Power electronic handbook

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22 Electronic Ballasts 571

Line

Glow

Switch

(a)

Line

Starter

(b)

Line

Starter

(c)

Ballast Ballast

Ballast Starting Transformer

Line

(d)

CWA

Air Gapped

Core

FIGURE 22.8 Typical electromagnetic ballast used to supply discharge lamps at low frequency.

inductive ballast, the CWA also exhibits higher input power

factor, lower line extinguishing voltage and lower line starting

currents.

The main advantage of electromagnetic ballasts is their

simplicity, which in turn provides low cost and high reliabil-

ity. However, since they operate at line frequencies, typically

50–60 Hz, they also feature high size and weight. Other

important drawbacks of electromagnetic ballasts are as follows:

•

Low efﬁciency, especially for those ballasts featuring good

lamp power regulation against line voltage variation.

• Low reliability for ignition and re-ignition. If the voltage

spike is not well located within the line period the ignition

of the lamp can fail.

• Difﬁcult to control the lamp luminous ﬂux (dimming).

• Lamp operating point changes due to lamp aging process,

thus reducing lamp life.

• Low input power factor and high harmonic distortion.

Large capacitors are needed across the line input to

increase power factor.

• Over-current risk due to ballast saturation caused by rec-

tifying effect of some discharge lamps, specially at the end

of their life.

• Flickering and stroboscopic effect due to low frequency

supply. The energy radiated by the lamp is a function

of the instantaneous input power. Therefore, when sup-

plied from an AC line an instantaneous variation of

the light output occurs, which is called ﬂicker. For a

line frequency of 60 Hz the resulting light frequency

is 120 Hz. This variation is too fast for the human

eye, but when rapidly moving objects are viewed under

these lamps, the objects seem to move slowly or even

halted. This is called stroboscopic effect, and can be very

dangerous in industrial environments. A ﬂicker index

is deﬁned with values from 0 to 1.0 [1]. The higher

the ﬂicker index, higher is the possibilities of noticeable

stroboscopic effect.

• Unsuitable for DC applications (emergency lighting,

automobile lighting, etc.).

22.2 High Frequency Supply of

Discharge Lamps

22.2.1 General Block Diagram of Electronic

Ballasts

Figure 22.9 shows the general block diagram of a typical

electronic ballast. The main stages are the following:

• EMI ﬁlter. This ﬁlter is mandatory for commercial elec-

tronic ballast. Usually it consists of two coupled inductors

and a capacitor. The input ﬁlter is used to attenuate

the electro magnetic interference (EMI) generated by the

high frequency stages of the ballasts. It also protects the

ballast against possible line transients.

• AC–DC converter. This stage is used to generate a DC

voltage level from the AC line. Normally a full-bridge

diode rectiﬁer followed by a ﬁlter capacitor is used.

However, this simple rectiﬁer provides low input power

factor and poor voltage regulation. In order to obtain

a higher power factor and a regulated bus voltage, active

converters can be used as expounded later in this chapter.

• DC–AC inverter and high frequency ballast. These stages

are used to supply the lamp at high frequency. The

inverter generates a high frequency waveform and the

572 J. M. Alonso

EMI

FILTER

POWER

LINE

AC-DC

CONVERTER

BUS

DC-AC

CONVERTER

(H.F.)

H. F.

BALLAST

LAMP

CONTROL & PROTECTION

CIRCUIT

STARTING

CIRCUIT

FIGURE 22.9 Block diagram of a typical electronic ballast.

ballast is used to limit the current through the discharge.

Both inductors or capacitors can be used to perform

this function, with the advantage of low size and weight,

because they operate at high frequencies.

• Starting circuit. In most electronic ballast, specially those

for low-pressure discharge lamps, the high frequency bal-

last is used to both ignite the lamp and limit the lamp

current at steady state. Therefore, no extra starting cir-

cuit is necessary. However, when supplying high pressure

discharge lamps, the starting voltages are quite higher

and separate ignition circuits are needed, specially if hot

re-ignition is pursued.

