# ee_getCauerFromFoster

Get equivalent resistance and capacitance vectors for Cauer Thermal Model block from Foster Thermal Model block

## Syntax

``[RthVecCauer,CthVecCauer] = ee_getCauerFromFoster(RthVecFoster,CthVecFoster)``

## Description

````[RthVecCauer,CthVecCauer] = ee_getCauerFromFoster(RthVecFoster,CthVecFoster)` returns the equivalent resistance and capacitance vectors for a Cauer Thermal Model block from the resistance and capacitance vectors of a Foster Thermal Model block. The thermal models are equivalent because they have the same transfer function between the heat flow rate and the total temperature drop.The Foster transfer function, TFfoster(s), defines the relationship between the heat flow rate and the total temperature drop: $T{F}_{Foster}\left(s\right)=\sum _{i=1}^{N}\frac{{R}_{Foste{r}_{i}}}{1+{R}_{Foste{r}_{i}}{C}_{Foste{r}_{i}}s},$where RFoster is the Foster thermal resistance and CFoster is the Foster capacitance.To convert Foster resistances and capacitances to Cauer resistances and capacitances, the function uses the Euclid long division algorithm to express the Foster transfer function in the form of the Cauer transfer function, TFCauer,N(s): $T{F}_{Cauer,N}\left(s\right)=\frac{1}{s\text{\hspace{0.17em}}{C}_{Caue{r}_{N}}+\frac{1}{{R}_{Caue{r}_{N}}+\frac{1}{s\text{\hspace{0.17em}}{C}_{Caue{r}_{N-1}}+\frac{1}{{R}_{Caue{r}_{N-1}}+T{F}_{Cauer,N-2}\left(s\right)}}}},$where RCauer is the Cauer thermal resistance and CCauer is the Cauer capacitance.```

## Input Arguments

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Thermal resistance values of the Foster Thermal Model block, specified as a vector of positive elements. The size of this vector must be equal to the size of the `CthVecFoster` vector.

Capacitance values of the Foster Thermal Model block, specified as a vector of positive elements. The size of this vector must be equal to the size of the `RthVecFoster` vector.

## Output Arguments

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Equivalent thermal resistance values of the Cauer Thermal Model block, returned as a vector of positive elements.

Equivalent capacitance values of the Cauer Thermal Model block, returned as a vector of positive elements. The size of this vector is equal to the size of the `RthVecCauer` vector.

 Subhash Joshi, T. G., and Vinod John. Combined Transient Thermal Impedance Estimation for Pulse-Power Applications. In 2017 National Power Electronics Conference (NPEC), 42–47. Pune: IEEE, 2017. https://doi.org/10.1109/NPEC.2017.8310432.