Switch-Mode Power Supplies - ICE77 · Switch-Mode Power Supplies Switch-Mode Power Supplies (SMPSs) are a family of power circuits designed to deliver power to a load by scaling voltage

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Switch-Mode Power Supplies Switch-Mode Power Supplies (SMPSs) are a family of power circuits designed to deliver power to a load by scaling voltage levels from input to output. These circuits come in different versions and they can be used in a variety of devices ranging from computers to cars and aircrafts to cellphones. SMPSs can be DC/DC if they scale DC voltage to another DC voltage. Alternately, they can be called AC/DC if an additional first stage in the circuit rectifies AC voltage to DC voltage. They can be non-isolated or isolated, depending on whether galvanic isolation is used or not. Galvanic isolation is provided by a transformer which is an excellent solution for electrical separation since it avoids short circuits between input and output. The most important non-isolated SMPSs are:

1. Buck 2. Boost 3. Buck-Boost 4. Ćuk 5. SEPIC

The most important isolated SMPSs are:

1. Flyback 2. Forward 3. Push-pull 4. Half-bridge 5. Full-bridge

SMPSs are designed to operate above the audible frequency range (50kHz and above). They maintain a constant output voltage by means of a pulse width modulator (PWM) which provides a time-varying voltage signal to a switch that is typically implemented with a transistor (almost always a MOSFET). The output voltage of an SMPS is sampled, scaled down and compared to a reference voltage. In the simplest terms, the resulting signal is then compared to a ramp. The produced pulse is fed into the gate of the transistor and increases or decreases in width in order to maintain the output voltage constant under a specific output current load condition. SMPSs operate in the Continuous Conduction Mode (CCM) if the lowest/valley current through the inductor never goes to zero. SMPSs operate in the Discontinuous Conduction Mode (DCM) if the lowest/valley current through the inductor reaches zero.

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Voltage and current mode control The feedback circuit of an SMPS forms a closed loop and various control-loop approaches are used to regulate the output voltage. The feedback circuit is necessary because it provides sampling of the output, proper compensation and an appropriate PWM signal correction for the power stage (duty cycle modulation). Voltage-mode control (VMC) and current-mode controls (CMC) are the most common schemes although other variations exist and they are used in various ICs by different companies.

Buck converter voltage-mode control (left) and current-mode control (right)

Voltage-mode control (VMC) compares the signal produced by an error amplifier to a ramp and feeds the output of the comparator into a PWM that modulates the gate of one or two MOSFETs. Current-mode control (CMC) works in a similar way but it also feeds a sampled voltage across the sense resistor near the output inductor or across the output inductor itself into the aforementioned comparator. CMC comes in two variants: peak and valley. The second allows faster load transients and variable switching frequencies. The two control modes have a variety of advantages and disadvantages. Voltage-mode control uses more components which make compensation more challenging and it’s slower in terms of load transient recovery. Current-mode control uses fewer components which make compensation less challenging and it’s faster in terms of load transient recovery. Essentially, CMC is an evolution of VMC. Voltage-mode control uses one loop. Current-mode uses two loops, the second being voltage sensed across a sense resistor near the output inductor or across the output inductor itself.

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OA and OTA compensation SMPSs require compensation because, for instance, the Buck converter’s output LC filter causes an abrupt -180° phase shift at the resonating frequency and this drastically reduces phase margin which compromises circuit stability over frequency. Some ICs are internally compensated. Others require external compensation which can be of type II or type III. Compensation requires a set of carefully selected resistors and capacitors which are placed near operational amplifiers (OAs) or operational transconductance amplifiers (OTAs). The addition of these components introduces zeros and poles that, when they are strategically placed at the proper frequencies, provide an optimal phase boost which in turns improves stability and regulation of the control-loop. An OA produces an output voltage. An OTA produces an output current.

Type II compensation with OAs (left) and with OTAs (right)

Type III compensation zeros and poles over frequency

zeros

poles

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Power stage (CMC) The transfer function for the CMC Buck converter is:

1

1 1

where Avc, the gain, is given by:

∙∙

where As is the current-sense amplifier gain, Rs is the sense resistor, gm(ps) is the transconductance of the power stage and Rout is the load resistance. The transfer function of the CMC Buck converter has one zero (numerator) and two poles (denominator). The power stage of the CMC Buck converter has one zero (ωz) and two poles (ωp and ωL).

1∙

1∙

∙ ∙

∙

where Vslope is the peak-to-peak slope voltage (compared to the reference voltage). The dominating pole of the power stage (ωp) causes a -20dB/dec drop in magnitude and a -90° phase shift.

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Power stage (VMC) The transfer function for the VMC Buck converter is:

1

1 ∙

where Avc, the gain, is given by

Vramp is the peak-to-peak ramp voltage (compared to the reference voltage) and

where Rout is the load resistance. The transfer function of the VMC Buck converter has one zero (numerator) and two conjugate poles (denominator). The power stage of the VMC Buck converter has two conjugate poles (ω0) and one zero (ωz).

1

∙

1

∙

The conjugate poles (ω0) of the power stage cause a -40dB/dec drop in magnitude and a -180° phase shift.

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Type II and type III compensation Type II compensation with OTAs is shown below:

Note: the sharp drop in phase at the LC output filter resonating frequency is -180° so type II compensation cannot be used for voltage-mode control in CCM because, even with a theoretical phase boost of 90°, it still does not produce a sufficient amount of boost. Therefore, type II compensation is only used for CMC or for SMPSs in DCM. Type III compensation with OAs is shown below:

Note: the sharp drop in phase at the LC output filter resonating frequency is -180° and type III compensation provides a theoretical phase boost of 180° so this is the common scheme used for VMC. The design of SMPSs involves tradeoffs between component size, power, efficiency, noise, loop control and compensation schemes. Therefore, a specific application often depends on a specific topology.

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Linear Technology summarizes type II compensation with OTAs as follows:

where AVM is the DC gain, gm is the transconductance and R0 is the output impedance of the transconductance amplifier.

ωp0 is the low-frequency pole angular frequency (pole of the OTA) ωthz is the zero angular frequency (placed about one decade before the crossover

frequency) ωthp is the high-frequency pole angular frequency (placed at the ESRC frequency or at

½ the switching frequency) Note: recall that s=j2πf=jω. Using output capacitors with relatively high ESR (100-500mΩ) such as electrolytic/tantalum capacitors can bring the ESRC zero frequency to the left of the switching frequency. Using output capacitors with relatively low ESR (2-10mΩ) such as ceramic capacitors can push the ESRC zero frequency to the right of the switching frequency. Therefore, with output ceramic capacitors, it is not always necessary to add a high-frequency pole to attenuate noise.

ωp0

ωthz ωthp

∙1

1 1

∙

1∙

1

Error amplifier

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Linear Technology summarizes type III compensation with OAs as follows:

ω0 is the low-frequency pole angular frequency ωz1 is the first zero angular frequency (placed at the frequency of the dominant pole of

the power stage – the LC resonating frequency) ωz2 is the second zero angular frequency (placed at the frequency of the dominant pole

of the power stage – the LC resonating frequency) ωp1 is the first high-frequency pole angular frequency (placed at the ESRC frequency or at

½ the switching frequency) ωp2 is the second high-frequency pole angular frequency (placed at ½ the switching

frequency or at the ESRC frequency) Note: recall that ω=2πf. Note: the inverting input of the operational amplifier is also connected to a properly sized resistor that allows the output to be stepped down to a value that matches the reference voltage. However, since the lower resistor in the feedback network is not part of the transfer function, although it’s in every circuit, Linear Technology does not show it.

ω0

ωz1 ωz2

ωp1 ωp2

1 1

1 1

1 1

Power stage

Loop response

Error amplifier

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Loop response (CMC) The power stage and error amplifier Bode plots combine to produce the loop response (CMC). This is an example for a Buck converter.

Note: the zero (ωZEA) is placed one decade before the crossover frequency (fc) and the pole (ωHF) is placed at the ESR zero (ωZ). The crossover/bandwidth for this example is 10kHz.

Power stage

Error amplifier

Loop

+

=

-20dB/dec

-20dB/dec

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Loop response (VMC) The power stage and error amplifier Bode plots combine to produce the loop response (VMC). This is an example for a Buck converter.

Note: the zeros (ωZEA and ωFZ) are placed at the dominant pole of the power stage (ω0), the first high-frequency pole (ωFP) is placed at the ESR zero (ωZ) and the second high-frequency pole (ωHF) is added at ½ the switching frequency. The crossover/bandwidth for this example is 10kHz.

Power stage

Error amplifier

Loop

+

=

-40dB/dec

-20dB/dec

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Stability measurements The stability of a system can be inferred by looking at its output ripple voltage on an oscilloscope while load transients are applied and/or by examining Bode plots by injecting an AC signal while operating with a DC load. Output ripple voltage Typically, a system is stable if the load transient produces a fast recovery of the output ripple voltage without ringing (more than 45° of phase margin).

Typically, a system is marginally stable if the load transient produces a recovery of the output ripple voltage but some ringing is noticeable (around 45° of phase margin).

PM=46°

PM=59°

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Typically, a system is unstable if the load transient produces a slow recovery of the output ripple voltage and a considerable amount of ringing is clearly visible (less than 45° of phase margin).

For a converter, a 50% load transient is typical and an output ripple voltage of about ±3% of the output DC voltage is desirable during recovery from transient whereas ±1% of the output DC voltage is desirable during steady state. Bode plots Bode plots are one way to check for stability over frequency. The Bode plot setup looks like this:

Bode plot setup for a Buck converter with an OTA and Type II compensation

PM=33°

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A 10-50Ω “injection” resistor (Rt) is placed in series with the upper feedback resistor (R1) and a small AC sinusoidal signal (1-10% of the output DC voltage) is injected in the system by means of a transformer. At the same time both sides of the “injection” resistor are monitored on two separate channels (1 and 2) by a network analyzer or a frequency response analyzer. The AC signal is swept over frequency at different DC load conditions to generate the Bode plots which consist of gain and phase plots. A typical Bode plot provides bandwidth, gain and phase margins.

The above images are an example of a stable system with a 500kHz switching frequency with a bandwidth/crossover frequency of 80kHz (the point where the gain is 0dB or 1), a gain margin of -12dB at 200kHz (the point where the phase is 0°) and a phase margin of 60° at 80kHz (the point where the gain is 0dB). Bode plots can be hard to interpret but an easy rule is that the GM is calculated at the frequency where the phase is 0° by going from 0dB to the blue graph (downward in this case) and the PM is calculated at the frequency where the gain is 0dB by going from 0° to the red graph (upward in this case). When output ripple measurements or Bode plots show instability, the location of the aforementioned zeros and poles are changed by using a proper combination of resistors and capacitors. A circuit with higher bandwidth/crossover frequency will exhibit quicker transient response but also higher noise sensitivity. Bandwidth can be increased by using a larger value for the resistance used to introduce the first zero in the compensation network or by reducing the output capacitance. For a Buck converter a bandwidth (BW) of 1/10 to 1/6 of the switching frequency, a gain margin (GM) of at least -6dB at ½ switching frequency (fs) and a phase margin (PM) of 60° are typically desirable.

