$\begingroup$ I know, but the problem is that the unit step is defined like 1, for t>1 and 0, for 0= 0, and time can never be negative. Next, verify your results for both frequency response and unit step response by simulating the circuit in Fig. Drawing the circuit μ for 10^- 6 is entered as "u" on LTspice. A step by step derivation of this convolution would start with the following: f ( t) = ∫ − ∞ ∞ x ( τ) h ( t − τ) d τ = ∫ − ∞ ∞ e − α τ u ( τ) e − β ( t − τ) u ( t − τ) d τ. Step - For a step waveform, set V1 and V2 to the initial and stepped voltages of the waveform. In this example the resistor is 100kOhm at 27 ☌ (the default temperature for LTSPICE). And this is probably where you probably went on and tried to simplified the bounds on the integral with: f ( t) = ∫ 0 t e − α τ e. The tutorial for LTSpice is modified from this one, so if you found the layout of this one useful, you will probably find the LTSpice tutorial easy to follow.
PDF Transient Analysis of First Order RC and RL circuits 5.47. LTspice-Temperature Analysis(.temp) | Spiceman Steps may be linear, logarithmic, or specified as a list of values. SPICE Circuit Components LTspice Tips - Plot Manually Entered Functions - Motley. With the exception of the softlim (ip, lo, hi, sharp) function which must be copied and pasted by hand, all are immediately available to be used in expressions because they are built-in to LTspice. You'll need to have one simulation command, even if it's a DC operating point analysis.