Tristate Converters with Limited Duty Cycle

FELIX A. HIMMELSTOSS

Faculty of Electronic Engineering and Entrepreneurship,

University of Applied Sciences Technikum Wien,

Hoechstaedtplatz 6, 1200 Vienna,

AUSTRIA

Abstract: - Replacing the active switch of a DC/DC converter with a series connection of two active switches

and a diode which is connected to the connection point of the two switches, changes the converter into a tristate

one. The tristate concept changes the voltage transformation ratio of the original converter and influences the

dynamics. Starting from a topology for limited duty cycles, four converters can be derived. There are two

possibilities for the position of the second capacitor and so eight converter structures can be achieved. The

position of the second capacitor influences the input current, the inrush, the stored energy, and the voltage

stress of this component. When the input voltage has the other polarity, again eight converters can be designed.

Changing all active electronic switches by current bidirectional ones (an electronic switch with an antiparallel

diode) leads to bidirectional converters and increases the number of converters that are derived from the basic

topology to thirty-two. The function of the four basic structures is explained, and the voltage transformation

ratio calculated and graphically shown. The connections of the currents are explained. For one converter the

large and the small signal models and two transfer functions are calculated, and simulation of the dynamics are

shown.

Key-Words: - DC/DC converter, tristate, step-up, step-down, step-up-down, voltage transformation ratio

Received: February 16, 2023. Revised: November 25, 2023. Accepted: December 14, 2023. Published: December 31, 2023.

1 Introduction

The starting point of this review and study is the

paper, [1], which describes converters with limited

duty cycles. The basic topology is shown in

Figure 1. In the original paper the symbolic switches

SStr1 and SStr2 are current bidirectional switches,

voltage bidirectional switches, diodes, or AC

switches, or combinations of them. So one can

construct DC/DC, DC/AC, AC/DC, and AC/AC

converters. The second capacitor can be placed in

parallel to the load or between the input and the

output. In this paper, the tristate concept is applied

to the converter concept according to Figure 1.

Fig. 1: Basic structure

One switching structure SStr1 or SStr2 is

formed by a series connection of two electronic

switches S1 and S2 and a diode D1. The other

switching structure is formed only by a diode D2.

Using a positive input voltage four converters can

be designed according to Figure 1. For the second

capacitor there are two possibilities for their

placement, so one can get eight possible DC/DC

converters. When changing the polarity of the input

voltage, again eight DC/DC converters originate

from Figure 1. Replacing all electronic switches and

diodes with current bidirectional switches, two-

quadrant DC/DC converters are obtained. The

tristate concept changes the voltage transformation

ratio of the original converter.

The tristate concept was first applied to the

Boost converter, [2], [3], [4]. The application to the

Buck-Boost converter can be found in [5]. A very

interesting aspect is that with a constant duty cycle

of the second switch and controlling the converter

by the duty cycle of the first switch, in some cases

the converter can be treated as a phase minimum

system. The basics of Power Electronics can be

studied with the help of the textbooks, e.g. [6], [7],

[8]. The modeling and dynamic feedback

linearization of a 5-switch tristate Buck-Boost

bidirectional DC-DC converter is shown in [9]. A

practical applications of a tristate converter is shown

in [10], where the tristate converter is used to charge

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and discharge supercapacitors in a DC microgrid. It

should also be mentioned that the tristate concept

can be applied also to converter structures with

coupled coils, [11]. The bidirectional non-inverting

Buck-Boost converter can also be used as a tristate

converter, when both low-side switches are turned

on, [12].

2 The Four Basic Structures with a

Limited Duty Cycle

The four basic structures are shown in this chapter.

They are exemplarily drawn with MOSFETs as

electronic switches. The types are numbered by the

names that were used in the underlying patent and

also in the basic paper [1]. All circuits are shown

with C2 between input and output.

2.1 Step-up Converter Type 2b

The converter is depicted in Figure 2. The second

capacitor is placed between the input and the output.

