Continuous Voltage to a Device by Switching Virtually

Switch Duty Cycle

Switch duty cycle goes to zero if the VC pin is pulled to ground through a diode, placing the LT1070 in an idle mode.

From: Analog Circuit Design , 2011

LT1070 design manual

Carl Nelson , in Analog Circuit Design, 2011

Publisher Summary

LT1070 is a current mode switcher. This means that a switch duty cycle is directly controlled by the switch current rather than by the output voltage. Control of the output voltage is obtained by using the output of a voltage-sensing error amplifier to set the current trip level. This technique has several advantages. First, it has immediate response to input voltage variations, unlike ordinary switchers which have notoriously poor line transient response. Second, it reduces the 90° phase shift at mid-frequencies in the energy storage inductor. This greatly simplifies closed-loop frequency compensation under widely varying input voltage or output load conditions. Finally, it allows simple pulse-by-pulse current limiting to provide maximum switch protection under output overload or short conditions. A low dropout internal regulator provides a 2.3 V supply for all internal circuitry on LT1070. This low dropout design allows the input voltage to vary from 3 to 60 V with virtually no change in device performance. Several versions of LT1070 have been developed. LT1071 and LT1072 are identical to LT1070, except for switch current ratings 2.5 and 1.25 A, respectively. Designs which result in lower switch currents can take advantage of the cost savings of these smaller chips. Design equations for LT1071 and LT1072 are identical to the LT1070.

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A 500kHz, 6A monolithic boost converter

Karl Edwards , in Analog Circuit Design, Volume Three, 2015

Circuit description

The LT1370 is a current mode switcher. This means that switch duty cycle is directly controlled by the switch current rather than by the output voltage. This technique has several advantages: immediate response to input voltage variations, greatly simplified closed-loop frequency compensation, and pulse-by-pulse current limiting, which provides maximum switch protection. An internal low dropout regulator provides a 2.3V supply to all control circuitry. This low dropout design allows the input voltage to vary from 2.7V to 30V with virtually no change in device performance. An internal 500kHz oscillator is the basic clock for all timing. A bandgap provides the reference for the feedback error amplifier.

As with the LT1371, error amplifier circuitry allows the LT1370 to directly regulate negative output voltages. The NFB pin regulates at −2.48V, while the amplifier's output internally drives the FB pin to 1.245V. The error amplifier is a current output (g_m) type, so its output voltage, present on the V_C pin, can be externally clamped to lower the current limit. A capacitor-coupled external clamp provides soft start.

The S/S pin has two functions: synchronization and shutdown. The internal oscillator can be synchronized to a higher frequency by applying a TTL square wave to this pin. This allows the part to be synchronized to a system clock. If the S/S pin is held low, the LT1370 will enter shutdown mode. In this mode, all internal circuitry is disabled, reducing supply current to 12μA. An internal pull-up ensures start-up when the S/S pin is left open circuit.

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Some thoughts on DC/DC converters

Jim Williams , Brian Huffman , in Analog Circuit Design, 2013

Physiology of the LT1070

The LT1070 is a current mode switcher. This means that switch duty cycle is directly controlled by switch current rather than by output voltage. Referring to Figure C1, the switch is turned on at the start of each oscillator cycle. It is turned off when switch current reaches a predetermined level. Control of output voltage is obtained by using the output of a voltage-sensing error amplifier to set current trip level. This technique has several advantages. First, it has immediate response to input voltage variations, unlike ordinary switchers which have notoriously poor line transient response. Second, it reduces the 90° phase shift at mid-frequencies in the energy storage inductor. This greatly simplifies closed-loop frequency compensation under widely varying input voltage or output load conditions. Finally, it allows simple pulse-by-pulse current limiting to provide maximum switch protection under output overload or short conditions. A low dropout internal regulator provides a 2.3V supply for all internal circuitry on the LT1070. This low dropout design allows input voltage to vary from 3V to 60V with virtually no change in device performance. A 40kHz oscillator is the basic clock for all internal timing. It turns on the output switch via the logic and driver circuitry. Special adaptive antisat circuitry detects onset of saturation in the power switch and adjusts driver current instantaneously to limit switch saturation. This minimizes driver dissipation and provides very rapid turn-off of the switch.

Figure C1. LT1070 Internal Details

A 1.2V bandgap reference biases the positive input of the error amplifier. The negative input is brought out for output voltage sensing. This feedback pin has a second function; when pulled low with an external resistor, it programs the LT1070 to disconnect the main error amplifier output and connects the output of the flyback amplifier to the comparator input. The LT1070 will then regulate the value of the flyback pulse with respect to the supply voltage. This flyback pulse is directly proportional to output voltage in the traditional transformer-coupled flyback topology regulator. By regulating the amplitude of the flyback pulse the output voltage can be regulated with no direct connection between input and output. The output is fully floating up to the breakdown voltage of the transformer windings. Multiple floating outputs are easily obtained with additional windings. A special delay network inside the LT1070 ignores the leakage inductance spike at the leading edge of the flyback pulse to improve output regulation.

