**3.1 DC-DC converter circuits**

LED drivers often require step-up/step-down regulation DC/DC converters. The power converters supply constant current at a voltage from a not constant input voltage (actual battery source). The battery source voltage can be higher or lower than the load request. The converter output voltage can be regulated by the power switch duty ratio modulation strategy (PWM), taking into account a feedback adjustment by the output current [30]. Considering a single switch converter, a simple buck converter is a basic topology for the voltage and current control of the LED string (**Figure 7a**). It enables simple, efficient and cost-effective solutions for driving regular and high-brightness LEDs. In steady-state the duty cycle regulates the output voltage by the duty cycle (d) duration (3).

$$V\_0 = d \bullet V\_{\dot{m}} \tag{3}$$

structure achieves low input and output current ripples [31]. The presence of an inductor in the input stage of the circuit allows a smoothed input current waveforms. Furthermore, the LC filter in the output stage facilitates a smooth current waveform (**Figure 7d**). Moreover, this converter has four energy storage devices (two inductors and two capacitors) which can provide higher output power compared to other converters such as buck, boost and buck-boost of the same electrical characteristics. The disadvantage of this topology is a higher number of passive components and more complex control. Another interesting topology is the SEPIC converter [32]. It has the advantages of low input current ripple achievement due the presence of the LC filter in the input stage (**Figure 7e**). Furthermore, the output voltage is not inverted polarity. The drawbacks are as a Ćuk converter the higher number of passive components and more complex control due to fourth order dc-dc converter transfer function. Moreover, SEPIC converter has a higher voltage

*Non isolated converter for LED driver circuits. (a) Buck converter (b) boost converter, (c) Buck- boost*

To reduce the current ripple every converter described usually operated at constant current mode (CCM) and the power rate of these converter applications is

A basic control system to reach the requested LED brightness a peak current control (PCC) is widely used for drive based on Buck, Boost and Buck-Boost converter topologies. In the following, for simplicity, the Buck converter control strategy is investigated, but the considerations that will be made can be easily extended for the other topologies already described. In the Buck converter, the current sensing resistor can be connected to the source of MOSFET devices (**Figure 8a**). In this way, the current is only sensed during the on-state of the MOSFET switch compared to the sensing resistance located in load side, reducing power losses. Generally, the Buck converter topology can be rearranged in a

**3.2 Current control in LED driver DC-DC converter circuits**

*VS* ¼ *Vin* þ *V*<sup>0</sup> (6)

stresses on the power switch.

*converter, (d) Ćuk converter, (d) SEPIC converter.*

*Passive and Active Topologies Investigation for LED Driver Circuits*

*DOI: http://dx.doi.org/10.5772/intechopen.97098*

up to about 150 W.

**67**

**Figure 7.**

Multiple LEDs solution need an adequate voltage amount. Step-up (boost) LED drivers acting with a current control achieving a higher load voltage of the DC source available (**Figure 7b**). In this step-up converter, in steady-state conditions, the output voltage is higher than the input voltage as described by

$$V\_0 = \frac{1}{1-d} V\_{in} \tag{4}$$

In case of a wide input voltage range, a buck-boost topology is preferable. In the buck-boost converter, the output voltage is regulated by

$$\mathbf{V}\_0 = \left| \frac{d}{\mathbf{1} - d} \right| \bullet \mathbf{V}\_{in} \tag{5}$$

In this converter the output voltage has an opposite polarity than the input voltage (**Figure 7c**). Furthermore, the diode DS and C0 in the output stage can provide an LED short circuit protection feature. This circuit property, for example, is very crucial in automotive applications.

An improving alternative is the Ćuk converter. It is composed of a boost converter followed by a buck converter. As the buck-boost, it is suitable in applications where an input voltage from a continuous source (e.g. battery) can be greater or less than the requested output voltage. It maintains the same regulation law at steadystate of the traditional buck-boost converter with inverted polarity in the output voltage. The Ćuk converter features some benefits compared with the buck-boost converter in the matching of the LED driver design constraint. The topology

*Passive and Active Topologies Investigation for LED Driver Circuits DOI: http://dx.doi.org/10.5772/intechopen.97098*

#### **Figure 7.**

**3.1 DC-DC converter circuits**

*Block diagram of AC-DC LED driver circuits classification.*

*Light-Emitting Diodes and Photodetectors - Advances and Future Directions*

**Figure 6.**

the output voltage by the duty cycle (d) duration (3).

is very crucial in automotive applications.