The input voltage is applied to the connectors 3 and

4. The switch structure SStr1 is realized by a tristate

switch combination and the second switch structure

is formed only by a diode. The load, here

represented by a resistor, is connected between

terminals 1 and 2.

Fig. 2: Tristate step-up converter type 2b with

restricted duty cycle

In the steady state, the converter has three

modes which follow each other during the switching

period. In mode M1 both electronic switches S1 and

S2 are on, the output voltage U2, which is equal to

the sum of the voltage across C2 and the input

voltage U1, is across the coil L1, and the current

through it increases. When S1 is turned off, mode

M2 begins and the diode D1 turns on and the

voltage across L1 is nearly zero and the current

stays constant. Mode M3 starts when S2 is turned

off, too. Now diode D2 turns on and the voltage

across L1 is equal to the sum of the negative voltage

across C1 and the input voltage. The voltage across

C1 is equal to the output voltage (in the steady

state). The voltage-time balance is therefore:

 

22112 1dUUdU 

(1)

which leads to the voltage transformation ratio:

21

2

1

2

1

dd

d

U

M





(2)

with the restrictions:

1

21  dd

and

21 dd 

. (3)

The duty cycle of d2 must be greater or equal to

that of the switch S1 d1. From the voltage

transformation ratio, one can see that two

possibilities to change the output voltage are

feasible. Figure 3 shows the voltage transformation

ratio for the variable duty cycle of switch S1 and the

duty cycle of switch S2 as a parameter. In Figure 4

the duty cycle of S1 is the parameter and the duty

cycle of S2 is the variable.

Fig. 3: Voltage transformation ratio of the tristate

step-up converter type 2b with d2 as parameter and

d1 as variable

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Fig. 4: Voltage transformation ratio of the tristate

step-up converter type 2b with d1 as parameter and

d2 as variable

The connection between the currents through

the coils and the load current is also an important

feature of a converter. In the steady-state, the

currents through the capacitors are zero in the mean.

For the calculation, one can use the mean values of

the inductor currents. The current through the first

capacitor is the negative current through L2 in

modes M1 and M2, and during M3 the positive

current through L1. One can write the charge

balance according to:

)1( 2

1

_

2

_dIdI LL 

(4)

During the complete switching period, the

capacitor C2 is discharged by the load current.

During M1 it is also discharged by the current

through L1, and during the off-time of S1 (in the

modes M2 and M3) the current through L2 charges

the capacitor. The change of charge at the second

capacitor must also be zero:

 

01 1

2

_

1

_ dIdII LL

LOAD

(5)

From (4) and (5) one gets the connections:

21

2

1

_

1dd

d

I

LOAD

L





(6)

21

1

2

_

1

dd

d

I

LOAD

L







. (7)

The steady-state behavior is shown in Figure 5.

It shows the voltage across the capacitors, the input

current, the currents through the coils, the load

current, the output voltage, the input voltage, and

the control signals of the switches.

Fig. 5: Tristate step-up converter type_2b with

parasitic resistors, up to down: voltage across C1

(dark green), voltage across C2 (dark blue); input

current (dark violet), current through L1 (red),

current through L2 (violet), load current (brown);

output voltage (green), voltage across C2 (dark

blue), input voltage (blue), control signal of S2

(black, shifted), control signal of S1 (turquoise).

For this converter type, Figure 6 shows the

variant with the second capacitor in parallel to the

output and in Figure 7 one can see the important

voltages and currents in the steady state.

The input current is pulsating and is only

flowing when the switches S1 and S2 are off. The

peak of the input current is now also significantly

higher.

When a stable input source (batteries or DC

microgrid) is used, the variant with the capacitor

between input and output is preferable. When the

input source is unstable, it is better to use the variant

with the capacitor at the output.

