Lies, Damn Lies and Measurements

This paper describes some of the more unusual phenomena associated with RF/microwave measurements that have been investigated by the author over the past twelve years. It has been found that, from some high profile publications, microwave measurements have been either performed in error or their results wrongly interpreted. Four categories have been identified and two examples from each are discussed. Introduction Even when measurement equipment is working to specification and has been properly calibrated [1], unexpected results can sometimes be produced. With appropriate simulation software it is generally possible to investigate the causes of such phenomena. While unexpected results could mean disaster for some, for other they open up a window into new and exciting new areas of research. This paper describes some of the more unusual phenomena associated with RF measurements that have been investigated by the author over the past twelve years. Failure by Definition Ultra -high Q-factor [2] While it is accepted that superconductors can deliver unprecedented levels of Q-factor, the same can also be true of conventional active circuits. Non-superconducting monolithic inductors can have measured Q-factors that are orders of magnitude greater than those normally found with a purely passive implementation. At first sight, this may appear to be impossible. However, by exploiting the fundamental definition of Q-factor for a 1-port device, active inductors can be designed to have negligible (and even negative) effective series resistance. Fig. 1 shows the results of a monolithic tunable active inductor with measured unloaded Q-factor in excess of 15,000. resistance series reactance series factor Q Unloaded = − Fig. 1. Measured performance of a tunable active inductor at 2 GHz Power-Added Efficiency [3] Two definitions exist for the power-added efficiency of power amplifiers. The first is generic to any multi-input system and is simply the ratio of the total output power to total input power. The second definition is widely regarded as the industry standard for RF power amplifiers. A plot of the error between the definitions is given in Fig. 2, against power gain and basic efficiency DC OUT P P / = η . ( ) ( ) 2 # 1 # 2 # 1 # , ; ; ADD ADD ADD DC IN OUT ADD IN DC OUT ADD Errior P P P P P P η η η η η − = ∆ − = + = Fig. 2. Error characteristics in power-added efficiency calculations