The error signal developed at the comparator input is brought out externally. This pin (V_C) has four different functions. It is used for frequency compensation, current limit adjustment, soft-starting, and total regulator shutdown. During normal regulator operation this pin sits at a voltage between 0.9V (low output current) and 2.0V (high output current). The error amplifiers are current output (g_m) types, so this voltage can be externally clamped for adjusting current limit. Likewise, a capacitor-coupled external clamp will provide soft-start. Switch duty cycle goes to zero if the V_C pin is pulled to ground through a diode, placing the LT1070 in an idle mode. Pulling the V_C pin below 0.15V causes total regulator shutdown with only 50μA supply current for shutdown circuitry biasing. For more details, see Linear Technology Application Note 19, Pages 4-8.

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Theoritical considerations for buck mode switching regulators

Carl Nelson , in Analog Circuit Design, 2013

Block Diagram Description

A switch cycle in the LT1074 is initiated by the oscillator setting the R/S latch. The pulse that sets the latch also locks out the switch via gate G1. The effective width of this pulse is approximately 700ns, which sets the maximum switch duty cycle to approximately 93% at 100kHz switching frequency. The switch is turned off by comparator C1, which resets the latch. C1 has a sawtooth waveform as one input and the output of an analog multiplier as the other input. The multiplier output is the product of an internal reference voltage, and the output of the error amplifier, A1, divided by the regulator input voltage. In standard buck regulators, this means that the output voltage of A1 required to keep a constant regulated output is independent of regulator input voltage. This greatly improves line transient response, and makes loop gain independent of input voltage. The error amplifier is a transconductance type with a GM at null of approximately 5000μmho. Slew current going positive is 140μA, while negative slew current is about 1.1mA. This asymmetry helps prevent overshoot on startup. Overall loop frequency compensation is accomplished with a series RC network from V _C to ground.

Switch current is continuously monitored by C2, which resets the R/S latch to turn the switch off if an overcurrent condition occurs. The time required for detection and switch turn-off is approximately 600ns. So minimum switch on time in current limit is 600ns. Under dead shorted output conditions, switch duty cycle may have to be as low as 2% to maintain control of output current. This would require switch on time of 200ns at 100kHz switching frequency, so frequency is reduced at very low output voltages by feeding the FB signal into the oscillator and creating a linear frequency downshift when the FB signal drops below 1.3V. Current trip level is set by the voltage on the I_LIM pin which is driven by an internal 320pA current source. When this pin is left open, it selfclamps at about 4.5V and sets current limit at 6.5A for the LT1074 and 2.6A for the LT1076. In the 7-pin package an external resistor can be connected from the I_LIM pin to ground to set a lower current limit. A capacitor in parallel with this resistor will soft-start the current limit. A slight offset in C2 guarantees that when the I_LIM pin is pulled to within 200mV of ground, C2 output will stay high and force switch duty cycle to zero.

The shutdown pin is used to force switch duty cycle to zero by pulling the I_LIM pin low, or to completely shut down the regulator. Threshold for the former is approximately 2.35V, and for complete shutdown, approximately 0.3V. Total supply current in shutdown is about 150μA. A 10μA pull-up current forces the shutdown pin high when left open. A capacitor can be used to generate delayed startup. A resistor divider will program "undervoltage lockout" if the divider voltage is set at 2.35V when the input is at the desired trip point.

The switch used in the LT1074 is a Darlington NPN (single NPN for LT1076) driven by a saturated PNP. Special patented circuitry is used to drive the PNP on and off very quickly even from the saturation state. This particular switch arrangement has no "isolation tubs" connected to the switch output, which can therefore swing to 40V below ground.

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Power Supplies

Peter Wilson , in The Circuit Designer's Companion (Fourth Edition), 2017

7.1 General

A conceptual block diagram for the two common types of power supply—linear and switch-mode—is given in Fig. 7.1.

Figure 7.1. Power Supply Block Diagram.

7.1.1 The Linear Supply

The component blocks of a linear supply are common to all variants and can be described as follows:

•

input circuit: conditions the input power and protects the unit, typically voltage selector, fuse, on–off switching, filter, and transient suppressor

•

transformer: isolates the output circuitry from the ac input and steps down (or up) the voltage to the required operating level

•

rectifier and reservoir: converts the ac transformer voltage to dc, reduces the ac ripple component of the dc, and determines the output hold-up time when the input is interrupted

•

regulation: stabilizes the output voltage against input and load fluctuations

•

supervision: protects against overvoltage and overcurrent on the output and signals the state of the power supply to other circuitry; often omitted on simpler circuits

7.1.2 The Switch-Mode Supply

The advantage of the direct-off-line switch-mode supply is that it eliminates the 50   Hz mains transformer and replaces it with one operating at a much higher frequency, typically 30–300   kHz. This greatly reduces its weight and volume. The component blocks are somewhat different from a linear supply. The input circuit performs a similar function but requires more stringent filtering. This is followed immediately by a rectifier and reservoir that must work at the full line voltage and feeds the switch element which chops the high-voltage dc at the chosen switching frequency.

The transformer performs the same function as in a linear supply but now operates with a high-frequency square wave instead of a low-frequency sine wave. The secondary output needs only a small-value reservoir capacitor because of the high frequency. Regulation can now be achieved by controlling the switch duty cycle against feedback from the output; the feedback path must be isolated so that the separation of the output circuit from the mains input is not compromised. The supervision function, where it is needed, can be combined with the regulation circuitry.

