A first order high/low-shelf filter expressed as a continuous time transfer function in MATLAB.

circuitShelf.m

function [transferFunction] = circuitShelf(isHighShelf,R,C,f)
%%% CircuitShelf: A circuit informed shelf filter written as a continuous
%%% time transfer function.
% Author:   Ben Holmes
% Date:     2017/12/16
% License:  GPL v3

% Arguments:
%   - isHighShelf:  Boolean variable to switch between highpass and lowpass
%   - R:            2x1 vector of resistor values
%   - C:            Capacitor value
%   - f:            Frequencies at which to evaluate the transfer function

% Outputs:
%   - transferFunction: complex valued continuous time transfer function of
% the filter.

% Parameterisation: Gain and cutoff frequency can be used instead of
% circuit values.
% Let G be gain and fc be cutoff frequency
% R2 = R1*G/(1-G)
% For high-shelf: C = 1/(2*pi*(R1 + R2)*fc)
% For low-shelf:  C = 1/(2*pi*(R1*R2/(R1+R2))*fc);

% Find number of samples and pre-allocate output for speed.
Ns = length(f);
transferFunction = zeros(1,Ns);

% Select between high/low topology
if isHighShelf
    rIncidence = [1 -1 0;0 1 -1];
    cIncidence = [0 0 1];
    vIncidence = [1 0 0];
    X = [0; 0; 0; 1];
else
    rIncidence = [1 -1;0 1];
    cIncidence = [1 -1];
    vIncidence = [1 0];
    X = [0; 0; 1];
end

% Diagonalise the resistors into a 2x2 matrix
resistors = diag(1./R);

% Evaluate the transfer function at specified points
for nn=1:Ns
    capacitors = 2*pi*sqrt(-1)*f(nn)*C;
    
    S = [rIncidence.'*resistors*rIncidence+...
         cIncidence.'*capacitors*cIncidence ...
         vIncidence.';...
         vIncidence 0];
    
    transferFunctions = S\X;
    
    transferFunction(nn) = transferFunctions(2);
end

end