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Controllers, converters and modules SMPSs are made of a variety of components and semiconductor companies sell products that allow the designer to customize with different degrees of integration or flexibility.

Controller Converter Module Companies such as Texas Instruments, Analog Devices, Maxim Integrated, Monolithic Power Systems, Microchip Technology or ROHM Semiconductor use a variety of terms to refer to similar circuits, primarily for marketing and sales purposes. However, they more or less converge to the same terminology. The section of a circuit that hosts the PWM that drives the MOSFETs is typically called a “controller”. When controller and MOSFETs are combined they are called a “converter”. When a converter and inductors are in the same package, they are called a “module” (most companies call them “power modules”, except for Analog Devices which uses the term “μModule”). Note: most of what follows is labeled “converter” but the term is used in a general sense as a synonym of “SMPS” (whether it’s a controller, a proper converter or a module) and it includes input/output capacitors.

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Non-isolated topologies Below are some of the most common non-isolated topologies:

Buck (non-synchronous)

Buck (synchronous)

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Boost

Inverting Buck-Boost

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Ćuk

SEPIC

The simulations for the circuits presented below imply steady-state condition and introduce soft-start for a smooth start-up. The efficiency of each circuit depends primarily on MOSFET, diode and inductor which lower overall efficiency so a proper choice of components is crucial. The current through the inductor has a DC component and an AC component. The DC component will go through the load and the AC component will go through the capacitor.

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Buck converter (CCM) This circuit converts a DC voltage from a higher level to a lower level. It is generally used for applications that require up to 1000W. This specific example shows an asynchronous Buck converter in CCM operation.

Buck converter (CCM)

Ideally, in

out

V

VD

Input and output waveforms at start-up

Transient waveforms for CCM

This converter has an input of 12V and an output of 5V. The output current is 3A so the output power is 15W.

The MOSFET is modeled with the following parameters: W=0.92 L=2μ.

C2

66uF

L1

6uH

1 2

0 0 00

R2

15m

C1

30uF

0

R1

5m

V1

TD = 1ns

TF = 10nsPW = 10mPER = 20ms

V1 = 0V

TR = 1ms

V2 = 12V

R3

2m

D1MBR1035

M1M2N6796

I1

3Adc

V2

TD = 1ns

TF = 10nsPW = 902nsPER = 2us

V1 = 0V

TR = 10ns

V2 = 10V

V-

V+

VV

I

I

I

I

V-V+V

Time

0s 0.2ms 0.4ms 0.6ms 0.8ms 1.0ms 1.2ms 1.4ms 1.6ms 1.8ms 2.0msV(C1:2) V(C2:2)

0V

5V

10V

13V

Time

1.9960ms 1.9964ms 1.9968ms 1.9972ms 1.9976ms 1.9980ms 1.9984ms 1.9988ms 1.9992ms 1.9996ms 2.0000msID(M1) I(D1) I(L1) -I(C2)

0A

2.0A

4.0AV(V1:+) V(R2:1) V(M1:g,M1:s) V(M1:s) V(M1:s,L1:2)

-10V

0V

10V

SEL>>

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Buck converter in CCM states

On-time state

During the on-time the MOSFET is on and the diode is not conducting.

Off-time state

During the off-time the MOSFET is off and the diode is conducting. Note: the diode shown in the circuit could be replaced by a MOSFET (n-type) which would make the circuit synchronous and, therefore, more efficient. In that case, the low-side MOSFET should have a lower on-resistance compared to the high-side MOSFET because the low-side MOSFET is on the majority of the time (the off-time is typically longer).

C2

66uF

L1

6uH

1 2

0 0 0 0

R2

15m

0

C1

30uF

R1

5m

V1

TD = 1ns


V1 = 0V

TR = 1ms

V2 = 12V

R3

2m

M1M2N6796

I1

3Adc

V2

TD = 1ns


V1 = 0V

TR = 10ns

V2 = 10V

C2

66uF

L1

6uH

1 2

0 0 00

R2

15m

C1

30uF

0

R1

5m

V1

TD = 1ns


V1 = 0V

TR = 1ms

V2 = 12V

R3

2m

D1MBR1035

I1

3Adc

V2

TD = 1ns


V1 = 0V

TR = 10ns

V2 = 10V

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The specifications for the Buck converter in CCM are the followings:

VVin 1410 VVout 5 AIout 3 VVD 42.0

500 ∆ 40% 1.2 ∆ _ 50% 1.5 mR ONDS 220)( ∆ 100 ∆ 1% 50

∆ _ 3% 150 The 2N6796 MOSFET has an RDS(ON) of 220mΩ so the voltage drop across the device during the on-time is:

∙ ∙ 3 ∙ 220 ∙512

275

The duty cycle is:

0.426 1 1 0.426 0.574

The average input current is given by:

∙ 3 ∙ 0.426 1.279 The period is:

1 1500

2

On-time and off-time are:

0.426 ∙ 2 852 1 0.574 ∙ 2 1.147

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The inductance is calculated at high line which is when the voltage across the MOSFET is largest, the duty cycle is smallest and the off-time is largest:

14 275 13.725

.0.364 1 1 0.364 0.636

1 ∙ 0.636 ∙ 2 1.272

∙ ∆∆

∙∆

5 0.42 ∙ 1.2721.2

5.745 → 6

The minimum output capacitance for steady state is given by:

18∙

∆∙ ∆

18∙

1.2500 ∙ 50

6

However, in order to compensate for a sudden increase or decrease of load current at the output, additional capacitance will be needed. The minimum output capacitance for a 50% load transient and 150mV overshoot/undershoot is given by:

∆2 ∙ ∙ ∆

1.52 ∙ 50 ∙ 150

31.831 → 66

where fc, the bandwidth, is 1/10 of the switching frequency. The corner frequency of the LC output filter is given by:

1

2 ∙

1

2 6 ∙ 667.998

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The maximum ripple current through the inductor is:

∆∙ ∆ ∙ 5 0.42 ∙ 1.272

61.149

The peak current through MOSFET, inductor and diode is given by:

12∆ 3

121.149 3.574

Inductor ripple current (Vin=12V)

The maximum RMS output ripple current through the capacitor has an inductive shape:

12∆

√3

∆

√12

1.149

√12332

Therefore, a capacitor with an RMS current rating of at least 332mA must be selected.

Time

1.9960ms 1.9964ms 1.9968ms 1.9972ms 1.9976ms 1.9980ms 1.9984ms 1.9988ms 1.9992ms 1.9996ms 2.0000msI(L1)

2.5A

3.0A

3.5A

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The input ripple voltage is a combination of two terms: ∆ ∆ ∆ The first term is produced by the capacitive component of the input capacitor:

10 275 9.725

59.725

0.514

1 1 0.514 0.486

∙ ∙ 1∆ ∙

3 ∙ 0.514 ∙ 0.486100 ∙ 500

15 → 30

∆∙ ∙ 1

∙3 ∙ 0.514 ∙ 0.48630 ∙ 500

50

Note: this means that increasing capacitance or switching frequency will reduce the input ripple voltage. The second term is produced by the resistive component of the input capacitor (ESR): ∆ ∙ 3 ∙ 5 Ω 15 Combining the terms gives the total input ripple voltage: ∆ ∆ ∆ 50 15 65 The maximum RMS input current occurs at Vin=10V and it’s given by this equation:

35 10 5

101.5

Therefore, a capacitor with an RMS current rating of at least 1.5A must be selected. Note: the maximum RMS input current occurs at Vin=2Vout (D=50%).

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The output ripple voltage is a combination of two terms: ∆ ∆ ∆ The first term is produced by the output capacitor:

∆18∙∆

∙18∙

1.14966 ∙ 500

4.4

Note: this means that increasing capacitance or switching frequency will reduce the output ripple voltage. The second term is produced by the resistive component of the output capacitor (ESR): ∆ ∆ ∙ 1.149 ∙ 2 Ω 2.3 Combining the terms gives the total output ripple voltage: ∆ ∆ ∆ 4.4 2.3 6.6 Either one of the two terms above can dominate over the other. If ∆ dominates over ∆ the output will look sinusoidal. If ∆ dominates over ∆ the output will look triangular.

Output ripple voltage

Note: in this case ∆ is larger than ESRV so the output looks sinusoidal.

The implementation of the Buck converter shown above features a MOSFET and a diode. A more commonly used implementation is the so-called synchronous Buck converter topology which replaces the diode with an n-type MOSFET. 2 MOSFETs make the circuit synchronous.

Time

1.9960ms 1.9964ms 1.9968ms 1.9972ms 1.9976ms 1.9980ms 1.9984ms 1.9988ms 1.9992ms 1.9996ms 2.0000msV(I1:+)

4.996V

4.998V

5.000V

5.002V

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An example of a Buck circuit is the Texas Instruments LMR36006, a 4.2-60V input 1-28V/600mA output synchronous Buck converter that operates at 1 or 2.1MHz.

Typical application

Block diagram

Note: the diode is replaced by a MOSFET and both MOSFETs are integrated in the converter.

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The transfer function for the Buck circuit is

LC

d

LCs

L

r

RCs

rCs

sV

sVsF

i

o

~

2 111

where r is the equivalent series resistance (ESR) of the capacitor and ~

d is the

small-signal duty cycle perturbation [ tdDtd~

]. The equations that describe the operation of the Buck converter in CCM are:

outFETinLHi VVVV outDLLo VVV

o

oooL V

P

R

VII

L

tVVI offDout

L

LLL IIi

LoLC IIii

where LI is the inductor ripple current. The equations for the Buck converter at the edge of CCM and DCM are:

2

12

12

offLs

L

s

Lc

tRDT

RD

f

RL

offs

scL t

L

DT

L

D

LfR

2

1

2

1

2

where (c) stands for critical.

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Buck converter (DCM) This specific example shows a non-synchronous Buck converter in DCM operation. The average current going to the load is 400mA. The peak current through the inductor at 12V is 900mA. Since half of the ripple or 450mA is greater than 400mA, the inductor current will eventually reach zero. This is an instance of light load condition.

Buck converter (DCM)

Ideally, ∙ ∙ ∙ ∙

∙


Transient waveforms for DCM

This converter has an input of 12V and an output of 5V at 400mA. The MOSFET is modeled with the following parameters: W=0.92 L=2μ.

C2

66uF

L1

6uH

1 2

0 0 00

I1

400mAdc

V2

TD = 1ns


V1 = 0V

TR = 10ns

V2 = 10V

0

C1

30uF

R1

5m

R2

15m

V1

TD = 1ns


V1 = 0V

TR = 1ms

V2 = 12VD1

MBR1035

V

V

I

I

I

V-V+VV-

V+

I

I

M1M2N6796

R3

2m

Time

0s 0.5ms 1.0ms 1.5ms 2.0ms 2.5ms 3.0ms 3.5ms 4.0ms 4.5ms 5.0msV(V1:+) V(C2:2)

0V

5V

10V

13V

Time

4.9960ms 4.9964ms 4.9968ms 4.9972ms 4.9976ms 4.9980ms 4.9984ms 4.9988ms 4.9992ms 4.9996ms 5.0000msID(M1) I(D1) I(L1) -I(C2) I(I1)

-0.5A

0A

0.5A

1.0A

SEL>>

V(V1:+) V(I1:+) V(M1:g,M1:s) V(M1:s) V(M1:s,L1:2)-10V

0V

10V

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Note: decreasing the value of the load current will decrease the inductor current and if the ripple current through the inductor is large enough, during the off-time, the inductor current will reach zero and the converter will operate in DCM. Since the circuit operates in DCM, the current through the inductor will go to zero during the off-time as shown below:

Inductor ripple current


Time


0A

0.5A

1.0A

Time

4.9960ms 4.9964ms 4.9968ms 4.9972ms 4.9976ms 4.9980ms 4.9984ms 4.9988ms 4.9992ms 4.9996ms 5.0000msV(I1:+)

4.996V

4.998V

5.000V

5.002V

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Buck converter in DCM states

On-time state

During the on-time the MOSFET is on and the diode is off.

