Abstract
Forward and reverse modeling of RF circuit blocks are useful approaches in design space exploration. The underlying idea of forward modeling is the creation of accurate surrogate models, which can be used to predict the circuit performances replacing (expensive) circuit simulations. On the other hand, reverse modeling concerns multiobjective optimization to explore relevant trade-offs between performances. This paper provides a discussion of application of surrogate models and multiobjective optimization to narrow-band low noise amplifier design. We discuss numerical difficulties encountered when the forward model is derived by using surrogate models of low noise amplifier admittances to compute performance figures via analytical equations. Afterward, we provide an example where direct performace modeling leads to a more accurate result even when the simplest surrogate model type (a lookup table) is used. Finally, a detailed tutorial of the normal boundary intersection optimization method is provided.
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Notes
- 1.
The subscript ‘n’ indicates that design variables W and L m have been normalized such that they vary between −1 and 1.
- 2.
Admittances and noise functions are the elements of the vector b introducted in Sect. 5.1.
- 3.
Z s , Z l and L m are elements of the vector y introduced in Sect. 5.1.
- 4.
IIP2 is expressed in dBm, i.e. logarithmic scale.
- 5.
Maximization of a performance p is equivalent to minimization of −p.
- 6.
It is worthwhile to note that only 100 circuit simulations corresponding to different values of W need to be performed to generate the table, since the variability of L m is taken into account in the analytical performance equations, being L m an element of the vector y introduced in Sect. 5.1. Specific LNA performance equations are not included in this paper, because they can be found in any relevant text-book.
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Acknowledgements
This work was supported by the European Commission through the Marie Curie Actions of its Sixth Framework Program under the contract number MTKI-CT-2006-042477.
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Tommasi, L.D., Rommes, J., Beelen, T., Sevat, M., Croon, J.A., Dhaene, T. (2011). Forward and Reverse Modeling of Low Noise Amplifiers Based on Circuit Simulations. In: Benner, P., Hinze, M., ter Maten, E. (eds) Model Reduction for Circuit Simulation. Lecture Notes in Electrical Engineering, vol 74. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-0089-5_5
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