**66**

LED drivers often require step-up/step-down regulation DC/DC converters. The power converters supply constant current at a voltage from a not constant input voltage (actual battery source). The battery source voltage can be higher or lower than the load request. The converter output voltage can be regulated by the power switch duty ratio modulation strategy (PWM), taking into account a feedback adjustment by the output current [30]. Considering a single switch converter, a simple buck converter is a basic topology for the voltage and current control of the LED string (**Figure 7a**). It enables simple, efficient and cost-effective solutions for driving regular and high-brightness LEDs. In steady-state the duty cycle regulates

Multiple LEDs solution need an adequate voltage amount. Step-up (boost) LED

drivers acting with a current control achieving a higher load voltage of the DC source available (**Figure 7b**). In this step-up converter, in steady-state conditions,

*<sup>V</sup>*<sup>0</sup> <sup>¼</sup> <sup>1</sup>

In case of a wide input voltage range, a buck-boost topology is preferable.

1 � *d*

In this converter the output voltage has an opposite polarity than the input voltage (**Figure 7c**). Furthermore, the diode DS and C0 in the output stage can provide an LED short circuit protection feature. This circuit property, for example,

An improving alternative is the Ćuk converter. It is composed of a boost converter followed by a buck converter. As the buck-boost, it is suitable in applications where an input voltage from a continuous source (e.g. battery) can be greater or less than the requested output voltage. It maintains the same regulation law at steadystate of the traditional buck-boost converter with inverted polarity in the output voltage. The Ćuk converter features some benefits compared with the buck-boost converter in the matching of the LED driver design constraint. The topology

 

*<sup>V</sup>*<sup>0</sup> <sup>¼</sup> *<sup>d</sup>*

 

the output voltage is higher than the input voltage as described by

In the buck-boost converter, the output voltage is regulated by

*V*<sup>0</sup> ¼ *d* ∙*Vin* (3)

<sup>1</sup> � *<sup>d</sup>Vin* (4)

<sup>∙</sup>*Vin* (5)

*Non isolated converter for LED driver circuits. (a) Buck converter (b) boost converter, (c) Buck- boost converter, (d) Ćuk converter, (d) SEPIC converter.*

structure achieves low input and output current ripples [31]. The presence of an inductor in the input stage of the circuit allows a smoothed input current waveforms. Furthermore, the LC filter in the output stage facilitates a smooth current waveform (**Figure 7d**). Moreover, this converter has four energy storage devices (two inductors and two capacitors) which can provide higher output power compared to other converters such as buck, boost and buck-boost of the same electrical characteristics. The disadvantage of this topology is a higher number of passive components and more complex control. Another interesting topology is the SEPIC converter [32]. It has the advantages of low input current ripple achievement due the presence of the LC filter in the input stage (**Figure 7e**). Furthermore, the output voltage is not inverted polarity. The drawbacks are as a Ćuk converter the higher number of passive components and more complex control due to fourth order dc-dc converter transfer function. Moreover, SEPIC converter has a higher voltage stresses on the power switch.

$$V\_S = V\_{\rm in} + V\_0 \tag{6}$$

To reduce the current ripple every converter described usually operated at constant current mode (CCM) and the power rate of these converter applications is up to about 150 W.

#### **3.2 Current control in LED driver DC-DC converter circuits**

A basic control system to reach the requested LED brightness a peak current control (PCC) is widely used for drive based on Buck, Boost and Buck-Boost converter topologies. In the following, for simplicity, the Buck converter control strategy is investigated, but the considerations that will be made can be easily extended for the other topologies already described. In the Buck converter, the current sensing resistor can be connected to the source of MOSFET devices (**Figure 8a**). In this way, the current is only sensed during the on-state of the MOSFET switch compared to the sensing resistance located in load side, reducing power losses. Generally, the Buck converter topology can be rearranged in a

As demonstrated in (9) the LED current depends on Vin. A large variation of Vin

affects the ILED,Ave losing control accuracy with respect to the Ipeak reference. A more accurate control should contain compensation for the variation of the input voltage Vin in order to keep the LED current closer to the reference value Ipeak.

• Constant switching frequency strategy, with constant switching losses.

