tfer_1C.m

% TFER_1C	Evaluates the transfer function for a PMA in Case B.
% Author:	Timothy Sipkens, 2019-03-21
% 
% Inputs:
%   sp          Structure defining various setpoint parameters 
%               (e.g. m_star, V). Use 'get_setpoint' method to generate 
%               this structure.
%   m           Particle mass
%   d           Particle mobility diameter
%   z           Integer charge state
%   prop        Device properties (e.g. classifier length)
%
% Outputs:
%   Lambda      Transfer function
%   G0          Function mapping final to initial radial position
%=========================================================================%

function [Lambda, G0] = tfer_1C(sp, m, d, z, prop)

[tau, C0] = parse_inputs(sp, m, d, z, prop);
        % parse inputs for common parameters

%-- Taylor series expansion constants ------------------------------------%
C3 = tau .* ([sp.alpha]' .^ 2 * prop.rc + ...
    2 .* [sp.alpha]' .* [sp.beta]' ./ prop.rc + [sp.beta]' .^ 2 ./ (prop.rc^3) - C0 ./ (m .* prop.rc));
C4 = tau .* ([sp.alpha]' .^ 2 - 2 .* [sp.alpha]' .* [sp.beta]' ./ (prop.rc^2) - ...
    3 .* [sp.beta]' .^ 2 / (prop.rc^4) + C0 ./ (m .* (prop.rc^2)));


%-- Evaluate G0 and transfer function ------------------------------------%
G0 = @(r) prop.rc + (r - prop.rc + C3 ./ C4) .* ...
    exp(-C4 .* prop.L ./ prop.v_bar) - C3./C4;

ra = min(prop.r2, max(prop.r1, G0(prop.r1)));
rb = min(prop.r2, max(prop.r1, G0(prop.r2)));

Lambda = (1 ./ (2 .* prop.del)) .* (rb - ra);

end