitor at the output must have a different value from that at the input. With a l : n2 impedance transformer, for instance, it must be n2 times smaller than the capacitor at the input. Sometimes two or more transformers must be connected in cascade. In such a case low frequency compensation is possible if a high-pass -filter section is used (Fig.14). When the parallel inductance of the transformers at the interconnecting point are both approximately equal to L, the capacitance of CL must be L/2R2. handbook, halfpage CL R L E L R MGL222 Fig.14 Equivalent diagram of cascaded transformers with compensation. 5.2 Compensation at High Frequencies This is only necessary when the characteristic resistance of the transmission line differs from the required value. A situation often met with in practice is that in which the required characteristic resistance is lower than that of the available line. Taking the simple case of the phase reversing transformer (Fig.15) with a required characteristic resistance equal to R, we find that compensation for an actual value equal to r x R can be made as follows. In parallel with the load resistance, we connect a capacitor of such a value that at the highest frequency the real part of the input admittance becomes 1/R. The resulting imaginary part of the input admittance is tuned out by means of a capacitor in parallel with the input. Both capacitors turn out to have the same value; given by 2 1 C H = --------------------------------- { 1 - 1 - r 2 - 1 tan l } max rRtanl in which max = 2 times the maximum frequency. The schematic diagram is shown in Fig.15. 1998 Mar 23 12 Philips Semiconductors Design of HF wideband power transformers Application Note ECO6907 handbook, halfpage R CH E CH R MGL223 Fig.15 Phase reversing transformer with high frequency compensation. The result of this compensation is an exact match at the maximum frequency. There will be however, a slight mismatch at lower frequencies which is many times smaller than that at the maximum frequency without compensation. A combination of high and low frequency compensation is of course possible. 6 TRANSFORMER CONFIGURATION Because of the variety of the existing configurations it is hardly possible to give a complete survey. Therefore a restriction will be made to some principally different types. 6.1 Phase Reversing Transformer This type has already been discussed in the previous section. 6.2 Balanced to Unbalanced Transformer The schematic diagram is shown in Fig.16. This type can be considered as a modification of the phase reversing transformer. The primary inductance in this case is 4 times the inductance of the winding between the points A and B because of the voltage division. If low frequency compensation is used, a capacitor equal to 2CL must be placed in series with each input connection (see Section 5.1) to preserve symmetry, and one capacitor equal to CL in series with the output (point B). handbook, halfpage +V +1/2 V A B R -1/2 V MGL224 Fig.16 Balanced to unbalanced transformer. 1998 Mar 23 13 Philips Semiconductors Design of HF wideband power transformers 6.3 Symmetrical(1) 1 : 4 Impedance Transformer Application Note ECO6907 The schematic diagram is given in Fig.17. Two cables each having a characteristic resistance of 2R, can be wound on a common core. The direction of the windings follows from the voltage division. Low frequency compensation can be made with a capacitor equal to 2CL (see Section 5.1) in each of the input leads and a capacitor equal to 1/2CL in each of the output leads. handbook, 1 halfpage + /2 V +V 0 4R -V MGL225 R -1/2 V A B Fig.17 Symmetrical 1 : 4 impedance transformer. 6.4 Asymmetrical 1 : 4 Impedance Transformer If, in the 1 : 4 impedance transformer of Section 6.3, the points A and B are connected to earth it is no longer possible to wind the two lines on a common core. In fact the lower line may be wound on an `air core' because there is no voltage difference between the points A and B. The logical next step is to omit the lower line completely (with a consequent slight phase difference between the lines). Then we get the transformer shown in Fig.18. The characteristic resistance of the transmission line has again an optimum value of 2R. But even if this value is chosen the input impedance is not constant as a