Unwind di Power Electronics - 5 di 5

Buck-boost PFC and flyback converter

The buck-boost PFC full topology is the following: Remig Tg eLritti VoVOLTAGEPWM COMPENSATOR. Obviously, the output capacitor must be designed according to PFC theory so it must not filter out the switching harmonics but it has to filter out harmonics in order to exchange power with the rest of the circuit. In this model, there is no internal loop to regulate the Rem.

One disadvantage of this topology is that the buck-boost converter generates an inverted output voltage and sometimes it’s required some type of galvanic isolation between the load and the AC grid. For these reasons, it is not used the buck-boost converter but the isolated version of the buck-boost converter, the so-called flyback converter.

Flyback converter structure

In the flyback converter, the inductor is built around a magnetic core composed of a ferromagnetic material whose magnetic permeability is much larger than the magnetic permeability of the void:

Air gap: One thing needed when an inductor is built is an air gap, which is a region of the core where the core is interrupted, and the magnetic permeability of this air gap is similar to the magnetic permeability of the void. The reason why this air gap is needed is that the inductor needs to store magnetic energy, and to store magnetic energy it’s needed a region of space in which it can build a magnetic field, and this cannot be done with a solid core that saturates immediately and cannot store any significant magnetic energy.

The described model is the following:

• Inductor
• Air gap
• Core

In a flyback converter, the inductor is transformed into a mutual inductor just by adding a second winding, so the circuit becomes:

Vg e Vo. In this case, in the converter, there is a galvanic isolation between input and output which is very often required. Due to the fact that input and output sides are separated, some simplifications can be applied to the circuit. For example, the primary switch can now be referred to the ground and so moved below:

Mi MrVg Voe. Note that the right side of the circuit is just flipped upside-down.

The mutual inductor is called a mutual transformer, but it’s not a transformer because its purpose is to store and release magnetic energy in a periodic session, and this is not the behavior of a transformer because the behavior of a transformer is to be completely transparent to the electrical power, and in fact, a magnetic transformer doesn’t have air gaps while mutual transformers have.

The converter obtained acts like a buck-boost converter and, in particular, in DCM it behaves like a LFR so this topology can be used as a PFC. The flyback PFC converter topology is the following:

mi Ma Veviti VOLTAGEPWM COMPENSATOR. Note that a voltage is sensed at the secondary side to drive something at the primary side so some opto isolator must be used between the voltage compensator and the PWM. This type of PFC has some problems, one of which is that it must operate in DCM, and in this operating point, the current stresses are typically large, so the flyback converters are used for low power levels while topologies that behave in CCM (and with low current stresses) can be used also for high power levels. Another important problem of this topology is that there is a switch on the primary side, so the current at the primary side is discontinuous and this behavior increases the quantity of harmonics at the primary side.

Generating a sinusoid voltage using a half-bridge inverter

Let's see how to generate a sinusoid voltage using a half-bridge inverter:

LESSON #29

Vdc sa15Vdc si Usc2 02iot Vov 0152 15µVide2 52. The output voltage is:

tivVdc2 To t2 IoVdc To 2 2z Si0N5 OFF0Nsa52 OFF. This type of output is called square-wave modulation because the output voltage is exactly a square wave. It’s important to note that the output voltage frequency is equal to the frequency of the switches. If the output voltage must have a frequency f0, the switches must be opened and closed with a frequency f0:

f fas. This type of behavior presents some problems, first of all, the output voltage is not a sinusoid (no inverter can create a perfect output sinusoidal voltage) but more important there is some low-frequency distortion. The output voltage is a periodic function so it can be written in a Fourier expansion:

Not vqnsinkw.ttdieki. Where Vo,k is the amplitude of the k-th harmonic. As any square wave with duty-cycle equal to 50%, the output voltage contains only odd order harmonics:

• Kk VE0Va NEtiri ODDvento

The amplitude of the fundamental harmonic is Vo,1 and its expression is:

4 theVoi 2T. The fundamental harmonic is represented as follows:

tvolive2AVdc2 tVoxZlive2N. In general, the amplitude of the fundamental harmonic is larger (not so much) than the amplitude of the corresponding square-wave. The amplitude of the other harmonics is:

iVan Y. The amplitude of the successive harmonics decreases as 1/k. The spectrum of vo(t) is:

V ielive2A ffa fa fa fa fa fa7 953 ti. This type of inverter presents some advantages. First of all, it is very simple to implement, in fact, there are no modulators, the switches must be opened and closed in the right way to generate a square wave and the switching losses (losses proportional to the switching rate) are very low. Note that a distorted output is not always a disadvantage because if the goal is to heat up a resistor, a distorted output is perfect. The very big disadvantage of this topology is that the amplitude of the fundamental harmonic cannot be regulated as desired because it only depends on the DC voltage that can never be controlled, in fact, Vdc is usually a constant every time.

