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MODELING AND ANALYSIS OF THYRISTOR AND DIODE REVERSE

RECOVERY IN RAILGUN PULSED POWER CIRCUITS∗ ∗

J. Bernardes

Naval Surface Warfare Center, Dahlgren Division

Dahlgren, VA 22448

S. Swindler

Naval Surface Warfare Center, Carderock Division

Philadelphia, PA 19112

Abstract

As pulsed-power systems used to drive EM launchers

evolve from laboratory to operational environments, high-

power solid-state devices are emerging as the leading

switch technology for these systems. These devices,

specifically high-power thyristors and diodes, offer the

advantages of improved energy efficiency, reduced

volume, and reduced auxiliaries over spark-gaps and

ignitrons. Proper application of these devices requires

understanding of their behavior both during forward

conduction and during reverse recovery.

The semiconductor device models available in most

circuit simulation software packages do not accurately

characterize large power thyristors and diodes for thermal

management and snubber design. A semiconductor-

device model is presented that captures device reverse-

recovery and on-state conduction behavior utilizing a

time-varying resistance that depends on the solid-state

device properties and operating circuit parameters. The

information needed to construct this model can be

extracted from the device datasheet or obtained from the

manufacturer.

This circuit model is used to analyze pulsed-power

circuits typically used to drive railguns. Of key interest in

these simulations are the voltage transients and energy

losses in the solid-state devices during the reverse-

recovery process. This behavior is analyzed for different

circuit element values and device parameters such as peak

reverse current, and reverse recovery charge.

I. INTRODUCTION

In capacitor-based pulsed power circuits used to drive

railguns, the large energy store is normally divided into

modules. Groups of these modules are sequentially

switched into the launcher to tailor pulse shape and

amplitude. Figure 1 shows the two basic types of module

circuits, with the main difference being the location of the

crowbar diode.

∗ Work supported in part by NAVSEA PMS-405 and Office of Naval Research

Figure 1. Two common circuit configuration for railgun

capacitor-based pulsed power modules.

This type of circuit produces a current pulse with a

sinusoidal rise to peak current, followed by an exponential

decay. The initial part of the pulse is the result of the

charged capacitor discharging through an underdamped,

series, RLC circuit. At peak current, which corresponds

to capacitor zero voltage, all the energy is stored in the

system inductances, and, under ideal conditions, the

crowbar diode prevents voltage reversal across the

capacitor. This leads to current decaying exponentially as

the inductor discharges through the diode and the load.

Each of the two module-circuit topologies has advantages

and disadvantages that impact the switch design. In

Figure 1(a), where the diode is directly across the

capacitor, the switch must conduct during the entire

current pulse. In Figure 1(b), where the diode is on the

load side of the switch, the switch only conducts during

the current rise, greatly reducing switch losses and

heating. However, because of unavoidable stray

inductance between the capacitor and the diode, and

because of thyristor reverse recovery behavior; there is a

possibility for the generation of significant and potentially

damaging transient voltages across the thyristor. Proper

understanding of the thyristor reverse recovery behavior

and the resultant voltage transients is essential when

applying this circuit configuration.

This paper describes a circuit model for the thyristor

that was specifically developed to facilitate transient

Load

Load

(a)

(b)

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behavior analysis of the capacitor module circuit during

thyristor reverse recovery. This model can, however, also

be adapted to any series RLC circuit containing a solid-

state rectifier that experiences reverse conduction.

Figure 2. Rectifier approximate reverse-current behavior.

II. RECTIFIER REVERSE RECOVERY

Solid-state rectifier devices such as thyristors and

diodes conduct in the reverse direction to some degree

during commutation. As the current passes through zero,

the device continues to conduct due to excess minority

carriers remaining in the device. These carriers require a

certain amount of time be removed by reverse current

flow and by recombination with opposite charge carriers.

This reverse-conduction behavior, known as reverse

recovery and illustrated in Figure 2, is a function of

device properties and the current derivative (dI/dt) at the

current zero crossing.

The reverse current can be approximated by a

waveform with constant slope from zero to peak reverse

current, followed by an exponential decay, with a time

constant, τ, derived from the specific device properties

[1]. Two dI/dt-dependent parameters, peak reverse

current, Irr, and reverse charge, Qrr, define the device

reverse recovery behavior. These parameters are obtained

from the device data sheet. Qrr equals the integral of the

reverse current, or, graphically – as shown in Figure 2, the

area under the reverse current waveform. By integrating

the reverse current, the following expression for Qrr can be

obtained in terms of the various waveform parameters.

I

Q

=

2

τ

rr

rr

dI

rr

I

dt

+

2

(1)

Solving the above equation for τ yields the following:

Q

rr

=

τ

dt

dI

I

I

rr

rr

2

−

(2)

τ gives a measure of how quickly the reverse current

decays back to zero, and is a function of the device

properties, Qrr and Irr. A smaller τ leads to a larger

decaying-current derivative, and this results in higher

voltage transients due to the presence of inductance in the

circuit.

