MEBS 6000 2010 Utilities services M.Sc.(Eng) in building ...

MEBS 6000 2010 Utilities services M.Sc.(Eng) in building services

Faculty of Engineering University of Hong Kong

K.F. Chan (Mr.) of 38 July 2010

Introduction

Power electronics applies electronic techniques to the control of electric power. This

field is not new because vacuum tubes have long been used for this purpose. However,

more recently, power electronics has grown rapidly because solid state devices have

been developed, at decreasing price, to control electric power, specifically, power

transistors, silicon controlled rectifiers (SCR), and gate turnoff thyristors (GTO).

Switch

A switch is a device that has two stable states, ON and OFF. When ON, the switch has

an impedance much smaller than its load, and when OFF, it has an impedance much

larger than its load.

The concept depicted in the above diagram showing the relationship between current

through a switch against the voltage across it is important – semiconductors try to

simulate a mechanical switch using purely electronic technique. We will come back

on this.




Semiconductors

Semiconductors are neither good conductors nor good insulators. Semiconductors are

made from materials that have four valence electrons in their outer orbits.

Insulator Semi-conductor

[Adopted from Herman S.L. Industrial Motor Control]

Germanium and silicon are the most common semiconductor materials. Among the

two, silicon is used more often because of its ability to withstand heat.




Pure semiconductor material


When semiconductor materials are refined into a pure form, the molecules arrange

themselves into a crystal structure with a definite pattern. This is called a lattice

structure. To make semiconductor material useful, it is mixed with an impurity.

When pure semiconductor material is mixed with an impurity that has only three

valence electrons, such as indium or gallium, the lattice structure changes, leaving a

hole in the material




P-type semiconductor material


This hole is caused by a missing electron. Since the material now lacks an electron, it

has a positive charge – this is called a p-type material.

When a semiconductor material is mixed with an impurity that has five valence

electrons, such as arsenic or antimony, the lattice structure has an excess of

electrons – the material has a negative charge. It is called an n-type material.




N-type semiconductor material


All solid state devices are made from combination of p- and n-type materials. The

number of layers and the thickness of each layer play an important part in determining

characteristics of the device formed.




Transistors

Transistors can be used as either amplifiers or electronic switches. In power

applications, transistors are used mainly as electronic switches. Two types of

transistors are commonly used in power applications: the bipolar transistor and the

field effect transistor (FET). Other power devices, such as the insulated gate bipolar

transistor (IGBT), are hybrids of these two types. The following figure shows various

sizes of bipolar power transistors.

Bipolar transistor

The bipolar transistor consists of three layers of semiconductor materials in the n-p-n

or p-n-p structure as shown in the following figure:




The ratings of these transistors can be as high as a few hundred amperes. The

operation of the bipolar transistor is based on the capability of the p-n junction to

inject or collect minority carriers. When the emitter is forward biased, electrons are

injected from the n (emitter) to the p (base) region. If the other n layer (collector) is

reverse biased, the electrons in the p layer are collected in that n layer.

The base layer is very thin compared to the layers of the emitter or collector because it

is an obstacle to the flow of current. However, it serves a very useful purpose – it

controls the flow of electrons from emitter to collector. If a base current is injected in

the p junction, more current is allowed to pass from the emitter to the collector. The

relationship between the base and collector currents, however, is nonlinear.

The collector is positive biased with respect to the emitter or base, and the base

voltage is positive with respect to the emitter. The base-emitter junction is a simple

diode. Hence, the voltage difference between the base and emitter is very small (about

0.6V)

The basic equations of the bipolar transistor can be written as

CEOBC III += β

CBE III +=

BECBCE VVV +=

where β is the current gain (ratio of collector to base currents), and CEOI is the

leakage current of the collector-emitter junction. Because the leakage current is very

small compared with BIβ it is often ignored.




A transistor can be connected in a common-base or common-emitter form. The above

figure shows the characteristic of an n-p-n transistor connected in the common emitter.

The base characteristic is very similar to that of the diode. In the forward direction,

the base-emitter voltage is below 0.7V. A substantial increase in the base current

occurs at a slightly higher value of the base-emitter voltage.

The collector characteristics can be divided into three basic regions:

- the linear region,

- the cutoff region, and

- the saturation region.