• Intrinsic short circuit protection. MOSFET failure for over current can be

• In converter application with isolating transformer, the saturation problems

• Easy LED driver module application capability. The modules can be connected in parallel with equal current sharing providing equal current control for each

Finally, the current regulation of LED to obtain a dimming effect combine the PCC strategy and an adjustable PWM signal. A conventional circuit structure is

To avoid inaccuracy in the controlled current a hysteresis-current control (HCC) technique can be implemented. In HCC strategy is necessary to control the on and off current value. The controlled current is always included within a defined hysteresis band [33]. In this control solution, the sensing resistor can be positioned in series to

the LED, thus the high-side MOSFET buck layout may be used, as shown in **Figure 11a**, to allocate the sensing resistor with a grounded pin [35]. The sensing

*Schematic of driver circuit with PCC strategy combined and PWM control signal to act the dimming effect.*

The CPM technique achieves the following advantages

controlled by limiting the maximum reference current;

• Simply control circuit implementation and robust;

*Passive and Active Topologies Investigation for LED Driver Circuits*

*DOI: http://dx.doi.org/10.5772/intechopen.97098*

can be reduced;

As disadvantages have

• Susceptibility to noise;

• Sensitive to the wide Vin variation.

module.

shown in **Figure 10**.

**Figure 10.**

**69**

#### **Figure 8.**

*Buck converter with MOSFET with the sensing resistance layout arrangement in the traditional in (a) high-side location and in (b) low-side position. (c) Switching waveforms of command signal Vq and the main converter currents.*

different way to reduce the noise signal, positioning the sensing resistor with a pin to ground (**Figure 8b**). The capacitor C0 in some industrial application, in low side MOSFET solution, is removed as highlighted in **Figure 8b** (LUMILED HB-LED arrangement) [33]. The main switching current waveforms and the gate control voltage Vq in steady state conditions are reported in **Figure 8c**.

The operating principle of the PCC control is shown in **Figure 9** in the condition with the low-side MOSFET and the sensing resistor between source and ground.

The current control works as follows. The clock signal leads the control signal Vq high and the current in the inductor ramps up. When the transduced MOSFET current Ics reaches the reference Ipeak, the comparator resets the command signal and at the next clock signal, the control cycle is repeated [34]. The schematic of the PCC control is depicted in **Figure 9a**. The main control waveforms and the LED current are reported in **Figure 9b**. From **Figure 9b** the current ripple, ΔIL, is evaluated by:

$$
\Delta I\_L = \frac{V\_{in} - V\_0}{L\_S} t\_{on} = \frac{V\_0}{L\_S} t\_{off} \tag{7}
$$

The average LED current ILED,Ave can be calculated as

$$I\_{LED,Ave} = I\_{peak} - \frac{\Delta I\_L}{2} = I\_{peak} - \frac{V\_0}{2L\_S} t\_{off} \tag{8}$$

$$I\_{LED,Ave} = I\_{peak} - \frac{V\_0 T\_{sw}}{2L\_S} \left(1 - \frac{V\_0}{V\_{in}}\right) \tag{9}$$

#### **Figure 9.**

*Peak current control technique (a) circuit schematic of the control method and Buck in low side MOSFET solution. (b) Main control signal and led current behavior.*

## *Passive and Active Topologies Investigation for LED Driver Circuits DOI: http://dx.doi.org/10.5772/intechopen.97098*

As demonstrated in (9) the LED current depends on Vin. A large variation of Vin affects the ILED,Ave losing control accuracy with respect to the Ipeak reference.

A more accurate control should contain compensation for the variation of the input voltage Vin in order to keep the LED current closer to the reference value Ipeak.

The CPM technique achieves the following advantages


As disadvantages have

different way to reduce the noise signal, positioning the sensing resistor with a pin to ground (**Figure 8b**). The capacitor C0 in some industrial application, in low side MOSFET solution, is removed as highlighted in **Figure 8b** (LUMILED HB-LED arrangement) [33]. The main switching current waveforms and the gate control

*Buck converter with MOSFET with the sensing resistance layout arrangement in the traditional in (a) high-side location and in (b) low-side position. (c) Switching waveforms of command signal Vq and the main converter*

The operating principle of the PCC control is shown in **Figure 9** in the condition with the low-side MOSFET and the sensing resistor between source and ground. The current control works as follows. The clock signal leads the control signal Vq

