ita_tubeimpedance_transformation.m 8.56 KB
 Jan-Gerrit Richter committed Jul 29, 2016 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 ``````function varargout = ita_tubeimpedance_transformation(varargin) %ITA_TUBEIMPEDANCE_TRANSFORMATION - Transmission line impedance transformation for tubes % This function transforms the input impedance of a tube into the load impedance, % resp. the load impedance of a tube into the input impedance, according to the % transmission line theory. For small tubes (diameter 20mm and smaller), % a lossy transformation will be executed. % % There are two cases: % 1. The (load) impedance Z(0) is known, so the (input) impedance Z(l) % one would see at x=l has to be computed. % 2. The (input) impedance Z(l) is known, so the (load) impedance Z(0) % at x=0 (which would cause Z(l) )has to be computed. % % Instructions for the two cases: % Case 1: % Specify the length with a positive sign. % Case 2: % Specify the length with a negative sign. % % Sketch (One is looking from the l plane into the transmission line): % % | x=l (l plane) | x=0 (0 plane) % |___________________________________| % | | % Input imp >>> negative l >>> Load imp % Z(l) | <<< positive l <<< Z(0) % |___________________________________| % | | % % % Call: Z_trans = ita_tubeimpedance_transformation(Z_known, diameter, length, temp, [option]) % Z_known : itaAudio % diameter : numeric in [m] % length : numeric in [m] % temp : numeric in [�C] % option : optional string ('lossless' for transformation type override) % % Example: % Z_0 = ita_make_impedance('Z_0',100,44100,16); % Load impedance % Z_L = ita_tubeimpedance_transformation(Z_0,0.03,0.01,30);% Get input impedance % % % Note: Keep in mind that due to the numerical computation, slight % errors occur, which grow with the value of the transformed impedance. % Try for instance: % % Z_0 = ita_make_impedance('Z_0',inf,44100,16); % Z_L = ita_tubeimpedance_transformation(Z_0,0.03,0.01,30); % Z_0_new = ita_tubeimpedance_transformation(Z_L,0.03,-0.01,30); % ita_plot_spk(Z_0_new); % % You will will see spots where Z_0_new is not exactly inf (but in the % range of 400dB, which is probably almost inf...). This is worse for the % lossy transformation. % % The formulas for the lossy transformation for small tubes were taken % from 'Mathematical predictions of electroacoustic frequency response of % in situ hearing aids' by David P. Egolf (J. Acoust. Soc. Am. 63, 264-271, (1978)). % % % See also ita_impedance_parallel, ita_make_impedance. % % Reference page in Help browser % doc ita_impedance_transformation % % This file is part of the application TPA-TPS for the ITA-Toolbox. All rights reserved. % You can find the license for this m-file in the application folder. % % Author: Johannes Klein -- Email: johannes.klein@akustik.rwth-aachen.de % Created: 04-Mar-2009 % Modified: 10-Mar-2009 - klein - Vast performance improvement % Modified: 21-Jun-2009 - klein - Introducing lossy transmission, work in progress % Modified: 26-Jun-2009 - klein - Lossy transmission, work pretty much done %% Get ITA Toolbox preferences and Function String verboseMode = ita_preferences('verboseMode'); %#ok Use to show additional information for the user thisFuncStr = [upper(mfilename) ':']; %#ok Use to show warnings or infos in this functions %% Initialization and Input Parsing narginchk(4,5); sArgs = struct('pos1_Z_known','itaAudio','pos2_diameter','integer','pos3_length','integer','pos4_temp','integer','pos5_option','anything'); [Z_known,diameter,length,temp,option,sArgs] = ita_parse_arguments(sArgs,varargin); %#ok if ~ischar(option) clear option; option = 'none'; end %% Paramters - TODO: Outsource computing of std. parameters (see also "medium constants" for lossy transformation below)- klein % Probe constants