Off-time state with inductor current

During the off-time the MOSFET is off and the diode is on.

Off-time state with no inductor current

During the off-time the current in the inductor will reach zero and the circuit will reduce to an RC circuit.

C2

66uF

L1

6uH

1 2

0 0 0 0

I1

400mAdc

V2

TD = 1ns


V1 = 0V

TR = 10ns

V2 = 10V

0

C1

30uF

R1

5m

R2

15m

V1

TD = 1ns


V1 = 0V

TR = 1ms

V2 = 12V

M1M2N6796

R3

2m

C2

66uF

L1

6uH

1 2

0 0 00

I1

400mAdc

V2

TD = 1ns


V1 = 0V

TR = 10ns

V2 = 10V

0

C1

30uF

R1

5m

R2

15m

V1

TD = 1ns


V1 = 0V

TR = 1ms

V2 = 12VD1

MBR1035R3

2m

C2

66uF

0 0 0 0

I1

400mAdc

V2

TD = 1ns


V1 = 0V

TR = 10ns

V2 = 10V

0

C1

30uF

R1

5m

V1

TD = 1ns


V1 = 0V

TR = 1ms

V2 = 12V

R3

2m

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Boost converter This circuit converts a DC voltage from a lower level to a higher level. It is generally used for applications that require up to 5000W.

Boost converter

Ideally, out

in

V

VD 1



This converter has an input of 12V and an output of 24V. The output current is 3A so the output power is 72W. The MOSFET is modeled with the following parameters: W=.7 L=2µ.

C2

47uF

L1

6uH

1 2

0 0 000

R3

1m

D1

MBR1045

M1

IRF121V2

TD = 1ns

TF = 10nsPW = 1.100usPER = 2us

V1 = 0V

TR = 10ns

V2 = 10V

I1

3Adc

V1

TD = 1ns


V1 = 0V

TR = 2ms

V2 = 12V

R2

15m V VV V-V+

V

I

I

I

I

C1

15uF

0

R1

10m

Time

0s 0.5ms 1.0ms 1.5ms 2.0ms 2.5ms 3.0ms 3.5ms 4.0ms 4.5ms 5.0msV(C1:2) V(D1:2)

0V

10V

20V

25V

Time

4.9950ms 4.9955ms 4.9960ms 4.9965ms 4.9970ms 4.9975ms 4.9980ms 4.9985ms 4.9990ms 4.9995ms 5.0000msI(L1) ID(M1) I(D1) -I(C2)

0A

5.0A

-6.0ASEL>>

V(V1:+) V(C2:2) V(M1:g) V(V1:+,R2:2) V(M1:d)-20V

0V

20V

31 www.ice77.net

Boost converter states

On-time state


Off-time state


C2

47uF

L1

6uH

1 2

0 0 0 00

R3

1m

M1

IRF121V2

TD = 1ns


V1 = 0V

TR = 10ns

V2 = 10V

I1

3Adc

V1

TD = 1ns


V1 = 0V

TR = 2ms

V2 = 12V

R2

15m

0

C1

15uF

R1

10m

C2

47uF

L1

6uH

1 2

0 0 000

R3

1m

D1

MBR1045

V2

TD = 1ns


V1 = 0V

TR = 10ns

V2 = 10V

I1

3Adc

V1

TD = 1ns


V1 = 0V

TR = 2ms

V2 = 12V

R2

15m

C1

15uF

0

R1

10m

32 www.ice77.net

The specifications for the Boost converter in CCM are the followings:


500 mVVout 240%1 ∆ 40% mR ONDS 240)(

89% The output power is:

∙ 24 ∙ 3 72 The current through the inductor is the sum of the input current through the MOSFET and the output current through the diode. The average input current is:

∙

7212 ∙ 0.89

6.742

Therefore, the ripple current through the inductor will be as follows: ∆ 40% ∙ 0.4 ∙ 6.742 2.697 The IRF121 MOSFET has an RDS(ON) of 240mΩ and an average of 6.742A will flow through it during the on-time so the voltage drop across the device is:

∙ 6.742 ∙ 240 1.618 The duty cycle is:

1 1 . 0.567 1 1 0.567 0.433

The period is:

1 1500

2

On-time and off- time are:

0.567 ∙ 2 1.135 1 ∙ 0.433 ∙ 2 865

33 www.ice77.net

The inductance is calculated at high line which is when the voltage across the MOSFET is largest, the duty cycle is smallest and the on-time is smallest:

14 1.618 12.382

1 1.

0.484 1 1 0.484 0.516

∙ 0.484 ∙ 2 968

∙ ∙

∆ % ∙ ∙0.89 ∙ 14 ∙ 0.4840.4 ∙ 500 ∙ 72

5.864 → 6

The load resistance is:

.8

3

7222 A

W

I

PR

out

outL or

8

72

24 22

W

V

P

VR

out

outL

The minimum output capacitance is calculated at low line:

10 1.618 8.382

1 1.

0.651 1 1 0.651 0.349

∙ 0.651 ∙ 2 1.302

∙∙ ∆

3 ∙ 0.651500 ∙ 240

16.269 → 47

The corner frequency of the LC output filter is given by:

1

2 ∙

0.433

2 6 ∙ 474.1

34 www.ice77.net


∆∙ ∆ ∙ 14 1.618 ∙ 968

61.998

The peak current through MOSFET, inductor and diode is given by:

12∆

∙12∆

7210 ∙ 0.89

121.998 9.089


The maximum RMS output ripple current through the capacitor has a trapezoidal shape:

13

0.6510.349

4.095

Therefore, a capacitor with an RMS current rating of at least 4.095A must be selected (the high current figure may imply that two or more parallel capacitors could be used).

Time


6.0A

7.0A

8.0A

5.5A

8.5A

35 www.ice77.net

The output ripple voltage is a combination of two terms: ∆ ∆ ∆ The first term is produced by the capacitive component of the output capacitor:

∆1 1

473 ∙ 0.651 ∙ 2 83.1

Note: this means that increasing capacitance will reduce the output ripple voltage. The second term is produced by the resistive component of the output capacitor (ESR):

∆1

12∆ ∙

30.349

12∙ 1.998 ∙ 1 9.59

Combining the terms gives the total output ripple voltage: ∆ ∆ ∆ 83.1 9.59 92.7 Either one of the two terms above can dominate over the other. If ∆ dominates over ESRV the output will look triangular.

If ESRV dominates over ∆ the output will look trapezoidal.


Note: in this case ∆ dominates over ESRV so the output looks triangular.

The implementation of the Boost converter shown above features a MOSFET and a diode. A more commonly used implementation is the so-called synchronous Boost converter topology which replaces the diode with an n-type MOSFET. 2 MOSFETs make the circuit synchronous.

Time

4.9950ms 4.9955ms 4.9960ms 4.9965ms 4.9970ms 4.9975ms 4.9980ms 4.9985ms 4.9990ms 4.9995ms 5.0000msV(D1:2)

23.95V

24.00V

24.05V

36 www.ice77.net

An example of a Boost circuit is the Monolithic Power Systems MP3418, a 0.6-4V input 1.8-4V/400mA output synchronous Boost converter that operates at 1.2MHz.

Typical application

Block diagram

Note: the diode is replaced by a MOSFET and both MOSFETs are integrated in the converter.

37 www.ice77.net

The transfer function for the Boost circuit is

~

2

2 1

1

11

1d

D

sR

L

CLCL

sL

r

RCs

rCs

sV

sVsF

e

eee

i

o

where 21 D

LLe

The equations that describe the operation of the Boost converter in CCM are:

FETinLHi VVV DoutinLLo VVVV

o

oooL V

P

R

VII

L

tVVVI offinDout

L

LLL IIi

oLCHi Iii oCLo Ii

The equations for the Boost converter at the edge of CCM and DCM are:

2

1

2

1

2

1 222onLsL

s

Lc

tDRDDTR

f

DDRL

ons

scL

tD

L

DDT

L

DD

LfR

222 1

2

1

2

1

2

38 www.ice77.net

Inverting Buck-Boost converter This circuit converts a DC voltage to either a lower level or a higher level. It is generally used for applications that require up to 150W. This specific example shows CCM operation in Buck mode (output voltage is lower than input voltage).

Inverting Buck-Boost converter in Buck mode

Ideally, inout

out

VV

VD


Transient waveforms for CCM in Buck mode

This converter has an input of 14V and an output of -12V. The output current is 3A so the output power is 36W. Note: the polarity at the output is opposite to the one at the input.The MOSFET is modeled with the following parameters: W=.97 L=2μ.

C2

68uF

0 0 0

I1

3AdcL1

60uH

1

2

V2TD = 1ns


V1 = 0V

TR = 10ns

V2 = 14VV1

TD = 1ns


V1 = 0V

TR = 2ms

V2 = 14V

R31m

0

M1IRF132

D1

MBR1035V V

V+

V- V

I

I

I

I

C1

100uF

0

R11m

R210m

Time

0s 1ms 2ms 3ms 4ms 5ms 6ms 7ms 8ms 9ms 10ms 11ms 12ms 13ms 14ms 15msV(V1:+) V(C2:2)

-10V

0V

10V

-15V

15V

Time

14.990ms 14.991ms 14.992ms 14.993ms 14.994ms 14.995ms 14.996ms 14.997ms 14.998ms 14.999ms 15.000msID(M1) I(L1) I(D1) I(C2)

-5A

0A

5A

10A

SEL>>

V(V1:+) V(C2:2) V(M1:g,M1:s) V(M1:s)-20V

0V

20V

39 www.ice77.net

Inverting Buck-Boost converter states

On-time state


Off-time state


C2

68uF

0 0 0

I1

3AdcL1

60uH

1

2

V2TD = 1ns


V1 = 0V

TR = 10ns

V2 = 14VV1

TD = 1ns


V1 = 0V

TR = 2ms

V2 = 14V

R31m

0

M1IRF132

C1

100uF

R11m

0

R210m

C2

68uF

0 0 0

I1

3AdcL1

60uH

1

2

V2TD = 1ns


V1 = 0V

TR = 10ns

V2 = 14VV1

TD = 1ns


V1 = 0V

TR = 2ms

V2 = 14V

R31m

0

D1

MBR1035C1

100uF

0

R11m

R210m

40 www.ice77.net

The specifications for the inverting Buck-Boost converter in CCM in Buck mode are the followings:

