# How to create Spice / LTSpice repeatable damped sinusoid

Is there a more elegant and/or simpler method to model a repeating, damped sinusoid from SPICE or LTSpice rather than chaining the damped SINE sources in series? Below is a schematic and the waveform I am attempting to recreate ad infinitum.

I'm attempting to simulate switching noise from a DC/DC converter from within LTSpice. The area of interest is the PCB parasitics which cause a repeating, damped sinusoid superimposed on the switching frequency output ripple.

The only method I have found to model a repeating, damped sinusoid is to use a series chain of SINE sources, each offset in time by 1/2 the switching frequency, and include a damping factor for the decay. For a short chain length this is manageable; however for a longer transient sim, the thing would become unwieldy.

Any ideas how to make this repeatable forever?

• You could try an LCR circuit of some sort and use a square-wave on it. Rising edge will produce a decayed ringing and ditto trailing edge. – Andy aka Apr 21 '14 at 18:23
• Tried that, and although it does work, creating different rising and falling edge oscillatory behavior proves to be difficult. My insticts tell me there must be a way to simulate a (for ..) loop inside LTSpice or at least set up behavioral voltage sources to repeat a certain time segment of another source over and over again. – smoothVTer Apr 24 '14 at 18:45
• You can create different falling edge ringing frequencies and damping ratios by using a switch contact triggered on the falling edge. – Andy aka Apr 24 '14 at 19:20

[Sorry for the necromancy]

Even if it has been answered, there is a much simpler, better, and faster way to do it:

V2 acts as a control source who outputs pulses with very narrow Toff. V1 has the trigger keyword which allows an external source turn on V1 when V(ctl) >= 0.5 and off when V(ctl) < 0.5. The trigger voltage can also have a specified value, for example [...] trigger V(ctl)<1.3. This provides an exact sine with an exact 1-exp(-x) decaying shape, set in V1.

This should be possible with arbitrary behavioural voltage sources. For a linear dampening you just need a modulo and a sine function. Sine is fortunately already there, just modulo must be defined on your own:

.function mod(x,y) { (x/y)-int(x/y) }


You can then set your voltage source to

V=(1-mod(time*100,5))*sin(time*1000)


and this will produce:

If you need this more often you can make your own function that takes sine frequency and cycle as a parameter.

A little more complex this could be

V=sinh((1-mod(time*20,5))*5)*sin(time*1000)


which will produce

If you need more complex dampening behaviour, simply setup another voltage source that has this behaviour and use that voltage as a multiplicator for a sine wave.