radius = diameter/2; % density = 1.1769*(1-0.00335*(temp-26.85)); velocity = 347.23*(1+0.00166*(temp-26.85)); f = Z_known.freqVector; f(1,1) = 1; % Brute force fix to prevent division by zero later on. % This does not matter, because the first bin will be set to zero at the end. omega = 2*pi*f; %% Preparations for resulting itaAudio original_name = Z_known.comment; Z_trans = ita_generate('flat',1,Z_known.samplingRate,Z_known.fftDegree); Z_trans.channelUnits{1} = 'kg/s m^2'; Z_trans.comment = [original_name '(trans)']; Z_trans.channelNames{1} = Z_trans.comment; nBins = Z_known.nBins; if diameter > 2e-2 || strcmp(option, 'lossless') %% Transformation for big tubes % Abbreviations k = omega./velocity; sine = sin(k.*length); cosine = cos(k.*length); % Characteristic impedance of the tube Z_c = ones(1,nBins).*density.*velocity; % Transformation components b2 = 1i; a2 = 1i; else %% Transformation for small tubes % Medium constants sigma = (0.8410*(1-0.0002*(temp-26.85)))^2; % Prandtl number of fluid medium mu = ((temp+273.15)/273.15)^1.5*(273.15+110.4)/(temp + 273.15 + 110.4)*1.71e-5; % Dynamic (absolute) viscosity ratio = 1.4017*(1-0.00002*(temp-26.85)); % Ratio of specific heats of the fluid medium (c_p/c_v) % Propagation constants alpha = sqrt(-1i.*omega.*density.*sigma./mu); % Attenuation part of propagation operator beta = sqrt(-1i.*omega.*density./mu); % Phase part of propagation operator % Abbreviations ar = alpha.*radius; br = beta.*radius; % Propagation operator gamma_pre = 1i.*omega./velocity; % Prefactor of gamma equation gamma_num = 1+2.*(ratio-1).*((bessel(1,ar))./(ar.*bessel(0,ar))); % Inner numerator of gamma equation gamma_den = 1-(2.*bessel(1,br))./(br.*bessel(0,br)); % Inner denominator of gamma equation gamma = gamma_pre.*sqrt(gamma_num./gamma_den); % Complete gamma % Characteristic impedance of the tube Z_c_pre = (density.*velocity); % Prefactor of Z_c equation Z_c_first = 1-(2.*bessel(1,br))./(br.*bessel(0,br)); % First inner factor if Z_c equation Z_c_second = 1+(2.*(ratio-1).*bessel(1,ar))./(ar.*bessel(0,ar)); % Secondinner factor if Z_c equation Z_c = Z_c_pre./sqrt(Z_c_first.*Z_c_second); % Complete gamma % Further abbreviations sine = sinh(gamma.*length); cosine = cosh(gamma.*length); % Transformation components b2 = 1; % Contrary to lossless no factor "1i" a2 = 1; % Contrary to lossless no factor "1i" end %% Computation of Z_trans % In case of Z_known=inf, Z_known is not needed for the computation of the % resulting element. A simplified equation is used: % (Z_trans.spk=dens*vel*cos_kl/sin_kl) or % (Z_trans.spk=dens*vel*cosh_gl/sinh_gl), respectively . fin_vec = ~isinf(Z_known.spk); % Vector with "1" at finite positons of Z_known Z_known.spk(~fin_vec) = 1; % Set inf Z_known elements to 1 (see explanation above) b0 = Z_c; b1 = Z_known.spk; b2 = b2.*Z_c; a1 = Z_c; a2 = a2.*Z_known.spk; b2 = b2.*fin_vec; % Set elements at Z_known=inf positions to 0 (simplification, see explanation above) a1 = a1.*fin_vec; % Set elements at Z_known=inf positions to 0 (simplification, see explanation above) Z_trans.spk = b0.*(b1.*cosine+b2.*sine)./(a1.*cosine+a2.*sine); % The final formula %% Check for zero frequency Z_trans.spk(:,1) = 0; %% Check for Nyquist Z_trans.spk(:,end) = real(Z_trans.spk(:,end)); %% Add history line Z_trans.header = ita_metainfo_add_historyline(Z_trans.header,mfilename,varargin); %% Check header Z_trans = ita_metainfo_check(Z_trans); %% Find output parameters if nargout == 0 %User has not specified a variable % Do plotting? Z_medium = ita_generate('flat',(density*velocity),44100,Z_trans.fftDegree); Z_medium.comment = 'Z(medium)'; Z_medium.channelNames{1} = Z_medium.comment; ita_plot_freq_phase(Z_trans/Z_medium); else % Write Data varargout(1) = {Z_trans}; end %end function end``````