VVin 14(max) VVout 12 AIout 3 VVD 42.0

kHzf s 200 mVVout 120%1 ∆ 10% mR ONDS 160)(

%96 The output power is:

WAVIVP outoutout 36312

The current through the inductor is the sum of the input current through the MOSFET and the output current through the diode. The average current through MOSFET and inductor during the on-time is:

∙36

14 ∙ 0.963 5.679

The IRF132 MOSFET has an RDS(ON) of 160mΩ and an average of 5.679A will flow through it during the on-time so the voltage drop across the device is:

mVmARIV ONDSaveLFET 909160679.5)()(

The minimum duty cycle is:

478.09091412

12

(max)min

mVVV

V

VVV

VD

FETinout

out

522.0478.011 min D


∙ 5.679 ∙ 0.478 2.716 The period is:

skHzf

Ts

s 5200

11


ssTDt son 391.25478.0min(min) ssTDt soff 609.25522.01 min(max)

41 www.ice77.net

The minimum inductance is calculated at high line which is when the voltage across the MOSFET is largest, the duty cycle is smallest and the on-time is smallest:

∙ ∙

∆ % ∙ ∙ ∙ | | ∙ | |

0.96 ∙ 14 ∙ 12

0.1 ∙ 200 ∙ 36 ∙ 14 12 0.96 ∙ 14 12

56.894 → 60 The load resistance is:

4

3

3622 A

W

I

PR

out

outL or

4

36

12 22

W

V

P

VR

out

outL

The minimum output capacitance at high line is given by:

| | ∙

∙ ∆12 ∙ 2.3914 ∙ 120

59.781 → 68

The corner frequency of the LC output filter is given by:

1

2 ∙

0.522

2 60 ∙ 681.3

42 www.ice77.net


∆∙ ∆ | | ∙ 14 0.42 ∙ 2.609

60540

The current through the inductor is the sum of the input current through the MOSFET and the output current through the diode. The peak current through MOSFET, inductor and diode is given by:

12∆

∙12∆

∙ .

3 540 5.949


The RMS output ripple current through the capacitor has a trapezoidal shape:

13

0.4780.522

2.872


Time


5.6A

5.8A

6.0A

6.2A

43 www.ice77.net


∆1 1

683 ∙ 0.478 ∙ 5 105.5


∆1

12∙ ∆ ∙

30.522

12∙ 540 ∙ 1 6

Combining the terms gives the total output ripple voltage: ∆ ∆ ∆ 105.5 6 111.5 Either one of the two terms above can dominate over the other. If ∆ dominates over ESRV the output will look triangular.




Time

14.990ms 14.991ms 14.992ms 14.993ms 14.994ms 14.995ms 14.996ms 14.997ms 14.998ms 14.999ms 15.000msV(C2:2)

-12.08V

-12.04V

-12.00V

-11.96V

-11.92V

44 www.ice77.net

This specific example shows CCM operation in Boost mode (output voltage is higher than input voltage).

Inverting Buck-Boost converter in Boost mode

Ideally, inout

out

VV

VD


Transient waveforms for CCM in Boost Mode

This converter has an input of 10V and an output of -12V. The output current is 3A so the output power is 36W. Note: the polarity at the output is opposite to the one at the input. The MOSFET is modeled with the following parameters: W=.97 L=2μ.

R510m

V+

VV

I

I

I

I

VV-

V3

TD = 1ns


V1 = 0V

TR = 2ms

V2 = 10V

M2IRF132

D2

MBR1035 C4

80uF

00 0

I2

3AdcL2

45uH

1

2

C3

100uF

V4TD = 1ns


V1 = 0V

TR = 10ns

V2 = 10V

R41m

0

R61m

0

Time

0s 1ms 2ms 3ms 4ms 5ms 6ms 7ms 8ms 9ms 10ms 11ms 12ms 13ms 14ms 15msV(V3:+) V(C4:2)

-10V

0V

10V

-15V

15V

Time

14.990ms 14.991ms 14.992ms 14.993ms 14.994ms 14.995ms 14.996ms 14.997ms 14.998ms 14.999ms 15.000msID(M2) I(L2) I(D2) I(C4)

-5A

0A

5A

10A

SEL>>

V(V3:+) V(C4:2) V(M2:g,M2:s) V(M2:s)-20V

0V

20V

45 www.ice77.net

The specifications for the inverting Buck-Boost converter in CCM in Boost mode are the followings:

VVin 10(min) VVout 12 AIout 3 VVD 42.0

kHzf s 200 mVVout 120%1 ∆ 10% mR ONDS 160)(



The current through the inductor is the sum of the input current through the MOSFET and the output current through the diode. The average current through MOSFET and inductor during the on-time is:

∙36

10 ∙ 0.963 6.75


VmARIV ONDSaveLFET 08.116075.6)()(

The maximum duty cycle is:

574.008.11012

12

(min)max

VVV

V

VVV

VD

FETinout

out

426.0574.011 max D


∙ 6.75 ∙ 0.574 3.782 The period is:

skHzf

Ts

s 5200

11


46 www.ice77.net

ssTDt son 868.25574.0max(max)

ssTDt soff 132.25426.01 max(min)

The minimum inductance at low line is given by:

∙ ∙

∆ % ∙ ∙ ∙ | | ∙ | |

0.96 ∙ 10 ∙ 12

0.1 ∙ 200 ∙ 36 ∙ 10 12 0.96 ∙ 10 12

40.404 → 45 The load resistance is:

4

3

3622 A

W

I

PR

out

outL or

4

36

12 22

W

V

P

VR

out

outL

The minimum output capacitance is calculated at low line which is when the voltage across the MOSFET is smallest, the duty cycle is greatest and the on-time is largest:

| | ∙

∙ ∆12 ∙ 2.8684 ∙ 120

71.702 → 80

The corner frequency of the LC output filter now is:

1

2 ∙

0.426

2 45 ∙ 801.131

47 www.ice77.net


∆∙ ∆ | | ∙ 12 0.42 ∙ 2.132

45588

The current through the inductor is the sum of the input current through the MOSFET and the output current through the diode. The peak current through MOSFET, inductor and diode is given by:

12∆

∙12∆

∙ .

3 588 7.044


The RMS output ripple current through the capacitor has a trapezoidal shape:

13

0.5740.426

3.48


Time


7.0A

7.2A

7.4A

7.6A

7.8A

48 www.ice77.net


∆1 1

803 ∙ 0.574 ∙ 5 107.6


∆1

12∙ ∆ ∙

30.426

12∙ 588 ∙ 1 7.3

Combining the terms gives the total output ripple voltage: ∆ ∆ ∆ 107.6 7.3 114.9 Either one of the two terms above can dominate over the other. If ∆ dominates over ESRV the output will look triangular.




Note: the inductance is calculated at high line whereas the capacitance at the output is calculated at low line. Note: the maximum ripple current through the inductor occurs at high line whereas the maximum ripple voltage at the output occurs at low line.

Time


-12.08V

-12.04V

-12.00V

-11.96V

-11.92V

49 www.ice77.net

Note: the circuit should use a 60µH inductor and 80µF of capacitance at the output to meet the requirements. This will reduce the maximum ripple current through the inductor from 588mA to 540mA at low line.

50 www.ice77.net

Inverting Buck-Boost converter (revisited) The Buck-Boost converter can be used to produce a negative voltage which is sometimes desirable and this can be accomplished by swapping the inductor and the diode voltage references of a Buck converter. This example shows an inverting Buck-Boost converter in CCM in Boost mode.

Inverting Buck-Boost converter

Ideally, inout

out

VV

VD



This converter has an input of 10V and an output of -12V. The output current is 3A so the output power is 36W. The MOSFET is modeled with the following parameters: W=0.92 L=2μ.

V-

V+

V

V

I

I

I

I

V-V+V

C2

80uF

L1

60uH

1 2

0

R2

10m

0

C1

100uF

R1

1m

V1

TD = 1ns


V1 = 0V

TR = 1ms

V2 = 10V

R3

1m

D1MBR1035

M1M2N6796

I1

3Adc

V2

TD = 1ns


V1 = 0V

TR = 10ns

V2 = 10V

0

Time

0s 0.5ms 1.0ms 1.5ms 2.0ms 2.5ms 3.0ms 3.5ms 4.0ms 4.5ms 5.0msV(C1:2) V(I1:-)

-10V

0V

10V

-15V

Time

4.988ms 4.989ms 4.990ms 4.991ms 4.992ms 4.993ms 4.994ms 4.995ms 4.996ms 4.997ms 4.998msID(M1) I(D1) I(L1) -I(C2)

-5.0A

0A

5.0A

V(C1:2) V(I1:-) V(M1:g,L1:1) V(L1:1) V(L1:1,L1:2)

0V

10V

-14VSEL>>

51 www.ice77.net

Swapping the voltage references between output and ground for a Buck converter produces the inverting Buck-Boost converter.

Buck converter

Inverting Buck-Boost converter (A)

Inverting Buck-Boost converter (B)

The inverting Buck-Boost converter discussed here is essentially the same inverting Buck-Boost converter previously presented. A is just a redrawn and equivalent version of B (note the inductor and diode are swapped just like ground and output current direction).

C2

66uF

L1

6uH

1 2

0 0 00

R2

15m

C1

30uF

0

R1

5m

V1

TD = 1ns


V1 = 0V

TR = 1ms

V2 = 12V

R3

2m

D1MBR1035

M1M2N6796

I1

3Adc

V2

TD = 1ns


V1 = 0V

TR = 10ns

V2 = 10V

V-

V+

VV

I

I

I

I

V-V+V

V-

V+

V

V

I

I

I

I

V-V+V

C2

80uF

L1

60uH

1 2

0

R2

10m

0

C1

100uF

R1

1m

V1

TD = 1ns


V1 = 0V

TR = 1ms

V2 = 10V

R3

1m

D1MBR1035

M1M2N6796

I1

3Adc

V2

TD = 1ns


V1 = 0V

TR = 10ns

V2 = 10V

0

R510m

V+

VV

I

I

I

I

VV-

V3

TD = 1ns


V1 = 0V

TR = 2ms

V2 = 10V

M2IRF132

D2

MBR1035 C4

80uF

00 0

I2

3AdcL2

45uH

1

2

C3

100uF

V4TD = 1ns


V1 = 0V

TR = 10ns

V2 = 10V

R41m

0

R61m

0

52 www.ice77.net

Inverting Buck-Boost converter states (revisited)

On-time state


Off-time state


C2

80uF

0

L1

60uH

1 2

R2

10m

0

C1

100uF

R1

1m

V1

TD = 1ns


V1 = 0V

TR = 1ms

V2 = 10V

R3

1m

M1M2N6796

I1

3Adc

V2

TD = 1ns


V1 = 0V

TR = 10ns

V2 = 10V

0

C2

80uF

L1

60uH

1 2

0

R2

10m

0

C1

100uF

R1

1m

V1

TD = 1ns


V1 = 0V

TR = 1ms

V2 = 10V

R3

1m

D1MBR1035

I1

3Adc

V2

TD = 1ns


V1 = 0V

TR = 10ns

V2 = 10V

0

53 www.ice77.net

The design procedure for this circuit is identical to the one previously presented.