III. RECTIFIER RECOVERY MODEL

A number of papers have presented thyristor and diode

device models that capture some of the devices’ complex

behavior [2]-[8], but these were not convenient to use in

railgun simulations. Semiconductor physics-based

models [2] were not easily implemented in simulation

packages and required knowledge of parameters not

readily available to device users. Some papers did not

address reverse recovery adequately [3]-[5]. Others did

address reverse recovery but were considered overly

complex and difficult to implement [6]-[8].

A recovery model for high-power silicon rectifiers was

developed to produce the desired reverse-recovery

behavior in a transient circuit model. This model consists

of a time-varying resistance that increases at the

appropriate rate to force the recovery current to decay in

the time scale dictated by the device parameters and the

zero-crossing dI/dt. This model is derived specifically for

the thyristor used as a switch in a railgun pulsed power

module with the crowbar diode forward of the switch.

Similar procedures can be used to derive comparable

expressions for the crowbar diode in this circuit, or for

devices in other circuit configurations.

During forward conduction and up to peak reverse

current, the rectifier can modeled as a constant resistance,

as a resistance in series with a dc threshold voltage, or

using a more complex voltage drop model provided by the

manufacturer. After Irr is reached, an expression is

derived for the rectifier effective resistance. This is done

by first writing the following voltage loop equation for the

circuit in Figure 3, which represents the module circuit

during reverse recovery.

− ∫

dSCRa

a

aa

VRI

dt

dI

LRIdtI

C

V

−++=

1

0

(3)

Figure 3. Module circuit used to derive the reverse

recovery resistance.

C is the energy storage capacitor, and V0 is the negative

voltage on the capacitor resulting from the reverse

conduction in the interval prior to Irr being reached. L is

Irr

Irr

tt

ττ

Qrr

Qrr

ττ

tt

rrrraa

eeIIII

−−

==

dI/dtdI/dt

RSCR

RSCR

RSCR

RSCR

ZZZZZZ

Vd

Vd

Vd

Vd

Vd

Vd

++++++

------

Ia

Ia

Ia

Ia

Ia

Ia

RRRRRRLLLLLL

CCCCCC

++++++

------

Railgun

LoadLoadLoadLoadLoadLoad

RailgunRailgunRailgunRailgun Railgun

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the stray inductance between the switch and the capacitor,

and Ia is the reverse current from Irr forward. The recovery

current can be modeled as a decaying exponential of the

form shown below [1].

Substituting this expression into (3), solving the

derivative and integral, and rearranging terms, yields the

following equation for the rectifier recovery resistance.

VV

R

rr

This resistance has the form of an increasing exponential

with a time constant, τ.

IV. CIRCUIT MODEL ANALYSIS

The rectifier resistor model was evaluated in a test

circuit using Microcap circuit analysis software. The

selected circuit is that of a capacitor-store railgun module

with the diode on the load side of the switch. Since, in

this particular circuit, the diode does not experience

reverse recovery, only the thyristor switch was modeled

using the variable resistor. This circuit, shown in Figure

4, models a thyristor switch composed of two series ABB

5STP-26N6500 devices. Parallel resistor R23 represents

static sharing resistors.

τ

t

rra

eII

−

=

(4)

τ

τ

C

τ

L

Re

I

t

d

SCR

+−+

+

=

)(

0

(5)

Figure 4. Microcap circuit model used to simulate

Thyristor (SCR) reverse recovery behavior.

To facilitate running different parametric cases that

change the rectifier zero-crossing dI/dt, expressions are

generated for Irr and Qrr as a function of dI/dt. This is

done through curve fitting data points obtained from the

device data sheet. This also allows easy extrapolation of

these curves to higher dI/dt outside of the data specified,

which is normally required when these devices are used in

railgun pulsed power applications. As shown in Figure 5,

a power-type curve fit achieves a good match to the data.

In order to automate the process for different circuit

conditions, the circuit model captures several parameters

during the simulation. The first is the zero-crossing dI/dt,

from which Irr and Qrr are calculated. This is followed

capturing the time when the reverse current reaches Irr.

These parameters are then used to calculate the rectifier

recovery resistance in equation (5).

Figure 5. Curve fit to Irr for ABB 5STP-26N6500

thyristor.

Figure 6 shows a set of waveforms generated by this

circuit simulation. Figure 6(a) shows the thyristor and

diode currents, the sum of which constitutes the

sinusoidally rising, exponentially decaying load current.

Note the reverse thyristor current with the characteristic

initial constant dI/dt followed by the exponential decay to

zero. As a check, integrating the reverse recovery current

gives the recovery charge, Qrr, and this value should

match the initially selected Qrr. Figure 6(b) shows the

capacitor voltage and the thyristor voltage. Capacitor-

voltage zero crossing coincides with thyristor peak

current. The fall time of the thyristor current determines

the degree of reverse voltage on the capacitor. The

thyristor reverse voltage is in effect a pulse, due to the

“snap back” of the recovery current, superimposed on the

capacitor reverse voltage. Ultimately, the main functions

of this type of simulation are: (1) to determine the reverse

voltage on the thyristor to insure that rated reverse voltage

magnitude is not exceeded; (2) if reverse-voltage

mitigation is necessary, determine the value and impact of

adding snubber components, and (3) determine the losses

in the rectifier during the reverse recovery period.

