Compact SPICE Simulator using ODE Solvers

Written in conjunction with Ariana Bruno (amb633) for a programming assignment in ECE4960.

Summary This program focuses on building ODE solvers for SPICE-like circuit simulation. Three different one-step solvers (Euler, Standard Runge-Kutta, and Adaptive Runge-Kutta) were built and tested. The main program builds all relevant functions in the C++ language. A succint implementation on MATLAB is included to cross-check that the values obtained are accurate.

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Usage

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The program is simple to use for user's looking to run individual runs to generate results to solve a specific system's ODEs with various ODE Solver methods. To run the program it takes the standard format:

./program Argument#1 - Argument#2 - Argument#3

• Argument#1: Pick the ODE Solver method to use
  • ForwardEuler, RK34, RK34A
  • TEST --> sending the argument only will run the test mode
• Argument#2: Pick the system to solve
  • Exponential, Simple, Amplifier
• Argument#3: Pick the size of the time step
  • 1, 0.2

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Part 0 - Utility Functions

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Overview: Common utility functions that will be accessed and used commonly throughout the assignment. All functions have been resused from previous programming assignments.

Documentation:

• add_vectors( a , b , sum ): element-wise addition of vectors a and b with result being stored in sum
• scaleVector( scalar , a , result ): multiplies vector a by a constant scalar and stores it in result
• shiftVector( scalar , a , result ): adds a constant scalar to vector a and stores it in result
• expVector( result , input ): takes the element-wise exponential of the elements in input and stores it in result
• vectorMultiplication ( a , b , result ): element-wise multiplication of vectors a and b
• vectorProduct( results , A , b ): matrix product of a matrix A and a vector b
• print_full_vec( a ): prints all elements in vector a to screen
• calculateNorm ( a ): calculates the norm of vector a

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Part 1 - Differential Functions

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Overview: Implementation of ODE functions that will be solved using the three methods discussed in Part 2.

Documentation: All functions have to create/ call the standard function signature:

• phi: vector<double> for storing the slope of the function at the current time step
• xi: vector<double for sending the values of the function at the current time step
• time: double value for sending the current time step
• march: double value for sending the time interval (march) value at each iteration

exponential_function(): exponential test function as detailed in the hacker practices

simple_RC_circuit(): differential equations for simple circuit given in Figure 03 of handout

amplifier_circuit(): differential equations for common source amplifier given in Figure 5a of handout

Other helper functions:

• generate_current_input( time ): returns the current at the given time, following the function given in Figure 6
• calculate_ID( vgs , vds ): returns the ID,EKF current for the given parameters, as defined in Equation 1 of the handout - reused from Programming Assignment 03

Testing functions:

• test_current_generator(): testing function to check that generate_current_input( time ) returns the correct values
• test_simple_RC_circuit(): testing function to check that simple_RC_circuit() returns the correct values - values are cross-referenced with the MATLAB implementation
• test_amplifier_circuit(): testing function to check that the amplifier_circuit() returns the correct values - values are cross-referenced with the MATLAB implementation

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Part 2 - ODE Solver Methods

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Overview: Implementation of ODE Solver methods that solve the systems defined in Part 1.

Documentation: All functions have to create/ call the these variables:

• *function: for passing the phi function that corresponds to the system that will be solved (i.e. simple_RC_circuit())
• slope: vector<double> for storing the slope (phi) of the function at the current time step
• values: vector<double for sending the (current) values to the function to calculate the next iterative values
• time: double value for sending the current time step (t)
• march: double value for sending the time interval (h) value at each iteration

forward_euler(): solves for phi at each time step using the forward euler method and the system's ODE given as a pointer.

The Runge Kutta method functions have to create/ call these additional variables:

• k1, k2, k3, k4: vector<double> for calculating the intermediate k values to calculate the phi at each time step
• adaptivity: bool to decide when to enable adaptive time steps, which calculats the new time step size using the k values, x_i+1, and a relative error of 1e-4

RK34_function(): solves for phi at each time step using the Runge Kutta 3-4 method and the system's ODE given as a pointer.

ODE_Solver(): solves x_i+1 for given the current time step, and calculates phi using the function pointer which provided based which system is being solved.