# OTL Circuit Function

The six-dimensional OTL circuit function computes the mid-point voltage of an output transformerless (OTL) push-pull circuit. It has been used as a test function in metamodeling (Ben-Ari and Steinberg, 2007) and sensitivity analysis for screening (Moon, 2010) exercises.

## Description

The mid-point voltage (V_m) of an OTL push-pull circuit is computed using the following analytical expression:

V_m = f(\mathbf{x}) = \frac{(V_{b1} + 0.74) \beta (R_{c2} + 9)}{\beta (R_{c2} + 9) + R_f} + \frac{11.35 R_f}{\beta (R_{c2} + 9) + R_f} + \frac{0.74 R_f \beta (R_{c2} + 9)}{(\beta (R_{c2} + 9) + R_f) R_{c1}},

where:

V_{b1} = \frac{12 R_{b2}}{R_{b1} + R_{b2}},

and \mathbf{x} = \{R_{b1}, R_{b2}, R_{f}, R_{c1}, R_{c2}, \beta\}​ is the vector of input variables described in the table below.

## Inputs

For computer experiment purposes, the input variables are modeled as six independent uniform random variables.

No Variable Distribution Parameters Description
1 R_{b1} Uniform R_{b1,\min} = 50,
R_{b1,\max} = 150
Resistance b1 [\text{k}\Omega]
2 R_{b2} Uniform R_{b2,\min} = 25,
R_{b2,\max} = 70
Resistance b2 [\text{k}\Omega]
3 R_{f} Uniform R_{f,\min} = 0.5,
R_{f,\max} = 3
Resistance f [\text{k}\Omega]
4 R_{c1} Uniform R_{c1,\min} = 1.2,
R_{c1,\max} = 2.5
Resistance c1 [\text{k}\Omega]
5 R_{c2} Uniform R_{c2,\min} = 0.25,
R_{c2,\max} = 1.2
Resistance c2 [\text{k}\Omega]
6 \beta Uniform \beta_{\min} = 50,
\beta_{\max} = 300
Current gain [\text{A}]

## Resources

The vectorized implementation of the OTL circuit function in MATLAB as well as the script file with the model and probabilistic inputs definitions of the function in UQLAB can be downloaded below:

uq_otlCircuit.zip (2.4 KB)

The contents of the file are:

Filename Description
uq_otlCircuit.m vectorized implementation of the OTL circuit function
uq_Example_otlCircuit.m definitions for the model and probabilistic inputs in UQLab
LICENSE license for the function (MIT)

## References

• E. N. Ben-Ari and D. M. Steinberg, “Modeling Data from Computer Experiments: An Empirical Comparison of Kriging with MARS and Projection Pursuit Regression,” Quality Engineering, vol. 19, pp. 327–338, 2007. DOI:10.1080/08982110701580930
• H. Moon, “Design and analysis of computer experiments for screening input variables,” Ohio State University, 2010. URL