Fig. 6: Tristate step-up converter type 2b, the second

capacitor in parallel to the output

Fig. 7: Tristate step-up converter type 2b and the

second capacitor in parallel to the output with

parasitic resistors, up to down: voltage across C1

(dark green), voltage across C2 (dark blue); input

current (dark violet), current through L1 (red),

current through L2 (violet), load current (brown);

output voltage (green), voltage across C2 (dark

blue), input voltage (blue), control signal of S2

(black, shifted), control signal of S1 (turquoise).

2.2 Step-down Converter Type 2c

The circuit diagram is depicted in Figure 8.

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Fig. 8: Tristate step-down converter type 2b with

limited duty cycle

The second switching structure is replaced by

the tristate switch. The input voltage is connected to

the terminals 1 and 2 and the load is connected to

the terminals 3 and 4. The first switching structure is

the single diode D2.

During mode M1 the voltage across C2 lies

across the inductor L2, during M2 the voltage across

L2 is zero, and during M3 the voltage across C1 is

negative across the coil L2. From the loop U1, L2,

C1, and L1 one can see that the voltage across C1

must be equal to the input voltage in a steady state.

The voltage across C2 is equal to the difference

between the input voltage and the output voltage.

The voltage-time balance across L2 can now be

written as:

 

21121 1)( dUdUU 

(8)

and that leads to the voltage transformation ratio:

1

21

1

21

d

dd

U

M



(9)

with the limitations:

1

21  dd

and

12 dd 

. (10)

Figure 9 shows the voltage transformation ratio

for the variable duty cycle of switch S1 and the duty

cycle for switch S2 as a parameter. In Figure 10 the

duty cycle for S1 is the parameter and the duty cycle

of S2 is the variable.

Fig. 9: Voltage transformation ratio of the tristate

step-down converter type 2b with d2 as parameter

and d1 as variable

Fig. 10: Voltage transformation ratio of the tristate

step-down converter type 2b with d1 as parameter

and d2 as variable

The connections between the load current and

the mean values of the currents through the coils can

be again calculated with the help of the currents

through the capacitors. The charge balances for C1

and C2 are:

 

2

_

2

1

_

1dIdI LL 

(11)

 

2

_

1

2

_

1

_

1)( dIdIII LOADLL

LOAD 

, (12)

respectively, and leading to the connections:

1

2

10

_

1

d

I

LOAD

L



(13)

1

2

_

d

I

LOAD

L

. (14)

Figure 11 shows the input current which is now

continuously compared to the variant where the

second capacitor is in parallel to the output and

where the current is pulsating, furthermore, it shows

the currents through the coils, the load current, the

input and the output voltages and the control

signals. Figure 12 shows the same signals for the

variant, where the second capacitor is in parallel to

the output.

Fig. 11: Tristate step-down converter type 2c with

parasitic resistors, up to down: input current (dark

violet); current through L2 (violet), load current

(brown), current through L1 (red); output voltage

(green), control signal of S2 (black, shifted), control

signal of S1 (turquoise)

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Fig. 12: Tristate step-down converter type 2c second

capacitor in parallel to the load with parasitic

resistors, up to down: input current (dark violet);

current through L2 (violet), load current (brown),

current through L1 (red); output voltage (green),

control signal of S2 (black, shifted), control signal

of S1 (turquoise)

2.3 Step-up-down Converter Type 3d

The input voltage is connected to terminals 3 and 4,

the switching structure SStr2 is a tristate switch and

SStr1 is now a diode (Figure 13). The second

capacitor is connected between the input and the

output.

Fig. 13: Tristate step-up-down converter with

limited duty cycle type 3d

When both switches are on, the voltage across

coil L2 is equal to the voltage across C2 which is

equal to the sum of the input and the output

voltages. When S1 is turned off, the voltage across

L2 is zero and when S2 is also turned off, diode D2

turns on and the voltage across L2 is equal to the

negative voltage across C1. It is easy to see that the

voltage across C1 is equal to the output voltage in

the steady state. The voltage-time balance across L2

is equal to:

   

22121 1dUdUU 

(15)

leading to the voltage transformation ratio:

21

1

2

1dd

d

U

M



(16)

with the limitations:

1

21  dd

and

12 dd 

. (17)

Figure 14 shows the voltage transformation

ratios of the duty cycle of switch S2 as constant and

the duty cycle of switch S1 as variable.

