SLUAAL2 Application note

SLUAAL2 june 2023 UCC256402 , UCC256403 , UCC256404

1.1 For the Time Domain Simulation and Fundamental Harmonic Analysis of LLC Resonant Converters, What Model of the Transformer Should be Used?

The LLC topology can be realizable with the following:

An external inductor and a tightly coupled transformer, or
With a integrated transformer with a poor coupling which integrates both resonant and magnetizing inductors.

In both of these implementations, the transformer can be modeled as T-type [1] or APR models which are shown in the following images. These two models can be used for both time domain simulation and also for fundamental harmonic analysis. Equation 1, Equation 2, Equation 3 describe the behavior of all the models given in Figures 1 to 4. Reference [2] shows the different transformer model derivations from a coupled inductor transformer model. Also, the videos given here: Clarifying Coupled Inductor and Transformer Modeling, Transformer leakage in LLC converters, Leakage models of multi-winding transformer and implications to LLC converter demonstrates different transformer models and their performance using spice simulation tool.

Figure 1-1 Mutual Inductance Model

Figure 1-3 T Type Transformer Model Considering Coupling Coefficient k

Figure 1-2 T Type Transformer Model

Figure 1-4 All Primary Referred (APR) Model

Equation 1.

v_{1} = L_{1} \frac{d i_{1}}{d t} + M \frac{d i_{2}}{d t}

Equation 2.

v_{2} = L_{2} \frac{d i_{2}}{d t} + M \frac{d i_{1}}{d t}

Equation 3.

k = \frac{M}{\sqrt{L_{1} L_{2}}}

where L₁, L₂, M, k are primary open circuit inductance, secondary open circuit inductance, mutual inductance, coupling coefficient respectively.

The parameters of the models shown above can be calculated from the transformer data sheet parameters where primary open circuit Inductance (L_p) and primary inductance when secondaries are short (L_lk), turns ratio are provided.

Equation 4.

k = \sqrt{1 - \frac{L_{l k}}{L_{p}}}

Equation 5.

L_{1} = L_{p}

Equation 6.

n = turns ratio

Figure 1-5 T-type Transformer Model for LLC Design and Analysis

Figure 1-6 APR-Type Transformer Model for LLC Design and Analysis

To validate models, a closed loop simplis simulation with both T-type model shown in Figure 1-5 and APR model shown in Figure 1-6 has been built with the same transformer parameters as that of UCC25640x EVM hardware [3] where integrated transformer from Wurth Electronics [4] is used. In the transformer data sheet, L_p, L_lk, n are given as 510uH, 82uH, 16.5 respectively. From Equation 4, Equation 5, Equation 6, the parameters of the transformer obtained as k =0.916, L₁=510uH, n=16.5, k*n=15.115. Figure 1-7 shows the comparison between EVM measurements and closed loop Simplis models. We can observe that in all the cases the operating frequency is almost same for a given input voltage.

Figure 1-7 Input Voltage vs Switching Frequency From Closed Loop Simulation Model and From the EVM Measurements at 12 V, 15 A Load