Reprogrammable Analog Ordinary Differential Equation Solver

Team: Taryn Pike and Evan Gobien

Sponsor: TRCP Medical

Project

Problem Description and Motivation

Solving high-order differential equations digitally can be slow and computationally intensive especially in real-time systems.

We built a real time reprogrammable analog computer that solves up to 8th-order linear ODEs using op-amp circuits and digitally controlled resistors, with synchronized configuration via FPGA.

Why It Matters

Our system provides fast, hardware-based solutions ideal for real-time simulation.

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System

System flow diagram

Methods

  • We used op-amp circuits for integrators, adders, and scalers, with 17 digital potentiometers setting coefficients. An FPGA (DE10-Nano) controlled all 17 SPI channels in parallel for synchronized updates, chosen for its high GPIO count.
  • A custom PCB was designed to match the FPGA’s footprint, using surface-mount ICs to keep the layout compact—through-hole components would have made it significantly larger.
  • We simulated the full circuit in EveryCircuit (SPICE) to validate behavior before hardware implementation.
Final PCB Design

Final PCB Design

Conclusion

model
  • Our analog solver matched results from MATLAB and SPICE, validating accuracy for 3rd–5th order ODEs. Higher-order verification (up to 8th) is harder to confirm due to simulation limits but appears consistent.
  • We achieved real-time, reprogrammable ODE solving with FPGA-driven SPI control. The project also taught us advanced surface-mount PCB design, enabling a compact board footprint.
  • Next steps:
    • Confirm full 8th-order accuracy
    • Explore non-linear/time-varying systems
    • Implement Practical User Interface
    • Miniaturize for embedded/educational tools