In the linear region, the transistor operates as an amplifier, where β is almost

constant and in the order of a few hundreds. Any base current is amplified a few

hundred times in the collector circuit. This is the region in which most audio

amplifiers operate when using bipolar transistors. However, on a continuous basis,

power transistors do not operate in the linear region because losses of the transistor

are excessive in this region and can lead to thermal damage of the transistor.

The cutoff region is the area of the characteristic in which the base current is zero. In

this case, the collector current is negligibly small regardless of the value of the

collector-emitter voltage.

In the saturation region, the collector-emitter voltage is very small at high base

currents.

When used as a switch, a transistor operates in two regions only, viz, cutoff and

saturation. In the cutoff region, the transistor acts as an open switch, where the

collector current is almost zero regardless of CEV . In the saturation region, the

transistor operates as a closed switch because the voltage across the switch is very

small, and the external circuit determines the magnitude of the collector current.




The above figure explains the operation of a transistor in switching circuit. The

transistor is connected to an external circuit that consists of a dc source CCV and a

load resistance LR . The base circuit of the transistor is connected to a current source

to produce the base current of the transistor.

The loop equation of the collector circuit is represented by:

CLCECC IRVV +=

This equation, which demonstrates a linear relationship between CI and CEV , is

known as the load line equation. This load line equation has a negative slope and

intersects the CEV axis at a value equal to CCV and the CI axis at a value equal to

L

CC

R

V.

If the base current is set equal to zero, the operating point of the circuit is in the cutoff

region point 1. The collector current in this case is very small and can be ignored. The

collector emitter voltage of the transistor is almost equal to the source voltage CCV .

This operation resembles an open mechanical switch.




Now, assume that the base current is set to the maximum value. The transistor

operates in the saturation regions at point 2. The voltage drop across the

collector-emitter terminals of the transistor is small and can be ignored. The collector

(or load) current is almost equal to L

CC

R

V. In this case, the transistor is equivalent to a

closed mechanical switch.

The bipolar transistor is a current-driven device. To open the transistor, the base

current should be set to zero. To close the transistor, the base current should be set as

high as the ratings permit. Keep in mind that the base current must exist for as long as

the transistor is closed. Because β is small in the saturation region and the collector

current is high in power applications, the base current is also high in magnitude. This

situation creates two major problems: the first is that there are relatively high losses in

the base circuit. The second is that the driving circuit must be capable of producing a

large base current for as long as the transistor is closed. Such a circuit is large, of low

efficiency, and complex to build.

Even with the disadvantages of requiring high base current, thus requiring high power

base drive circuits and higher switching and operating losses than SCRs, power

bipolar transistor switches are gaining popularity especially in IGBT construction.

The main advantage is that turn ON and turn OFF are controlled by the base current,

and no forced-commutation circuit is required. Bipolar junction transistors do not

offer as high switching frequency as MOSFETs or IGBTs – high switching frequency

is very important in ac motor controller circuits. Therefore in LV (<200V)

installations, MOSFETs are more popular. However, BJT still plays an important role

in power electronics.




Example

A transistor has 1β =200 in the linear region and 2β =10 in the saturation region.

Calculate the base current when the collector current is equal to 10A, assuming that

the transistor operates in the linear region. Repeat the calculation for the saturation

region.

Answer

In the linear region

mAI

I CB 50

200

10

1

===β

In the saturation region,

mAI

I CB 1000

10

10

2

===β

Note that the base current in the saturation region is 20 times of that in the linear

region. This ratio is same as the ratio of 2

1β

β




Field Effect Transistor (FET)

Field effect transistors (FETs) are widely used as electronic switches in computer and

logic circuits. There are several subspecies of FETs. The most common are the

junction gate FET (JFET), the metal oxide semiconductor FET (MOSFET), and the

insulated gate FET (IGFET).

The operation of FETs is based on the principle that the current near the surface of a

semiconductor material can be changed when an electric field is applied at the

surface.

In the above example, two n-junctions (source and drain) are embedded in a p

material. The gate, which is metal, is connected to the positive side of a dc supply.