Inductor ripple current


Time


7.0A

7.2A

7.4A

7.6A

Time

4.988ms 4.989ms 4.990ms 4.991ms 4.992ms 4.993ms 4.994ms 4.995ms 4.996ms 4.997ms 4.998msV(I1:-)

-12.08V

-12.04V

-12.00V

-11.96V

-11.92V

54 www.ice77.net

An example of an inverting Buck-Boost circuit is the Analog Devices ADP5074, a 2.8-15V input (Vin-39V)/2.4A output synchronous inverting Buck-Boost converter that operates at 1.2MHz or 2.4MHz.

Typical application

Block diagram

Note: the MOSFET is integrated in the converter.

55 www.ice77.net

The transfer function for the inverting Buck-Boost circuit is

~

2

2 1

1

11

1d

D

sR

DL

CLCL

sL

r

RCs

rCs

sV

sVsF

e

eee

i

o

where 21 D

LLe

The equations for the Buck-Boost converter in CCM are as follows:

FETinLHi VVV DoutLLo VVV

o

ooo V

P

R

VI

L

tVVI offDout

L

LLL IIi

oLCHi Iii oCLo Ii

The equations for the Buck-Boost converter at the edge of CCM and DCM are:

2

1

2

1

2

1 22

)(offLLs

s

Lc

tRDRDT

f

RDL

offs

scL tD

L

DT

L

D

LfR

1

2

1

2

1

222

56 www.ice77.net

Non-inverting Buck-Boost converter The implementation of the inverting Buck-Boost converter features a polarity at the output that is opposite to the one at the input. The fact the MOSFET does not have a terminal ground complicates the PWM circuit that turns the transistor on and off and a DC offset is required.

A popular variant of the circuit with a slightly different implementation is the so-called non-inverting 4-switch Buck-Boost converter topology which replaces the diode with a MOSFET and introduces 2 more MOSFETs.

The 4 MOSFETs make the circuit synchronous. Also, the output of the circuit has the same polarity of the input because the current flows towards the output. The circuit, depending on the voltage and the input and the output operates in either Buck or Boost modes. In the Buck mode M4 is always on, M3 is always off and M1/M2 turn on alternately. The circuit is, effectively, a Buck converter (inductor connected to the output). In the Boost mode M1 is always on, M2 is always off and M3/M4 turn on alternately. The circuit is, effectively, a Boost converter (inductor connected to the input).

1

2

0

-+

1 2

0

+

0

+

M4

M3M2

M1

57 www.ice77.net

An example of a non-inverting Buck-Boost circuit is the Maxim Integrated MAX8625A, a 2.5-5.5V input 1.25-4V/800mA output synchronous Buck-Boost converter that operates at 1MHz.

Typical application

Block diagram

Note: the MOSFETs are integrated in the converter. In the Buck mode P2 is always on, N2 is always off and P1/N1 turn on alternately. The circuit is a Buck converter (inductor connected to the output). In the Boost mode P1 is always on, N1 is always off and P2/N2 turn on alternately. The circuit is a Boost converter (inductor connected to the input).

58 www.ice77.net

Ćuk converter The Ćuk converter is named after Slobodan Ćuk of the California Institute of Technology who first presented the circuit in 1976. This converter has the same transfer function of the Buck-Boost converter as well as opposite polarity for input and output. This circuit can also provide an output voltage higher or lower than the input. Unlike the previous converters, this one features two inductors and an additional capacitor between them. The inductors are not coupled in this example.

Ćuk converter

Ideally, inout

out

VV

VD



C3

100uF

L1

83uH

1 2

0 0 00

M1

IRFR012

L2

35uH

1 2

D1

SD41

C2

4.7uF

0

I1

3Adc

V+

I

V

I

V

VV-V+VVV-

I

I

I

I

I

V2

TD = 1ns


V1 = 0V

TR = 10ns

V2 = 10V

V1

TD = 1ns


V1 = 0V

TR = 1ms

V2 = 12V

R2

15m

R3

1m

R4

10m

R51m

C1

100uF

0

R11m

0

Time

0s 0.2ms 0.4ms 0.6ms 0.8ms 1.0ms 1.2ms 1.4ms 1.6ms 1.8ms 2.0msV(R4:2)

-2.5V

0V

-6.0VSEL>>

V(V1:+)0V

5V

10V

15V

Time

9.990ms 9.991ms 9.992ms 9.993ms 9.994ms 9.995ms 9.996ms 9.997ms 9.998ms 9.999ms 10.000ms-I(C1) I(L1) ID(M1) -I(C2) I(D1) -I(L2) I(C3)

-5.0A

0A

5.0A

SEL>>

V(V1:+) V(I1:-) V(V2:+) V(V1:+,R2:1) V(M1:d) V(D1:1) V(D1:1,L2:2)

-20V

0V

20V

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Unlike the Buck converter, the Ćuk converter is lighter because instead of having one bulky inductor, it has two smaller inductors. If the inductors are coupled, the amount of inductance will be halved. The ripple voltage across the coupling capacitor is proportional to the input voltage. A capacitance that yields about a 10% ripple voltage is typical. This converter has an input of 12V and an output of -5V (inverted Buck mode). The output current is 3A so the output power is 15W. Note: the polarity at the output is opposite to the one at the input. The MOSFET is modeled with the following parameters: W=900µ L=45n.

Inductor ripple currents


Time

9.980ms 9.982ms 9.984ms 9.986ms 9.988ms 9.990ms 9.992ms 9.994ms 9.996ms 9.998ms 10.000msI(L1) I(L2)

2.0A

2.5A

3.0A

3.5A

Time

9.980ms 9.982ms 9.984ms 9.986ms 9.988ms 9.990ms 9.992ms 9.994ms 9.996ms 9.998ms 10.000msV(I1:-)

-5.002V

-5.001V

-5.000V

-4.999V

-4.998V

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Ćuk converter states

On-time state

During the on-time the MOSFET is on and the diode is off. The current through the MOSFET is the sum of the currents through the inductors.

Off-time state

During the off-time the MOSFET is off and the diode is on. The current through the diode is the sum of the currents through the inductors.

C3

100uF

L1

83uH

1 2

0 0 00

M1

IRFR012

L2

35uH

1 2C2

4.7uF

0

I1

3AdcV2

TD = 1ns


V1 = 0V

TR = 10ns

V2 = 10V

V1

TD = 1ns


V1 = 0V

TR = 1ms

V2 = 12V

R2

15m

R3

1m

R4

10m

R51m

C1

100uF

0

R11m

0

C3

100uF

L1

83uH

1 2

0 0 00

L2

35uH

1 2

D1

SD41

C2

4.7uF

0

I1

3AdcV2

TD = 1ns


V1 = 0V

TR = 10ns

V2 = 10V

V1

TD = 1ns


V1 = 0V

TR = 1ms

V2 = 12V

R2

15m

R3

1m

R4

10m

R51m

C1

100uF

0

R11m

0

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An example of a Ćuk circuit is the Linear Technology LTM8045, a 2.8-18V input -2.5V to -15V/700mA output Ćuk micromodule that operates between 200kHz and 2MHz.

Typical application

Block diagram

Note: most of the components are inside the micromodule which can be configured to work like a SEPIC circuit.

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SEPIC SEPIC stands for Single-Ended Primary Inductor Converter. This circuit looks very much like the Ćuk converter because it’s derived from it. The main differences between the two circuits is that D1 and L2 are swapped at their respective position so that the output for the SEPIC is no longer negative. This circuit can also provide an output voltage higher or lower than the input. The inductors are not coupled in this example.

SEPIC

Ideally, inout

out

VV

VD



C3

100uF

L1

83uH

1 2

0 0 00

D1

SD41

M1

IRFR012I1

3Adc

L2

35uH

1

2

C2

4.7uF

0

V2

TD = 1ns


V1 = 0V

TR = 10ns

V2 = 10V

V1

TD = 1ns


V1 = 0V

TR = 1ms

V2 = 12V

R2

15m

R3

1m

R410m

R51m

C1

100uF

0

R11m

V+

V

I

I

I

I

V VVV- VI

I

I

0

Time

0s 0.2ms 0.4ms 0.6ms 0.8ms 1.0ms 1.2ms 1.4ms 1.6ms 1.8ms 2.0msV(I1:+)

2.5V

5.0V

-1.0VSEL>>

V(V1:+)0V

5V

10V

15V

Time

1.990ms 1.991ms 1.992ms 1.993ms 1.994ms 1.995ms 1.996ms 1.997ms 1.998ms 1.999ms 2.000ms-I(C1) I(L1) ID(M1) -I(C2) -I(L2) I(D1) -I(C3)

0A

5.0A

-6.0ASEL>>

V(V1:+) V(I1:+) V(M1:g) V(V1:+,R2:1) V(M1:d) V(L2:1)

-10V

0V

10V

20V

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The positive polarity of the voltage at the output is generally desired so this circuit is more popular than the Ćuk converter. Unlike the Buck converter, the SEPIC is lighter because instead of having one bulky inductor, it has two smaller inductors. If the inductors are coupled, the amount of inductance will be halved. The ripple voltage across the coupling capacitor is proportional to the input voltage. A capacitance that yields about 10% ripple voltage is typical. This converter has an input of 12V and an output of +5V (Buck mode). The output current is 3A so the output power is 15W. Note: the polarity at the output is the same as the one at the input. The MOSFET is modeled with the following parameters: W=900µ L=45n.

Inductor ripple currents


Time

1.980ms 1.982ms 1.984ms 1.986ms 1.988ms 1.990ms 1.992ms 1.994ms 1.996ms 1.998ms 2.000msI(L1) I(L2)

2.0A

2.5A

3.0A

3.5A

Time


4.96V

4.98V

5.00V

5.02V

5.04V

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SEPIC converter states

On-time state

During the on-time the MOSFET is on and the diode is off. The current through the MOSFET is the sum of the currents through the inductors.

Off-time state

During the off-time the MOSFET is off and the diode is on. The current through the diode is the sum of the currents through the inductors.

C3

100uF

L1

83uH

1 2

0 0 00

M1

IRFR012I1

3Adc

L2

35uH

1

2

C2

4.7uF

0

V2

TD = 1ns


V1 = 0V

TR = 10ns

V2 = 10V

V1

TD = 1ns


V1 = 0V

TR = 1ms

V2 = 12V

R2

15m

R3

1m

R410m

R51m

0

C1

100uF

R11m

0

C3

100uF

L1

83uH

1 2

0 0 00

D1

SD41

I1

3Adc

L2

35uH

1

2

C2

4.7uF

0

V2

TD = 1ns


V1 = 0V

TR = 10ns

V2 = 10V

V1

TD = 1ns


V1 = 0V

TR = 1ms

V2 = 12V

R2

15m

R3

1m

R410m

R51m

C1

100uF

0

R11m

0

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An example of a SEPIC circuit is the Linear Technology LTM8049, a dual 2.6-20V input +2.5V to +24V/1A output SEPIC micromodule that operates between 200kHz and 2.5MHz.

Typical application

Block diagram

Note: most of the components are inside the micromodule which can be configured to work like a Ćuk circuit (as shown above where one output is +12V (SEPIC) and the other is -12V (Ćuk).