The application of square-wave modulation can be applied to a full-bridge inverter and it’s more useful:

IdcVac 5 52 io bce tvoVoc2 suSa. Note that the input DC voltage is usually not split. The represented split DC voltage is just a manipulation used to simplify the calculations. The generated output voltage is:

itvVdc To tVdc ToTo 2 252Si 54 53. Differently, from the half-bridge inverter, the output voltage is Vdc and the amplitudes of the first and of the other harmonics are:

4 iVoi Van Yvuoie. The fundamental harmonic is doubled too. It’s important to note that the full-bridge rectifier can create not only a perfect square wave but using its switches combination can also put to 0 the output voltage. Let’s use the node O as follows:

Idc Va VbNoVac 5 52 Nao Vb oio bce tVa vo2 suSatTaoVoc2 To tTo2Vox2 tIoVoc2 To tTo2Vox2 tvoVdc To tVdc. The two legs generate the output of a half-bridge rectifier but the second leg generates a shifted output voltage. This shift is indicated with alpha. The corresponding time interval (the corresponding time delay) is:

LL Wo. The output voltage is a three-level waveform and can be seen as the superposition of the two output voltages produced by the two legs that sometimes cancel out each other. A first advantage of this behavior is that the output voltage can be modulated using the control variable alpha that can change the shape of vo(t). In fact, the fundamental harmonic of the output voltage is a function of alpha. Let’s use the following definitions:

leia tiii. The voltages vao1(theta) and vbo1(theta) are the first-order sinusoids of the square waves generated by the two legs of the full-bridge inverter. In order to calculate the first-order sinusoid of the output voltage, it can be just done by the difference between the two expressions:

V lla Q a 0toTaoNo dsin 5inV 0 0 dsin sinV 0 0sin sin E4 44 4X X5in 5intVI tVa 44 44t Cossin sin sin sinCos Cos Cos2Il 40 0sin sin2 cos cosVI a. Clearly, the output voltage is a function of alpha. If alpha becomes 0, the amplitude of the output voltage is maximum and equal to Vdc, while if alpha becomes equal to pi, the two square waves are one the opposite of the other and their superposition generates a constant 0 waveform, so the output voltage is every time 0.

Let’s sketch the behavior of the fundamental harmonic as a function of alpha:

dVoi l4 ti 2. The output voltage can so be controlled. If the operation of control is not very important but it’s important to reduce the Total Harmonic Distortion (THD), the best alpha is more or less of 46°: 46I EL 29vThisThis result is a little bit better than the THD of a pure square wave that is: I 487l'Ha.

Pulse Width Modulation (PWM) inverters

Let’s see now the class of Pulse Width Modulation (PWM) inverters. These topologies generate a very clean output voltage (there is a very low low-frequency distortion) and give the opportunity to control the output voltage. The used topologies are the following:

Vide µSi2e eioNotVdc Vr2 52 èOSCILLATORf fas. In the PWM topologies, there is obviously a pulse width modulator that uses a symmetric carrier so not a saw-tooth signal but a purely triangular waveform. It’s important to note that the behavior of the PWM is not real because usually, it’s used a dead-time between the commutations of c(t) and c’(t) in order to be sure that the switch is completely off before turning on the successive switch. Some block is used to generate this dead-time. The carrier shape is a triangular symmetrical bipolar (can assume positive or negative values) waveform, while let’s firstly assume that the modulating signal u(t) is constant:

Ut tOr µ lVaU t.ve. The output voltage is:

V t tTON. The output voltage is a two-level voltage. The time Ton is the time used by the switch S1 conducts and can be calculated just using similarities between the following two triangles:

U b hor Ht ut B Ts 2kUtaTon Ve iUD I g2KUt. The ratio between the bases is equal to the ratio between the heights:

Ton dit.frII Eff tuTs. The obtained result can be seen as the duty cycle of the switch. Note that the modulating signal U can assume any value between +Vr and -Vr. The corresponding value of the duty cycle can assume any value between 0 and 1:

VrVr U o 1D