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International Journal of Microwave Science and Technology
Volume 2012 (2012), Article ID 865625, 4 pages
Research Article

Invariance Property of the 𝜇 Stability Test with respect to the Characteristic Impedance

1Electronics Engineering Department, American University in Cairo, Cairo, Egypt
2Army Research Laboratory, Adelphi, MD 20783, USA

Received 21 December 2011; Revised 18 February 2012; Accepted 20 February 2012

Academic Editor: Chien-Jen Wang

Copyright © 2012 Amr A. Ibrahim et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Stability of electrical amplifiers is of crucial importance. Among the popular stability tests is the μ-test which has many advantages over other tests like the K-Δ test. However, the value of μ parameter is dependent on the input/output terminal characteristic impedance 𝑍 𝑜 used and this raises the concern that the predictions of the test are dependent on the choice of 𝑍 𝑜 . This paper proves that the conclusions of the μ-test regarding stability/instability remain invariant with 𝑍 𝑜 . This proof is necessary for gaining confidence in the results of the μ-test and should benefit circuit designers. Similar proofs should be extended to all other stability tests for additional insights into their validity under different circuit termination.