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Isolated topologies

Below are some of the most common isolated topologies:

Flyback

Forward (single switch)

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Push-pull

Half-bridge

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Full-bridge

The simulations for the circuits presented below imply steady-state condition and introduce soft-start for a smooth start-up. The isolated topologies include a transformer which allows to step up or step down the voltage from input to output. The efficiency of each circuit depends primarily on MOSFET, diode and inductor which lower overall efficiency so a proper choice of components is crucial. The current through the inductor has a DC component and an AC component. The DC component will go through the load and the AC component will go through the capacitor.

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Except for the Flyback converter, all the other converters are simulated with a Ferroxcube TN33/20/11 toroidal core made of 2P90 material with an inductance index of 87nH/T2. Coupling is non-linear.

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Flyback converter This circuit is a variation of the Buck-Boost converter. The input inductor is coupled with another inductor to form a power transformer which provides isolation and voltage level shift. At the same time the power transformer stores energy. The duty cycle is typically limited to less than 50%. This is done to ensure the energy stored on the primary side of the power transformer is discharged during the off-time. This circuit typically operates in DCM and it’s used for applications that require up to 250W.

Flyback converter

Ideally, ∙

∙


C2100uF

0

0

I1

3AdcR2

2m

V

V

I

I

I

V

VV

D1

DMBRB1645T4G

1 2

V2TD = 1ns


V1 = 0V

TR = 10ns

V2 = 10V

V1TD = 1ns

TF = 10nsPW = 10msPER = 20ms

V1 = 0V

TR = 1ms

V2 = 24V

C133uF

R1

10m

0

0

0

L1

3.5uH

L2

600nH

M1

IRF140

K K1

COUPLING = 0.99K_Linear

R3

20m

R4

5m

12 : 5

Time

0s 0.5ms 1.0ms 1.5ms 2.0ms 2.5ms 3.0ms 3.5ms 4.0ms 4.5ms 5.0msV(V1:+) V(D1:2)

0V

10V

20V

25V

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Transient waveforms for DCM

This converter has an input of 24V and an output of 5V. The output current is 3A so the output power is 15W. The MOSFET is modeled with the following parameters: W=.97 L=2µ.

Time

4.9960ms 4.9964ms 4.9968ms 4.9972ms 4.9976ms 4.9980ms 4.9984ms 4.9988ms 4.9992ms 4.9996ms 5.0000msID(M1) I(D1) -I(C2)

0A

10A

20AV(V1:+) V(I1:+) V(V2:+) V(R3:2) V(D1:1)

0V

25V

50V

SEL>>

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Flyback converter states

On-time state


Off-time state


C2100uF

0

0

I1

3AdcR2

2m

V2TD = 1ns


V1 = 0V

TR = 10ns

V2 = 10V

V1TD = 1ns


V1 = 0V

TR = 1ms

V2 = 24V

C133uF

R1

10m

0

0

0

L1

3.5uH

L2

600nH

M1

IRF140

K K1


R3

20m

R4

5m

12 : 5

C2100uF

0

0

I1

3AdcR2

2m

D1

DMBRB1645T4G

1 2

V2TD = 1ns


V1 = 0V

TR = 10ns

V2 = 10V

V1TD = 1ns


V1 = 0V

TR = 1ms

V2 = 24V

C133uF

R1

10m

0

0

0

L1

3.5uH

L2

600nH

K K1


R3

20m

R4

5m

12 : 5

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The specifications for the Flyback converter in DCM are the followings:


kHzfs 500 mVVout 50%1 mR ONDS 70)( 0.375



The input power is:

WWP

P outin 231.19

78.0

15

The inductance of the primary side of the transformer is calculated at low line:

∙

2 ∙ ∙22 ∙ 0.375

2 ∙ 500 ∙ 19.2313.3539 → 3.5

The turns ratio is defined as follows:

∙1

225 0.4

∙0.4

1 0.3752.444

A choice of Np=12 and Ns=5 is acceptable:

125

2.4 → 0.416

The inductance of the secondary side of the transformer is given by:

3.5 ∙ 0.416 607 → 600

The peak current on the primary side of the transformer is:

∙

∙22 ∙ 0.375

3.5 ∙ 5004.714

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The average current through the MOSFET during the on-time has a triangular shape and its average value is:

24.714

22.357


∙ 2.357 ∙ 70 165 The voltage across the primary side of the transformer at Vin=24V is:

24 165 23.835 The duty cycle is:

∙

∙

5 0.4 ∙ 2.45 0.4 ∙ 2.4 24 154

0.349

1 1 0.349 0.651 The average input current is given by:

∙ 2.357 ∙ 0.349 0.823 The period is:

1 1500

2


0.349 ∙ 2 698 1 ∙ 0.651 ∙ 2 1.302 The peak current on the secondary side of the transformer is:

4.714 ∙ 2.4 11.314

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The voltage across the primary side of the transformer at Vin=22V is:

22 165 21.835 The maximum duty cycle is:

∙

∙

5 0.4 ∙ 2.45 0.4 ∙ 2.4 22 165

0.369

1 1 0.369 0.631 Maximum on-time and minimum off-time are:

0.369 ∙ 2 737 1 ∙ 0.631 ∙ 2 1.262

The time it takes for the secondary side of the transformer to discharge is:

∙ 600 ∙ 11.3145 0.4

1.257

The sum of the maximum on-time and the time it takes for the transformer to discharge must be less than the period because the transformer must have time to fully discharge:

737 1.257 1.995 2

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Voltage spike and resonance at the drain of the MOSFET

At the beginning of the off-time the drain of the MOSFET sees a voltage spike of 61.7V and experiences resonance caused by the combination of leakage inductance of the transformer and the output capacitance of the MOSFET (red box). If the voltage spike at the drain of the MOSFET is near or above the drain-to-source rating of the MOSFET, an RC snubber can be placed across the MOSFET or an or RDC snubber can be placed across the primary side of the transformer. At the end of the off-time the drain of the MOSFET experiences resonance caused by the combination of the magnetizing inductance of the transformer and the output capacitance of the MOSFET (blue box). The current in the MOSFET increases linearly during the on-time. The current in the diode decreases linearly during the off-time. If the current spikes are not considered, the peaks in current in the MOSFET and the diode are directly related by the turns ratio of the transformer. The peaks occur when energy is transferred from the primary side to the secondary side of the transformer. Since the circuit operates in DCM, the current through the diode will go to zero during the off-time as shown below:

The current through the diode reaches zero during the off-time

Time

4.9960ms 4.9964ms 4.9968ms 4.9972ms 4.9976ms 4.9980ms 4.9984ms 4.9988ms 4.9992ms 4.9996ms 5.0000msV(V1:+) V(D1:2) V(V2:+) V(L1:2) V(D1:1)

0V

40V

-20V

70V

Time

4.9960ms 4.9964ms 4.9968ms 4.9972ms 4.9976ms 4.9980ms 4.9984ms 4.9988ms 4.9992ms 4.9996ms 5.0000msID(M1) I(D1) -I(C2)

0A

10A

20A

-5A

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∆∙∙

3 ∙ 0.369100 ∙ 500

22.1

Note: this means that increasing capacitance or switching frequency will reduce the output ripple voltage. The second term is produced by the resistive component of the output capacitor (ESR):

∆∙ 1 3 ∙ 0.631

29.5

Combining the terms gives the total output ripple voltage: ∆ ∆ ∆ 22.1 9.5 31.6


It is important to reduce the ESR on the output side because the leading edge of the output ripple voltage waveform will spike and, therefore, increase the overall output ripple voltage.

Time


4.98V

5.00V

5.02V

5.04V

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An example of a Flyback circuit is the Linear Technology LT3748, a 5-100V input Flyback controller.

Typical application

Block diagram

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Forward converter This circuit is a variation of the Buck converter. The introduction of a power transformer provides isolation and voltage level shift. The major difference between the Forward converter and the Flyback converter is that energy is not stored in the transformer but it’s passed on directly to the load (the word forward derives from this behavior). Another difference between the Forward and Flyback converters is one additional inductor and one additional diode. A few variants of the Forward converter exist. The one presented here is the so-called single-switch with resonant reset version which allows the power transformer to reset as the energy stored in the magnetizing inductance during the on-time dissipates during the off-time through the combination of the output capacitance of the MOSFET, the capacitance of the forward diode and any snubber capacitances in the circuit (sometimes added across MOSFET and secondary side of transformer). The advantages of the resonant reset variant of the Forward converter is that an additional dedicated reset winding for the power transformer and a diode on the primary side can be eliminated. This reduces the complexity of the power transformer, it lowers cost of the converter and the duty cycle for the circuit can exceed 50%. This circuit is used for applications that require up to 200W.

Ideally, ∙

Forward converter

TX1

TN33_20_11_2P90

L1_TURNS = 20L2_TURNS = 10

VV

I

I

V-V+VV

V

V

I

I

I

I

C2

100uF

00

V1TD = 1ns


V1 = 0V

TR = 1ms

V2 = 24VR5

5mR250m

R320m

34.8uH : 8.7uH

V2TD = 1ns


V1 = 0V

TR = 10ns

V2 = 10V

D1

MBR1045

D2

MBR1045

0

0

M1

IRF140

L1

6uH

1 2

R4

10m

I1

3Adc

C1

33uF

R1

10m

0

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This converter has an input of 24V and an output of 5V. The output current is 3A so the output power is 15W. The MOSFET is modeled with the following parameters: W=.97 L=2u.

Time

0s 0.2ms 0.4ms 0.6ms 0.8ms 1.0ms 1.2ms 1.4ms 1.6ms 1.8ms 2.0ms 2.2ms 2.4ms 2.6ms 2.8ms 3.0msV(TX1:1) V(C2:2)

0V

10V

20V

25V

Time

2.9960ms 2.9964ms 2.9968ms 2.9972ms 2.9976ms 2.9980ms 2.9984ms 2.9988ms 2.9992ms 2.9996ms 3.0000ms-I(C1) ID(M1) I(D1) I(D2) I(L1) -I(C2)

0A

2.0A

4.0AV(C1:2) V(R4:1) V(V2:+) V(R2:2) V(D1:1) V(L1:1) V(L1:1,L1:2)

0V

50V

100V

SEL>>

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Forward converter states

On-time state

During the on-time the MOSFET is on. The forward diode is on and the freewheeling diode is off.

Off-time state

During the off-time the MOSFET is off. The forward diode is off and the freewheeling diode is on. The circuit looks like a Buck converter during the off-time.