function of frequency. From theory (see Ref.5) it is: 2cosl + jrsinl Z in = R x ------------------------------------------------1 1 + cosl + j -- sinl r in which r = ratio between the actual characteristic resistance and 2R. (1) Terminology in normal use is employed to describe the various transformer configurations. However the terms `symmetrical', `balanced' and `push-pull' are used here synonymously to mean `antiphase port signals having equal amplitudes with respect to ground', while likewise `asymmetrical', `unbalanced' and single-ended' are synonymous with `one port terminal grounded'. Strictly defined, the terms `asymmetrical, and `unbalanced' also apply to unequal port terminal values with respect to ground. 1998 Mar 23 14 Philips Semiconductors Design of HF wideband power transformers Application Note ECO6907 handbook, halfpage V 2V V 4R R - MGL226 Fig.18 Asymmetrical 1 : 4 impedance transformer. If r > 1 high frequency compensation is sometimes possible. A capacitor C1 given by: 1 + cosl - ( 1 + cosl ) - r sin l C 1 = ---------------------------------------------------------------------------------------------- max rRsinl 2 2 2 2 + cosl - ( 1 + cosl ) - r sin l must then be connected across the input and a capacitor C2 given by: C 2 = ----------------------------------------------------------------------------------------------4 max rRsinl 2 2 2 must be connected across the output. 6.5 Symmetrical 9 : 1 Impedance Transformer The schematic diagram is given in Fig.19. The two transmission lines have an optimum characteristic resistance of 3R. They can again be wound on a common core, and the third line omitted as in the previous case. The input impedance is 4 + 5cosl + j6rsinl given by: Z in = 9R x ----------------------------------------------------6 9cosl + j -- sinl r in which r is the ratio between the actual characteristic resistance and 3R. If r > 1 high frequency compensation is sometimes possible. A capacitor C1 given by: 4 + 5cosl - 9 3cos 2 l + 4cosl + 2 - 36r 2 sin 2 l C 1 = ----------------------------------------------------------------------------------------------------------------------------------------6 max rRsinl must than be connected across the low impedance side, and a capacitor C2, given by: 9cosl - 9 3cos 2 l + 4cosl + 2 - 36r 2 sin 2 l C 2 = ------------------------------------------------------------------------------------------------------------------------------54 max rRsinl must be connected across the high impedance side. 1998 Mar 23 15 Philips Semiconductors Design of HF wideband power transformers Application Note ECO6907 +1/2 V handbook, halfpage +1/6 V 9R -1/6 V -1/2 V MGL227 +1/6 V R -1/6 V Fig.19 Symmetrical 9:1 impedance transformer. 6.6 Asymmetrical 1 : 9 Impedance Transformer In this transformer (see Fig.20), two transmission lines are required, each having an optimum characteristic resistance of 3R. Although these lines can be wound on a common core, the upper line must have twice the number of turns of the lower line, because of the voltage division. The third line has again been omitted. High frequency compensation follows the same principle as that used in previous sections. handbook, halfpage V 2V R V 3V 9R MGL228 Fig.20 Asymmetrical 1 : 9 impedance transformer. 1998 Mar 23 16 Philips Semiconductors Design of HF wideband power transformers Application Note ECO6907 handbook, halfpage 2R A B R E1 1/2R R E2 MGL229 Fig.21 Single-ended hybrid. 6.7 Single-ended Hybrid This circuit (see Fig.21) permits the combination of two signals in a common load (R/2) in such a way that the signal sources do not influence each other. When the two signals have different frequencies the power is equally divided between the resistors R/2 and 2R. When the two signals have the same frequency, phase and amplitude, all the power is delivered to R/2. The optimum value of the characteristic impedance of the transmission line is equal to R. At the low frequency end of the band the isolation between the sources depends on the inductance of the winding. When the R isolation is expressed as a power ratio S the inductance between the points A and B must be: L = -------------- S - 1 8 min Even when the optimum characteristic impedance is chosen, high frequency compensation has been found to have a marked influence on the