Irr

y = 0.0011x0.7873

R2 = 0.9997

10

1.0E+06

100

1000

10000

100000

1.0E+071.0E+081.0E+09

Irr-max-Data (A)

Power (Irr-max-

Data (A))

C1C1

Cbank Cbank

L1L1

LindLind

L4L4

LstrayLstray

R14R14

5m5m

SCR SCR

RscrRscr

R18R18

Rd Rd

R19

1m1m

R20R20

Rc Rc

R23R23

100k100k

L8L8

10nH10nH

D1 D1

.define Lstray (Lc+Lbus)

.define Lind 14uH

.define Rd 0.2m

.define C 4.08e-3

.define Rc 3.3m.define Rc 3.3m .define Rd 0.2m

.define Lc 300nH

.define Lbus 700nH .define Lbus 700nH

.define Qrr if(I(L4)<0,(8e-7*(v(didt)*-1)^0.591),0)

.define Irr ((1.1e-3*(V(didt)*-1)^0.7873)*-1).define Irr ((1.1e-3*(V(didt)*-1)^0.7873)*-1)

PULSE-FORMING NETWORKPULSE-FORMING NETWORK

.define volt 6kV

.define Lc 300nH

.define Cbank 4.08e-3 IC = volt

.define C 4.08e-3

REVERSE RECOVERY PARAMETERSREVERSE RECOVERY PARAMETERS

11

22334455

66

77

88

99

R19

.define Lstray (Lc+Lbus)

.define Lind 14uH

.define Qrr if(I(L4)<0,(8e-7*(v(didt)*-1)^0.591),0)

.define volt 6kV.define Cbank 4.08e-3 IC = volt

Page 4

Figure 6. Sample waveforms showing thyristor reverse

recovery, and the impact of varying stray inductance

between capacitor and thyristor from 1 to 4 µH in steps of

1 µH.

Figure 6 shows another feature of this self-contained

simulation approach, the stepping of component values in

order to analyze trends. Figure 6 shows the impact of

varying the stray inductance between the capacitor and

the thyristor. Thyristor and diode currents along with

capacitor and thyristor voltages are displayed for stray

inductance values of 1, 2, 3, and 4 mH. This inductance

is controlled by the geometry of the buswork, and is

therefore driven by component layout. Increasing

inductance results in longer fall times in thyristor current,

and consequently lower dI/dt. This leads to lower Irr and

Qrr values, higher capacitor reverse voltages, and, not

necessarily intuitive, larger transient voltage pulsed on the

thyristor voltage. Overall this example analysis indicates

that it is advantageous to reduce this stray inductance.

V. SUMMARY

A rectifier circuit model was developed that includes

reverse recovery behavior. This model was implemented

and demonstrated for a commercial high-power thyristor

in a typical railgun pulsed-power circuit. The two main

advantages of this modeling approach are: (1) the ability

model both forward conduction and reverse recovery in a

single simulation run, and (2) the ability to quickly

perform parametric analysis. This simulation approach is

a tool for designing circuits where transients from the

reverse recovery of solid-state rectifiers are a concern.

VI. REFERENCES

[1] J. Waldmeyer, B. Backlund, “Design of RC Snubbers

for Phase Control Applications,” ABB Document 5SYA

2020-01, Feb. 2001.

[2] P. Lauritzen, C. Ma, “A simple diode model with

reverse recovery,” IEEE Transactions on Power

Electronics, Apr. 1991.

[3] S. Taib, L. Hulley, Z. Wu, W. Shepherd, “Thyristor

switch model for power electronic circuit simulation in

modified SPICE 2,” IEEE Transactions on Power

Electronics, Jul. 1992.

[4] Y. Liang, V. Gosbell, “A versatile switch model for

power electronics SPICE2

Transactions on Industrial Electronics, Volume 36, Issue

1, Feb. 1989.

[5] P. McEwan, “Modelling of thyristors using

manufacturers data,” IEE Colloquium on Power

Electronics and Computer Aided Engineering, Jan. 1994

[6] Z. Gang, C. Xiangxun, Z. Jianchao, W. Chengqi, “A

Macro-Model of SCR for Transient Analysis in Power

Electronic System,” POWERCON '98. Aug. 1998.

[7] N. Losic, “Modeling of Thyristor Circuits in

Computer-Aided Analysis and Design,” APEC '88. Feb.

1988.

[8] F. Gracia, F. Arizti, F. Aranceta, “A nonideal

macromodel of thyristor for transient analysis in power

electronic systems,” IEEE Transactions on Industrial

Electronics, Dec. 1990.

simulations”, IEEE

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