The source and drain are connected to another dc supply, with the drain on the

positive side and the source on the negative side. The voltage difference between the

drain and source creates a current flowing in the channel. The magnitude of the

current is affected by strength of the electric field from the gate. Thus, the gate

voltage controls the drain current, which makes the FET much easier to control than

the bipolar transistor.




Several characteristics can be obtained from the many FET subspecies. The difference

between the two in the above two figures is that a MOSFET designed for

enhanced/depletion mode has a narrow-doped conducting layer diffused into the

channel. The presence of this layer results in current DI flowing inside the channel

even if the gate-to-source voltage GSV is negative.

The main advantage of FETs over bipolar transistors is in the way the current in the

switching circuit is controlled. The FETs are voltage-driven devices, unlike the

current-driven bipolar transistors. The gate voltage controls the drain current DI of a

FET, which is relatively easy to implement. For LV installations (<200V) MOSFET is

more popular than bipolar junction transistors.




Thyristors

Thyristor is a name given to a family of devices that include the silicon-controlled

rectifier (SCR), the bi-directional switch (triac), and the gate turnoff SCR (GTO).

These devices can handle large currents and are widely used in power applications.

Although not commonly used, other thyristor devices are also available for low

current control circuits, such as the silicon unilateral switch (SUS) and the bilateral

diode (diac).

Four level diode

The following shows the symbol and structure of a four level diode.

(Adopted from COGDELL, J.R. Foundations of Electric Power)

The structure consists of four alternating layers of p- and n-type semiconductor,

forming three pn junctions. 2 of the pn junctions face the same direction, and the

middle one faces the opposite direction. Thus one might anticipate that the device will

operate as three diodes in series, with the middle one turned around. Hence, no current

ought to flow in either direction, because at least one of the diodes will always be

reverse biased.




The characteristic displayed above reveals that no current flows for a negative

voltages, where 2 pn junctions are reverse biased, nor does current flow for positive

voltages, where the middle pn junction is reverse biased, until a threshold voltage or

breakdown voltage, VBO, is reached. After this threshold voltage is exceeded, the four

level diode begins to conduct freely: It “fires” acting as if the middle pn junction has

disappeared. The threshold phenomenon occurs because the doping levels in the fours

layers differ greatly. The outside p and n materials are doped heavily; hence they have

many carrier holes and electrons, respectively, available to diffuse into the middle n

and p regions, which are lightly doped only. Once the breakdown occurs in the middle

junction at VBO, the holes from above and the electrons from below flood into the

depletion region of the middle junction, where the electric field due to uncovered

charges reinforces their movement across the junction. Thus, this middle depletion

region effectively disappears due to the carriers from the forward biased junctions,

and we are left with two forward biased junctions in series. The small voltage for the

pnpn diode in the ON stage results from the contributions from each ON junction. The

turn ON voltage is typically less than 0.7V because the excess carriers from each

junction help each other.

If the current is reduced below a certain value called holding current Ih, the device

opens, and the current drops to zero. The voltage across the device is now equal to the

source voltage. This process is called commutation.




Thus, the pnpn has two states. It is OFF for negative voltage, and remains OFF for

positive voltage until the threshold voltage is reached, after which it turns ON. It

remains ON until the current is reduced to a small value, after which it turns OFF

again. The value of the threshold voltage, VBO, can be controlled over a modest range

by the semiconductor design. Typical pnpn diodes have threshold voltage from 6 to

32V. Thus, this device, like the pn junction diode, is a voltage controlled switch,

except that the four level diode requires much more than 0.7V to turn ON.




Silicon controlled rectifier (SCR)

The following figure shows the symbol and structure of a silicon-controlled rectifier

(SCR), which is sometimes simply called a thyristor.


The SCR has a pnpn structure with an external gate to turn ON the device. With no

gate current, the SCR characteristic is like that of a four level diode. The important

difference, however, is that the breakdown threshold occurs at a much higher voltage,

indeed, high enough that the SCR should never conduct because the input voltage will

never exceed its threshold. On the contrary, the forward biased SCR should fire only

when a pulse of current is delivered to the gate. This is shown by the IG>0

characteristic in the following figure; in effect, the threshold is reduced to a very small

value when the gate conducts.




Physically, the gate injects holes into the lightly doped p region and floods the

depletion region with carriers, thus initiating breakdown.