Fig. 14: Voltage transformation ratio of the tristate

step-up-down converter type 3d with d2 as

parameter and d1 as variable

In Figure 15 the parameter is a constant duty

cycle of S1 and the variable is the duty cycle of S2.

Fig. 15: Voltage transformation ratio of the tristate

step-up-down converter type 3d with d1 as

parameter and d2 as variable

For the connections between the load current

and the mean values of the current through the coils

one gets from the charge balances

)1( 2

2

_

2

1

_dIdI LL 

(18)

)1)(()( 1

1

_

1

2

_dIIdII LOAD

LL

LOAD 

(19)

21

2

1

_

1

dd

d

I

LOAD

L







(20)

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21

2

_

1dd

d

I

LOAD

L





. (21)

Figure 16 shows the signals input current,

currents through the coils, input and output voltages,

and the control signals of the active switches. One

can again see that the input current is continuous

when the second capacitor is between the output and

the input.

Fig. 16: Tristate step-up-down converter type 3d

with parasitic resistors, up to down: input current

(dark violet); current through L2 (violet), load

current (brown), current through L1 (red); output

voltage (green), control signal of S2 (black, shifted),

control signal of S1 (turquoise)

2.4 Step-up-down Converter Type 2a

The input voltage is connected to the terminals 1

and 2, the load is connected to the terminals 3 and 4.

The second capacitor is placed between the input

and the output. The switching structure SStr1 is now

the tristate switch and SStr2 is replaced by a diode

(Figure 17).

Fig. 17: Tristate step-up-down converter with

limited duty cycle type 2a

From the circuit diagram one can obtain for the

steady state that the voltage across C1 must be equal

to the input voltage and the voltage across C2 must

be equal to the sum of the input voltage and the

output voltage. During mode M1 (both active

switches are on) the input voltage is across the coil

L1. During mode M2 (S2 and D1 are on) the coil L1

is short-circuited and the voltage across it is zero.

During M3 (only D2 is conducting) the voltage

across L1 is the negative sum of the voltage across

C1 (which is equal to the input voltage) and the

output voltage. The voltage-time balance across L1

is therefore:

  

22111 1dUUdU 

(22)

2

21

1

2

1

d

dd

U

M





(23)

with the limitations:

1

21  dd

and

12 dd 

. (24)

Figure 18 shows the voltage transformation

ratios for the duty cycle of switch S2 as constant and

the duty cycle of switch S1 as variable.

Fig. 18: Voltage transformation ratio of the tristate

step-up-down converter type 2a with d2 as

parameter and d1 as variable.

In Figure 19 the parameter is a constant duty

cycle of S1 and the variable is the duty cycle of S2.

Fig. 19: Voltage transformation ratio of the tristate

step-up-down converter type 2a with d2 as

parameter and d1 as variable

The charge balance of C1 can be written as:

 

2

1

_

2

_

1dIdI LL 

. (25)

For C2 one gets:

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)1( 2

2

_

1

_

2dIIIdI LOAD

LL

LOAD 













(26)

leading to:

2

10

_

1d

d

I

LOAD

L





(27)

1

2

_



LOAD

L

I

. (28)

The steady-state behavior is shown in Figure 20.

The signals are input current, currents through the

coils, input and output voltages, and the control

signals.

Fig. 20: Tristate step-up-down converter type 2a

with parasitic resistors, up to down: input current

(dark violet); current through L2 (violet), load

current (brown), current through L1 (red); output

voltage (green), control signal of S2 (black, shifted),

control signal of S1 (turquoise)

The input current is pulsating and when only

switch S2 is on current is fed back to the source.

Compared to the variant with the second capacitor

parallel to the load the peak current is reduced and

the time during which the current is fed back to the

source is shorter. This is shown in Figure 21. If one

wants to avoid reverse current into the source it is

better to use the topology according to type 3d.

