Real-time-capable Emulation of Nonlinear Analog Circuits by Means of Novel Wave Digital Filters
Final Report Abstract
Within the scope of the project, crucial contributions for convergence speed acceleration of linear Wave Digital Filters (WDFs) with non-computable topological loops as well as of WDFs containing multiple or multi-port nonlinearities could be achieved. For this purpose, the concept of Automatic Differentiating WDFs (ADWDFs) was introduced to determine optimal convergence matrices. Regarding linear WDFs, the fixed point iteration procedure can be solved directly after one step and is completely independent of freely selectable artificial port resistances. In addition, no termination criterion is required, since the fixed point is always determined exactly. Regarding nonlinear WDFs, the convergence speed using ADWDFs could be significantly accelerated and remains almost independent of freely selectable port resistances. Furthermore, the method offers easy parallelization, since certain initialization procedures for the determination of optimal convergence matrices can be carried out independently of each other, whereas with the fixed point iteration procedure only sequential processing is possible. Further, the scalability of the linear WDFs mentioned could be reduced to the simple scaling of a matrix-vector product. Regarding nonlinear WDFs, scalability is due to a linear system of equations to be solved. A split-modular approach was presented using separate forward and reverse conducting diodes within the Ebers-Moll model for bipolar transistors as a topological (parallel) junction in the WD domain. Thereby, noncomputable loops that inevitably arise from multiple or multi-port nonlinearities are resolved simultaneously by means of ADWDFs, which was verified on an actual emitter-follower circuit. The presented approach can be directly applied to circuits containing, for example, additional bipolar transistors and can be solved without further topology-related considerations, thus solving two problems simultaneously. An FPGA implementation of WDFs containing multiple exp-based nonlinearities was realized. A diode-clipper circuit with single floating-point precision was implemented, and a suitable efficient look-up-table-design was proposed in combination with an iterative approach for real-time function evaluation of the Lambert W function. Further, two variants of the circuit were implemented, namely a sequential and a concurrent one, for each of which FPGA resource utilization and a rule for the latency were determined as a function of the required iteration steps. It was shown that although the Halley method generally converges faster, the overall latency for the Newton method is the same, while the latter achieves the same accuracy while being more resource-efficient. With the developed demonstrator the theoretical results can be experienced practically and in real-time.
Publications
- (2019). An Improved Multi-Dimensional Approach to Wave Digital Filters with Topology-Related Delay-Free Loops using Automatic Differentiation. 2019 IEEE 62nd International Midwest Symposium on Circuits and Systems (MWSCAS), 1163–1166
Kolonko, L., Velten, J. & Kummert, A.
(See online at https://doi.org/10.1109/MWSCAS.2019.8885341) - (2020). Optimization of Artificial Port Reflectances for Wave Digital Filters with Topology-Related Delay-Free Loops. 2020 IEEE 63rd International Midwest Symposium on Circuits and Systems (MWSCAS), 170–173
Kolonko, L., Velten, J. & Kummert, A.
(See online at https://doi.org/10.1109/MWSCAS48704.2020.9184701) - (2021). A Split-Modular Approach to Wave Digital Filters containing Bipolar Junction Transistors. 2021 IEEE International Midwest Symposium on Circuits and Systems (MWSCAS), 840–843
Kolonko, L., Musiol, B., Velten, J. & Kummert, A.
(See online at https://doi.org/10.1109/MWSCAS47672.2021.9531789) - (2021). Automatic Differentiating Wave Digital Filters with Multiple Nonlinearities. 2020 28th European Signal Processing Conference (EUSIPCO), 146–150
Kolonko, L., Velten, J. & Kummert, A.
(See online at https://doi.org/10.23919/Eusipco47968.2020.9287674) - (2021). FPGA Implementation of Wave Digital Filters with Multiple exp-based Nonlinearities. 2021 IEEE International Midwest Symposium on Circuits and Systems (MWSCAS), 507–510
Kolonko, L., Velten, J., Kummert, A. & Musiol, B.
(See online at https://doi.org/10.1109/MWSCAS47672.2021.9531724)
