f[x_] := 2 t /; 0 <= t < T/2;
f[x_] := 2 - 2 t /; t/2 <= t < T;
(*PERIOD*)T := 1;
Plot[f[x], {t, 0, T}];

(*this is the part were if I increase the fundamental period to be plotted I have an error "Iteration limit of 4096 exceeded."*)
f[x_] := f[t - T] /; t > T;
f[x_] := f[t + T] /; t < 0
T := 1;
Plot[f[x], {t, -T, T}]}

Clear[f]
f[t_, T_] /; Mod[t, T] <= T/2 := 2 Mod[t, T]
f[t_, T_] := 2 - 2 Mod[t, T]

With[{T = 1}, Plot[f[t, T], {t, -2 T, 2 T}]]