Fig. 21: Tristate step-up-down converter type 2a, C2

in parallel to the output, with parasitic resistors, up

to down: input current (dark violet); current through

L2 (violet), load current (brown), current through

L1 (red); output voltage (green), control signal of S2

(black, shifted), control signal of S1 (turquoise)

3 Topologies of the Four Converters

Supplied by a Negative Input

Voltage

To construct converters for a negative input voltage

one has to change the polarity of the

semiconductors. Again only the converters with the

second capacitor between input and output are

shown. The number of the topologies correlates with

[1]. The results are the same as for the

corresponding ones in paragraph 2. Figure 22 shows

the step-up converter for negative input voltage.

Figure 23 is the step-up converter, Figure 24 is the

step-down converter, and Figure 25 is the second

possible step-up-down converter for negative input

voltage.

Fig. 22: Tristate step-up-down converter type 3a

Fig. 23: Tristate step-up converter type 3b

Fig. 24: Tristate step- down converter type 3c

Fig. 25: Tristate step-up-down converter type 2d

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4 Further Interesting Aspects

The voltages across the coils are equal to each other,

therefore one can combine the two coils on one

magnetic core (integrated magnetics). One can also

combine two converters in parallel to increase the

power. In this case, the control signals for the

second converter should be shifted by a half period.

When more than two converters work together, the

signals should be shifted by 120 degrees for three

converters or by 90 degrees, when four converters

are working together. For increasing the voltage

transformation ratio two (or more) converters can be

cascaded.

4.1 Model of the Converter Type 2b

The model of the converter for ideal components is

derived for the continuous mode. The equivalent

circuit for mode M1 (both active switches are on) is

depicted in Figure 26.

Fig. 26: Equivalent circuit mode M1

The state equations are given by

1

12

1L

uu

dt

di C

L



(29)

2

1

2L

u

dt

di C

L

(30)

1

2

1

C

i

dt

du L

C

(31)

 

2

11212 /

C

Ruui

dt

du CLC 



. (32)

For mode M2 (S2 is still on and D1 is

conducting) the equivalent circuit is shown in

Figure 27.

Fig. 27: Equivalent circuit mode M2

The state equations are now given by:

1

1"0"

Ldt

diL

(33)

2

121

2)(

L

uuu

dt

di CC

L



(34)

1

2

1

C

i

dt

du L

C

(35)

 

2

11222 /

C

Ruui

dt

du CLC 



. (36)

The equivalent circuit of mode M3 (only diode

D2 is conducting) can be seen in Figure 28.

Fig. 28: Equivalent circuit mode M3

1

11

1L

uu

dt

di C

L



(37)

2

2L

u

dt

di C

L

(38)

1

C

i

dt

du L

C

(39)

 

2

11222 /

C

Ruui

dt

du CLC 



. (40)

The three sets of equations can be combined

into one describing matrix differential equation.

This is possible when the switching period of the

converter is much shorter than the time constants of

the converter. The equations are weighted by the

duty cycles (the time at which they are valid divided

by the switching period). Mode M1 is weighted by

d1, mode M2 is weighted by (d2-d1), and M3 is

weighted by (1-d2). This leads to:

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 

1

21

2

21

1

21

2

1

2

1

212

1

2

1

2

1

2

1

2

1

2

1

2

1

0

1

0

1

00

1

00

1

00

u

CR

L

dd L

dd

u

i

CRC

d

C

dC

d

C

dL

d

L

dL

d

L

d

u

i

dt

d

C

L

C

L



























































. (41)

From this equation, one can get the operation

point connections and the small signal model. (41)

is a nonlinear differential equation. To get transfer

functions and Bode plots which are very helpful for

the controller design, one has to linearize the

equation around the working point. The variables

are substituted by the sum of the working point

value, written with capital letters and a zero in the

index, and the disturbance, written with small letters

and a roof on top. The working point connections

result in the voltages in:

   

011 10201020101020  UDDUDUD CC

(42)

   

01 10201020101020  UDDUDUD CC

. (43)

For the current one obtains:

 

01 20201020  LL IDID

(44)

 

01

1

10

1

20

20101010  R

U

R

U

IDID C

LL

. (45)

For the connections of the capacitor voltages

and the output voltage referred to as the input

voltage one gets:

2010

20

1

10

1

DD

D

U

UC







, (46)

2010

10

1

20

1DD

D

U

UC





, (47)

2010

20

2010

10

1

20

1

1DD

D

DD

D

U











, (48)

respectively.