7.1.3 Specifications

The technical and commercial considerations that apply to a power supply can add up to a formidable list. Such a list might run as follows:

•

input parameters: minimum and maximum voltage, maximum allowable input current, surge and continuous, frequency range, for ac supplies, permissible waveform distortion, and interference generation

•

efficiency: output power divided by input power, over the entire range of load and line conditions

•

output parameters: minimum and maximum voltage(s), minimum and maximum load current(s), maximum allowable ripple and noise, load and line regulation, transient response

•

abnormal conditions: performance under output overload, performance under transient input conditions such as spikes, surges, dips and interruptions, performance on turn-on and turn-off: soft-start, power-down interrupts

•

mechanical parameters: size and weight, thermal and environmental requirements, input and output connectors, screening

•

safety approval requirements

•

cost and availability requirements

7.1.4 Off the Shelf Versus Roll Your Own

The first rule of power supply design is: do not design one yourself if you can buy it off the shelf. There are many specialist power supply manufacturers who will be only too pleased to sell you one of their standard units or, if this does not fit the bill, to offer you a custom version.

The advantages of using a standard unit are that it saves a considerable amount of design and testing time, the resources for which may not be available in a small company with short timescales. This advantage extends into production—you are buying a completed and tested unit. Also your supplier should be able to offer a unit, which is already known to meet safety and electromagnetic compatibility (EMC) regulations, which can be a very substantial hidden bonus.

Costs

The major disadvantage will be unit cost, which will probably though not necessarily be more than the cost of an in-house designed and built power supply. The supplier must, after all, be able to make a profit. The exact economics depend very much on the eventual quantity of products that will be built; for lower volumes of a standard unit it will be cheaper to buy off the shelf, for high volumes or a custom-designed unit it may be cheaper to design your own. It may also be that a standard unit will not fulfill your requirements, though it is often worth bending the requirements by judicious circuit redesign until they match. For instance, the vast majority of standard units offer voltages of 3.3 or 5   V (for logic) and ±12 or 15   V (for analog and interface). Life is much easier if you can design your circuit around these voltages.

A graph of unit costs versus power rating for a selection of readily available single output standard units is shown in Fig. 7.2. Typically, you can budget for £1 per watt in the 50–200   W range. There is little cost difference between linear and switch-mode types. On the assumption that this has convinced you to roll your own, the next section will examine the specification parameters from the standpoint of design.

Figure 7.2. Price Versus Power Rating for Standard Power Supplies.

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Isolated Active Waveshaping Techniques for Power Quality Improvements in Variable Frequency AC Drive

Sanjeet Kumar Dwivedi , in Modeling and Control of Power Electronics Converter System for Power Quality Improvements, 2018

6.3.3 Design of AC-DC Flyback converter

Fig. 6.3 shows the circuit diagram of AC-DC Flyback converter. The design of components is given for the operation of Flyback converter in the discontinuous conduction mode (DCM) of current operation. In DCM the converter acts as a voltage follower with inherent PFC at the input AC mains. An AC-DC Flyback converter equivalent circuit is shown in Fig. 6.9. The operating modes of the high frequency transformer isolated AC-DC Flyback converter in discontinuous current mode are shown in Fig. 6.10A (i–iii) and the resulting input voltage, input current and output current waveforms are given in Fig. 6.10B–D. All these values are referred to the secondary side of the Flyback transformer. The modes of operation are subdivided into three stages.

Figure 6.9. Equivalent circuit of high frequency isolated AC-DC Flyback converter.

Figure 6.10. (A) Two different operating stages (i) and (ii) of Flyback converter in DCM of operation and its (B) voltage waveforms (C) and (D) switch and diode current waveform.

1.

First Stage of Operation: The first stage is defined by the on time t _on of switch S ₁ and is shown in Fig. 6.10 A(i). In the first stage of converter operation the peak input current (i _pk) refers to the secondary, for 0<t<t _on and can be defined as:

(6.64) $i_{\mathrm{pk}}=\frac{v_{1\mathrm{r}}d{T}_{\mathrm{s}}}{n{L}_{\mathrm{m}}}$

where n is turn ratio of the transformer, L _m is Flyback transformer magnetizing inductance referred to the secondary ( $L_{\mathrm{m}}=\frac{{L\prime }_{\mathrm{m}}}{n^2}$ ). d is switch duty cycle, T _s is switching period, and v _1r is absolute value of sinusoidal input voltage (v _1r=|v _s|=V _s|sinωt|).

The average input current (i _avg) of the converter is calculated from Fig. 6.10A as:

(6.65) $i_{\mathrm{avg}}=\frac{1}{T_{\mathrm{s}}}{\int }_0^{T_{\mathrm{s}}}{i}_{\mathrm{s}}(t)\mathrm{d}t$

By solving Eq. (6.65) the average current is given as:

(6.66) $i_{\mathrm{avg}}==\frac{d{i}_{\mathrm{pk}}}{2n}$

By substituting Eq. (6.64) into Eq. (6.66) the average current becomes:

(6.67) $i_{\mathrm{avg}}=\frac{v_{1\mathrm{r}}}{R_{\mathrm{e}}}$

(6.68) $R_{\mathrm{e}}=\frac{2n^2{L}_{\mathrm{m}}}{d^2{T}_{\mathrm{S}}}$

where R _e is the effective resistance at the converter input.

