Rising knowledge heart energy calls for are driving server end-equipment producers to succeed in increased power-conversion efficiencies with the intention to cut back the thermal footprint of their techniques. The transition from a 12-V energy distribution bus to a 48-V bus creates the necessity for a high-efficiency, small-footprint step-down converter (48 V to 12 V). Gallium nitride (GaN) subject impact transistors (FETs) are the first enablers for the dimensions reductions and efficiencies wanted in these techniques.
In Energy Tip #122, I offered an summary of a high-efficiency 1kW bus converter design that addresses this want utilizing high-performance GaN switches [1]. That design makes use of a matrix transformer-based inductor-inductor-capacitor (LLC) converter and an built-in printed circuit board (PCB) transformer.
On this energy tip, I need to unpack the customized design of the transformer and clarify how I derived it. Particularly, I need to present the way to analytically predict the transformer dimensions that may yield the transformer with the smallest footprint and highest converter effectivity, which would require equations for some currents within the system together with estimates of the winding resistances as a perform of the geometry, each shared in shared in Energy Tip #122. With this knowledge, I’ll clarify the way to make this prediction utilizing a software resembling Mathcad.
Determine 1 is a high-level schematic for the LLC converter that’s the focus of this text. Desk 1 lists the corresponding specs. The built-in matrix transformer that I’m going to optimize is proven in grey in Determine 1.
Determine 1 LLC converter with the built-in matrix transformer that shall be optimized on this article (proven in grey). Supply: Texas Devices
|
Parameter |
Minimal |
Typical |
Most |
|
Vin |
40 V |
48 V |
60 V |
|
Vout |
9.5 V |
12 V |
15 V |
|
Pout |
1 kW |
||
|
Peak effectivity |
98 % |
||
|
Transformer turns ratio |
4-to-1 |
||
|
fs |
1 MHz |
||
|
Lm, magnetizing inductance |
2 µH |
||
|
Lr, resonant inductance |
16 nH |
||
|
Cr, resonant capacitance |
3.52 µF |
||
|
Type issue |
One-eighth brick |
||
|
Main GaN FETs |
LMG2100R044 |
||
|
Secondary GaN FETs |
EPC2066 |
||
|
Controller |
F2800157QRHBRQ1 or UCD3138ARJAT |
||
Desk 1 Working specs for the bus converter proven in Determine 1.
The mathematical prediction of the minimal measurement and most effectivity would require equations for the losses within the system. These losses should be parameterized in such a approach as to be a perform of the transformer geometry. In actuality, you’ll must accommodate losses from many alternative sources; nevertheless, in an effort to make this text digestible, I’m solely going to cowl 4 loss parts. Desk 2 lists the loss parameters of those parts, together with an outline of every.
|
Parameter |
Method |
Description |
|
Pcore |
 |
Transformer core loss. ok, α, and β are materials constants from the fabric knowledge sheet. Ve is the amount of the core materials and is a perform of the core geometry dimensions. |
|
Pcu |
 |
Transformer winding loss. Ilr,rms and Isec,rms are offered in Energy Tip #122 together with the AC resistance time period. |
|
Pfet,pri |
 |
Main and secondary GaN FET losses. For the reason that system is zero voltage switched, solely the Rds,on-related losses are required. The currents will be derived as described in Energy Tip #122 and are listed as (1) and (2) under. |
|
Pfet,sec |
 |
Desk 2 LLC loss parameters and an outline of every.
The entire system losses can then be outlined as Pcomplete(w,r) = Pcore(w,r)+ Pcu(w,r)+Pfet,pri+Pfet,sec. The Pcore and Pcu parameters are proven as express features of the transformer winding geometry. The parameters w and r are placeholders in the mean time and shall be substituted for the related geometric parameters.
Determine 2 exhibits a mockup of the board and core. The sunshine purple area signifies the overall PCB measurement. The inexperienced space is the world taken up by the transformer windings, and the grey materials is the gapped transformer core.
Determine 2 Board mannequin the sunshine purple area is the overall PCB measurement, inexperienced is the world taken up by the transformer windings, and darkish grey is the gapped transformer core. Supply: Texas Devices
Determine 3 exhibits probably the most important geometric parameters for the transformer windings. This drawing is a prime view of 1 copper layer of the inexperienced area proven in Determine 2. For simplicity, Determine 3 doesn’t present any vias or layer cuts, though these shall be crucial for implementation.
