Computationally Efficient Design of an LNA Input Matching Network Using Automatic Differentiation

We present a method for the design of an LNA input matching network using automatic differentiation (AD), a technique made popular by machine learning. The input matching network consists of a non-uniform suspended stripline transformer, directly optimized with AD-provided gradients. Compared to the standard approach of finite-differences, AD provides orders of magnitude faster optimization time for gradient-based solvers. This dramatic speedup reduces the iteration time during design and enables the exploration of more complex geometries. The LNA designed with this approach improves over a previous two-section uniform-line design, achieving an average noise temperature of (11.53 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\pm$</tex-math></inline-formula> 0.42) K over the frequency range of 0.7 GHz to 2 GHz at room temperature. We optimized the geometry in under 5 s, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$40$</tex-math></inline-formula>x faster than optimizing with finite-differences.