isolation. Practically it has been found that a small capacitor must be connected in parallel with R/2. To illustrate the degree of isolation that may be expected in a practical design, an example is given of a hybrid transformer designed for the frequency band of 1.6 to 28 Mhz. The requirement was to combine two signals of different frequency and equal power (3 W in 100 ) in a single 50 load with a minimum isolation of 40 dB between the sources. R From the equation L = -------------- S - 1 , it follows that L must be 125 H minimum. Because of this high inductance it was 8 min decided to choose 3H1 material. An available 23 x 14 x 7 mm toroid belonged to `group 5' which meant that the minimum r was 2680(1). The required number of turns was 9. The optimum value of the characteristic resistance is 100 , but for reasons of convenience 150 miniature twin lead was used. The calculated value of Bmax was 87 gauss at 1.6 MHz. High frequency compensation was achieved by means of a 33 pF capacitor in parallel with the 50 load resistance. The isolation between the sources measured as a function of frequency is given in Table 1 below, illustrating that the minimum isolation requirement of 40 dB has been fulfilled over the desired frequency band. (1) For the convenience of the user the toroids of ferroxcube 3H1 are delivered sorted into groups of approximately equal -value. The -value is indicated by the colour of the cicumference of the toroids, see "Data Handbook System". Groups are not separately available. 1998 Mar 23 17 Philips Semiconductors Design of HF wideband power transformers Table 1 f (MHz) 0.5 1 1.6 5 15 28 40 6.8 Push-pull Hybrid 33 41 42.5 40.5 41 43 32 Application Note ECO6907 ISOLATION (dB) Two different versions will be discussed. In the first one the impedance level is stepped-up by a factor of two and in the second the impedance level is stepped-down by a factor of two. 6.8.1 IMPEDANCE STEP-UP TYPE The two transmission lines (see Fig.22) have an optimum characteristic resistance equal to R and they can be wound on a common core. handbook, halfpage +1/2 V1 R +1/2 V2 R R -1/2 V1 A B R C D -1/2 V2 E +1/2 (V1 + V2) 0 2R F -1/2 (V1 + V2) MGL230 Fig.22 Push-pull hybrid with impedance step-up. A hybrid can always be used in two ways. The first way has been mentioned in Section 6.7. The second way is the inverse of the first i.e. the power from a single source is equally divided between two loads which are isolated from each other. The latter arrangement allows a more convenient calculation of the lower frequency limit. To do this we must know the effective inductance in parallel with 2R. The voltage across this resistor is 4 times the voltage between the points D and F and therefore the effective inductance in parallel with 2R is 16 times the inductance between the points D and F. For low frequency compensation the effective inductance in parallel with 2R can be considered as two equal inductances in series - one between points E and O and one between points F and O - each having a value of 8 times the inductance between points D and F. The hybrid can then be considered as two balanced to unbalanced transformers on a common core and the compensation can be made as described in Section 6.2. 1998 Mar 23 18 Philips Semiconductors Design of HF wideband power transformers 6.8.2 IMPEDANCE STEP-DOWN TYPE Application Note ECO6907 This hybrid (see Fig.23) is identical to the previous one except that the transmission lines on one side have been connected in parallel instead of in series. When this hybrid is used for the combination of two signals which have the same frequency, phase and amplitude, the ferrite core will not be magnetized. However when V2 becomes zero, the voltage across each winding will be V1/4 and the voltage across R/2 will be V1/2. This means that the effective inductance in parallel with R/2 becomes 4 times the inductance of a single winding. A similar approach must be used in finding the winding V/turn when calculating Bmax. handbook, halfpage +1/2 V1 R +1/2 V2 R R -1/2 V1 R -1/2 V2 +1/4 (V1 + V2) 1/2 R -1/4 (V1 + V2) MGL231 Fig.23 Push-pull hybrid with impedance step-down. 7 PRACTICAL EXAMPLES It is possible to combine some of the functions, mentioned in Chapter 6, in one transformer. In the two examples given simple calculations show the method used in designing for a particular application. 