• Control and protection circuit. This stage includes the

main oscillator, error ampliﬁers to regulate lamp current

or power, output over-voltage protection, timers to con-

trol the ignition times, over-current protection, lamp fail-

ure protection, etc. It can vary from very simple circuits,

those used in self-oscillating ballasts, to very complicated

ones, which sometimes include a microprocessor-based

control circuit.

There are several important topics when designing elec-

tronic ballasts:

•

Operating frequency. The operating frequency should be

high in order to take beneﬁt of the lower size and weight

of the reactive elements used to stabilize the discharge.

Usually, the operating frequency should be higher than

20 kHz to avoid audible frequencies, which can produce

annoying noises. On the other hand, a higher frequency

produces higher switching losses and a practical limit of

the switching frequency is about 100 kHz when using

MOSFET switches. It is also important to avoid frequen-

cies in the range 30–40 kHz, because these frequencies are

normally used in IR remote controls and could generate

some kind of interference.

• Lamp current waveform. In order to attain the maximum

lamp life, it is important to drive the lamp with symmet-

rical alternating currents, thus making use of both the

lamp electrodes alternately. Also, an important parame-

ter is the lamp current crest factor (CF), which is the ratio

of the peak value to the rms value of the lamp current.

In case of electronic ballasts, the peak value of the low

frequency modulated envelope to the rms value should

be used. The higher the CF, the lower the lamp life. The

ideal situation is to supply the lamp with a pure sinusoidal

waveform. Usually, a CF lower than 1.7 is recommend to

avoid early aging of the lamp.

• Lamp starting procedure. This is a very important issue

when developing commercially available electronic bal-

lasts. The reason is that the life of the lamp greatly

depends on how well the lamp starting is performed,

specially for hot-cathode ﬂuorescent lamps. During the

starting process, electrodes must be warmed up to the

emission temperature, about 800

◦

C, and no high volt-

age should be applied until their temperature is sufﬁ-

ciently high, thus avoiding sputtering damage. Once the

electrodes reach the emission temperature, the starting

voltage can be applied to ignite the lamp. For lamps with

cold cathodes, the starting voltage must be applied rapidly

to prevent harmful glow discharge and cathode sputter-

ing. In any case, starting voltage must be limited to the

minimum value to ignite the lamp, since higher volt-

ages could provide undesirable starting conditions which

would reduce the life of the lamp.

• Dimming. This is an important feature which allows the

ballast to control lamp power and thereby lighting out-

put. Usually the switching frequency is used in solid-state

ballasts as a control parameter to provide dimming capa-

bility. Variations in frequency affect the high frequency

ballast impedance and allow to change the discharge cur-

rent. For example, if an inductor is used as high frequency

ballast, a frequency increase yields an increase in the bal-

last impedance, thus decreasing lamp current. Dimming

should be carried out smoothly, avoiding abrupt changes

in lamp power when passing from one level to another. In

an eventual power cutoff, the lamp should be re-started

22 Electronic Ballasts 573

at maximum lighting level and then slowly reduced to

the required output level.

• Acoustic resonance. The HID lamps exhibit an unsta-

ble operation when they are supplied at high frequency.

At a certain operating frequencies the arc ﬂuctuates and

becomes unstable, what can be observed as a high ﬂicker

due to important changes in the lamp power and thus in

the lighting output. This can be explained by the depen-

dence of the damping of acoustic waves on the plasma

composition and pressure. More information about this

topic can be found in [2]. The avoidance of acoustic

resonance is mandatory to implement commercial elec-

tronic ballasts. This can be performed by selecting the

operating frequency in a range free of acoustic reso-

nances, typically below 1 kHz and over 100 kHz. Other

methods are frequency modulation, square wave opera-

tion and sine-wave superposed with the third harmonic

frequency [3, 4].