The average current of the Flyback converter obeys the ohm's law and the effective resistance R _e is controllable by the variation of the duty cycle of the switch S ₁ as given in Eq. (6.68).

The average output current (i _avg) of the converter is computed as:

(6.69) $i_{\mathrm{avg}}=\frac{1}{T_{\mathrm{s}}}{\int }_0^{T_{\mathrm{s}}}{i}_{\mathrm{o}}(t)\mathrm{d}t$

By solving Eq. (6.69) the average current (i _avg) can be given as:

(6.70) $i_{\mathrm{avg}}=\frac{d_2{i}_{\mathrm{pk}}}{2}$

where d ₂ is on time duty ratio (t _don/T _s) of the diode.

The diode duty ratio d ₂ can be calculated by solving for time (d+D ₂)T _S at which the magnetizing current reaches zero as:

(6.71) $d_2=d\left(\frac{v_{1r}}{n{v}_{\mathrm{DC}}}\right)$

where v _DC is voltage of the DC link ( $v_{\mathrm{DC}}={v\prime }_{\mathrm{DC}}/n$ ).

By substituting Eqs. (6.64), (6.68), and (6.71) into Eq. (6.70) and by rearranging the terms the average power is calculated as:

(6.72) $i{}_{\mathrm{avg}}v_{\mathrm{DC}}=\frac{v_{1\mathrm{r}}^2}{R_{\mathrm{e}}}$

The average power obtained is equal to the power consumed by the converter at the input side.

2.

Second Stage of Operation: The second stage is defined by the diode on time t _don of diode (D ₅) and shown in Fig. 6.10A(ii).

From Eq. (6.72) it is found that the Flyback converter operates as a perfect power factor preregulator (PFP) in the DCM as shown in Fig. 6.10 provided that the Flyback magnetizing inductance current ceases to zero before the end of switching period T _s, this can be represented as:

(6.73) $d_2<(1-d)$

or

(6.74) $d_2=d\left(\frac{v_{1\mathrm{r}}}{n{v}_{\mathrm{DC}}}\right)<1$

In Eq. (6.74) the switch duty ratio "d," the output voltage "v _DC" and the turns ratio of transformer "n," all presumed constant. The input rectified sine wave voltage "v _1r " varies between "0" and "V _s."

The necessary condition for the Flyback converter operation in DCM is given as:

(6.75) $d<\frac{1}{1+\left(\frac{V_{\mathrm{s}}}{n{v}_{\mathrm{DC}}}\right)}$

For the power balance condition of the converter operation, input power is equated to output power as:

(6.76) $\frac{v_{1\mathrm{r}}^2}{R_{\mathrm{e}}}=\frac{v_{\mathrm{DC}}^2}{R}$

From the Eq. (6.76) the output voltage can be calculated as:

(6.77) $v_{\mathrm{DC}}=v_{1\mathrm{r}}\sqrt{(R/R_{\mathrm{e}})}$

Substituting values of R _e from Eqs. (6.68) and (6.77) can be further simplified to

(6.78) $v_{\mathrm{DC}}=v_{1\mathrm{r}}\left(\frac{d}{n}\right)\sqrt{\frac{R{T}_{\mathrm{s}}}{2L_{\mathrm{m}}}}$

Therefore the duty ratio "d" of the switch can be given as:

(6.79) $d=\left(\frac{n{v}_{\mathrm{DC}}}{v_{1\mathrm{r}}}\right)\sqrt{2\mathrm{K}}$

where K is the conduction parameter of converter (2L _m/RT _s).

Equating Eqs. (6.75) and (6.79) and using the peak value of rectified sinusoidal input voltage, v _1r=V _s, solution for "K" is given as:

(6.80) $K<K_{\mathrm{crit}}=\frac{1}{2{\left\{1+\left(\frac{n{v}_{\mathrm{DC}}}{V_{\mathrm{s}}}\right)\right\}}^2}$

and from the conduction parameter of converter, the magnetizing inductance "L _m" is given as:

(6.81) $L_{\mathrm{m}}<L_{\mathrm{mcrit}}=\frac{R{T}_{\mathrm{s}}}{4{\left\{1\left(\frac{n{v}_{\mathrm{DC}}}{V_{\mathrm{s}}}\right)\right\}}^2}$

The extreme operating condition on the Flyback converter is its operation with the minimum value of load resistance "R" and with minimum peak line voltage "V _s." Therefore the critical value of magnetizing inductance of the high frequency transformer "L _m" referred to the secondary side must satisfy the relation as:

(6.82) $L_{\mathrm{m}}<L_{\mathrm{mcrit}}=R_{\min }\left[\frac{{\mathrm{T}}_{\mathrm{s}}}{4{\left\{1+\left(\frac{{\mathit{nv}}_{\mathrm{DC}}}{{\mathrm{V}}_{\mathrm{s}}}\right)\right\}}^2}\right]$

3.

