tfer_2S.m

% TFER_2S   Evaluates the transfer function for a PMA in Case C.
% 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_2S(sp, m, d, z, prop)

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

%-- Estimate device parameter --------------------------------------------%
lam = 2 .* tau .* ([sp.alpha]' .^ 2 - ...
    [sp.beta]' .^ 2 ./ (rs .^ 4)) .* prop.L ./ prop.v_bar;


%-- Taylor series expansion constants ------------------------------------%
C1 = 2 .* tau .* ([sp.alpha]' .^ 2 - ...
    [sp.beta]' .^ 2 ./ (rs .^ 4));
C2 = -2 .* tau .* ([sp.alpha]' .^ 2 ./ rs - ...
    5 .* [sp.beta]' .^ 2 ./ (rs .^ 5));


%-- Evaluate G0 and transfer function ------------------------------------%
G0 = @(r) rs + C1 .* (r - rs) .* exp(-lam) ./ ...
    (C2 .* (r - rs) + C1 - C2 .* (r - rs) .* exp(-lam));

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