# SCEPTRE: Simulation of Nonlinear Electrical Circuits

SCEPTRE was originally developed by IBM Federal Systems Division, Owego, New York, for the Air Force Weapons Laboratory, Kirtland AFB, New Mexico, in 1966 (see Resources 1-5). The development was assumed by GTE Sylvania, Waltham, Mass., in 1972. The program could be obtained from AFWL for certain mainframes.

Typical applications for the use of SCEPTRE are circuits with semiconductor devices. Equivalent circuits for these devices are available with any desired complexity (see Resources 5-8).

To demonstrate the wide range of SCEPTRE applications, I will present two examples from different areas. Other examples are included with the listings in the file ftp://ftp.linuxjournal.com/pub/lj/listings/issue63/3008.tgz.

1. High Voltage Impulse Generator

Voltage pulses of large amplitude are generated when
capacitors initially charged in parallel are series-connected with
the aid of spark gaps. Such a Marx-surge generator is illustrated
in Figure 3. For testing high voltage equipment, e.g., a power
transformer, the shape of the generated impulse must meet certain
requirements (rise and breakdown time). The shape is influenced
mainly by the resistors **RE** and
**RD**. To save computing time, the capacitors
**CS** in stages 1 and 2 are initially charged via
**INITIAL CONDITIONS** to the voltage of
**EH** (making **EH**
superfluous).

As the stages are identical, the **MODEL
DESCRIPTION** is used and each stage is included with a
simple statement in the **CIRCUIT DESCRIPTION**. To
avoid ambiguity of the element names in the main circuit, SCEPTRE
includes the model designation as a suffix (here S1 and S2) to the
component names. For simplicity, the spark is replaced by a
constant resistance **RF**, but any other nonlinear
function may be applied. For this example, the set of units chosen
were **kV, A, k omega**, nF, mH and
**mu**s. The voltage at the capacitor
**CB** is referred to as **VCB** and
is shown in Figure 4. The SCEPTRE input is shown in Listing
2.

Listing 2. Marx-Surge Generator Input to SCEPTRE

2. Rotational system

Figure 5 shows a rotational system with two degrees of
freedom. Two bearings with polar moments of inertia
**J_1** and **J_2** and viscous
frictions **c_1** and **c_2** are
coupled through a shaft with a spring constant
**k**. A driving torque **M** is
applied to the left bearing. It is desirable to find the angular
velocities **omega****_1** and
**omega****_2** of the bearings and
the torque M_w on the shaft.

One approach is to derive directly the mechanical relationship, which yields in the following differential equations (see Resources 3):

with the substitutions

This set of equations can be entered directly under
**DEFINED PARAMETERS**.

Another method for solving this problem is converting the non-electrical system to its electrical analog as shown in Figure 5. The corresponding mechanical and electrical analogs for this problem are shown in Table 2.

Listing 3. Rotating System Input to SCEPTRE

The SCEPTRE input to solve these two methods simultaneously
and independently is shown in Listing 3. The defined parameter
**PERAB3** has been introduced to monitor the
absolute error between the equivalent quantities
**PX3** and **VC1**. The functions of
time for these quantities are shown in Figure 6. The absolute error
**PERAB3** remains less than 1.5E-15 during the
complete simulation.

## Comments

## Whoa, 10 year old post!

Whoa, I just saw the date on this post and was quite surprised. No wonder it look somewhat familiar to me, as I was in school right around that time, probably in one of my physics classes.

-Jack