22.2.2 Classiﬁcation of Electronic Ballast

Topologies

Typical topologies used to supply discharge lamps at high fre-

quency can be classiﬁed into two main groups: non-resonant

ballasts and resonant ballasts.

22.2.2.1 Non-resonant Ballasts

These topologies are usually obtained by removing the output

diode of DC-to-DC converters, in order to supply alternat-

ing current to the lamp. Current mode control is normally

employed to limit the discharge lamp current. The lamp is

supplied with a square current waveform, which can exhibit a

DC level in some cases. A small capacitor is used to initially

ignite the lamp, but its effect at steady-state operation can be

neglected.

Examples of non-resonant electronic ballasts are shown

in Fig. 22.10. Figure 22.10a, illustrates a boost-based and a

ﬂyback-based ballasts, respectively. Other topologies, which

can supply symmetric alternating current through the lamp,

D1 D2

Lamp

(d)(c)(b)(a)

L1 L2

Lamp

FIGURE 22.10 Non-resonant electronic ballasts.

are shown in Fig. 22.10c (symmetric boost) and 22.10d

(push–pull).

These topologies present several drawbacks such as high-

voltage spikes across the switch, which necessitates the use of

high voltage transistors, and high switching losses due to hard

switching, which gives low efﬁciency specially for high powers.

Besides, since the ideal situation is the lamp being supplied

with a sine wave, these circuits produce an early aging of the

lamp. To conclude, typical applications of these topologies are

portable and emergency equipment, where lamp power is low

and the number of ignitions during its life is not very high.

Some applications of these circuits can be found in [5–8].

22.2.2.2 Resonant Ballasts

These ballasts use a resonant tank circuit to supply the lamp.

The resonant tank ﬁlters the high order harmonics, thus

obtaining a sine current waveform through the lamp. Resonant

ballasts can be classiﬁed into two categories:

A. Current-fed resonant ballasts

These ballasts are supplied with a DC current source, usu-

ally obtained by means of a choke inductor in series with the

input DC voltage source. The DC current is transformed into

an alternating square current waveform by switching power

transitors. Typical topologies of this type of ballasts are shown

in Fig. 22.11.

The topology shown in Fig. 22.11a corresponds to a class E

inverter. Inductor Le is used to obtain a DC input current

with low current ripple. This current supplies the resonant

tank through the power switch formed by Q1–D1. The reso-

nant tank used in this topology can vary from one ballast to

another; the circuit shown in Fig. 22.11a is one which is nor-

mally used. The main advantage of this topology is that zero

voltage switching (ZVS) can be attained in the power switch,

thus reducing the switching losses and making possible the

operation at very high frequencies, which can reach several

megahertz. This allows to drastically reduce the size and weight

of the ballast. However, the adjustment of the circuit parame-

ters to obtain the optimum operation results is quite difﬁcult,

specially for mass production. Another important drawback

is the high voltage stress across the switch, which can reach

574 J. M. Alonso

(a)

Lamp

(b)

Q1 Q2

(c)

Lamp

FIGURE 22.11 Two typical current-fed resonant inverters: (a) class E inverter; (b) current-fed push–pull inverter; and (c) current-fed full-bridge

resonant inverter.

values of three times the DC input voltage. For these reasons,

the main applications of this circuit are battery supply ballasts

with low input voltage and low lamp power, as those used

in emergency lighting and portable equipment. Typical power

range of this ballast varies from 5 to 30 W. Applications of this

circuit can be found in [9, 10].

Another typical topology in this group is the current-fed

push-pull inverter shown in Fig. 22.11b. In this circuit, a DC

input current is obtained by means of choke inductor Le. Tran-

sistors are operated with a 50% duty cycle, thus providing a

current square wave, which supplies the current-fed parallel

resonant circuit formed by the mutual inductance of the trans-

former and capacitor C. This circuit has the advantage of being

relatively easy to implement in a self-oscillating conﬁguration,

avoiding the use of extra control circuits and thereby reducing

the cost. Also, ZVS can be obtained in the power switches.