These results are equal to the results which were

obtained with the help of inspection, as shown in

paragraph 2.1.

From (41) one can also find the small signal

model of the converter around the working point.

The real values are found by adding the result of the

small signals with the operating point values. The

small signal model can be written according to:

)49(

0

1

00

1

0

1

00

1

00

1

00

2

1

2010

21

1

2010

2

1010

2

1020

2

2010

1

1010

1

1020

1

2010

2

1

2

1

212

10

2

10

1

20

1

20

2

10

2

20

1

10

1

20

2

1

2

1

















































































d

u

C

II

CR

C

II L

UU

L

UU

L

DD L

UU

L

UU

L

DD

u

i

CRC

D

C

DC

D

C

DL

D

L

DL

D

L

D

u

i

dt

d

LL

CC

C

L

C

L

Using abbreviations for the elements of the state

matrix and the input matrix:



































































2

1

4241

33

232221

131211

2

1

2

1

444241

3231

2423

1413

2

1

2

1

0

00

0

00

d

u

BB

B

BBB

u

i

AAA

AA

u

i

dt

d

C

L

C

L

(50)

and using the Laplace transformation:























































)(

0

00

)(

0

2

1

4241

33

232221

131211

2

1

2

1

444241

3231

2423

1413

sD

sU

BB

B

BBB

sU

sI

AsAA

sAA

AAs

C

L

(51)

one can calculate twelve transfer functions

between the four state variables and the three input

variables. The most important transfer functions are

those that show the influence on the voltage across

the second capacitor and the duty cycles. The

denominator is the same for all twelve transfer

functions and can be calculated by the determinant

of the coefficient matrix and leads to:

WSEAS TRANSACTIONS on CIRCUITS and SYSTEMS

DOI: 10.37394/23201.2023.22.24

Felix A. Himmelstoss

E-ISSN: 2224-266X

226

Volume 22, 2023

 

   

 

)52(.

31231431241342

32231432241341443223443113

3223

311342244114

2

44

34

AAAAAAA

AAAAAAAAAAAAAs

AA

AAAAAA

sAssDen

























The numerator of the transfer function between

the voltage across C2 and the duty cycle D1 can be

calculated with the method of Crammer to:

 

   

1231232231134212322322321341

423223423113

22421241

23

42

)53(

1_

BAABAAABAABAAA

BAABAAs

BABAssBDUCNUM







With the same method, the numerator for the

transfer function between the voltage across C2 and

the duty cycle of the second switch D2 can be

calculated and leads to:

 

)54(.

)(22_

133123

233113

4213322323321341

334223

334113

23421341

2

































BAA

ABAABAAA

BAA

sBABAsDUCNUM

The parameters used in all simulations are

L1=L2=47µH, C1=C2=330µF, and U1=24 V, (the

parasitic resistors are 4 mΩ for the coils and 10 mΩ

for the capacitors). The working point for the

calculation of the Bode plot is D10=0.3, D20=0.5,

UC10=60 V, UC20=36 V, ILOAD=2.4 A,

IL10=8.4 A, IL20=6 A, R=25 Ω.

Figure 29 shows the Bode plot of the voltage

across C2 in dependence on the duty cycle d1. The

transfer function is a non-phase minimum system

because one zero is on the right side of the complex

plane. The complex zero leads to a resonance at

904 Hz and is on the left side of the complex plane

and shifts the phase to +180o, the third zero is on the

right side and shifts the phase tending to -90o. The

complex poles are at 507 Hz and at 1228 Hz and can

be seen as the two positive spikes. On the whole the

phase tends now only to -270o.