Selection of Output DC Capacitor Filter: The value of output capacitance is selected as per Eq. (6.34) obtained earlier for the AC-DC Cuk converter.

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Interfacing Between an ESS and a Microgrid

David Wenzhong Gao , in Energy Storage for Sustainable Microgrid, 2015

3.2 DC-DC Converter

DC-DC converters are used to change the voltage level at the DC source input to the desired DC output voltage level. There are several different types of DC-DC converters, namely step-down converter, step-up converter, and bidirectional DC-DC converter. A step-down converter converts a high voltage DC source into a low voltage output, while a step-up converter increases the DC source voltage to a higher output voltage. The bidirectional DC-DC converter can do both step-down and step-up conversions, and the power can flow in either direction between input and output.

Many ESSs are DC power sources, e.g., batteries and supercapacitors. Also, the DC link appears in microgrids in between back-to-back converters. So, a DC-DC converter can connect DC ESSs to the DC link in a microgrid. In addition, for a photovoltaic (PV) microgrid, the ESS can work to mitigate the intermittency of the PV output through control of DC-DC converter.

In this section, several DC-DC converters will be introduced. They cover the categories of step-down converter, step-up converter and bidirectional DC-DC converter.

3.2.1 Buck Converter (Step-Down Converter)

Buck converter is a simple and widely used voltage step-down device with high efficiency (e.g., 95% or above). Figure 3.2 shows a typical circuit of a buck converter.

Figure 3.2. The circuit structure of buck converter.

In the buck converter, the inductor plays a major role to lower the input voltage. There are two states in the operation process of buck converter: the on-state and off-state of the switch S. During the on-state, the control signal closes the switch S. Since the source V _i is serially connected to the inductor and load, the current I _L through the inductor L is increasing. According to Faraday's law of induction, there will be a voltage V _L induced across the inductor. This opposing voltage V _L counteracts the voltage of the source and reduces the voltage on the load. At the same time, the inductor absorbs energy from the source and stores the energy in the form of a magnetic field.

On the other hand, if the switch S is opened by a control signal, this results in the off-state of the converter. In the off-state, the source voltage V _i is disconnected from the circuit by the switch. Due to the diode D, the current I _L through the inductor will continue to flow but its magnitude will drop. As a result, the induced voltage across the inductor will change its direction. Since there is energy stored in the inductor, the inductor becomes a source to supply the load by releasing its stored energy.

By switching between on-state and off-state constantly, the buck converter is able to decrease the voltage from the input to the output. If the current through the inductor never falls to zero during the whole process, the converter is said to be in continuous mode. Otherwise, it is in discontinuous mode. Figure 3.3 shows the current and voltage change during the continuous mode.

Figure 3.3. Voltage and current in continuous mode.

The voltage across the inductor is related to the change rate of its current, as given in Eq. (3.1).

(3.1) $V_{\mathrm{L}}=L\frac{d{I}_{\mathrm{L}}}{dt}$

Therefore, in continuous mode, the change of current can be calculated for both on-state and off-state. Equation (3.2) denotes the current change in on-state.

(3.2) $\mathrm{\Delta }{I}_{{\mathrm{L}}_{\mathrm{on}}}={\int }_0^{t_{\mathrm{on}}}\frac{V_{\mathrm{L}}}{L}dt=\frac{V_{\mathrm{i}}-V_{\mathrm{o}}}{L}{t}_{\mathrm{on}}$

Similarly, for the off-state, the decrease of current through the inductor is computed by Eq. (3.3)

(3.3) $\mathrm{\Delta }{I}_{{\mathrm{L}}_{\mathrm{off}}}={\int }_{t_{\mathrm{on}}}^T\frac{V_{\mathrm{L}}}{L}dt=\frac{-V_{\mathrm{o}}}{L}(T-t_{\mathrm{on}})=-\frac{V_{\mathrm{o}}}{L}{t}_{\mathrm{off}}$

If the converter operates in a steady state, during a cycle, the current through the inductor at the beginning of the on-state will be the same as the current at the end of the off-state. This means that the accumulated current change during one operational cycle (i.e., one period consisting of one on-state and one off-state) is zero.

(3.4) $\mathrm{\Delta }{I}_{{\mathrm{L}}_{\mathrm{on}}}+\mathrm{\Delta }{I}_{{\mathrm{L}}_{\mathrm{off}}}=\frac{V_{\mathrm{i}}-V_{\mathrm{o}}}{L}{t}_{\mathrm{on}}-\frac{V_{\mathrm{o}}}{L}{t}_{\mathrm{off}}=0$

Let $D=t_{\mathrm{on}}/T$ be the switch duty cycle, and 0< D<1. Equation (3.4) becomes:

(3.5) $\frac{V_{\mathrm{i}}-V_{\mathrm{o}}}{L}DT-\frac{V_{\mathrm{o}}}{L}(1-D)T=0$

(3.6) $\Rightarrow \frac{V_{\mathrm{o}}}{V_{\mathrm{i}}}=D$

So, by controlling the switch duty cycle of the converter, the output voltage V _o can be controlled. Also, as D is always blow 1, Eq. (3.6) shows that the output voltage is always lower than the input voltage.

