Voltage-fed Resonant Inverters

22.4.2 Voltage-fed Resonant Inverters

Some voltage-fed resonant inverters used to supply discharge

22.4.2.1 Series-Loaded Resonant Circuit

lamps were previously shown in Fig. 22.12. Basically, they use The output voltage corresponding to the n-order harmonic is two or more switches to generate a square voltage waveform. easily obtained as follows: The different topologies are mainly given by the type of reso- nant tank used to filter this voltage waveform. There are three

typical resonant tanks; their equivalent circuits are shown in

(22.19) Fig. 22.22. These circuits are the series-loaded resonant tank

V 0,n =V S,n

1 2 1 + 1 Q S (Fig. 22.22a), the parallel-loaded resonant tank (Fig. 22.22b), 2

i LC Fundamental (V

FIGURE 22.22 (a–c) Equivalent circuits of voltage-fed resonant inverters and (d) typical operating waveforms.

590 J. M. Alonso

FIGURE 22.23 Characteristics of series-loaded resonant inverter: (a) THD and (b) fundamental output voltage.

where Q S Q S , the THD tends to the value corresponding to a square wave. quency given by the following expressions:

The output voltage is always lower than the input voltage, and for frequencies around the natural frequency, the circuit acts

Q S = R/Z B = R (L/C S ) −1/2 = ω/ω 0 =ω LC S (22.20) as a voltage source, especially for the high values of Q S . This means that the lamp cannot be ignited and supplied in dis-

Figure 22.23a shows the THD of the series-loaded circuit and charge mode, maintaining a constant switching frequency. This Fig. 22.23b shows the fundamental output voltage, which is property is similar to that encountered for the current-fed reso- normally considered for design purposes.

nant inverter. The use of step-up transformers is mandatory In this circuit, the input and output currents are equal and to achieve lamp ignition, especially for the low input volt-

can be calculated by dividing the output voltage by the load ages. In order to maintain the operating frequency constant, impedance. This current is also circulating through the inverter

a series element will be necessary to limit the lamp current at switches and therefore represents an important parameter for normal discharge operation. A capacitor can also be used as

the design. Another important parameter is the phase angle expounded in the previous section. In summary, this circuit of the input current, which defines the type of commutations is mainly used in high input voltage and low-current applica- in the inverter switches. For the fundamental harmonic, the tions, and it is not very frequently used to implement electronic phase angle of the current circulating through the resonant ballasts. tank can be calculated as follows:

22.4.2.2 Parallel-loaded Resonant Circuit

ϕ = − tan −1

In this circuit, the output voltage corresponding to the n-order harmonic is given by the following expression:

At the natural frequency (ω 0 ), the input voltage and current

will be in phase, which means that there is no reactive energy

handled by the circuit and all the input energy is transferred

V 0,n =V S,n

to the load at steady-state operation. For frequencies higher

−1 than ω 0 , the current is lagged and some reactive energy will

be handled. In this case the inverter switches will present zero

where voltage switching (ZVS) [17]. For frequencies lower than ω 0 ,

the current is in advance and also some reactive energy will

= ω/ω 0 =ω LC P (22.23) current switching (ZCS).

be handled. In this case, the inverter switches will present zero

Q P = R/Z B = R (L/C P )

As can be seen in Fig. 22.23a, the THD is lower for the lower The THD and fundamental output voltage are shown in values of the normalized load and for frequencies close to the Fig. 22.24. This circuit has characteristics very much useful to natural frequency of the resonant tank. For the higher values of implement electronic ballasts than the series-loaded resonant

22 Electronic Ballasts 591 14

FIGURE 22.24 Characteristics of parallel-loaded resonant inverter: (a) THD and (b) fundamental output voltage.

circuit. First, the THD of the output voltage around the nat- is considered. The value of this fundamental current and its ural frequency is in general quite lower than that of the series phase angle can be obtained as follows: circuit. For the lower values of Q P , the THD tends to a value of 12%, which corresponds to the THD of a triangular wave. As

a result, the lamp voltage and current waveforms will be very

2 2 2 2 similar to a sine wave, which is an adequate waveform to supply (22.24) Z B +Q

−1 ) the lamp. Second, the frequency response of the output volt- age (Fig. 22.24b) makes it possible to both ignite the lamp and