Determine 3 Essentially the most important transformer winding geometry. A prime view of the inexperienced area proven in Determine 2. Supply: Texas Devices
The parameter rc is the radius of the transformer core publish. And rc,s is the spacing between the core and the PCB windings. wcu,1 and wcu,2 are the space from the PCB gap to the outer fringe of the winding. Utilizing these parameters lets you outline the overall loss as a perform of those parameters as Pcomplete(wcu,2,rc). Utilizing Determine 3, you may also outline the world of the transformer footprint as a perform of those identical parameters as proven in equation (3).
You should use Pcomplete(wcu,2,rc) and Axfmr(wcu,2,rc) to optimize the system for minimal energy loss and minimal measurement by making a contour plot of the effectivity equation (4), after which superimposing on that plot one other contour plot design with a relentless footprint space. See Determine 4.
Determine 4 Optimum transformer dimensions plot with a contour plot of the effectivity equation (4) and one other contour plot with a relentless footprint space superimposed on it. Supply: Texas Devices
In Determine 4, the curved traces characterize contours of fixed effectivity, whereas the straight traces sloping downward from left to proper characterize designs of fixed space. Pay attention to the truth that the smaller footprint designs are those furthest to the left within the plot. As well as, the purpose the place a relentless effectivity contour simply barely touches one in every of these traces is the purpose the place the design ends in the smallest footprint for that effectivity contour. Primarily based on this, you may visualize a line of small transformers, as proven by the darkish blue line. Any design on this line would be the smallest design potential for the goal effectivity—or, for those who desire, the very best effectivity you can obtain for a design of that measurement. The pink dot in Determine 4 exhibits the ultimate design dimensions chosen for the {hardware}.
It’s straightforward to generate contour plots resembling these in Determine 4 in instruments together with Matlab, Mathcad, or Mathematica. One of these evaluation is what occurs if you clear up a constrained optimization drawback utilizing Lagrange multipliers [4] and will be carried out with Equations 5, 6 and seven. Whereas fixing the issue this manner is extra mathematically intensive, the top result’s an identical to what you may obtain through the use of the contour plots.
Evaluating the loss within the transformer (as produced by the equations) to the transformer loss (produced by an unbiased simulation of the transformer utilizing finite aspect evaluation, or FEA) will validate this technique. The outcomes of the 2 fashions are inside 1% of one another. Moreover, the overall losses within the system in comparison with the prediction even have glorious correlation, as proven in Determine 5.
Determine 5 Loss comparability the place the overall losses within the system in comparison with the prediction even have glorious correlation. Supply: Texas Devices
On this energy tip, I introduced a technique for fixing a constrained optimization drawback that ends in the transformer parameter crucial to attain the smallest-size transformer and highest effectivity converter. The accuracy of the tactic was inside 1%, as demonstrated by FEA simulation. This technique doesn’t want the complicated derivatives to formally clear up a Lagrange multiplier drawback, permitting you to exactly zero in on higher options and additional leverage the dimensions and effectivity advantages of GaN switches.
Brent McDonald works as a system engineer for the Texas Devices Energy Provide Design Providers crew, the place he creates reference designs for quite a lot of high-power functions. Brent obtained a bachelor’s diploma in electrical engineering from the College of Wisconsin-Milwaukee, and a grasp’s diploma, additionally in electrical engineering, from the College of Colorado Boulder.
Associated Content material
References
- Texas Devices. n.d. 100-V 4.4-mΩ half-bridge GaN FET with built-in driver and safety. Accessed July 23, 2024.
- Liu, Ya. 2007. “Excessive Effectivity Optimization of LLC Resonant Converter for Huge Load Vary.” Grasp’s thesis, Virginia Polytechnic Institute and State College.
- Dowell, P.L. “Results of Eddy Currents in Transformer Windings.” Printed in Proceedings IEE (UK) 113, no. 8 (August 1966): pp. 1387-1394.
- n.d. Lagrange multiplier. Accessed July 23, 2024.