The turn on voltage, VTO, is dependent on the magnitude of the gate current – the

higher the gate current, the lower the turn on voltage. When the gate pulse is as high

as the rating permits, the SCR can be turned on at a very low anode-to-cathode

voltage. A general expression relating the turn on voltage VTO to the equivalent dc

gate current IG can be written as

KIBOTO

GeVV −=

where K is a constant whose value is dependent on the device characteristics. Note

that this equation is purely empirical, and specification of the particular device should

be consulted for accurate information about SCR triggering characteristics.




The popularity of the SCR is due to several factors, including the following:

- SCRs are cheaper to manufacture than other types of solid state switches, such as

the bipolar transistors and FETs

- A single pulse, instead of the continuous signal needed by a bipolar transistor,

can turn on a SCR. Hence, losses are reduced.

- In ac circuits, the SCR is self-commutated and may not need an external circuit to

turn it off.

- As SCR can have much larger current and voltage ratings than the transistor.

SCRs are usually found in large rating power electronic circuits, including large rating

circuits, but is becoming less popular in smaller variable frequency drives.

In some literature and in commercial applications, the terms thyristor and SCR are

frequently used interchangeably. Currently, SCRs are frequently used in power

electronic circuits. However, this may change in future as other devices such as the

IGBT are getting larger ratings and are easier to control.

Commutation

Commutation refers to the switching of a conducting device from the ON state to the

OFF state. An SCR must be commutated by reducing its current below the holding

current value required to sustain conduction. Normally, this is accomplished by

reverse biasing the device for a period of time. When in an ac cycle, the voltage

across an SCR changes from forward bias to reverse bias, the SCR ceases to pass

current and is line commutated.




When an auxiliary circuit is used to commutate the SCR independent of the line

voltage, the SCR has a forced, or device, commutation. A lot of efforts has be devoted

to design circuits for device commutation of SCR to ensure safe operation.

When the device is commutated by controlling the gate signal, it is self-commutated.

SCR cannot be self commutated and must be line commutated. On the other hand,

transistors has low reverse blocking ability, thus cannot be line commutated and must

be self commutated.




Example

A SCR is connected in series with an ac voltage source of 120V (rms value) and a

load resistance. The breakover voltage of the SCR VBO=200V, and K=0.2mA-1.

Calculate the approximate value of the dc gate current required to trigger the SCR at

30o.

Answer

The source voltage can be written as

( ) ( )tVs ωsin1202=

When the SCR is open, the voltage across the SCR is equal to the source voltage. For

a 30o triggering angle the voltage across the SCR is

( ) ( )30sin1202=sV

The dc triggering current can then be calculated as

KIBOTO

GeVV −=

( ) ( ) ( )2.020030sin1202 GIe−=⇒

mAIG 29.4=⇒




Gate turnoff thyristors (GTO)

GTOs are similar to SCRs except that conduction through the GTO can be stopped by

applying a negative voltage – negative with respect to the cathode – to the gate.


The above figure shows that the circuit symbol for a GTO is like a SCR symbol

except for a mark on the gate. The forward biased GTO is turned ON by a pulse of

positive current to its gate, but unlike the SCR, it is turned OFF by a pulse of negative

gate current. The negative current removes carriers from the cathode region, and the

inner pn junction blocks the forward current.

GTOs are thyristors able to handle a greater amount of current than transistors and are

used in large power rating power electronic circuits.




Diacs and triacs

The following diagram shows a non-rectifying power controller.


Diac is the short form for diode for alternating current. In the above diagram the

device replacing the four level diode is called a diac. It is like two parallel four level

diodes facing in opposite direction and fires in either direction. Most diac have a

breakdown voltage of about 30V.

[Adopted from HERMAN, Stephen L. Industrial Motor Control]




[Adopted from HERMAN, Stephen L. Industrial Motor Control]

Similarly, triac is the short form for triode for alternating current. In the above wiring

schematics, the device replacing the SCRs is called a triac, and it functions like two

parallel SCRs facing opposite directions, but with their gates joined together. Once

triggered, a triac continues to conduct until the current through it drops below the

threshold value, i.e. the holding current, at the end of a half cycle of an ac supply. This

makes the triac a very convenient switch allowing the control of very large power

flows with only small control current typically in the order of milliampere only.

