Why White Noise is not adding Uniformly to Signal?

I am adding noise,,generated through randn, to a signal However as seen in image the noise does not effect the low part of Input Signal. What can be the reason for it.

NOTE: Kindly ignore all parameters above in code.. you may focus from where i am adding noise (Mentioned in comments).

Its simply Multlipying an Input singnal added with noisr by transfer function and plotting the output

% clear all; format short e; close all;
fprintf('\n \n \n \n \n \n \n','%s');
% set(0,'DefaultAxesFontName','arial');
% set(0,'DefaultAxesFontSize',12);

global w f nfig k T;

nfig=0;
color1='-r';
color2='-k';
color10='-g';
color20='-b';

f=10e3:10e3:100e9;
w=2*pi*f;
k=13.8e-24;
T=300;

%%% Transistor Small-Signals Parameters %%% %%% %%% %%% %%% %%% %%% %%% %%%
Gmcsp=25e-3;
RFcsp=25e3;
ROcsp=1e6;
Cu=54.1283e-15;
Bcsp=13;                % 0-31
CFcsp=10*Cu+Bcsp*Cu;    %1.25 pF    1.248509 pF

%%% Transistor Small-Signals Parameters Shaper  %%% %%% %%% %%% %%% %%% %%%
Gmsh=25e-3;
RFsh=430e3;
Rsh=12.5e3;
ROsh=1e6;
Cush=9.47242e-15;
Bsh=6;                    % 0-15
CFsh=64*Cush+Bsh*Cush;    % 663e-15;

%%% Detector Parasitic Cap
CDE=60e-12;

%%% Transfer Function with Cf-CD %%% %%% %%% %%% %%% %%% %%% %%% %%% %%% %%%
syms gmcsp rocsp rfcsp cfcsp cde vocsp vcsp gmsh rosh rsh rfsh cfsh vosh vsh iin s

eq1= (vcsp-vocsp)*s*cfcsp + (vcsp-vocsp)/rfcsp + s*cde*vcsp -iin;
eq2= (vocsp-vcsp)*s*cfcsp + (vocsp-vcsp)/rfcsp + vocsp/rocsp + gmcsp*vcsp + (vocsp-vsh)/rsh;
eq3= (vsh-vosh)*s*cfsh + (vsh-vosh)/rfsh + (vsh-vocsp)/rsh;
eq4= (vosh-vsh)*s*cfsh + (vosh-vsh)/rfsh + vosh/rosh + gmsh*vsh;

tf=solve(eq1,eq2,eq3,eq4,vosh,vsh,vocsp,vcsp);
tf1=collect(tf.vosh,s);
fprintf('\n','%s');fprintf('vosh/iin(s) (NO CD-CGS1) \n','%s');fprintf('\n','%s');
pretty(tf1);

%%% Plot in s-Domain %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% vout/iin
nfig=nfig+1;
figure(nfig);
tfvosh=subs(tf.vosh,{gmcsp,rocsp,cfcsp,rfcsp,gmsh,rosh,rsh,rfsh,cfsh,cde,iin},{Gmcsp,ROcsp,CFcsp,RFcsp,Gmsh,ROsh,Rsh,RFsh,CFsh,CDE,1});
%[mag1,phase1]=plotting_from_system2(tfvosh,color1);

tfvocsp=subs(tf.vocsp,{gmcsp,rocsp,cfcsp,rfcsp,gmsh,rosh,rsh,rfsh,cfsh,cde,iin},{Gmcsp,ROcsp,CFcsp,RFcsp,Gmsh,ROsh,Rsh,RFsh,CFsh,CDE,1});
%[mag2,phase2]=plotting_from_system2(tfvocsp,color2);
ylabel('Magnitude - [dBOhm]');
title('vosh/qin');
legend('vosh','vocsp');

%%% Noise TF %%% %%% %%% %%% %%% %%% %%% %%% %%% %%% %%% %%% %%% %%% %%% %%
syms gmcsp rocsp rfcsp cfcsp cde vocsp vcsp gmsh rosh rsh rfsh cfsh vosh vsh vncsp s

eq1= (vcsp+vncsp-vocsp)*s*cfcsp + (vcsp+vncsp-vocsp)/rfcsp + s*cde*(vcsp+vncsp);
eq2= (vocsp-vcsp-vncsp)*s*cfcsp + (vocsp-vcsp-vncsp)/rfcsp + vocsp/rocsp + gmcsp*vcsp + (vocsp-vsh)/rsh;
eq3= (vsh-vosh)*s*cfsh + (vsh-vosh)/rfsh + (vsh-vocsp)/rsh;
eq4= (vosh-vsh)*s*cfsh + (vosh-vsh)/rfsh + vosh/rosh + gmsh*vsh;

tfn=solve(eq1,eq2,eq3,eq4,vosh,vsh,vocsp,vcsp);
tfn1=collect(tfn.vosh,s);
fprintf('\n','%s');fprintf('vn1 TF \n','%s');fprintf('\n','%s');
pretty(tfn1);

