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

Figure 3. Schematic of a Two-stage Marx-Surge 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 mus. 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

Figure 4. Output Voltage VCB

2. Rotational system

Figure 5. Rotating System with Two Degrees of Freedom, Electrical Analog of 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.

Figure 6. Output Voltage VC1 and Shaft Moment PX3