> *ton* <sup>¼</sup> *<sup>V</sup>*<sup>0</sup> *LS*

<sup>2</sup> <sup>¼</sup> *Ipeak* � *<sup>V</sup>*<sup>0</sup>

2*LS*

2*LS*

<sup>1</sup> � *<sup>V</sup>*<sup>0</sup> *Vin* 

*toff* (7)

*toff* (8)

(9)

high and the current in the inductor ramps up. When the transduced MOSFET current Ics reaches the reference Ipeak, the comparator resets the command signal and at the next clock signal, the control cycle is repeated [34]. The schematic of the PCC control is depicted in **Figure 9a**. The main control waveforms and the LED current are reported in **Figure 9b**. From **Figure 9b** the current ripple, ΔIL, is

> <sup>Δ</sup>*IL* <sup>¼</sup> *Vin* � *<sup>V</sup>*<sup>0</sup> *LS*

The average LED current ILED,Ave can be calculated as

*ILED*,*Ave* <sup>¼</sup> *Ipeak* � <sup>Δ</sup>*IL*

*ILED*,*Ave* <sup>¼</sup> *Ipeak* � *<sup>V</sup>*0*Tsw*

*Peak current control technique (a) circuit schematic of the control method and Buck in low side MOSFET*

*solution. (b) Main control signal and led current behavior.*

voltage Vq in steady state conditions are reported in **Figure 8c**.

*Light-Emitting Diodes and Photodetectors - Advances and Future Directions*

evaluated by:

**Figure 9.**

**68**

**Figure 8.**

*currents.*


Finally, the current regulation of LED to obtain a dimming effect combine the PCC strategy and an adjustable PWM signal. A conventional circuit structure is shown in **Figure 10**.

To avoid inaccuracy in the controlled current a hysteresis-current control (HCC) technique can be implemented. In HCC strategy is necessary to control the on and off current value. The controlled current is always included within a defined hysteresis band [33]. In this control solution, the sensing resistor can be positioned in series to the LED, thus the high-side MOSFET buck layout may be used, as shown in **Figure 11a**, to allocate the sensing resistor with a grounded pin [35]. The sensing

**Figure 11.**

*(a) HCC control scheme in high-side MOSFET Buck converter. (b) The controlled current behavior with a fixed hysteresis band in two different cases of the control signal Vq.*

current is compared with a reference current and the error is forward to a window detector with the band levels positive and negative requested. The controlled current behavior with a fixed hysteresis band in two different cases of the control signal Vq is reported in **Figure 11b**. The HCC technique is non-constant frequency control.

> It works with a DC power supply and therefore falls within the classification outlined. Usually, the Flyback converter is used attached to the grid to create singlestage AC/DC drivers, thus it will be more fully discussed in the next session.

> In the Flyback converter, the single switch use limits the power rate. Furthermore, a single switch does not make the best exploitation of the magnetic hysteresis loop, producing losses in the magnetic core [38]. In the field of higher powers, topologies based on Half-Bridge, Push-Pull and Full-Bridge converter are applied to supply high current. These converters all have high-frequency transformers that allow galvanic isolation. The high switching frequencies used (around hundreds of kHz with wide-bandgap devices) achieve a transformer volume reduction. An additional advantage of the transformer is the availability to feature several secondary windings. Therefore, several LED strings can be supplied at the same time also with different strings arrangement. The Half-Bridge converter (**Figure 12**) has

> > *V*<sup>0</sup> *Vin*

primary, switch voltage limited stress (equal to Vin).

*A qualitative estimation of the isolated application versus the power rate.*

*Passive and Active Topologies Investigation for LED Driver Circuits*

*DOI: http://dx.doi.org/10.5772/intechopen.97098*

MOSFET, high primary current stress.

<sup>¼</sup> *Ns Np*

To avoid devices cross conduction, the duty cycle must be d < 0.5. It has the

Cons: hard switching operation, floating driver circuit need for the high side

The Push-Pull converter operates in hard switching at d < 0.5. It has the same transfer function of the Half-Bridge converter multiplied by 2. In the Push-Pull converter the MOSFETs driver circuits are more simple because there are two switches in low side position (**Figure 12**). Push-Pull topology features lower input ripple than the Half-Bridge. On the other hand, at turn-off the switches have higher voltage stress are (2Vin). Furthermore, in the primary side the transformer is center

The Full-Bridge structure is composed of four switches (see **Figure 12**). It has a twice transfer voltage ratio as the Half-Bridge topology and operating with d < 0.5. It features twice the power rate than the Half-Bridge solution with equal MOSFETs

voltage stress (equal to Vin), but it has a more complex structure.

