# Smoothing a unit step function

I want to smooth a unit step function for use in NDSolve so this function is a smooth function of time (t). How can I do the smoothing? The unit step function is defined by:

α = π/6;
Vbusd[t_] := 5 (1 - Exp[-t]);
Vbusq[t_] := 3 Exp[-t];

n = UnitStep[Vbusd[t]*Cos[t - α - π/6] - Vbusq[t]*Sin[t - α - π/6]]  -
UnitStep[Vbusd[t]*Cos[t - α - (5 π)/6] - Vbusq[t]*Sin[t - α - (5 π)/6]];

• After a second look I think your question is a little unclear. What do you really want? Smoothen n with NDSolve or find a smooth approximation of n which is to be used in NDSolve? Jun 21 '15 at 9:17
• Thanks alot for help. finding a smooth approximation of n which is to be used in NDSolve.
– mard
Jun 21 '15 at 9:21
• I normally use Tanh Jun 21 '15 at 10:48

These are the transitions I usually use: (both are $C^{\infty}$)
f[x_] = Piecewise[{{(Erf[Sqrt[2 π] ArcTanh[x]] + 1)/2, -1 < x < 1}}, UnitStep[x]]