− (22.25) limit the lamp current at steady state, maintaining a constant

operating frequency. During ignition, the lamp shows a very high impedance, thus giving a high value of Q P . Under these The condition for the input voltage being in phase with the conditions, the parallel circuit can generate a very high output input current can be obtained by equaling Eq. (22.25) to voltage, provided that the operating frequency is close to the zero. This gives a value of the normalized frequency, which is natural frequency. Once the lamp is ignited, the normalized

load Q P decreases and the circuit can limit the lamp current ϕ =0 = 1 − 1/Q P . For a frequency greater than that value, without changing the operating frequency. In fact, the parallel the input current will lag the input voltage and the inverter

circuit operating close to the natural frequency acts as a current switches will present zero voltage switching. For frequencies source for the load, as will be shown later. This is adequate to lower than that value, the current will be in advance and zero supply discharge lamps because it assures a good discharge sta- current switching is obtained. The output voltage gain at that bility, avoiding the lamp being easily extinguished by transitory frequency is equal to Q P . power fluctuations.

Finally, it is very interesting to study the characteristic of The maximum value of the voltage gain shown in Fig. 22.24 this circuit for frequencies close to the natural frequency ω 0

can be calculated to be equal to Q 7 P 1 2 = 1), since this is the normal region selected to operate − 1/4Q P , and it for ballast applications. At this frequency, the output volt-

= 2 1 − 1/2Q

P . This means that a age gain is equal to Q P and then the output current will be

V S,1 /Z B . This means that when operated at the natural fre- maximum is only present if Q P is greater than 1 7√2 ≈ 0.71. quency, the parallel circuit acts as a current source, whose For the higher values of Q P , the maximum gain can be approxi- value only depends on the input voltage. At the natural fre- mated to Q P and the frequency of maximum gain can be

quency, the input current is equal to V S,1 1 +Q 2 P 7Z B and the The input current of the parallel resonant circuit is phase angle is equal to tan −1 ( −1/Q P ). The circuit is always another important parameter to calculate the current han- inductive, with ZVS, and the phase angle decreases when Q P

approximated to the natural frequency ω 0 .

dled by the inverter switches. Since the operating frequency is increases, which means that less reactive energy is handled by normally around resonance, only the fundamental component the circuit.

592 J. M. Alonso 20

FIGURE 22.25 Characteristics of series–parallel-loaded resonant inverter: (a) THD and (b) fundamental output voltage.

for α =0.5. As can be seen, the THD is also very low around This circuit is also very widely used to implement electronic the natural frequency, especially for the higher values of the

22.4.2.3 Series–Parallel-Loaded Resonant Circuit

ballasts. The fundamental output voltage is given by the fol- normalized load Q SP . Regarding the output voltage, this circuit lowing expression:

acts as a parallel circuit around the natural frequency ω 0 , with a maximum gain voltage of about Q SP /α. Around the natural fre-

V 0,1 =V S,1 (22.26) quency of the series circuit given by L and C S ,ω 0S =ω 0 1 −α,

Q SP 2 + α 2 −1

1 1 −α 2 1 2 2 the circuit acts as a series-loaded circuit with a maximum

voltage gain equal to unity.

The series–parallel circuit can also be used to both ignite and where

supply the lamp at constant frequency, since it also acts as a cur- rent source at the natural frequency. Besides, this circuit allows

Q SP = R/Z B = R (L/C E ) −1/2

= ω/ω o =ω LC E to limit the ignition voltage by means of the factor α, thus

α =C E /C P =1−C E /C S

avoiding sputtering damage of lamp electrodes. Also, the series (22.27) capacitor can be used to block any dc component of the inverter

square output voltage, as that existing in the asymmetric half- and C E =C S C P /(C S +C P ) is the series equivalent of the bridge. In summary, the series–parallel circuit combines the two capacitors present in this resonant circuit.

best features of the series-loaded and the parallel-loaded, and The fundamental input current and its phase angle are the this is the reason why it is used widely to implement electronic following:

ballasts.

