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###

Gaussian Pulse

- General Form:

`gpulse(`*v1 v2 td pw per td1 td2* ... )

- Examples:

`vsfq 0 0 gpulse(0 0 20p 2p 0 40p 60p)
`

vpulse 1 0 gpulse(0 1 100p 5p 100p)

**parameter** |
**description** |
**default value** |
**units** |

*v1* |
base value |
0.0 |
volts or amps |

*v2* |
pulse peak value |
*v1* |
volts or amps |

*td* |
delay time |
0.0 |
seconds |

*pw* |
pulse width |
`tstep` |
seconds |

*per* |
period |
0.0 |
seconds |

This generates a gaussian pulse signal, and as a special case, as a
voltage source will generate single flux quantum (SFQ) pulses.

The expression used to generate a pulse is

*value* =
*v*1 + (*v*2 - *v*1)^{ . }*exp*(- ((*time* - *td* )/*pw*)^{2})

The *td* delay value specifies the time of the initial pulse peak.
The *pw* defines the pulse width, as evident in the expression.
If the *per* is given a nonzero value larger than twice the *pw*, a train of pulses will be generated, the first being at *td*
and at time increments of *per* thereafter. A *per*
explicitly zero can be followed by any number of time values. A pulse
will be generated to peak at each of these values, in addition to the
*td* value.

If the amplitude is set to zero, i.e., *v2* = *v1*, the
amplitude will be computed from the pulse width to yield a single flux
quantum pulse. Such a pulse, as a voltage applied across an inductor,
will induce a single flux quantum of
=
*h*/(2^{ . })
= 2.06783fWb (*h* is Planck's constant, *e* is the electron
charge). With superconductors, the flux that threads superconducting
loops is quantized in increments of this value, due to the requirement
that the superconducting wave function meet periodic boundary
conditions around the loop. The computed amplitude is

*v*2 = *v*1 + /(*pw*^{ . })

where
is the flux quantum whose value is given above.

In superconducting electronics, single flux quantum pulses are
generated and received by logic circuits. A generator of SFQ pulses
is therefor a useful item when working with this technology.

Example

`* gaussian pulse
`

v1 1 0 gpulse(0 0 20p 2p 0 40p)

l1 1 2 10p

b1 2 0 100 jj3 area=.2

r2 2 0 2

.tran .1p 100p uic

.plot tran v(1) v(2) i(l1) ysep

`* Nb 4500 A/cm2
`

.model jj3 jj(rtype=1, cct=1, icon=10m, vg=2.8m, delv=0.08m,

+ icrit=1m, r0=30, rn=1.7, cap=1.31p)

In the example, the generator produces two SFQ pulses. The second
pulse causes the Josephson junction to emit a flux quantum, the
second one from the source is therefor expelled. The inductor
current shows the same value before and after the second pulse,
as expected.

** Next:** Piecewise Linear
** Up:** Tran Functions
** Previous:** Pulse
** Contents**
** Index**
Stephen R. Whiteley
2017-10-02