However, the switches also present a high voltage stress, about

three times the DC input voltage, which makes this topology

unsuitable for power line applications. This circuit is also nor-

mally used in battery-operated applications in a self-oscillating

arrangement. The typical power range is 4–100W. Applications

based on this circuit can be found in [11, 12].

Finally, Fig. 22.11c shows a current fed full-bridge resonant

inverter, which can be used for higher power rating. Also,

this circuit allows to control the output power at constant

frequency by switching the devices of the same leg simulta-

neously, generating a quasi-square current wave through the

resonant tank [13].

B. Voltage-fed resonant ballasts

At present, electronic ballast manufactures mostly use voltage-

fed resonant ballasts, specially for applications supplied from

the AC mains. The circuit is fed from a DC voltage source,

normally obtained by line voltage rectifying. A square wave

voltage waveform is then obtained by switching the transis-

tors with a 50% duty cycle, and used to feed a series resonant

circuit. This resonant tank ﬁlters the high/order harmonics

and supplies the lamp with a sine current waveform. One

advantage of the voltage-fed series resonant circuit is that the

starting voltage can be easily obtained without using extra igni-

tion capacitors by operating close to resonant tank frequency.

Figure 22.12 shows electrical diagrams of typical voltage-fed

resonant ballasts.

The voltage-fed version of the push–pull inverter is illus-

trated in Fig. 22.12a. This inverter includes a transformer,

which can be used to step up or down the input voltage in

order to obtain an adequate rms value of the output square

wave voltage. This provides higher design ﬂexibility but also

increases the cost. One disadvantage is that the voltage across

transistors is twice the input voltage, what can be quite high for

line applications. Therefore, this inverter is normally used for

low voltage applications. Another important drawback of this

voltage-fed inverter is that any asymmetry in the two primary

windings (different number of turns) or in the switching times

of power transistors would provide an undesirable DC level in

the transformer magnetic ﬂux, which in turn could saturate

the core or decrease the efﬁciency due to the circulation of DC

currents.

Figure 22.12b and 22.12c illustrates two possible arrange-

ments for the voltage-fed half-bridge resonant inverter. The

former is normally referred as asymmetric half-bridge, and

uses one of the resonant tank capacitors (C1 in the ﬁgure) to

block the DC voltage level of the square wave generated by

the bridge. This means that capacitor C1 will exhibit a DC

level equal to half the DC input voltage superimposed to its

normal alternating voltage. A transformer can also be used

in this inverter to step up or down the input voltage to the

required level for each application. In this case, the use of the

series capacitor C1 prevents from any DC current circulating

through the primary winding, thus avoiding transformer sat-

uration. This topology is widely used by ballast manufacturers

to supply ﬂuorescent lamps, especially in the self-oscillating

version which allows to drastically reduce the cost. When

supplying hot cathode ﬂuorescent lamps, the parallel capac-

itor C2 is normally placed across two electrodes, as shown in

Fig. 22.12b, in order to provide a preheating current for the

electrodes and achieve soft ignition. Figure 22.12c shows other

version of the half-bridge topology, using two bulk capacitors

22 Electronic Ballasts 575

(a)

Lamp

(b)

D1 D2

Lamp

(c)

C1 C2L1

Lamp

(d)

FIGURE 22.12 Typical voltage-fed resonant inverters: (a) push–pull; (b)–(c) half-bridge; and (d) full-bridge.

to provide a ﬂoating voltage level equal to half the input volt-

age. In this case, capacitor C1 is no longer used to block a DC

voltage, thus showing lower voltage stress.