When operated at frequency ω 0 , the output voltage gain is

equal to Q SP /α, and then the circuit acts as a current source

I S,1 = equal to V S,1 /αZ B , which is independent of the load. As stated

Z B 2 2 2 2 + 2 SP /α −1

previously, this current source behaviour is adequate to supply (22.28) discharge lamps because it allows the lamp current to be limited

all the time. The input current phase angle at this frequency is ⎧

SP ), and the input current always lags the tan

2 equal to tan (

−α/Q

input voltage, thus showing ZVS operation. ⎨

Finally, the condition to have input current in phase with the ϕ =

(22.29) input voltage can be obtained by equaling Eq. (22.27) to zero.

SP

This gives the following value:

if

C = 1 −α

2 −(1−α) THD of the output voltage and the fundamental output voltage

Figure 22.25 shows the characteristics corresponding to the

Q SP,ϕ =0 =

22 Electronic Ballasts 593

Equation (22.30) defines the borderline between the ZVS the operating frequency is adjusted to a value above the nat- and the ZCS modes. The output voltage gain in this border- ural frequency of the resonant tank. In this way, the heating line can be obtained by using Eq. (22.30) in Eq. (22.26), and it current can be adjusted to the necessary value, maintaining a is equal to α/ α (1

2 ). lamp voltage quite lower than the starting voltage. Since nor- mally MOSFET or bipolar transistors are used, the operation over the natural frequency is preferable because they provide

ZVS, and the slow parasitic diodes existing in these transistors The design methodology of a resonant inverter for discharge can be used. After a short period of time, the switching fre-

22.4.3 Design Issues

lamp supply can be very different depending on the lamp type quency is reduced until the starting voltage is obtained, and and characteristics, inverter topology, design goals, etc. Some then the lamp is ignited. Normally, the final operating point at guidelines, especially focused for supplying fluorescent lamps steady-state operation is adjusted to be at a switching frequency with voltage-fed resonant inverters are presented in this section equal to the natural frequency, so that a very stable operation to illustrate the basic design methodology.

for the lamp is assured.

A typical starting process for a hot-cathode fluorescent lamp Figure 22.27a shows a fluorescent lamp supplied using a is shown in Fig. 22.26. Initially, lamp electrodes are heated up series–parallel resonant tank. The input data for the design are

to the emission temperature. During this phase, the inverter normally the fundamental input voltage V S , the switching fre- should assure a voltage applied to the lamp not high enough quency in normal discharge operation (running) f S , the lamp to produce sputtering damage in lamp electrodes, thus avoid- voltage and current at high frequency V LA ,I LA , the electrode

ing premature aging of the lamp. Once electrodes reach the heating current I H , the maximum lamp voltage during heating emission temperature, the lamp can be ignited by applying process V H , and the lamp starting voltage V IG . the necessary starting voltage. Following this procedure, a soft

The equivalent circuit during the heating and ignition phase starting is achieved and a long lamp life is assured.

is shown in Fig. 22.27b. The current circulating in this circuit is

The best method to perform this soft starting is to control the electrode heating current, which can be calculated by using the inverter switching frequency, so that the lamp voltage and Q SP = ∞ in Eq. (22.24) current are always under control. During the heating process,

V S /Z B

V IG where the electrode resistance has been neglected for simplicity.

Ignition

For a given heating current I H , the necessary switching fre- quency is obtained from Eq. (22.31) as follows:

Heating H =

(22.32) 2Z B I H 2Z B I H

V HEAT Running

Regarding the heating voltage, it can be calculated from V LA

Q≈∞

Eq. (22.26) using Q SP =∞, and the following value is obtained: Q=R LA /Z B

V H = 2 (22.33)

H Ω −1

R Ω IG Ω H

FIGURE 22.26 Typical starting process of discharge lamps.

(c) FIGURE 22.27 (a) Fluorescent lamp supplied with a series–parallel circuit; (b) equivalent circuit during heating and ignition; and (c) equivalent

(a)

(b)

circuit during normal discharge mode.