3.2.2 Boost Converter (Step-Up Converter)

Like the buck converter, the boost converter has a simple structure, as shown in Figure 3.4. The function of a boost converter is to increase the input voltage to a higher output voltage. Again, the inductor in the circuit plays a major role to boost the input voltage.

Figure 3.4. The circuit structure of boost converter.

The boost converter also has an on-state and an off-state. In the on-state, the switch S is in closed position, I _D=0, the current I _L through the inductor L is increasing and the voltage across the inductor is equal to the source voltage. In this process, the inductor is storing energy from the source.

In the off-state, the switch is open. The load is reconnected to the source and the inductor. Hence, the current through the inductor will decrease, resulting in an induced voltage across inductor in the same direction of the source voltage. Now, the inductor becomes another source to supply the load by releasing its stored energy. Since the source and inductor are connected in series, the voltage on the load is the aggregation of the voltage on inductor and source voltage, which means the output voltage is higher than the source.

(3.7) $V_{\mathrm{o}}=V_{\mathrm{L}}+V_{\mathrm{i}}$

If the current through the inductor is always above zero, the converter is working in continuous mode. According to the relationship between the current and voltage of the inductor, the change of current during on-state and off-state can be obtained. In the on-state, only the source V _i influences the current through the inductor as Eq. (3.8) shows.

(3.8) $\mathrm{\Delta }{I}_{{\mathrm{L}}_{\mathrm{on}}}={\int }_0^{t_{\mathrm{on}}}\frac{V_{\mathrm{L}}}{L}dt=\frac{V_{\mathrm{i}}}{L}{t}_{\mathrm{on}}=\frac{V_{\mathrm{i}}}{L}DT$

where D is the duty cycle. In the off-state, both the source and the load are connected with the inductor in series. The inductor current change is given in Eq. (3.9).

(3.9) $\mathrm{\Delta }{I}_{{\mathrm{L}}_{\mathrm{off}}}={\int }_{t_{\mathrm{on}}}^T\frac{V_{\mathrm{L}}}{L}dt=\frac{V_{\mathrm{i}}-V_{\mathrm{o}}}{L}(1-D)T$

In the steady state, as Figure 3.5 shows, the current I _L at the beginning of on-state and at the end of the off-state will be the same, which means that the accumulated current change during a cycle is zero. Therefore, the following relationship of the current change through the inductor can be obtained:

Figure 3.5. Voltage and current in continuous mode.

(3.10) $\mathrm{\Delta }{I}_{{\mathrm{L}}_{\mathrm{on}}}+\mathrm{\Delta }{I}_{{\mathrm{L}}_{\mathrm{off}}}=\frac{V_{\mathrm{i}}}{L}DT+\frac{V_{\mathrm{i}}-V_{\mathrm{o}}}{L}(1-D)T=0$

which implies that

(3.11) $\frac{V_{\mathrm{o}}}{V_{\mathrm{i}}}=\frac{1}{(1-D)}$

Because the duty cycle D is less than 1, the ratio in Eq. (3.11) will always be bigger than 1. This implies that the output voltage V _o is always higher than the input V _i. The gain of the boost converter can be controlled by the duty cycle D.

3.2.3 Bidirectional Buck-Boost Converter

In a microgrid system, charging and discharging of BESS requires the DC-DC converter to be bidirectional so that the power flow can change direction between the ESS and the microgrid. Typically, the voltage at the ESS side is lower than that at the microgrid side. That means that the ESS voltage must be stepped up so that the ESS can discharge to supply power to the microgrid. Conversely, when the ESS is being charged, the higher voltage at the DC-bus of the microgrid needs to be stepped down to the rated voltage of the ESS.

Figure 3.6 shows the structure of a bidirectional DC-DC converter. The transistors in the converter work as switches to connect or disconnect the circuit. This bidirectional DC-DC converter can be considered as a combination of a buck converter and a boost converter. In the buck converter mode, the transistor T ₁ is always off, current flows from the DC-bus to the ESS source. By controlling the transistor T ₂, the converter can decrease the microgrid side voltage V _DC to charge the ESS. If the converter works in boost converter mode, the transistor T ₂ is always in its off-state and the diode on T ₂ facilitates current flow in one direction from the ESS source to the microgrid. By controlling the duty cycle D of the transistor T ₁, the converter is able to increase the output voltage V _ESS of the ESS so as to supply power to the microgrid.

Figure 3.6. Bidirectional buck-boost converter.

A case study of bidirectional buck-boost converter will be given at the end of this chapter.

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An overview of high voltage conversion ratio DC-DC converter configurations used in DC micro-grid architectures

T. Arunkumari , V. Indragandhi , in Renewable and Sustainable Energy Reviews, 2017

2.3.2 Three-phase current-fed push–pull bidirectional dc–dc converter

For fuel cell application active clamp current fed three phase push-pull dc-dc converter is proposed by Lee et al. The main advantage of this converter is transient surge voltage, natural zero voltage switching, zero current switching of clamp switches, duty cycle attained at lesser range [45]. Hugo et al. proposed the converter which works below 1/3 duty cycle range. The voltage fed three phase push pull converter has advantages such as less in volume, less weight, components used is less, maintains low voltage across the devices. The efficiency attained is 95% [46] Romero Leandro proposed the push pull converter with ZVS-PWM technique. This converter reduces the switching loss, increases the power density, and it requires the filter since it operates in higher frequency. Here the leakage energy is recycled which helps in improvement of the efficiency [47]. Satarupa Bal, proposed the snubberless soft switching current fed three phase converter, this converter is suitable to operate in ZVS and ZCS condition. The efficiency attained is 95.8% [48].

