Linearization of electronics

Linearization of electronics

Linearization of electronics group led by prof. Timo Rahkonen aims to analyze, understand, and minimize non-linear effects in electronics, and develop faster and more precise ways to analyze their effects.

Distortion contribution analysis

The main contribution  of the group has been  the development of a generic distortion contribution analysis technique called Volterra on Harmonic Balance (VoHB). It has been implemented to operate on top of normal Harmonic Balance simulation using any device models any any number of components, and the implementation has been done on commercial AWR-Aplac simulator. Fig.1 shows and example of the VoHB: an RF power amplifier is simulated using a non-linear device model.  VoHB fits a polynomial model for each non-linear I-V and Q-V source and calculates their contributions, e.g. showing how much of the total output 3rd-order intermodulation distortion (IM3) originates from Ids-Vgs and Qg-Vgs sources. Further, one can plot how the dominant contributions consist of non-linearities of different order, and results mixing from different harmonic bands. This aids the designer to minimize total distortion by a proper tuning of 2nd harmonic termination, for example. As another example, the tool has also been used to analyze the effect of the input impedance of the reconstruction filter to the  distortion generated in the output of a current-steering RF DA converter.

Error correction in AD and DA converters

Methods to characterize and minimize non-linearity errors in AD and DA converters have been developed. As an example, Fig. 2 shows the spectral location of spurious components generated in a multi-bit  delta-sigma converter, when input amplitude is swept.  The trajectory  of spurious components depends on the non-linearity of the DAC, and spurious components  generated at small signals can be pushed out from signal band simply re-ordering the DAC unit elements so that the DAC INL has minimum 2-cycle periodicity.

Design of  supply modulated RF transmitters

One efficient method to improve the power efficiency of RF transmitters is to modulate the power supply in real time. The group has developed a piecewise linear simulation technique, that greatly speeds up the simulation of modulated switch-mode power supplies, and  has studied non-linear effects both in supply modulators and in supply-modulated RF amplifiers. For example, switching class E amplifiers have a strong supply-dependent injection from output to the input of the amplifier. This alters the duty cycle of the input drive and causes negative resistance at the fundamental frequency, both of which need to be compensated by proper design of the input impedance. Fig. 3 shows a load-pull example, where the input damping network of an integrated switching amplifier  has be disconnected by laser cutting, and in the marked high modulation sidebands are seen, indicating emerging instability. The designed damping circuit cured the instability, and input a 2nd harmonic trap prevented duty cycle variotions.


Last updated: 15.8.2013