Finally, for the high power range (>200 W) the full-bridge

topology shown in Fig. 22.12d is normally used. The transis-

tors of each half-bridge are operated with a 50% duty cycle and

their switching signals are phase-shifted by 180

◦

. Thus, when

switches Q1 and Q2 are activated, direct voltage V

is applied

to the resonant tank, and when switches Q3 and Q4 are acti-

vated, the reverse voltage −V

is obtained across the resonant

circuit. One of the advantages of this circuit is that the switch-

ing signals of the two branches can be phase-shifted by angles

between 0 and 180

◦

, thus controlling the rms voltage applied

to the resonant tank ranging from 0 to V

. This provides an

additional parameter to control the output power at constant

frequency, the results are useful to implement dimming ballast.

22.3 Discharge Lamp Modeling

The low frequency of the mains is not an adequate power

source for supplying discharge lamps. At these low frequencies,

electrons and ionized atoms have enough time to recombine

at each current reversal. For this reason, the discharge must be

re-ignited twice within each line period. Figure 22.13a illus-

trates the current and voltage waveforms and the I–V char-

acteristics of a 150 W HPS lamp operated with an inductive

ballast at 50 Hz. As can be seen, the re-ignition voltage spike

is nearly 50% higher than the normal discharge voltage, which

is constant during the rest of the half-cycle.

When lamps are operated at higher frequencies (above

5 kHz), electrons and ions do not have enough time to recom-

bine. Therefore, charge carrier density is sufﬁciently high at

each current reversal and no extra power is needed to re-ignite

the lamp. The result is an increase in the luminous ﬂux com-

pared to that at low frequencies, which is especially high for

ﬂuorescent lamps (10–15%).

Figure 22.13b shows the lamp waveforms and I–V charac-

teristics for the same 150 W HPS when supplied at 50 kHz. It

is shown how the re-ignition voltage spikes disappear and the

lamp behavior is nearly resistive.

Figure 22.14 illustrates how the voltage waveforms change

in a ﬂuorescent lamp when increasing the supply frequency.

As can be seen, at a frequency of 1 kHz, the voltage is already

nearly sinusoidal and the lamp exhibits a resistive behavior.

Therefore, a resistor can be used to model the lamp at high

frequencies for ballast design purposes. However, most lamp

manufactures provide only lamp data for operating at low fre-

quencies, where the lamp behaves as a square wave voltage

source. Table 22.2 shows the low frequency electric data of

different discharge lamps provided by the manufacturer and

the measured values at high frequency for the same lamps. As

can be seen, a power factor close to unity is obtained at high

frequency.

The equivalent lamp resistance at high frequencies can be

easily estimated from the low frequency data. Lamp power at

576 J. M. Alonso

0 0.01 0.02 0.03 0.04 0.05

−200

−100

100

200

(V)

(A)

t (s)

−4

−2

Vla

Ila

0 100 200

−4

−2

Ila (A)

Vla (V)

(a)

0 10

−200

−100

100

200

t (µs)

Vla

Ila

(A)

−4

−2

20 30 40 50

(V)

−200 −100

0 100 200

−3

−1.5

1.5

Ila (A)

Vla (V)

(b)

−200 −100

FIGURE 22.13 150 W HPS lamp waveforms and I–V characteristics at: (a) 50 Hz and (b) 50 kHz.

100

200

500

1000

25000

Frequency

(Hz)

FIGURE 22.14 Voltage waveforms for a 36 W linear ﬂuorescent lamp

supplied through a resistive ballast at nominal power and different

operating frequencies. Vertical scale: 100 V/DIV.

any operating frequency can be expressed as follows:

= V

(22.2)

where V

and I

are the rms values of lamp voltage and

current, and FP

is the lamp power factor.

At line frequencies, the lamp power factor is low (typically

0.8), due to the high distortion in the lamp voltage waveform.

However, at high frequencies the lamp power factor reaches

nearly 1.0. Then, lamp voltage and current at high frequency

LA,hf

, I

LA,hf

) can be estimated from the following equation:

LA,hf

= P

(22.3)

where P

is the nominal lamp power provided by the

manufacturer.