7.1 12.5 Balanced to 50 Unbalanced Transformer In this case, the transformers described in Sections 6.2 and 6.3 have been combined. The schematic diagram is shown in Fig.24. A transformer of this type is required for a wideband s.s.b. transmitter in the frequency range of 1.6 to 28 MHz. It must be able to handle a peak envelope power of 80 W. The input impedance of 12.5 balanced and the output impedance is 50 unbalanced. The total amount of resistive and reflection losses is required to be below 5% (power). handbook, full pagewidth A +1/2 V 12.5 -1/2 V L1 B +V L3 +2 V 50 -V L2 MGL232 Fig.24 12.5 balanced to 50 unbalanced transformer. 1998 Mar 23 19 Philips Semiconductors Design of HF wideband power transformers Application Note ECO6907 The transformer has been wound on a single 4C4 toroid of 36 x 23 x 15 mm. Windings L1 and L2 must have a characteristic resistance of 25 ; they consist of two 50 coaxial cables of 2.8 mm diameter in parallel. Winding L3 must have a characteristic resistance of 50 ; a single 50 coaxial cable of 2.8 mm diameter has been used. The winding direction follows from the voltage division. From this it is also clear that windings L1 and L2 must have an equal number of turns and that winding L3 must have twice the number of winding L1. We can calculate the lower frequency limit from the effective inductance in parallel with the 50 load resistance. We allow a reactance of +j 200 at 1.6 Mhz, corresponding to an inductance of 20 H, in parallel with the 50 load (see Section 3.1). As the voltage between points A and B is 14 of the output voltage, the inductance between these points will be 20/16 = 1.25 H. The corresponding number of turns is: n= Lx1 --------------o r A in which 1/A = 9.42 cm-1 and r is taken to be 100. This gives: n = 3.06 We take = 3.5 turns, making the inductance in parallel with the 50 load resistance equal to: 3.5 2 20 ---------- = 26.2 H minimum 3.06 The measured value was actually 39 H, because the r of the core used was greater than 100. The maximum flux density Bmax can be calculated when the maximum voltage across the windings is known. The peak value of the voltage across the 50 load resistance for an 80 W power level is: Vp = 2 x 80 x 50 = 89.5V and between points A and B: 89.5/4 = 22.35 V. The ferrite cross section for this core is 0.976 x 10-4 m2. So at 1.6 MHz the maximum flux density is: V max -4 22.35 B max = ----------- = ------------------------------------------------------------------------------------------------ = 65.4 x 10 T or 65.4 gauss. 6 -4 An 2 x x 1.6 x 10 x 0.976 x 10 x 3.5 This corresponds to a Bmax x f product of 1.05 x 104 T. Hz. From Fig.5 it can be seen that up to this level the variation in core losses in only very small. The minimum value of the parallel loss resistance referred to the 50 level (see Fig.5) is: 9 9 26.2 x 10 L R p = ---- x 41 x 10 = ---------------------------- x 41 x 10 = 10.7 k r 100 -6 So the core losses are: 50/10 700 x 100% = 0.47% maximum. The cable can handle a power of 170 W at 28 MHz and it has a loss of 0.135 dB/m at this frequency. The length of the cable (the sum of L1 and L3) is about 60 cm, giving a maximum cable loss of approximately 1.9%. When the transformer was driven from an unbalanced 50 source and loaded with two resistors of 6.25 at the balanced side (connecting point of the resistors earthed) the power loss and asymmetry were so small that they could not be measured. The input impedance at the unbalanced side as a function of frequency is given in Table 2. 1998 Mar 23 20 Philips Semiconductors Design of HF wideband power transformers Table 2 f (MHz) 1.6 5 15 28 7.2 49.3 49.6 50.2 50.2 50 Unbalanced to 5.55 Balanced Transformer Rp () +j 395 +j 1250 +j 21200 -j 1060 Application Note ECO6907 Xp () In this case the transformers described in Section 6.2 and 6.5 have been combined. The schematic diagram is given in Fig.25. A transformer of this design is again required for a wideband s.s.b. transmitter in the frequency range of 1.6 to 28 MHz. The required peak envelope power handling is 5 W, with an input impedance of 50 unbalanced and an output impedance of 5.55 balanced. handbook, full pagewidth L2 +3 V 50 +11/2 V C1 -11/2 V L3 C2 +1/2 V 2.78 L1 2.78 -1/2 V MGL233 Fig.25 50 