TX1

TN33_20_11_2P90


0

C2

100uF

0

V1TD = 1ns


V1 = 0V

TR = 1ms

V2 = 24VR5

5mR250m

R320m

34.8uH : 8.7uH

V2TD = 1ns


V1 = 0V

TR = 10ns

V2 = 10V

D1

MBR1045

0

0

M1

IRF140

L1

6uH

1 2

R4

10m

I1

3Adc

C1

33uF

R1

10m

0

TX1

TN33_20_11_2P90


C2

100uF

00

V1TD = 1ns


V1 = 0V

TR = 1ms

V2 = 24VR5

5mR250m

R320m

34.8uH : 8.7uH

V2TD = 1ns


V1 = 0V

TR = 10ns

V2 = 10V

D2

MBR1045

0

0

L1

6uH

1 2

R4

10m

I1

3Adc

C1

33uF

R1

10m

0

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The specifications for the Forward converter in CCM are the followings:


kHzfs 500 mVVout 50%1 ∆ 40% 1.2 mR ONDS 70)(

5.0max D 2/87 NnHAL pFCoss 550 pFCref 300 where Coss is the output capacitance of the MOSFET and Cref is the estimated capacitance across the secondary side reflected to the primary side. The turns ratio is defined as follows:

022.244.05

5.022max(min)

VV

V

VV

DV

N

N

Dout

in

s

p

5.02 p

s

s

p

N

N

N

N

The average current through the MOSFET is:

AAN

NII

p

soutavep 5.15.03)(


∙ 1.5 ∙ 70 105 The voltage across the primary side of the transformer at Vin=24V is:

VmVVVVV FETinp 895.2310524

The duty cycle is:

455.02895.23

44.05

V

VV

N

N

V

VVD

s

p

p

Dout 545.0455.011 D


∙ 1.5 ∙ 0.455 0.683

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The period is:

1 1500

2


nssDTt son 9112455.0 ssTDt soff 089.12545.01

The inductance is calculated at high line which is when the voltage across the MOSFET is largest, the duty cycle is smallest and the off-time is largest:

VmVVVVV FETinp 895.2510526(max)(max)

420.02895.25

44.05

(max)min

V

VV

N

N

V

VVD

s

p

p

Dout 580.0420.011 min D

ssTDt soff 160.12580.01 min(max)

∙ ∆∆

∙

∆5 0.44 ∙ 1.160

1.25.259 → 6

The maximum ripple current through the inductor happens with the maximum off-time:

∆∙ ∆ ∙ 5 0.44 ∙ 1.160

61.052

Np is chosen to be 20 and Ns is chosen to be 10. The inductance of the secondary side of the transformer is:

HN

nHNAL pLp 8.342087 2

22

The inductance of the primary side of the transformer is:

HN

nHNAL sLs 7.81087 2

22

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The peak current on the secondary side of the transformer is:

12∆ 3

121.052 3.526

The maximum ripple current through the inductor reflected to the primary side of the transformer is given by:

∆ ∆ ∙ 1.052 ∙ 0.5 526

The maximum ripple current on the primary side of the transformer is calculated at high line which is when the voltage across the MOSFET is largest, the duty cycle is smallest and the on-time is smallest:

nssTDt son 8402420.0min(min)

mAH

nsV

L

tVI

p

onppT 625

8.34

840895.25(min))(

Combining the ripple currents of inductor and transformer on the primary side of the transformer produces this: ∆ ∆ ∆ 526 625 1.151 The peak current through the MOSFET is given by:

∙∆2

3.526 ∙ 0.51.151

22.339

The RMS output ripple current through the capacitor has an inductive shape:

12

∆

3

∆

√12

1.052

√12304

Therefore, a capacitor with an RMS current rating of at least 304mA must be selected. Selecting a 100μF capacitor, the corner frequency of the LC output filter is:

1

2 ∙

1

2 6 ∙ 1006.497

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During the off-time the voltage at the drain of the MOSFET increases dramatically. The voltage at the anode of the forward diode does the same thing but in the opposite direction. This behavior is caused by the transfer of the energy stored in the magnetizing inductance of the transformer to the parasitic capacitances mentioned above. The transformer resets as its drain voltage goes back to the input voltage well before the end of the off-time as shown below:

The drain voltage of the MOSFET goes back to the input voltage (transformer reset)

During the off-time the MOSFET sees a voltage of 90.2V. The anode of the forward diode dips to -33.1V. The output capacitance of the IRF140 MOSFET is 550pF and the junction capacitance of the MBR1045 diode at 30V (reverse) is 275pF.

550 275 825 The maximum voltage at the drain is given by the sum of the maximum input voltage on the primary side of the transformer and the maximum resonant reset voltage:

∙

2 ∙

25.89525.895 ∙ 840

2 34.8 ∙ 82525.895 64.211 90.106

The reverse voltage at the anode of the forward diode is given by the voltage across the primary side to the secondary side of the transformer:

∙ 64.211 ∙ 0.5 32.106

If the voltage at the drain of the MOSFET is near or above the drain-to-source rating of the MOSFET, an RC snubber can be placed across the MOSFET or an RCD snubber can be placed across the primary side of the transformer.

Time

2.9960ms 2.9964ms 2.9968ms 2.9972ms 2.9976ms 2.9980ms 2.9984ms 2.9988ms 2.9992ms 2.9996ms 3.0000msV(V1:+) V(R4:1) V(V2:+) V(M1:d) V(D1:1) V(D2:2) V(D2:2,L1:2)

0V

50V

100V

-40V

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∆18∙∆

∙18∙

1.051100 ∙ 500

2.6

Note: this means that increasing capacitance or switching frequency will reduce the output ripple voltage. The second term is produced by the resistive component of the output capacitor (ESR): ∆ ∆ ∙ 1.051 ∙ 5 Ω 5.3 Combining the terms gives the total output ripple voltage: ∆ ∆ ∆ 2.6 5.3 7.9 Either one of the two terms above can dominate over the other. If ∆ dominates over ∆ the output will look sinusoidal. If ∆ dominates over ∆ the output will look triangular.


Note: in this case ∆ is smaller than ESRV so the output looks triangular.

Time


4.996V

4.998V

5.000V

5.002V

5.004V

87 www.ice77.net

An example of a Forward circuit is the Linear Technology LT8310, a 6-100V input Forward controller.

Typical application

Note that the forward diode is referenced to ground and placed at the bottom of the schematic in the opposite direction. When the diodes are replaced by MOSFETs they make the circuit synchronous and therefore more efficient. By placing the MOSFET on the low side of the power transformer both MOSFETs are referenced to ground and they are easier to drive (turn on and off).

Block diagram

88 www.ice77.net

Push-pull converter This circuit uses two switches which are typically implemented by MOSFETs. It also has two transformers. The secondary side of the transformer is center-tapped. This circuit is used for applications that require up to 1000W.

Push-pull converter

Ideally, s

p

in

out

N

N

V

VD

2

1


V

I

II

I

I

I

V

V V

V

V

I

D1

SD51

D2

SD51

Q1

RCX200N20

1

2

3

0

R1

1m

I1

20Adc

Q2

RCX200N20

1

2

3

R2

2m

0

0

C1

100uF

V2

TD = 1ns


V1 = 0V

TR = 10ns

V2 = 10V

0

L1

3uH

1 2

V1

TD = 1ns


V1 = 0V

TR = 1ms

V2 = 48V

0

V3

TD = 2.5us


V1 = 0V

TR = 10ns

V2 = 10V

TX1

XFRM_NONLIN/CT-PRI/SEC

LP1_TURNS = 32LP2_TURNS = 32LS1_TURNS = 20LS2_TURNS = 20RP_VALUE = 30mRS_VALUE = 50m

0

R3

1m

C2

100uF

0

0

0

Time

0s 0.2ms 0.4ms 0.6ms 0.8ms 1.0ms 1.2ms 1.4ms 1.6ms 1.8ms 2.0msV(V1:+) V(I1:+)

0V

20V

40V

50V

89 www.ice77.net

Transient waveforms

This converter has an input of 48V and an output of 24V. The output current is 20A so the output power is 480W. The MOSFET is modeled with the following parameters: W=1 L=2µ.

Time

1.990ms 1.991ms 1.992ms 1.993ms 1.994ms 1.995ms 1.996ms 1.997ms 1.998ms 1.999ms 2.000ms-I(C2) I(Q1:DRAIN) I(Q2:DRAIN) I(D1) I(D2) I(L1) -I(C1)

0A

10A

20A

SEL>>

V(V1:+) V(I1:+) V(Q1:GATE) V(Q2:GATE) V(Q1:DRAIN) V(Q2:DRAIN)

0V

50V

100V

90 www.ice77.net

Push-pull converter states

Push state

During the push state the Q2 MOSFET and the D2 diode are on. Meanwhile, the Q1 MOSFET and the D1 diode are off.

Dead-time state

D2

SD51

0

R1

1m

I1

20Adc

Q2

RCX200N20

12

3

R2

2m

0

0

C1

100uF

V2

TD = 1ns


V1 = 0V

TR = 10ns

V2 = 10V

0

L1

3uH

1 2

V1

TD = 1ns


V1 = 0V

TR = 1ms

V2 = 48V

0

V3

TD = 2.5us


V1 = 0V

TR = 10ns

V2 = 10V

TX1



0

R3

1m

C2

100uF

0

0

0

D1

SD51

D2

SD51

0

R1

1m

I1

20Adc

R2

2m

0

0

C1

100uF

V2

TD = 1ns


V1 = 0V

TR = 10ns

V2 = 10V

0

L1

3uH

1 2

V1

TD = 1ns


V1 = 0V

TR = 1ms

V2 = 48V

0

V3

TD = 2.5us


V1 = 0V

TR = 10ns

V2 = 10V

TX1



0

R3

1m

C2

100uF

0

0

0

91 www.ice77.net

During the dead time both MOSFETs are off. Both diodes are on and they share current.

Pull state

During the pull state the Q1 MOSFET is and the D1 diode are on. Meanwhile, the Q2 MOSFET and the D2 diode are off. The duty cycle is given by:

12

122448

3220

0.4

The period is:

sTkHzf ss 5200

Therefore, the on-time is:

0.4 ∙ 5 2

D1

SD51

Q1

RCX200N20

1

2

30

R1

1m

I1

20Adc

R2

2m

0

0

C1

100uF

V2

TD = 1ns


V1 = 0V

TR = 10ns

V2 = 10V

0

L1

3uH

1 2

V1

TD = 1ns


V1 = 0V

TR = 1ms

V2 = 48V

0

V3

TD = 2.5us


V1 = 0V

TR = 10ns

V2 = 10V

TX1



0

R3

1m

C2

100uF

0

0

0

92 www.ice77.net

Q1 and Q2 turn on alternately and there is a dead time between V2 and V3. When Q1 is on and Q2 is off, current flows through D1. When Q2 is on and Q1 is off, current flows through D2. When either of the diodes is on, it carries the entire load current which in this case is 10A (average). During the dead time both diodes carry current.

MOSFET gate signals (top) and inductor, diodes and capacitor currents (bottom)


Time

1.990ms 1.991ms 1.992ms 1.993ms 1.994ms 1.995ms 1.996ms 1.997ms 1.998ms 1.999ms 2.000msI(D1) I(D2) I(L1) -I(C1)

0A

10A

20A

SEL>>

V(Q1:GATE) V(V2:+)0V

5V

10V

Time


24.000V

24.005V

24.010V

24.015V

Q1/D1 on

dead time

Q2/D2 on

93 www.ice77.net

An example of a Push-Pull circuit is the Linear Technology LT3999, a 2.7-36V input Push-Pull converter.

Typical application

Block diagram

94 www.ice77.net

Half-bridge converter This circuit is used for applications that require up to 2000W.