As can be seen in Table 22.2, ﬂuorescent lamps tend to

maintain nearly the same rms current at low and high fre-

quency, whereas high pressure discharge lamps tend to main-

tain nearly the same rms voltage. Based on these assumptions,

the equivalent lamp resistance at high frequency estimated

from the low frequency values are shown in Table 22.3.

22 Electronic Ballasts 577

TABLE 22.2 Electric data of different discharge lamps

Lamp

∗

Manufacturer @ 50 Hz Measured @ H.F.

V (Vrms) I (Arms) P (W) PF V (Vrms) I (Arms) P (W) PF

Fluorescent (TLD-36 W) 103 0.44 36 0.79 83.2 0.46 36 0.94

Compact ﬂuorescent (PLC-26 W) 105 0.31 26 0.80 82 0.32 26 0.99

Low-pressure sodium (SOX-55 W) 109 0.59 55 0.86 75 0.76 56 0.98

Mercury vapor (HPLN-125 W) 125 1.15 125 0.87 132 0.92 120 0.99

Metal-halide (MHN-TD-150 W) 90 1.80 150 0.93 92 1.63 146 0.97

High-pressure sodium (SON-T-150 W) 100 1.80 150 0.83 105 1.42 148 0.99

∗

Lamps aged for 100 h.

TABLE 22.3 Estimated electric data of discharge lamps at high

frequency

Lamp V

LA,hf

Fluorescent lamps P

LA,lf

High-pressure lamps V

LA,lf

Low-pressure sodium lamps neither maintain voltage nor

current, constant at high frequency, and also they exhibit

an equivalent resistance quite dependent on the frequency.

Therefore their equivalent resistance can only be obtained by

laboratory testing.

Note that the values given by Table 22.3 are only an

approximation to the real value, which should be obtained

by measurement at the laboratory. It can be used as the ﬁrst

starting point in the design of the electronic ballast, but ﬁnal

adjustments should be made at the laboratory.

Another important issue is that the lamp equivalent resis-

tance is strongly dependent on power delivered to the lamp,

which is specially important for designing electronic ballasts

with dimming feature. The characteristic lamp resistance vs

lamp power is different for each discharge lamp type and must

be obtained by laboratory testing. One of the best possibilities

to ﬁt the lamp resistance vs power characteristic is the hyper-

bolic approximation. For example, Mader and Horn propose

in [14] the following simple approximation:

) =

(22.4)

where R

is the equivalent lamp resistance, P

is the average

lamp power, and V

and P

are two parameters which depend

on each lamp. This characteristic has been plotted in Fig. 22.15

for a particular lamp with V

= 100 V and P

= 1W.

This model can be implemented very easily in circuit simu-

lation programs, such as SPICE-based programs. Figure 22.16

shows the electric circuit and the description used to model

0 5 10 15 20

2500

5000

7500

10000

(Ω)

(W)

=100 V

=1 W

FIGURE 22.15 Lamp resistance vs lamp power characteristic.

the lamp behavior in a SPICE-based simulation program. The

voltage-controlled voltage source EL is used to model the resis-

tive behavior of the lamp. The voltage source VS is used to

measure the lamp current so that the instantaneous and aver-

age lamp current can be calculated; for this reason its voltage

value is equal to zero. GP is a voltage-controlled current source

used to calculate the instantaneous lamp power, which is then

ﬁltered by RP and CP in order to obtain the averaged lamp

power. Finally, the hyperbolic relationship between the lamp

resistance and power is implemented by means of the voltage-

controlled voltage source EK. The time constant τ = RP·CP is

related to the ionization constant of the discharge.

Figure 22.17 illustrates some simulation results at low fre-

quency when the lamp is supplied from a sinusoidal voltage

source and stabilized with an inductive ballast.

The Mader–Horn model can also be used at high frequen-

cies obtaining a resistive behavior for the lamp. The equivalent

lamp resistance at high frequency will also exhibit a hyper-

bolic variation with the averaged lamp power and with a time

constant given by τ. This model is then useful to simulate

electronic ballast with dimming feature.