unbalanced to 5.55 balanced transformer. The transformer can be wound on a single 4C4 toroid of 23 x 14 x 7 mm. Winding L1 must have a characteristic resistance of 50 ; this has been approached by a twisted pair of enamelled copper wires of 0.45 mm diameter (Rc = 52 ). Windings L2 and L3 must have a characteristic resistance of 1623 . For this purpose four enamelled copper wires of 0.22 mm diameter have been twisted and diagonally interconnected as shown in Fig.26; the characteristic resistance was found to be 30 , making a high-frequency correction necessary. The required compensation, determined experimentally gave values for C1 of 22 pF and for C2 of 270 pF. handbook, halfpage MGL234 Fig.26 Interconnection of winding wires. In the cross-section shown, the two wires indicated by dots are interconnected, as are those indicated by crosses. This configuration gives a maximum winding capacitance, necessary for a low characteristic resistance. 1998 Mar 23 21 Philips Semiconductors Design of HF wideband power transformers Application Note ECO6907 From the voltage division it follows that winding L1 must have 112 times the number of turns of windings L2 and L3. The required number of turns can be calculated in the same way as in the previous section. To get a parallel input inductance of 20 H minimum, 9 turns are required for winding L1. The measured value was approx. 30 H. Calculation of Bmax according to the method of Section 7.1 gives a value of approx. 40 gauss at 1.6 MHz. This is so low that a smaller core could be chosen. The reason for not doing this is that the smaller core has not sufficient room for the windings. In Table 3 the input impedance is given as a function of frequency. Table 3 WITHOUT H.F. COMPENSATION Rp () 1.6 5 15 28 49 50 56 71 Xp () +j 300 +j 360 +j 220 +j 213 WITH H.F. COMPENSATION Rp () 48 49 50 51 Xp () +j 370 +j 840 +j 1400 -j 11000 If there is no high frequency compensation, the variation in impedance is rather large. This is caused by: * The characteristic resistance of the transmission lines L2 and L3 being 30 instead of 1623 . * The electrical length of the windings L2 and L3. Measurements have shown that the wave-length on these lines is only 41% of the wavelength in free space - the decrease in wave-length being caused by the twisting of the wires, the dielectric constant of the wire insulation and the influence of the r of the ferrite core. * The inductance of the load resistors. The power loss measured at 28 MHz was 0.34 dB. At lower frequencies it was too small to be measured accurately. Voltage asymmetry between both terminals was less than 4%. 8 REFERENCES 1. W. Hilberg; Einige grundsatzliche Betrachtungen zu Breitband-Ubertragern; N.T.Z. 1966, Heft 9, p. 527 - 538. 2. A. Muser, J. Zen, R. Armbruster; Transformateurs d'impulsions rapides a lignes de transmissions; L'onde electrique No. 446, Mai 1964, p. 520 - 529. 3. H. Nielinger; Optimale Dimensionierung von Breitbandanpassungsnetzwerken; N.T.Z. 1968, Heft 2, p. 88 - 91. 4. O. Pitzalis, Jr., T.P.M. Couse; Practical Design Information for Broadband Transmission Line Transformers; Proc. IEEE (Letters) April 1968, p. 738 - 739. 5. C.L. Ruthroff; Some Broad-Band Transformers; Proc. IRE August 1959, p. 1337 - 1342. 1998 Mar 23 22 Philips Semiconductors - a worldwide company Argentina: see South America Australia: 34 Waterloo Road, NORTH RYDE, NSW 2113, Tel. +61 2 9805 4455, Fax. +61 2 9805 4466 Austria: Computerstr. 6, A-1101 WIEN, P.O. Box 213, Tel. +43 160 1010, Fax. +43 160 101 1210 Belarus: Hotel Minsk Business Center, Bld. 3, r. 1211, Volodarski Str. 6, 220050 MINSK, Tel. +375 172 200 733, Fax. +375 172 200 773 Belgium: see The Netherlands Brazil: see South America Bulgaria: Philips Bulgaria Ltd., Energoproject, 15th floor, 51 James Bourchier Blvd., 1407 SOFIA, Tel. +359 2 689 211, Fax. +359 2 689 102 Canada: PHILIPS SEMICONDUCTORS/COMPONENTS, Tel. +1 800 234 7381 China/Hong Kong: 501 Hong Kong Industrial Technology Centre, 72 Tat Chee Avenue, Kowloon Tong, HONG KONG, Tel. +852 2319 7888, Fax. +852 2319 7700 Colombia: see South America Czech Republic: see Austria Denmark: Prags Boulevard 80, PB 1919, DK-2300 COPENHAGEN S, Tel. +45 32 88 2636, Fax. +45 31 57 0044 Finland: Sinikalliontie 3, FIN-02630 ESPOO, Tel. +358 9 615800, Fax. +358 9 61580920 France: 51 