The following figure shows how the load voltage varies.


This is the preferred circuit for light dimmers and universal motor tools, which do not

require dc voltage.




Darlington transistor

When a bipolar transistor operates as a switch, only the cutoff and saturation regions

are used. In the saturation region, the current gain β is very small. Hence, when the

transistor is closed, a large base current is needed. This base current must be

maintained for as long as the transistor is closed. The continuous large base current

results in high transistor losses and demands an extensive control circuit to provide.

For example:

Load current (emitter current) is 100A, β is 4, the base current must then be

( )β+1

100=20A

This base current is very large.

To reduce the base current, two transistors can be connected in Darlington fashion.

The emitter current of 1Q is ( ) 111 BIβ+ .

The emitter current of 2Q is ( ) 221 BIβ+ = ( )( ) 112 11 BIββ ++

Hence, the ratio of the emitter current of 2Q (which is the load current) and the base

current of 1Q (which is the triggering current of this Darlington transistor) is

( )( )121

2 11 ββ ++=B

E

I

I




For example:

1Q and 2Q are identical transistors with 1β = 2β =4. If the load current is also 100A,

then the base current for the Darlington transistor is ( )( )12 11

100

ββ ++=4A

This is only one fifth of the base current computed above for the single transistor.




IGBT (insulated gate bipolar transistor)

Bipolar transistors are current controlled devices with relatively low losses in the

power circuit (collector circuit) during the conduction period, due to their relatively

low forward drop CEV when closed. It is suitable for current ratings up to a few

hundred amperes. Bipolar transistors are more suitable for high switching frequencies

than SCRs. These are very desirable features for power applications. However, bipolar

transistors have very low current gains at the saturation region (when closed). Thus,

the base currents are relatively high, which makes the triggering circuits bulky,

expensive, and of low efficiency.

On the other hand, MOSFETs are voltage-controlled devices that require very small

input current. Consequently, the triggering circuit is much simpler and less expensive

to build. In addition, the forward voltage drop of DSV of a MOSFET is small for low

voltage devices (<200V). At this voltage level, the MOSFET is a fast-switching power

device. Because of these features, MOSFETs replace bipolar transistors in

low-voltage applications.

In high-voltage applications (>200V), both the bipolar transistor and the MOSFET

have desirable features and drawbacks. Combining the two in one circuit, as shown in

the following figure, enhances the desirable features and diminishes the drawbacks.

[Adopted from EL-SHARKAWI, Mohamed A.,

Fundamentals of Electric Drives.]

[Adopted from Murphy & Turnbull, Power Electronic Control of

AC Motors]




The MOSFET is placed in the input circuit and the bipolar transistor in the output

(power) circuit. The MOSFET is triggered by a voltage signal with a very low gate

current. Then the source current of the MOSFET triggers (closes) the bipolar

transistor. The losses of the output power circuit are relatively low even for

high-voltage applications. Furthermore, because the output circuit is a bipolar

transistor, it can be used in higher frequency switching applications (when compared

with thyristors). These two devices can now be included on the same wafer; the new

device is called the insulated gate bipolar transistor or IGBT.

As the name implies, IGBT has an “insulated” gate, i.e. very high impedance, so

IGBT is a voltage, not current, controlled device.

Frequency inverters using IGBT on the dc/ac inverter section does not use SCR in the

ac/dc conversion section, thus subject to less problem of line harmonics. This

self–commutating device is available up to 300-Ampere current ratings, has good

turn-on and turn-off ability (its voltage control feature needs only 3 to 5 Volts of

energy to turn on) and has switching speeds of up to 18 kHz. It is cost effective to

manufacture and can be implemented into an electric circuit at relatively low costs.

All these features make the IGBTs gain popularity in VFDs today.




With costs and performance driving the semiconductor industry, more efficient

versions of IGBTs are coming out very year, and VFD designs change very often.

The following diagram depicts the general performance limits and application range

of different power electronic devices.

