In order to model a high gain converter containing a transformer or coupling inductor， Tapped Inductance Switcher modeling method（TIS）proposed a general nonlinear block consisting of a pair of complementary switches and three terminals with a coupled inductor。Static and dynamic model of such TIS blocks are presented.By changing the block internal parameters such as equivalent winding ratio defined as“a”，the coupled inductors in a block can be represented as ordinary inductors and isolated transformers or tapped inductors.
Once the topology of the switching power supply is expressed by a general nonlinear block, the model can be transformed into a personalized external linear network and a general nonlinear component model when the nonlinear general modeling component is used for modeling，just as shown in the Fig. 1 .
And the modeling of nonlinear block has been completed in advance. Researchers only need to apply the modeled nonlinear block to analyze the simple linear network, then the overall topological circuit model can be obtained directly, which is very convenient.
Fig.1： The TIS block and The TIS block portrayed as a “black box”
By changing the paramaters of the block，the TIS block can represent different topologies，But for different topologies，the embed mode is different .So the definition of the paramaters and the rules about the TIS block are given。
1):TIS Block Terminal
TIS block has 3 terminals, which represented by the numbers 0,1,2, each terminal includes two variables: voltage and current.And so the block characteristics can be fully expressed by six electrical variables.Voltage sources represent the voltage applied by the peripheral circuit at various terminals on a TIS block, current sources represent the port current.Just as shown the figure 1. The terminal 1 connectes switching device is an active switch,it's PWM control signal is K(d). The terminal 2 connectes switching device is an passive switch or complementary active switch,it's PWM control signal is K‘ (d’). The terminal 0 don't connet any switch.
2):TIS Block paramaters
a):Magnetic inductor Lm is depended by the effective winding ratio N10 and inductor L1 of the original coupled inductor winding N1 :
b): Effective winding ratio a is the ratio of the effective winding ratio N10 to N20:
According to the converter topology and coupling inductance winding mode, the effective winding ratio is also different. The specific content can be seen from the reference.
As for the converter with ordinary inductor,the paramaters are:
Example about buck converter :
The buck converters paramaters are as follow:
Fig2：buck converter paramaters
The TIS block about buck converter shown as follow：
Fig3：The TIS block with buck converters and the TIS block portrayed as a “black box”
First，we will use the static model to solve the output voltage and the current of the inductor，just shown
Fig4：the steady model of the buck converter based on the TIS block
According to the steady value of the steady model, and then plug it into the small signal model,Connet the model shown as the figure 3, By using the tool "linear analysis system" in the Simulink, we will know the control-to-output frequency response,shown as the figure :
Fig5：the dynamic model of the buck converter and the control to output frequency response
Finally，bu using the simulation software PSIM and contrast the simulation and the theortical result with the TIS block ，we can find the theortical result is good agreement with the simulation。
Fig6：Comparison of the theortical result by TIS block vs.simulated results of BUCK converter