Pro: better transformer utilization, best application up to 500 W, single winding

∙ *d* (11)

the following transfer function

following pro and cons.

**Figure 12.**

tapped [39].

**71**

The advantages of this control strategy are


The main disadvantage is the non-constant frequency control. It means a switching losses variable and generally higher compared with the previous control method. But with the new generation of wide-bandgap devices such as GaN, the switching losses are strongly reduced and this control method is more attractive [36].

A further hardware arrangement to achieve switches losses reduction in buck converter is the use of a MOSFET (or GaN) devices to replace the diode DS working in a synchronous way with the high-side switch [36].

#### **3.3 Higher power LED driver DC-DC converter and galvanic insolation feature**

As the power required for driving LEDs increases, more complex topologies and galvanic isolation is required to isolate the DC source from the LED strings, increasing safety and protection against short circuits on the load side. In the field of medium power (up to about 100 W) the Flyback topology is usually the one most used for the reduced number of components, low cost, together with efficiency even above 90% (**Figure 12**). The increase in efficiency depends on the type of switch selected, whether pure silicon or wide-bandgap devices [37]. The presence of two inductances coupled to transfer energy between the primary side and the secondary side allows the galvanic isolation required in many applications. The Flyback converter is an isolated arrangement of the Buck-Boost converter. The output voltage depends on the ratio of the number of windings on the primary side and secondary side and maintains the Buck-Boost converter duty cycle dependence (10).

$$V\_0 = \frac{N\_s}{N\_p} \cdot \frac{d}{1 - d} \cdot V\_{in} \tag{10}$$

*Passive and Active Topologies Investigation for LED Driver Circuits DOI: http://dx.doi.org/10.5772/intechopen.97098*

**Figure 12.**

current is compared with a reference current and the error is forward to a window detector with the band levels positive and negative requested. The controlled current behavior with a fixed hysteresis band in two different cases of the control signal Vq is reported in **Figure 11b**. The HCC technique is non-constant frequency control.

*(a) HCC control scheme in high-side MOSFET Buck converter. (b) The controlled current behavior with a*

• Fixed band hysteresis control does not present stability problems

The main disadvantage is the non-constant frequency control. It means a switching losses variable and generally higher compared with the previous control method. But with the new generation of wide-bandgap devices such as GaN, the switching losses are strongly reduced and this control method is more

A further hardware arrangement to achieve switches losses reduction in buck converter is the use of a MOSFET (or GaN) devices to replace the diode DS working

**3.3 Higher power LED driver DC-DC converter and galvanic insolation feature**

increasing safety and protection against short circuits on the load side. In the field of medium power (up to about 100 W) the Flyback topology is usually the one most used for the reduced number of components, low cost, together with efficiency even above 90% (**Figure 12**). The increase in efficiency depends on the type of switch selected, whether pure silicon or wide-bandgap devices [37]. The presence of two inductances coupled to transfer energy between the primary side and the secondary side allows the galvanic isolation required in many applications. The Flyback converter is an isolated arrangement of the Buck-Boost converter. The output voltage depends on the ratio of the number of windings on the primary side and secondary side and maintains the Buck-Boost converter duty cycle

galvanic isolation is required to isolate the DC source from the LED strings,

*<sup>V</sup>*<sup>0</sup> <sup>¼</sup> *Ns Np* � *d*

<sup>1</sup> � *<sup>d</sup>* � *Vin* (10)

As the power required for driving LEDs increases, more complex topologies and

• low software requirements in digital form implementation,

*Light-Emitting Diodes and Photodetectors - Advances and Future Directions*

The advantages of this control strategy are

*fixed hysteresis band in two different cases of the control signal Vq.*

• high reliability, and less tracking error.

in a synchronous way with the high-side switch [36].

attractive [36].

**Figure 11.**

dependence (10).

**70**

*A qualitative estimation of the isolated application versus the power rate.*

It works with a DC power supply and therefore falls within the classification outlined. Usually, the Flyback converter is used attached to the grid to create singlestage AC/DC drivers, thus it will be more fully discussed in the next session.