(Adopted from BARNES, M. Variable speed drives and power electronics)




Device Current ON/OFF Ideal switch Bidirectional Instantaneous turn on / turn off 0 on state impedance, infinite off

state impedance Diode Unidirectional Forward voltage turn on / reverse voltage

turn off

SCR Unidirectional Turned on by a +ve gate pulse, cannot be self commutated

Forward and reverse blocking ability, thus can be line commutated

In absence of gate pulse, can also be turned on at high anode to

cathode voltage, or high dt

dv

GTO Unidirectional Turned on by +ve gate pulse, can be turned off by negative pulse at gate or by line commutation

Forward and reverse blocking ability, thus can be line commutated

A variant, asymmetric GTO, has low reverse blocking voltage

Triac Bidirectional Turn on: +ve or –ve gate pulse associated with corresponding forward or reverse voltage. Turn off: line commutation

Symmetrical forward & reverse blocking. Ideally suited to phase angle firing. Low voltage, low power, low frequency (<400Hz)

BJT Unidirectional +ve gate current to turn on, removal of gate current to turn off

Low reverse blocking ability, need to be self commutated

MOSFET Unidirectional +ve gate voltage to turn on, removal of gate voltage to turn off


Very fast switching frequency

IGBT Unidirectional +ve gate voltage to turn on, removal of gate voltage to turn off


Low on state losses, high switching frequency

[Table adopted from SHEPHERD, W., ZHANG, L. Power converter circuits.]




Snubbing circuit

To protect a power electronic switch against excessive dt

dv and

dt

di, a snubbing

circuit must be used. From the instant when voltage is applied to a switch, there is a small delay before the

switch turns ON, and there is a rate of rise of the switch current dt

di, which can cause

device failure due to localized heating in the junction. If it is not limited by load inductance, an external inductor must be added in series with the switch to limit the

dt

di of the gate.

Also critical is the rate of voltage rise of the switch in its OFF state. In certain applications, a rapid voltage increase can initiate conduction, independent of the gate

signal, and cause device malfunction. The snubber circuit limits the dt

dv across the

gate. With the switch OFF, the small (10 to 100Ω ) resistor in series with the capacitor

and the inductance in the load circuit limit the dt

dv across the switch, and the

capacitor blocks dc current. When the switch fires, the energy stored in the capacitor is dissipated in the resistor and the switch.




Let us first assume that the load has the following impedance:

LLLL Cj

LjRZω

ω 1++=

Now look at the path of the current 1i , which can be written in the Laplace form as

( ) ( )

++=

sCsLR

sVsI

11

where sL RRR +=

sL LLL +=

sL CC

C11

1

+=

and the subscripts L and s refer to the load and the snubber respectively. Suppose that there is a step input of source voltage, hence

( )s

VsV =

where V is the magnitude of the step change of voltage. Thus

++=

sCsLR

sVI

1/

1

++=

LCs

L

Rs

LVI

1/

21

Now let natural frequency of oscillation be

LCn

1=ω (note that this is not synchronous speed of motor)

and damping coefficient be

L

CR

2=ζ

So that

21nC

Lω=

nL

R ζω2= , and

21nLC

ω=




The s-domain equation can thus be re-written as

[ ]22

2

12 nn

n

ss

VCI

ωζωω

++=

The inverse Laplace transform of this equation will give the time-domain function of the current 1i (inverse Laplace transform can be found by looking up table):

( )[ ] teVC

ntn n 2

21sin

1ζω

ζω ζω −

−−

Differentiating this equation with respect to t will give

( )[ ] ( )[ ] teVCteVC

dt

din

tnn

tn nn 222

2

2

1cos1sin1

ζωωζωζ

ζω ζωζω −+−−

−= −−

Let us assume that the capacitors are initially uncharged. Furthermore, the charge on

the capacitors cannot instantly change. The maximum dt

di then occurs at the initial

time (t=0). By substituting t=0 into the above equation, hence

L

V

dt

di =max

The snubbing inductor is then calculated as

L

mas

s L

dt

di

VL −=

For adequate protection, sL should be selected so that it can V will not exceed the

breakover voltage, BOV of the device, and dt

di will not exceed, say, half the

maximum dt

di rating of the device. Therefore,

L

rated

s L

dt

di

VL −

=

5.0

This should be adequate in protecting the device from excessive dt

di due to supply

surges. This is only one of the three transients that a device should be able to

withstand without damage. The other two are the dt

dv and

dt

di created by the RC

snubbing circuit itself when the device is turn ON.




