65 dB is a high enough SNR that you can't tell the difference visually between a signal with no noise and a signal with noise 65 dB down added to it:
SNR = 65;
t = linspace(0,20,10000);
Ia = sin(2*pi*1000*t);
Ia_noise = awgn(Ia,SNR);
figure
plot(t,Ia,'LineWidth',2);
hold on
plot(t,Ia_noise,':');
But if you drop SNR down (to around 35-40 or lower in this particular example), you can see the difference:
SNR = 35;
t = linspace(0,20,10000);
Ia = sin(2*pi*1000*t);
Ia_noise = awgn(Ia,SNR);
figure
plot(t,Ia,'LineWidth',2);
hold on
plot(t,Ia_noise,':');