Half-bridge converter

Ideally, s

p

in

out

N

N

V

VD


I1

30Adc

0

R1

1m

0

C3

100uF

0

V+

V

V

V

I

I

V-

V+

V-

V+

V-

I

I

I

I

L1

3uH

1 2

V1

TD = 1ns


V1 = 0V

TR = 1ms

V2 = 120V

0

R2

1m

R3

1m

R4

2m

TX1

XFRM_NONLIN/CT-SEC

LP_TURNS = 28

LS1_TURNS = 20

LS2_TURNS = 20

RP_VALUE = 50m

RS_VALUE = 80m

Q1RCX200N20

1

2

3

Q2RCX200N20

1

2

3

V2

TD = 0us


V1 = 0V

TR = 10ns

V2 = 10V

C2

100uF

C1

100uF

V3

TD = 2.5us


V1 = 0V

TR = 10ns

V2 = 10V

0

D1

SD51

D2

SD51

Time

0s 0.2ms 0.4ms 0.6ms 0.8ms 1.0ms 1.2ms 1.4ms 1.6ms 1.8ms 2.0msV(V1:+) V(C3:2)

0V

50V

100V

125V

95 www.ice77.net

Transient waveforms


Time

1.990ms 1.991ms 1.992ms 1.993ms 1.994ms 1.995ms 1.996ms 1.997ms 1.998ms 1.999ms 2.000msI(Q1:DRAIN) I(Q2:DRAIN) I(D1) I(D2) I(L1) -I(C3)

10A

20A

30A

-5ASEL>>

V(Q2:DRAIN) V(I1:+) V(Q1:GATE) V(Q2:GATE,Q1:DRAIN) V(Q1:DRAIN,0) V(Q2:DRAIN,Q1:DRAIN)

0V

50V

100V

96 www.ice77.net

Half-bridge converter states

First state

During the push state the Q2 MOSFET and the D2 diode are on. Meanwhile, the Q1 MOSFET and the D1 diode are off.

Dead-time state

During the dead time both MOSFETs are off. Both diodes are on and they share current.

I1

30Adc

0

R1

1m

0

C3

100uF

0

L1

3uH

1 2

V1

TD = 1ns


V1 = 0V

TR = 1ms

V2 = 120V

0

R2

1m

R3

1m

R4

2m

TX1

XFRM_NONLIN/CT-SEC

LP_TURNS = 28

LS1_TURNS = 20

LS2_TURNS = 20

RP_VALUE = 50m

RS_VALUE = 80m

Q2RCX200N20

1

2

3

V2

TD = 0us


V1 = 0V

TR = 10ns

V2 = 10V

C2

100uF

C1

100uF

V3

TD = 2.5us


V1 = 0V

TR = 10ns

V2 = 10V

0

D2

SD51

I1

30Adc

0

R1

1m

0

C3

100uF

0

L1

3uH

1 2

V1

TD = 1ns


V1 = 0V

TR = 1ms

V2 = 120V

0

R2

1m

R3

1m

R4

2m

TX1

XFRM_NONLIN/CT-SEC

LP_TURNS = 28

LS1_TURNS = 20

LS2_TURNS = 20

RP_VALUE = 50m

RS_VALUE = 80m

V2

TD = 0us


V1 = 0V

TR = 10ns

V2 = 10V

C2

100uF

C1

100uF

V3

TD = 2.5us


V1 = 0V

TR = 10ns

V2 = 10V

0

D1

SD51

D2

SD51

97 www.ice77.net

Third state

During the pull state the Q1 MOSFET and the D1 diode are on. Meanwhile, the Q2 MOSFET and the D2 diode are off. The duty cycle is given by:

36120

2820

0.42

The period is:

sTkHzf ss 5200


0.42 ∙ 5 2.1

I1

30Adc

0

R1

1m

0

C3

100uF

0

L1

3uH

1 2

V1

TD = 1ns


V1 = 0V

TR = 1ms

V2 = 120V

0

R2

1m

R3

1m

R4

2m

TX1

XFRM_NONLIN/CT-SEC

LP_TURNS = 28

LS1_TURNS = 20

LS2_TURNS = 20

RP_VALUE = 50m

RS_VALUE = 80m

Q1RCX200N20

1

2

3

V2

TD = 0us


V1 = 0V

TR = 10ns

V2 = 10V

C2

100uF

C1

100uF

V3

TD = 2.5us


V1 = 0V

TR = 10ns

V2 = 10V

0

D1

SD51

98 www.ice77.net

Q1 and Q2 turn on alternately and there is a dead time between V2 and V3. When Q1 is on Q2 is off and current flows through D1. When Q2 is on Q1 is off and current flows through D2. When either of the diodes is on, it carries the entire load current which in this case is 30A (average). During the dead time both diodes share current.



Time


10A

20A

30A

-5ASEL>>

V(Q1:GATE) V(Q2:GATE,V2:-)0V

5V

10V

Time


36.000V

36.004V

35.997V

36.006V

Q1/D1 on

dead time

Q2/D2 on

99 www.ice77.net

An example of a Half-Bridge circuit is the Vishay Siliconix Si9122A, a 28-75V input Half-Bridge controller.

Typical application

Block diagram

100 www.ice77.net

Full-bridge converter This circuit is used for applications that require up to 5000W.

Full-bridge converter

Ideally, s

p

in

out

N

N

V

VD

2

1


C2

100uF

R2

1m

0

TX1

XFRM_NONLIN/CT-SEC

LP_TURNS = 42LS1_TURNS = 21LS2_TURNS = 21RP_VALUE = 70mRS_VALUE = 100m

I1

40Adc

0

C1

100uF

0

L1

3uH

1 2

V5

TD = 1ns


V1 = 0V

TR = 10ns

V2 = 10V

Q4RCX200N20

1

2

3

V2

TD = 2.5us


V1 = 0V

TR = 10ns

V2 = 10V

0

Q1RCX200N20

1

2

3

D1

SD51

D2

SD51

V3

TD = 2.5us


V1 = 0V

TR = 10ns

V2 = 10V

Q2RCX200N20

1

2

3

0

V4

TD = 1ns


V1 = 0V

TR = 10ns

V2 = 10V

Q3RCX200N20

1

2

3

V1

TD = 1ns


V1 = 0V

TR = 1ms

V2 = 120V

0

R1

1m

R3

2m

V

V-

V+

V

V-

V+

V-

V+

V-

V+

V-

V+

I

I

I

I

I

V

V-

V+V

I

I

I

I

Time

0s 0.2ms 0.4ms 0.6ms 0.8ms 1.0ms 1.2ms 1.4ms 1.6ms 1.8ms 2.0msV(Q2:DRAIN) V(I1:+)

0V

50V

100V

125V

101 www.ice77.net

Transient waveforms


Time

1.990ms 1.991ms 1.992ms 1.993ms 1.994ms 1.995ms 1.996ms 1.997ms 1.998ms 1.999ms 2.000ms-I(C2) I(Q3:DRAIN) I(Q4:DRAIN) I(Q1:DRAIN) I(Q2:DRAIN) I(D1) I(D2) I(L1) -I(C1)

-10A

0A

10A

20A

30A

V(Q4:DRAIN) V(C1:2) V(Q3:GATE) V(Q4:GATE,V5:-) V(Q1:GATE) V(Q2:GATE,Q2:SOURCE) V(Q2:SOURCE,0) V(Q4:DRAIN,V5:-) V(V5:-,0)V(Q4:DRAIN,Q2:SOURCE)

50V

100V

-10VSEL>>

102 www.ice77.net

Full-bridge converter states

First state

During the first state the Q3/Q4 MOSFETs and the D2 diode are on. Meanwhile, the Q2/Q1 MOSFETs and the D1 diode are off.

Dead-time state

During the dead time all MOSFETs are off. Both diodes are on and they share current.

C2

100uF

R2

1m

0

TX1

XFRM_NONLIN/CT-SEC


I1

40Adc

0

C1

100uF

0

L1

3uH

1 2

V5

TD = 1ns


V1 = 0V

TR = 10ns

V2 = 10V

Q4RCX200N20

1

2

3

V2

TD = 2.5us


V1 = 0V

TR = 10ns

V2 = 10V

0

D2

SD51

V3

TD = 2.5us


V1 = 0V

TR = 10ns

V2 = 10V

0

V4

TD = 1ns


V1 = 0V

TR = 10ns

V2 = 10V

Q3RCX200N20

1

2

3

V1

TD = 1ns


V1 = 0V

TR = 1ms

V2 = 120V

0

R1

1m

R3

2m

C2

100uF

R2

1m

0

TX1

XFRM_NONLIN/CT-SEC


I1

40Adc

0

C1

100uF

0

L1

3uH

1 2

V5

TD = 1ns


V1 = 0V

TR = 10ns

V2 = 10V

V2

TD = 2.5us


V1 = 0V

TR = 10ns

V2 = 10V

0

D1

SD51

D2

SD51

V3

TD = 2.5us


V1 = 0V

TR = 10ns

V2 = 10V

0

V4

TD = 1ns


V1 = 0V

TR = 10ns

V2 = 10V

V1

TD = 1ns


V1 = 0V

TR = 1ms

V2 = 120V

0

R1

1m

R3

2m

103 www.ice77.net

Third state

During the last state the Q1/Q2 MOSFETs and the D1 diode are on. Meanwhile, the Q3/Q4 MOSFETs and the D2 diode are off. The duty cycle is given by:

12

1248120

4221

0.4

The period is:

sTkHzf ss 5200


0.4 ∙ 5 2

C2

100uF

R2

1m

0

TX1

XFRM_NONLIN/CT-SEC


I1

40Adc

0

C1

100uF

0

L1

3uH

1 2

V5

TD = 1ns


V1 = 0V

TR = 10ns

V2 = 10V

V2

TD = 2.5us


V1 = 0V

TR = 10ns

V2 = 10V

0

Q1RCX200N20

1

2

3

D1

SD51

V3

TD = 2.5us


V1 = 0V

TR = 10ns

V2 = 10V

Q2RCX200N20

1

2

3

0

V4

TD = 1ns


V1 = 0V

TR = 10ns

V2 = 10V

V1

TD = 1ns


V1 = 0V

TR = 1ms

V2 = 120V

0

R1

1m

R3

2m

104 www.ice77.net

Q1/Q4 and Q2/Q3 turn on alternately and there is a dead time between V2/V3 and V4/V5. When Q1/Q4 are on Q2/Q3 are off and current flows through D1. When Q2/Q3 are on Q1/Q4 are off and current flows through D2. When either of the diodes is on, they carry the entire load current which in this case is 40A (average). During the dead time both diodes carry current.



Time


25A

50A

-10ASEL>>

V(Q3:GATE) V(Q4:GATE,V5:-) V(Q1:GATE) V(V3:+,Q3:DRAIN)0V

5V

10V

Time


48.000V

48.010V

48.020V

48.025V

Q1/Q2/D1 on Q3/Q4/D2 on

dead time

105 www.ice77.net

An example of a Full-Bridge circuit is the Texas Instruments LM5045, a 14-100V input Full-Bridge controller.

Typical application

Block diagram

Documents

Switch-Mode Power Supplies - ICE77 · Switch-Mode Power Supplies Switch-Mode Power Supplies (SMPSs) are a family of power circuits designed to deliver power to a load by scaling voltage