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A review of DC/DC converter-based electrochemical impedance spectroscopy for fuel cell electric vehicles

Hanqing Wang , ... Daniel Hissel , in Renewable Energy, 2019

3.4 Power converters based on auxiliary voltage-boost circuit

In purpose of increasing the voltage gain ratio of conventional non-isolated converters, different kinds of auxiliary circuits are widely applied to this type of topologies. Table 4 presents the comparisons of non-isolated DC/DC converters integrated with the auxiliary voltage-boost structure; the topologies are presented in Fig. 6 respectively.

Table 4. Comparisons of non-isolated DC/DC converters with auxiliary voltage-boost structure.

Ref.	Voltage gain	Power level	Vin	Vout	Efficiency	Quantity of components	Special characteristic
[57]	2/(1-D)	1.6 kW	50–120 V	400 V	∼96.6%	7	Input-parallel Output-series boost converter.
[59]	1/[(1-D1)*(1-D2)]	200 W	40 V	300 V	∼90%	6	New Cascade boost converter.
[66]	[(1 + D)/(1-D)]2	–	12 V	100 V	<90%	12	3-Z-Network based boost converter.
[62]	2/(1-D)	3 kW	20–35 V	250 V	∼94%	8	2-phase IBC combined with switched capacitor.
[63]	2/(1-D)	1.2 kW	26–43 V	200 V	∼95%	8	2-phase IBC combined with voltage doubler circuit.
[64]	2/(1-D)	1 kW	24 V	250 V	–	9	2-phase IBC combined with voltage double circuit.
[60]	2/(1-D)	100 W	24 V	240 V	∼95.8%	8	High step-up converter.
[67]	2/(3–4*D)	1.2 kW	60–150 V	400 V	∼95.66%	10	Three level Q-Z source boost converter.

Fig. 6. Schematics of non-isolated DC/DC converters for FCEVs application integrated with the auxiliary voltage-boost circuit.

The Input-Parallel Output-Series structure is interesting to be considered by the conventional Boost converter according to the study of Wang et al. [57]. An interleaved structure based on two inductors is chosen on the input side of this structure to reduce input current ripple. In addition, the two capacitors at the output side are connected in series to obtain a high voltage gain. Cascade Boost converter is another solution to achieve a high voltage gain ratio when the galvanic isolation is not necessary [58]. Nejad et al. [59] proposed a new cascade Boost converter; it can not only retain the advantages of the conventional cascade Boost converter but also reduce the conduction losses of semiconductors. Al-Saffar et al. [60 ] proposed a new single-switch step-up DC/DC converter which was derived from the conventional Boost converter integrated with self-lift Sepic converter for providing high voltage gain without extreme switch duty cycle.

Voltage Doubler Circuit (VDC) is well known due to its simple structure and principle. The basic operation of VDC has been discussed in detail by Ref. [61]. As presented in Refs. [62–64], some studies have integrated VDC with interleaved DC/DC converters in order to increase the voltage gain ratio. Fuzato et al. [64] analyzed the effect of the parasitic resistances on the static voltage gain of the 2-phase IBC combined with VDC using the final value theorem. Cardenas et al. [62] proposed a 3-kW DC-DC-AC power electronic interface for PEMFC application. A relatively high voltage gain (higher than 10 times) without transformer has been achieved. Wu et al. [63] proposed a power electronic interface based on a DC/DC converter and a DC/AC inverter which focused on grid-connected fuel cell generation system. In this study, the DC bus voltage has been set to 200 V while the maximum input voltage was only 40 V.

To realize a high voltage gain in DC/DC converters, Z-Source Impedance (ZSI) networks are also applied to boost the voltage due to the possibility of working in the shoot-through mode [65]. Zhang et al. [66] proposed a 3-Z-Network Boost converter that only utilized a single power switch; therefore easy to be controlled. The voltage gain could be higher than 9 times. Whereas, the maximum efficiency of the proposed converter was below 88% due to the high reverse recovery losses which are introduced by the high quantity of Si schottky diodes. A Boost Three Level DC/DC Synchronous Rectification Q-Z source converter (BTL-SRqZ) has been proposed by Zhang et al. [67]. The advantages such as lower voltage stress for the power semiconductors, the common ground between the input and output sides, as well as the wide range of voltage-gain with modest duty cycles [0.5, 0.75] for the power switches have been achieved. In order to compare the voltage gains of each topology more clearly, the voltage gain ratios are calculated as the function of duty cycles as presented in Fig. 7.

Fig. 7. The comparison of voltage gain ratio of the power converters combined with auxiliary voltage-boost circuit in an ideal case (without taking into account the internal resistance of inductors).