594 J. M. Alonso The frequency at which the starting voltage is achieved can

also be obtained using Q SP =∞ in Eq. (22.26), giving the following value:

FIGURE 22.28 Resonant circuit using a PTC resistor. Once the lamp is ignited, the new operation circuit is shown in Fig. 22.27c. Normally, the switching frequency is selected to

be very close to the natural frequency, and the circuit char- In the circuit shown in Fig. 22.28, the PTC is initially =1. Thus, as stated cold and capacitor C P1 is practically short-circuited by the previously, the circuit acts as a current source of the following PTC. The resonant tank under these conditions is formed by value:

L −C S −C P2 , which can be designed to heat the lamp electrodes with a heating voltage low enough to avoid lamp cold ignition.

I LA =

(22.35) Since the PTC is also heated by the circulating current, after α Z B a certain period of time, it reaches the threshold temperature

and trips. At this moment, the new resonant tank is formed From this equation, the impedance Z B needed to provide a by L, C S , and the series equivalent of C P1 and C P2 . This cir-

lamp current equal to I LA is easily obtained cuit can be designed to generate the necessary ignition voltage and to supply the lamp in normal discharge mode. Once the

(22.36) lamp is ignited, the PTC maintains its high impedance since

α I LA

the dominant parallel capacitor in this phase is C P1 (usually

C P1 ≪C P2 ).

Using Eqs. (22.31)–(22.36), the design procedure can be per- formed as follows:

Step 1 Steady-state operation. Choose a value for the fac-

22.5 High-Power Factor Electronic

tor α; normally a value of 0.8–0.9 will be adequate for most

Ballasts

applications. From Eq. (22.36), calculate the value of Z B for

the resonant tank. Since the natural frequency is equal to the As commented in a previous section, when electronic bal- switching frequency, the reactive elements of the resonant tank lasts are supplied from the ac line, an ac–dc stage is necessary can be calculated as follows:

to provide the dc input voltage of the resonant inverter (see Z B 1 1 Fig. 22.9). Since the introduction of harmonic regulations, as

(22.37) IEC 1000-3-2, the use of a full-bridge diode rectifier followed

2π f 2π f α Z

SS

B 2π f S (1 −α)Z B by a filter capacitor is no longer applicable for this stage due to the high harmonic content of the input current. Therefore,

Step 2 Heating phase. From Eq. (22.32), calculate the switching the use of an ac–dc stage showing a high input power factor

frequency for a given heating current I H . Then, calculate the

(PF) and a low total harmonic distortion (THD) of the input

value of the heating voltage V H from Eq. (22.33).

current is mandatory. The inclusion of this stage can signifi- Check if the heating voltage is lower than the maximum cantly increase the cost of the complete ballast, and therefore value allowed to avoid electrode sputtering. If the voltage is the search for low-cost high-power factor electronic ballasts is too high, choose a lower value of α and repeat steps 1 and 2. presently an important field of research. Also, the maximum heating frequency can be limited to avoid Figure 22.29a shows a first possibility to increase the input excessive frequency variation. The lower the α the lower is the power factor of the ballast by removing the filter capacitor frequency variation from heating to ignition, since the out- across the diode rectifier. However, since there are no low- put voltage characteristics are narrower for the lower values frequency storage elements inside the resonant inverter, the of α. output power instantaneously follows the input power, thus

Step 3

The described procedure to achieve lamp soft ignition producing an annoying light flicker. Besides, the resulting lamp requires the use of a voltage-controlled oscillator to control the current crest factor is very high, which considerably decreases switching frequency. This can increase the cost of the ballast. lamp life.

A similar soft ignition can be achieved using the resonant cir- In order to avoid flicker and increase lamp current crest cuit shown in Fig. 22.28. This circuit is very often used in factor, continuous power must be delivered to the lamp. self-oscillating ballasts, where the switches are driven from the This can only be accomplished by using a PFC stage with resonant current using a current transformer [18].

a low-frequency storage element. This solution is shown in

22 Electronic Ballasts 595

Lamp v

Lamp

g Resonant LA

v g PFC

C 0 Resonant v LA

FIGURE 22.29 High power factor ballasts.

Fig. 22.29b, where capacitor C 0 is used as energy storage ele- TABLE 22.4 IEC 1000-3-2. Harmonic limits for class c equipment ment. The main drawback of this solution is that the input

power is handled by the two stages, which reduces the efficiency Maximum permissible harmonic current expressed as

Harmonic order

a percentage of the input current at the fundamental

of the complete electronic ballast.

frequency (%) 2 2