%%% Noise Plot in s-Domain
%%% vout/vn
nfig=nfig+1;
figure(nfig);
tfnvosh=subs(tfn.vosh,{gmcsp,rocsp,cfcsp,rfcsp,gmsh,rosh,rsh,rfsh,cfsh,cde,vncsp},{Gmcsp,ROcsp,CFcsp,RFcsp,Gmsh,ROsh,Rsh,RFsh,CFsh,CDE,1});
%[magn1,phasen1]=plotting_from_system2(tfnvosh,color1);

tfnvocsp=subs(tfn.vocsp,{gmcsp,rocsp,cfcsp,rfcsp,gmsh,rosh,rsh,rfsh,cfsh,cde,vncsp},{Gmcsp,ROcsp,CFcsp,RFcsp,Gmsh,ROsh,Rsh,RFsh,CFsh,CDE,1});
%[magn2,phasen2]=plotting_from_system2(tfnvocsp,color2);
title('vosh/vnoise');
legend('vosh','vocsp');

%%% Equivalent Input Charge
Q=-5e-15;%:-1e-15:-10e-15;

QIN=Q;
QTIME=0.3e-9;

%%% Plot in Time-Domain %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% TIME AXIS
syms t;
wu=1/(RFsh*CFsh);

I=QIN/QTIME;
Tp=2/wu;
N=1000;

time=1:1:N;
time=Tp*time/N;

to1=1e-9;
to2=to1+1*QTIME; %to1+1*QTIME;

%%% Input Signal Laplace Transform
xins=(exp(-s*to1))*1/s-(exp(-s*to2))*(1/s);
xins=I*xins;
xint=ilaplace(xins);
xint=subs(xint,{t},{time});


%
noisevec =.055e-8*sqrt(0.707)*randn(size(time));
noisevecs=laplace(sym(noisevec));


% Output Signal
xinss=xins+noisevecs;       %%%%%%Adding Noise to Signal
yss_sh=xinss*tfvosh;        %%% Multipluing With Transfer function
%

%%% Output Signal
ys_sh=xins*tfvosh;
ys_csp=xins*tfvocsp;

%%% CFEQ=CF*(1+(1+RF/RL)*(CD/CF)/(Gm1*RL));

ysshtid=ilaplace(yss_sh);

yshtid=ilaplace(ys_sh);
ycsptid=ilaplace(ys_csp);

ysh=subs(yshtid,{t},{time});
yssh = zeros(size(time), 'sym');
for idx = 1 : numel(time);
yssh(idx) = subs(ysshtid(idx), t, time(idx));
end


ycsp=subs(ycsptid,{t},{time});

%%% Plot in Time-Domain %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
nfig=nfig+1;
figure(nfig);
plot(time*1e9,-yssh*1e3,color2,'LineWidth',1);
hold on;
plot(time*1e9,-ysh*1e3,color1,'LineWidth',2);
hold on;

plot(time*1e9,ycsp*1e3,color2,'LineWidth',2);
xlabel('Time - [nsec]');ylabel('Voltage - [mV]');
title('vosh/Iin');
grid on;
legend('vosh','vocsp');

[Adam Danz]

What's this?

time = time Tp * / N;

[Syed Adeel]

Tp*time/N

[Adam Danz]

FYI, I commented-out these 3 lines at the top of the code so users don't unintentionally make these changes to thier local systems by copying and executing all of your code.

% clear all; format short e; close all;
fprintf('\n \n \n \n \n \n \n','%s');
% set(0,'DefaultAxesFontName','arial');
% set(0,'DefaultAxesFontSize',12);

[Adam Danz]

I think your transfer function is scaling down the added noise but I haven't dug too deeply to verify that. I would start troubleshooting there.

[Syed Adeel]

I hope you come out with some solution as it has taken alot of time and I am in dire need of it.

Also notice the for loop I have used for subs as both the vectors are not of same lenght. (If thats correct way to do it)?adding noise in s domain , ilaplace and substiting thn gives a long vector making it unequat to time vector.

If I add the noise direct to output thn it works fine as in attached picture(both vectors are of same lenght in this case)

Answer 1

[Sulaymon Eshkabilov]

In your plot section, you are plotting three sets instead of four and thus, the noise added signal is not showing up.

See:

plot(time*1e9,-yssh*1e3,color2,'LineWidth',1);  % noise added signal
hold on;
plot(time*1e9,-ysh*1e3,color1,'LineWidth',2);   % clean signal
hold on;
plot(time*1e9,ycsp*1e3,color2,'LineWidth',2);   % Clean signal
                                                % Noise added signal: ys_csp is missing  

[Syed Adeel]

no. noise appera on red signal, to which i have added moise. the problem is initially there is no noise and later its get added.

not interested in csp output