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Interfacing renewable energy sources for maximum power transfer—Part II: Dynamics

Sergei Kolesnik , ... Alon Kuperman , in Renewable and Sustainable Energy Reviews, 2015

3 Generalized source-converter-load dynamics

In a generalized form, the small-signal open-loop transfer function matrix C={C _ij }, i=1,2; j=1,2,3 of any PPI with single input terminal and single output terminal, fed by a REG and terminated by a voltage-type load can be represented by (Laplace variable is omitted here and thereafter) [38]

(13) $\left[\begin{array}{c}{\tilde{v}}_{in}\\ {\tilde{i}}_{out}\end{array}\right]=\left[\begin{array}{ccc}{C}_{11}& C_{12}& C_{13}\\ C_{21}& -C_{22}& C_{23}\end{array}\right]\left[\begin{array}{c}{\tilde{i}}_{in}\\ {\tilde{v}}_{out}\\ {\tilde{u}}_c\end{array}\right]=\mathbf{C}\left[\begin{array}{c}{\tilde{i}}_{in}\\ {\tilde{v}}_{out}\\ {\tilde{u}}_c\end{array}\right],$

where ${\left[\begin{array}{ccc}{\tilde{i}}_{in}& {\tilde{v}}_{out}& {\tilde{u}}_c\end{array}\right]}^T$ is the three system input variables vector, ${\left[\begin{array}{cc}{\tilde{v}}_{in}& {\tilde{i}}_{out}\end{array}\right]}^T$ is the two system output variables vector (the subscript 'in' denotes an input-terminal variable, the subscript 'out' denotes an output-terminal variable and the subscript 'c' denotes a control variable), as shown in Fig. 3 . System input and output variables can be either voltages or currents, depending on the application of the converter while the control variable is either switch duty cycle (in case of voltage-mode control) or inductor peak or average current (in case of current-mode control). Note that the entry corresponding to transfer function C ₂₂ is negative if the current flows out of the output terminal. In addition, ${\tilde{v}}_{in}$ is PPI input voltage (controlled variable), ${\tilde{i}}_{out}$ —PPI output current, ${\tilde{i}}_{in}$ —PPI input current and ${\tilde{v}}_{out}$ —PPI output voltage.

Fig. 3. Combined source-converter-load system.

As mentioned in the previous section, small-signal representations of REG and load are governed by internal resistances, which may significantly affect the dynamic performance of the converter in terms of transient behavior and stability. Considering small-signal representation of a combined source-converter-load system, shown in Fig. 3, the overall open-circuit dynamics is derived by performing subsequent substitutions,

(14) ${\tilde{i}}_{in}={\tilde{i}}_{REG},{\tilde{v}}_{in}={\tilde{v}}_{REG},{\tilde{i}}_{out}={\tilde{i}}_L,{\tilde{v}}_{out}={\tilde{v}}_L,$

followed by combining (13) with (3) and (8) as

(15) $\left[\begin{array}{c}{\tilde{v}}_{in}\\ {\tilde{i}}_{out}\end{array}\right]=\left[\begin{array}{c}\frac{\left|R_{dyn}\right|\left(C_{13}+C_{12}{C}_{23}{R}_L+C_{13}{C}_{22}{R}_L\right)}{\left|R_{dyn}\right|+C_{11}+C_{11}{C}_{22}{R}_L+C_{12}{C}_{21}{R}_L+C_{22}\left|R_{dyn}\right|R_L}\\ \frac{C_{11}{C}_{23}-C_{13}{C}_{21}+C_{23}\left|R_{dyn}\right|}{\left|R_{dyn}\right|+C_{11}+C_{11}{C}_{22}{R}_L+C_{12}{C}_{21}{R}_L+C_{22}\left|R_{dyn}\right|R_L}\end{array}\right]{\tilde{u}}_c=\left[\begin{array}{l}{P}_{11}\\ P_{12}\end{array}\right]{\tilde{u}}_c.$

Apparently, combined open-loop dynamics is influenced by both source and load internal resistances. Denominator of (15) must be thoroughly investigated to assess combined plant stability.

According to the control engineering principles, only one of the two output variables can be independently controlled (since there is a single control input). Since MPP tracking operation is considered here, ${\tilde{v}}_{in}$ is the controlled variable and the corresponding closed-loop transfer function matrix is given by

(16) $\left[\begin{array}{c}{\tilde{v}}_{in}\\ {\tilde{i}}_{out}\end{array}\right]=\left[\begin{array}{c}\frac{L}{P_{se}(1+L)}\\ \frac{P_{21}L}{P_{se}{P}_{11}(1+L)}\end{array}\right]{\tilde{v}}_{r-in},$

where $L=P_{se}{P}_a{P}_c{P}_{11}$ is the control-to-input voltage loop gain, $P_{se}$ , $P_a$ and $P_c$ are the input-voltage sensor gain, modulator gain and controller transfer function, respectively. The variable ${\tilde{v}}_{r-in}$ is the reference command for the controlled variable ${\tilde{v}}_{in}$ . The stability of the combined closed loop system depends on the roots of (1+L) as well as on zeros of P ₁₁. As a consequence, the stability is ensured when the product L satisfies Nyquist stability criterion, where the boundary condition for instability corresponds to L=−1, and P ₁₁ is minimum phase.

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