## A Simple Spice Simulation for Illustrating the Operational Concept of Nonlinear Magnetic Transmission Lines

### By Vaughn P. McDowell

An interesting application of ferrites is in the use of nonlinear magnetic transmission lines, as described in Ref 1, for reducing the rise time of Marx generator output pulses from a few nanosecond to about 380 ps. Based on Refs 2 & 3 and considering the use of nonlinear ferrites the principle of operation seems to be based upon the propagation velocity increasing for portions of the pulse's amplitude that nears magnetic saturation traveling faster than the portions of its amplitude below saturation. As the wave travels down the line the shape of the pulse changes such that the peak moves or shifts forward catching up with the lower base portion of the pulse; as a result the shape of the pulse's leading edge sharpens. To simplify the spice simulation the transmission line is replaced with discrete LC components as used in pulse forming networks, see Figure 1:

Figure 1: A Simplified Model of a nonlinear magnetic transmission line

The component values used is not meant to represent actual values used; only for the purpose of illustrating the operation. V1 represents the applied input pulse while the voltage appearing across R1 is the output. If the input amplitude is below saturation then its velocity is (LC)-1/2, Ref. 2. At saturation the inductance in (LC)-1/2 decreases causing the velocity to increase. Figure 2 shows the result of the simulation run for the circuit above. The input pulse is represented by the Teal color plot of V(4) with a 5 nsec rise while the leading edge of the output at V(24), the Maroon plot, sharpened significantly.

Figure 2 Simulated INPUT (Teal) and OUTPUT (Maroon) Pulse

For simplicity I didn't include in the simulation a magnetic bias current as described in Ref. 1 for setting the hysteresis initial operating point.

Below is the main schematic circuit netlist; I have also included the listing of one of the general purpose nonlinear magnetic core defined subcircuit models that I used based on Refs 4 & 5. Model properties shows the values used for the total saturation flux is in VSEC, the unsaturated inductance, and saturated value. Extreme inductance values were used for illustrative purposes.

Main Circuit:

***** main circuit
V1 4 0 EXP( 0.0e+000 2.5e+005 5.0e-009 5.0e-009 3.0e-008 2.0e-009)
XX1 4 2 3 X_CORE2
C1 2 0 10p ic = 0
C10 27 0 10p ic = 0
R1 24 0 90
C9 25 0 10p ic = 0
XX11 27 24 21 X11_X_CORE2_1
XX10 25 27 20 X10_X_CORE2_1
C8 22 0 10p ic = 0
XX9 22 25 19 X9_X_CORE2_1
C7 15 0 10p ic = 0
XX8 15 22 9 X8_X_CORE2_7
C6 13 0 10p ic = 0
XX7 13 15 10 X7_X_CORE2_7
C5 11 0 10p ic = 0
XX6 11 13 18 X6_X_CORE2_7
XX5 8 11 17 X5_X_CORE2_7
XX4 7 8 16 X4_X_CORE2_7
C4 8 0 10p ic = 0
XX3 5 7 12 X3_X_CORE2_8
C3 7 0 10p ic = 0
XX2 2 5 14 X2_X_CORE2_8
C2 5 0 10p ic = 0

.TRAN 1E-10 1E-7 0 1E-9 uic

.OPTIONS gmin = 1E-12 temp = 27 itl1 = 2000 itl4 = 100
+ rshunt = 1G
.end

Core2 Subcircuit:

***** subcircuit definitions

.subckt X11_X_CORE2_1 8 1 4
g1 1 4 8 1 1
r1 2 1 5.000000000000e-001
b1 8 1 i = v(5,2)/.01
r3 5 2 .01
d1 12 13 dclamp1
c3 1 4 2.000000000000e-007 ic= 0.000000000000e+000
r4 4 1 10meg
e1 5 1 4 1 1
d2 13 11 dclamp1
v1 1 12 250
v2 11 1 250
r5 2 13 5.000000000000e-003
c1 1 2 0.004uf ic=0
.model dclamp1 d is = 2.55e-9 rs = 0.042 n = 1.75 tt = 5.76e-10 cjo = 9.554140127389e-010
+ vj = 25 m = 0.333 bv = 100KV ibv = 9.86e-5
.ends

References:

1) "A high-voltage, short-rise time pulse generator based on a ferrite pulse sharpener"
N. Seddon and E.Thornton; Review of Scientific Instruments, Volume 59, Issue 11, November 1988, pp.2497-2498

2) "Non-Linear Transmission Lines for Pulse Shaping in Silicon"
E. Afshari and A. Hajimiri California Institute of Technology (Caltech) Pasadena, CA, USA Caltech MC 136-93, 1200 E. California blvd., Pasadena, CA 91125

3) "Generation of kilovolt-subnanosecond pulses using a nonlinear transmission line" R J Baker, 0 J Hodder, B P Johnson, PC Subedi and 0 C Williams Department of Electrical Engineering, University of Nevada, Reno, Nevada 89557,USA Meas. Sci. Techno!. 4 (1993) 893-895. Printed in the UK DESIGN NOTE Received 6 April 1993, accepted for publication 4 May 1993

4) "SPICE Models For Electronics" L.G. Meares & Charles E. Hymowitz

5) "Magnetics-The Core Model (Beige Bag Software..."), Harvey Morehouse

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