NOTICE: Due to a lapse in annual appropriations, most of this website is not being updated. Learn more.
Form submissions will still be accepted but will not receive responses at this time. Sections of this site for programs using non-appropriated funds (such as NVLAP) or those that are excepted from the shutdown (such as CHIPS and NVD) will continue to be updated.
An official website of the United States government
Here’s how you know
Official websites use .gov
A .gov website belongs to an official government organization in the United States.
Secure .gov websites use HTTPS
A lock (
) or https:// means you’ve safely connected to the .gov website. Share sensitive information only on official, secure websites.
A new causal power-normalized waveguide equivalent-circuit theory determines uniquely both the magnitude and phase of the characteristic impedance of a waveguide.
Causality, characteristic impedance, microwave circuit theory
Citation
Williams, D.
and Alpert, B.
(1999),
Characteristic Impedance, Power, and Causality, IEEE Microwave and Guided Wave Letters, [online], https://doi.org/10.1109/75.766757
(Accessed October 10, 2025)