In the Flyback converter, the single switch use limits the power rate. Furthermore, a single switch does not make the best exploitation of the magnetic hysteresis loop, producing losses in the magnetic core [38]. In the field of higher powers, topologies based on Half-Bridge, Push-Pull and Full-Bridge converter are applied to supply high current. These converters all have high-frequency transformers that allow galvanic isolation. The high switching frequencies used (around hundreds of kHz with wide-bandgap devices) achieve a transformer volume reduction. An additional advantage of the transformer is the availability to feature several secondary windings. Therefore, several LED strings can be supplied at the same time also with different strings arrangement. The Half-Bridge converter (**Figure 12**) has the following transfer function

$$\frac{V\_0}{V\_{in}} = \frac{N\_s}{N\_p} \bullet d \tag{11}$$

To avoid devices cross conduction, the duty cycle must be d < 0.5. It has the following pro and cons.

Pro: better transformer utilization, best application up to 500 W, single winding primary, switch voltage limited stress (equal to Vin).

Cons: hard switching operation, floating driver circuit need for the high side MOSFET, high primary current stress.

The Push-Pull converter operates in hard switching at d < 0.5. It has the same transfer function of the Half-Bridge converter multiplied by 2. In the Push-Pull converter the MOSFETs driver circuits are more simple because there are two switches in low side position (**Figure 12**). Push-Pull topology features lower input ripple than the Half-Bridge. On the other hand, at turn-off the switches have higher voltage stress are (2Vin). Furthermore, in the primary side the transformer is center tapped [39].

The Full-Bridge structure is composed of four switches (see **Figure 12**). It has a twice transfer voltage ratio as the Half-Bridge topology and operating with d < 0.5. It features twice the power rate than the Half-Bridge solution with equal MOSFETs voltage stress (equal to Vin), but it has a more complex structure.

To reduce power losses with increasing efficiency, in higher power driver converter topologies, solutions with soft switching operation have been increasingly used. In these circuit types, the LLC resonant converter in half-bridge and fullbridge topologies are the most studied and applied [40]. The LLC resonant converter operation will be better discussed in the next section.

components compared with other isolated converters, and many studies have been conducted on the grid connection to obtain high PF and low THD [42, 43]. In the LED driver application, the operative conditions usually used is a critical conduction mode (CRM) or the discontinuous conduction mode (DCM) [44]. In DCM (or CRM) the switch turn-on can be driven when the transformer is completely demagnetized, thus transformer saturation is avoided. The efficiency of the Flyback converter can be increased using the soft-switching technique exploiting the parasitic components present in the structure of the converter and of the power switch (**Figure 14a**). The quasi-resonant (QR) mode is used in the Flyback application to reduce the switching losses despite the non-constant frequency operation. Moreover, the QR operation allows has an enhanced transient response in DCM opera-

In addition, the QR Flyback LED driver has higher safety properties under output short circuit conditions. In the QR operation, the MOSFET is not turned on until the primary windings are fully demagnetized. On the other hand, a high ripple output current and high output diode and switch conduction losses in comparison to the fixed frequency driver. A further drawback well know is the high voltage

Where Vr is the output voltage reflected in the primary side and Vstray is the peak voltage of the ringing at turn-off transient due to the equivalent primary inductance Lps and the equivalent parasitic capacitance (Cps) composed by the output MOSFET capacitor and the equivalent primary side stray capacitor

*frs* <sup>¼</sup> <sup>1</sup>

*(a) Schematic of Flyback converter with the stray inductance and capacitance reported on the primary side.*

*(b) DCM operation at td constant. (c) DCM in QR operation with k = 1.*

2*π* ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

*V*<sup>0</sup> þ *Vstray* ¼ *Vin* þ *Vr* þ *Vstray* (12)

*Lps* <sup>∙</sup>*Cps* <sup>p</sup> (13)

*Np Ns*

tion and it features a smaller EMI filter [45].

*Passive and Active Topologies Investigation for LED Driver Circuits*

*DOI: http://dx.doi.org/10.5772/intechopen.97098*

*VDS*,*peak* ¼ *Vin* þ

(**Figure 14a** and **b**). The resonant frequency *f*rs is

stress on the switch given by

**Figure 14.**

**73**

In **Figure 12** qualitative estimation of the isolated power converter topologies versus the output power rate are shown.