The RC circuit ( sR and sC ) can protect the device from the other two transients. Let

us assume that the charge on the capacitor sC is zero when the voltage V is applied.

With this assumption, the voltage across the device SCRV at the initial time is

1iRV sSCR = Then

dt

diR

dt

dVs

SCR 1=

But now L

V

dt

di =max

at time t=0, so

L

VR

dt

dVs

SCR =

This shows that the smaller the resistance sR , the smaller the dt

dv across the device.

However, sR is needed to limit the dt

di created by the snubbing capacitor.

Let us assume that the device is triggered. The current going through the device has two components, one is 1i and the other is 2i from the snubbing capacitor. We have

already discussed the dt

di attributed to 1i . The current 2i will also cause a

dt

di and

must also be limited to a tolerable value. Now

( )ssCRt

s

eR

Vi /02

−=(see Appendix 1)

where 0V is the capacitor voltage due to its initial charge before the device is

triggered. We may assume the worst case value for 0V as BOV . The dt

di of the

circuit is then

ssCRt

ss

eCR

V

dt

di −−= 202

The maximum dt

di2 occurs at time t=0. Hence

ss CR

V

dt

di2

0

max

2 −=




As in the previous case for dt

di1 , dt

di2 should also be limited to say, half of the

device’s rating.

Now if sR is small, dt

dv is small but then

dt

di2 will be large, a compromise shall be

made.




Example A SCR is connected between an ac source and a resistive load. The maximum allowable current transient of the SCR is 100sA µ , the maximum non-repetitive forward blocking voltage is 300V. Maximum allowable voltage transient of the SCR is 1500 sV µ . Calculate the value of the resistance, inductance and capacitance of the snubbing circuit to protect the SCR from excessive voltage transient and limit the current transient to half of the maximum rating. Answer

L

rated

s L

dt

di

VL −

=

5.0

As the load is resistive, LL =0, so

( )( )6101005.0

300

×=sL

hLs µ6≥ Now

L

VR

dt

dVs

SCR =

66

106

300101500 −×

=× sR

Ω≤ 30sR Also

ss CR

V

dt

di2

0

max

2 −=

( )( )sC2

6

30

300101005.0 =×

FCs µ0067.0≥ To reduce the size of the inductor, iron core material could be used. The problem with iron core inductors, however, is the core saturation, which reduces the values of the inductance at high current values. Air core inductors do not suffer from saturation but are bulky. Nevertheless, air core inductors are normally used for snubbing circuits. A sR of Ω30 will incur excessive power loss in the switch, we would manipulate

within the allowable figures. Let’s choose hLs µ10=

sAL

V

dt

di µ301010

3006

1 =×

== −




This is less than the rating of 100 sA µ , thus acceptable. If we choose, sC as Fµ1

ss CR

V

dt

di2

0

max

2 −=

( )( )( )66 101101005.0

300−××

=⇒ sR

Ω=⇒ 45.2sR Then

sVL

VR

dt

dVs

SCR µ5.731010

30045.2

6=

×== −

This is less than the rating of 1500 sV µ thus acceptable. Another factor that should be considered is the losses of the snubbing circuit due to the presence of sR . When the SCR is not triggering, the current 1i causes losses in

the snubbing circuit in the form of sRi 21 . A bypass diode can be used in parallel with

sR to reduce the losses. This diode will also reduce the voltage transient. [Text and figures mostly adopted from SHEPHERD, W., ZHANG, L. Power converter circuits, and EL-SHARKAWI, Mohamed A., Fundamentals of Electric Drives.]




Appendix 1 Voltages across the resistor, capacitor and the switch can be written as:

( ) ( ) ( )∫+= dttiC

tiRtvs

s 220

1

Taking Laplace transform

( ) ( ) ( )s

s sC

sIsIRsV 2

2 +=

( )

ss sC

R

sVI

10

2

+=

Now suppose that there is a step input of voltage of magnitude 0V , hence

( )s

VsV 0

0 =

Therefore

ss sC

R

sVI

10

2

+=

sCR

VCI

ss

s

+=

10

2

Taking inverse Laplace transform

( ) ( )ssCRt

ss

s eCR

VCti /0

2−=

( ) ( )ssCRt

s

eR

Vti /0

2−=⇒

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