Fig. 29: Bode plot voltage across C2 in dependence

on D1 (solid line: gain response, dotted line: phase

response)

Fig. 30: Bode plot voltage across C2 in dependence

on D2 (solid line: gain response, dotted line: phase

response)

Figure 30 shows the Bode plot for the voltage

across C2 in dependence on the duty cycle of switch

S2. The transfer function of the voltage across C2

and D2 is a non-phase minimum system. The

complex zero is on the right half of the complex

plane and shifts the phase by a further minus 180o.

So the phase tends to be minus 540o.

Fig. 31: Simulation circuit

WSEAS TRANSACTIONS on CIRCUITS and SYSTEMS

DOI: 10.37394/23201.2023.22.24

Felix A. Himmelstoss

E-ISSN: 2224-266X

227

Volume 22, 2023

Figure 31 shows the LTSpice simulation circuit

with parasitic resistors included in the models of the

coils and the capacitors. The pulse width modulation

is generated with the help of the comparators U1

and U2. The voltage sources V3 and V6 produce the

duty cycles which are compared with the saw tooth

signal of V4. The comparators must be supplied by

plus and minus 5 V. Therefore, the drivers E1 and

E2 which control the MOSFETs must amplify the

control signals. The isolated drivers are modeled by

voltage-controlled voltage sources.

Fig. 32: Current through L2 (violet), load current

(brown); current through L1 (red); output voltage

(green), voltage across C2 (turquoise), input voltage

(blue).

Figure 32 and Figure 33 show the results.

Fig. 33: Up to down: duty cycle for switch S2 (dark

blue); duty cycle for switch S1 (grey); output

voltage (green), voltage across C2 (turquoise), input

voltage (blue)

The input voltage is a stable voltage that is

turned on within 0.5 ms. In this case, there is a short

inrush peak and some damped ringing. After 10 ms

a soft-start begins and the duty cycles for the two

electronic switches increase linearly in the next

20 ms. The duty cycle for S1 makes a step at 40 ms

up and down at 50 ms. At 70 ms the duty cycle of

S2 makes a step up and returns to the original value

20 ms later. At 110 ms the input voltage makes a

step up and returns after 20 ms. The lowest graph

shows the output voltage, the voltage across C2, and

the input voltage. Each step shows a damped ringing

as a reaction. The currents through the coils show a

more pronounced transient.

5 Conclusion

Starting from the structure Figure 1, four new

converters were generated and described. When the

input voltage is negative, again four new converters

can be designed and the circuits are shown. The

function is the same as for the converters with

positive input voltage. The new converters can be

connected in parallel and controlled in an

interleaved way to improve the input current. Two

possible positions of C2 lead to eight new

converters. Using bidirectional switches instead of

the active and the passive switches leads to

bidirectional converters and generates 16 additional

DC/DC converters.

The converters have several interesting features:

 Additional degree of freedom in the voltage

transformation ratio

 Limited duty cycle

 Interesting voltage transformation ratios

 Possibility to couple and combine the coils

on one magnetic core

 Input current is influenced depending on the

position of the second capacitor.



The converters can be applied for solar and DC

microgrids and other applications.

References:

[1] F. A. Himmelstoss, and M. Jungmayer, A

Family of Modified Converters with Limited

Duty Cycle, 2021 International Aegean

Conference on Electrical Machines and

Power Electronics (ACEMP) & 2021

International Conference on Optimization of

Electrical and Electronic Equipment

(OPTIM), Brasov, Romania, 2021, pp. 246-

253.

[2] K. Viswanathan, R. Oruganti and D.

Srinivasan, Dual-mode control of tri-state

WSEAS TRANSACTIONS on CIRCUITS and SYSTEMS

DOI: 10.37394/23201.2023.22.24

Felix A. Himmelstoss

E-ISSN: 2224-266X

228

Volume 22, 2023

boost converter for improved performance,

IEEE Transactions on Power Electronics, vol.

