In physical design, human designers typically place macros via trial and error, which is a Markov decision process. Reinforcement learning (RL) methods have demonstrated superhuman performance on the macro placement. In this paper, we propose an extension to this prior work [1]. We first describe the details of the policy and value network architecture. We replace the force-directed method with DREAMPlace for placing standard cells in the RL environment. We also compare our improved method with other academic placers on public benchmarks.

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We have developed a new expression for the frequency-dependent surface impedance of a rectangular bar that is easily used, and is numerically efficient. By dividing the metal bar into rectangular and square sections, skin depth-induced current crowding to the surfaces and corners can be accurately modeled. Comparison to measured data shows excellent agreement over a wide frequency range, covering the transition from dc-like behavior to skin-depth limited behavior.

A new approximation technique to find the total series impedance per unit length for quasi-TEM transmission limes including conductor loss has been developed. It is shown through the use of conformal mapping that both frequency dependent skin-depth and proximity effects can be accurately modeled. Comparison between experimental measurements and calculations for twin-lead, coplanar strips, parallel square bars, and coplanar waveguide all show excellent agreement. This technique is easily generalized to any transmission line making use of polygonal cross-section conductors.

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