Rue Carnot, BP317, 92156 SURESNES Cedex, Tel. +33 1 40 99 6161, Fax. +33 1 40 99 6427 Germany: Hammerbrookstrae 69, D-20097 HAMBURG, Tel. +49 40 23 53 60, Fax. +49 40 23 536 300 Greece: No. 15, 25th March Street, GR 17778 TAVROS/ATHENS, Tel. +30 1 4894 339/239, Fax. +30 1 4814 240 Hungary: see Austria India: Philips INDIA Ltd, Band Box Building, 2nd floor, 254-D, Dr. Annie Besant Road, Worli, MUMBAI 400 025, Tel. +91 22 493 8541, Fax. +91 22 493 0966 Indonesia: see Singapore Ireland: Newstead, Clonskeagh, DUBLIN 14, Tel. +353 1 7640 000, Fax. +353 1 7640 200 Israel: RAPAC Electronics, 7 Kehilat Saloniki St, PO Box 18053, TEL AVIV 61180, Tel. +972 3 645 0444, Fax. +972 3 649 1007 Italy: PHILIPS SEMICONDUCTORS, Piazza IV Novembre 3, 20124 MILANO, Tel. +39 2 6752 2531, Fax. +39 2 6752 2557 Japan: Philips Bldg 13-37, Kohnan 2-chome, Minato-ku, TOKYO 108, Tel. +81 3 3740 5130, Fax. +81 3 3740 5077 Korea: Philips House, 260-199 Itaewon-dong, Yongsan-ku, SEOUL, Tel. +82 2 709 1412, Fax. +82 2 709 1415 Malaysia: No. 76 Jalan Universiti, 46200 PETALING JAYA, SELANGOR, Tel. +60 3 750 5214, Fax. +60 3 757 4880 Mexico: 5900 Gateway East, Suite 200, EL PASO, TEXAS 79905, Tel. +9-5 800 234 7381 Middle East: see Italy Netherlands: Postbus 90050, 5600 PB EINDHOVEN, Bldg. VB, Tel. +31 40 27 82785, Fax. +31 40 27 88399 New Zealand: 2 Wagener Place, C.P.O. Box 1041, AUCKLAND, Tel. +64 9 849 4160, Fax. +64 9 849 7811 Norway: Box 1, Manglerud 0612, OSLO, Tel. +47 22 74 8000, Fax. +47 22 74 8341 Philippines: Philips Semiconductors Philippines Inc., 106 Valero St. Salcedo Village, P.O. Box 2108 MCC, MAKATI, Metro MANILA, Tel. +63 2 816 6380, Fax. +63 2 817 3474 Poland: Ul. Lukiska 10, PL 04-123 WARSZAWA, Tel. +48 22 612 2831, Fax. +48 22 612 2327 Portugal: see Spain Romania: see Italy Russia: Philips Russia, Ul. Usatcheva 35A, 119048 MOSCOW, Tel. +7 095 755 6918, Fax. +7 095 755 6919 Singapore: Lorong 1, Toa Payoh, SINGAPORE 1231, Tel. +65 350 2538, Fax. +65 251 6500 Slovakia: see Austria Slovenia: see Italy South Africa: S.A. PHILIPS Pty Ltd., 195-215 Main Road Martindale, 2092 JOHANNESBURG, P.O. Box 7430 Johannesburg 2000, Tel. +27 11 470 5911, Fax. +27 11 470 5494 South America: Al. Vicente Pinzon, 173, 6th floor, 04547-130 SAO PAULO, SP, Brazil, Tel. +55 11 821 2333, Fax. +55 11 821 2382 Spain: Balmes 22, 08007 BARCELONA, Tel. +34 3 301 6312, Fax. +34 3 301 4107 Sweden: Kottbygatan 7, Akalla, S-16485 STOCKHOLM, Tel. +46 8 632 2000, Fax. +46 8 632 2745 Switzerland: Allmendstrasse 140, CH-8027 ZURICH, Tel. +41 1 488 2686, Fax. +41 1 488 3263 Taiwan: Philips Semiconductors, 6F, No. 96, Chien Kuo N. Rd., Sec. 1, TAIPEI, Taiwan Tel. +886 2 2134 2865, Fax. +886 2 2134 2874 Thailand: PHILIPS ELECTRONICS (THAILAND) Ltd., 209/2 Sanpavuth-Bangna Road Prakanong, BANGKOK 10260, Tel. +66 2 745 4090, Fax. +66 2 398 0793 Turkey: Talatpasa Cad. No. 5, 80640 GULTEPE/ISTANBUL, Tel. +90 212 279 2770, Fax. +90 212 282 6707 Ukraine: PHILIPS UKRAINE, 4 Patrice Lumumba str., Building B, Floor 7, 252042 KIEV, Tel. +380 44 264 2776, Fax. +380 44 268 0461 United Kingdom: Philips Semiconductors Ltd., 276 Bath Road, Hayes, MIDDLESEX UB3 5BX, Tel. +44 181 730 5000, Fax. +44 181 754 8421 United States: 811 East Arques Avenue, SUNNYVALE, CA 94088-3409, Tel. +1 800 234 7381 Uruguay: see South America Vietnam: see Singapore Yugoslavia: PHILIPS, Trg N. Pasica 5/v, 11000 BEOGRAD, Tel. +381 11 625 344, Fax.+381 11 635 777 For all other countries apply to: Philips Semiconductors, International Marketing & Sales Communications, Building BE-p, P.O. Box 218, 5600 MD EINDHOVEN, The Netherlands, Fax. +31 40 27 24825 (c) Philips Electronics N.V. 1998 Internet: http://www.semiconductors.philips.com SCA57 All rights are reserved. Reproduction in whole or in part is prohibited without the prior written consent of the copyright owner. The information presented in this document does not form part of any quotation or contract, is believed to be accurate and reliable and may be changed without notice. No liability will be accepted by the publisher for any consequence of its use. Publication thereof does not convey nor imply any license under patent- or other industrial or intellectual property rights. Printed in The Netherlands Date of release: 1998 Mar 23 |
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