Tristate Converters

FELIX A. HIMMELSTOSS

Faculty of Electronic Engineering and Entrepreneurship,

University of Applied Sciences Technikum Wien,

Hoechstaedtplatz 6, 1200 Vienna,

AUSTRIA

Abstract: - In the continuous inductor current operation the tristate DC/DC converters have three modes. In the

converters and the Buck and the Buck-Boost converters are shown. It is also possible to apply the concept to

converters of higher order. Here the Cuk, Zeta, and SEPIC are treated. It is also possible to apply it to quadratic

converters and the d-square converter is taken as an example. A converter with a reduced duty cycle is also

treated and a modification that avoids the inrush current is also shown. Finally, an improved superlift converter

is treated. The position of the zero of the transfer function is exemplarily studied.

cycle

Received: September 24, 2022. Revised: September 15, 2023. Accepted: Ocotber 17, 2023. Published: November 20, 2023.

topology with little reduced forward-losses is treated

switching (ZVS) can be found in, [8]. Another ZVS

concept is treated in, [9]. An interesting topology for

an inverting tristate Buck-Boost converter is shown

topologies are described in all the textbooks on

Power Electronics, (e.g., [11], [12], [13]). It should

be mentioned that other concepts exist to achieve

tristate converters, [14]. The circuit diagram of the

voltage U1 is across the inductor L1, and the current

increases. When S1 is turned off, the second mode

M2 begins. Now diode D1 turns on and the inductor

L1 is short-circuited. The current through the coil

converter is that the voltage transformation ratio is

now linear for a constant duty cycle of switch S2. In

the figure also the transformation ratio of the normal

Boost converter is shown (the nonlinear line).

Fig. 2: Voltage transfer ratio for the tristate Boost

simulations are done with capacitor values of

330 µF and inductor values of 47 µH, an input

voltage of 48 V, except when other values are given.

Fig. 3: Tristate Boost converter (up to down):

voltage across coil L1 (grey); current through the

inductor L1 (red), current through the load (violet);

output voltage (green), input voltage (blue), a

control signal for switch S2 (black, shifted), a

2.1 Tristate Buck

The tristate Buck converter is shown in Figure 4.

When both switches are on, the difference between

the input voltage and the output voltage is across the

(3)

one can

. (5)

nearly constant, and when S2 turns off too, the

negative voltage across C1 is across the inductor

and the current decreases. The voltage across C1 is

equal to the output voltage during steady-state (the

loop C1, L2, C2, L1 is always valid, and the mean

value of the voltages across the coils must be zero).

Fig. 10: Tristate Zeta converter

The voltage-time balance across L1 can be written

leading again to the voltage transformation ratio of

the Buck-Boost converter (Figure 9)

. (11)

. (12)

leading again to the voltage transformation ratio of

the Buck-Boost converter (Figure 9)

input and the output voltages, and the control

signals of the switches in the steady state.

Fig. 13: Tristate CUK converter (up to down):

voltage across the inductor L1 (grey); current

through the inductor L1 (red), current through the

inductor L2 (violet); output voltage (green), input

voltage (blue), control signal for switch S2 (black,

shifted), control signal for switch S1 (turquoise)

also turned off, the input voltage minus the sum of

the voltages across the output and the capacitor C1

is across L1. Now one can write for the voltage-time

balance across L1

(15)

which leads to the voltage transformation ratio

. (16)

Fig. 14: Tristate Sepic converter

M3, the negative output voltage is across L2. The

voltage-time balance is therefore

The voltage transformation ratio can now be given

according to

Fig. 17: Voltage transfer ratio for the tristate d-

ratio for d2 as a parameter and d1 as the

independent variable. The most interesting feature

of this converter is that the voltage transformation

modified converters with reduced duty cycle are

presented in, [17], and can also be transformed into

tristate ones. Figure 25 shows the inrush into this

converter. The modification of the position of the

second capacitor avoids a large inrush current which

stresses all components. The voltage transformation

ratio is shown in Figure 20.

Fig. 24: Modified tristate (2d-1)/(1-d) converter type

2A

Fig. 25: Tristate (2d-1)/(1-d) converter type 2A,

inrush (up to down): input current (red); input

voltage (blue), output voltage (green)

Fig. 26: Tristate (2d-1)/(1-d) converter type 2A, (up

to down): voltage across L1 (grey); current through

L1 (red), current through L2 (violet); load current

(brown); input voltage (blue), control signal for S2

Figure 29 shows the voltage across the coil L1,

the current through the inductors L1 and L2, the

input and the output voltages, and the control

signals for the switches in the steady state. Also, the

current through the inductor L2 which charges the

capacitor C1 is depicted.

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

output voltage (green)

4 Position of the Zero

Converters with the possibility to increase the

output voltage over the input voltage, like the Boost,

further negative phase shifts. To stabilize the

and the whole system gets slower.

To calculate the zero, a linear dynamic model

must be derived and the transfer functions

ascertained. This is shown now for the tristate Buck-

Boost converter. The state equation during M1 are

during M2

, (28)

and during M3

.