20, no. 4, pp. 790-797, July 2005, doi:

10.1109/TPEL.2005.850907.

[3] K. Viswanathan, R. Oruganti and D.

Srinivasan, A novel tri-state boost converter

with fast dynamics, IEEE Transactions on

Power Electronics, vol. 17, no. 5, pp. 677-

683, Sept. 2002, doi:

10.1109/TPEL.2002.802197.

[4] S. K. Viswanathan, R. Oruganti and D.

Srinivasan, Dual mode control of tri-state

boost converter for improved performance,

IEEE 34th Annual Conference on Power

Electronics Specialist, Acapulco, Mexico,

2003, pp. 944-950 vol.2, doi:

10.1109/PESC.2003.1218182.

[5] N. Rana and S. Banerjee, Interleaved Tri-state

Buck-Boost Converter with Fast Transient

Response and Lower Ripple, 2019 IEEE

Transportation Electrification Conference

(ITEC-India), Bengaluru, India, 2019, pp. 1-5.

[6] N. Mohan, T. Undeland and W. Robbins,

Power Electronics, Converters, Applications

and Design, 3rd ed. New York: W. P. John

Wiley & Sons, 2003.

[7] F. Zach, Power Electronics, in German:

Leistungselektronik, Frankfurt: Springer, 6th

ed., 2022.

[8] Y. Rozanov, S. Ryvkin, E. Chaplygin, P.

Voronin, Power Electronics Basics, CRC

Press, 2016.

[9] G. R. Broday, G. Damm, W. Pasillas-Lépine

and L. A. C. Lopes, Modeling and dynamic

feedback linearization of a 5-switch tri-state

buck-boost bidirectional DC-DC converter,

2021 22nd IEEE International Conference on

Industrial Technology (ICIT), Valencia,

Spain, 2021, pp. 427-432, doi:

10.1109/ICIT46573.2021.9453569.

[10] A. Choubey and L. A. C. Lopes, A tri-state 4-

switch bi-directional converter for interfacing

supercapacitors to DC micro-grids, 2017

IEEE 8th International Symposium on Power

Electronics for Distributed Generation

Systems (PEDG), Florianopolis, Brazil, 2017,

pp. 1-6, doi: 10.1109/PEDG.2017.7972507.

[11] M. A. Vaghela and M. A. Mulla, Tri-State

Coupled Inductor Based High Step-Up Gain

Converter Without Right Hand Plane Zero, in

IEEE Transactions on Circuits and Systems

II: Express Briefs, vol. 70, no. 6, pp. 2291-

2295, June 2023, doi:

10.1109/TCSII.2023.3237679.

[12] Q. Wang, A. Choubey and L. A. C. Lopes,

"Mode Transition for Increased Voltage Gain

Range of a 4-Switch DC-DC Converter with

Tri-State and Single Duty Cycle Control,"

2021 IEEE 12th International Symposium on

Power Electronics for Distributed Generation

Systems (PEDG), Chicago, IL, USA, 2021,

pp. 1-6, doi: 10.1109/PEDG51384.2021

9494256.

Contribution of Individual Authors to the

Creation of a Scientific Article (Ghostwriting

Policy)

The author contributed to the present research, in all

stages from the formulation of the problem to the

final findings and solution.

Sources of Funding for Research Presented in a

Scientific Article or Scientific Article Itself

No funding was received for conducting this study.

Conflict of Interest

The author has no conflicts of interest to declare.

Creative Commons Attribution License 4.0

(Attribution 4.0 International, CC BY 4.0)

This article is published under the terms of the

Creative Commons Attribution License 4.0

https://creativecommons.org/licenses/by/4.0/deed.en

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DOI: 10.37394/23201.2023.22.24

Felix A. Himmelstoss

E-ISSN: 2224-266X

229

Volume 22, 2023