578 J. M. Alonso

EK RK

30 40

GP RP CP

(a)

(b)

EK 30 20 Value={Vo*Vo/(V(40,20)+Po)}

.subckt lamp 10 20

+ params: Vo=100 Po=1 Tau=0.3m

EL 10 15 Value={V(30,20)*I(VS)}

VS 15 20 0

RK 30 20 1

GP 20 40 Value={V(10,20)*I(VS)}

RP 40 20 1

CP 40 20 {Tau}

.ends

++ +

FIGURE 22.16 (a) Mader–Horn linear model for discharge lamps and (b) SPICE description of the model.

20ms 25ms 30ms 35ms 40ms 45ms 50ms 55ms 60ms

Time

v(2) i(lb)*50 v(1)

200

−200

−150V −100V −50V −0V 50V 100V 150V

v(2)

i(lb)

3.0A

2.0A

1.0A

−1.0A

−2.0A

(b)

(c)

LAMP

=100 V

=1 W

τ = 0.3 ms

Vg 1 0 SIN(0 325 50)

Rb 1 2a 100

Lb 2a 2 500mH

XLA 2 0 LAMP

.tran 0.1m 60m 0 0.1m

(a)

FIGURE 22.17 (a) Example of simulation with an inductive ballast at low frequency; (b) operating waveforms; and (c) lamp I–V characteristics.

Discharge lamp modeling has become an important subject,

since its results are very useful to optimize the electronic ballast

performance. Some improvements on the Mader–Horn model

and other interesting models can be found in the literature

[14–16].

22.4 Resonant Inverters for Electronic

Ballasts

Most modern domestic and industrial electronic ballasts use

resonant inverters to supply discharge lamps. They can be

implemented in two basic ways: current-fed resonant inverters

and voltage-fed resonant inverters.

22.4.1 Current-fed Resonant Inverters

One of the most popular topologies belonging to this cate-

gory is the current-fed push–pull resonant inverter, previously

shown in Fig. 22.11. For this reason, this inverter will be stud-

ied here to illustrate the operation of the current-fed resonant

ballasts.

The current-fed push–pull inverter uses an input choke to

obtain a DC input current with low current ripple. This current

is alternatively conducted by the switches so that a parallel

22 Electronic Ballasts 579

−

−I

Fundamental (I

s,1

)

(a) (b)

2π

ωt

FIGURE 22.18 (a) Equivalent circuit of a current-fed parallel resonant inverter and (b) operating waveforms.

resonant tank can be supplied with a current square wave.

Figure 22.18 shows the equivalent circuit and the operating

waveforms of a current-fed parallel resonant inverter.

The input current can be expressed as a Fourier series in the

following way:

(t) =



n=1,3,5...

S,n

sin nωt =



n=1,3,5...

nπ

sin nωt (22.5)

S,n

being the peak value of each current harmonic and I

the

DC input current of the inverter. The output voltage for each

current harmonic is obtained by multiplying the input current

S,n

by the equivalent parallel impedance Z

E,n

, this is:

0,n

= I

S,n

E,n

= I

S,n

1/R +jnωC − j(1/nωL)

(22.6)

Usually, normalized values are employed in order to provide

more general results. Then, the output voltage can be expressed

as follows:

0,n

= I

S,n

1/Q +jn −j(1/n)

(22.7)

where Z

is the base impedance of the resonant tank, Q is the

normalized load,  is the normalized frequency, and ω

is the

natural frequency of the resonant circuit, given by:

√

L/CQ= R/Z

 = ω/ω

= ω

√

LC ω

= 1/

√

(22.8)

From Eq. (22.7) the peak output voltage V

0,n

and phase angle

can be obtained for each harmonic:

0,n

= I

S,n



1/Q

+(n −1/n)

(22.9)

=−tan

−1

Q(n −1/n) (22.10)

The total harmonic distortion (THD) of the output voltage

can be calculated as follows:

THD(%) =





n=3,5,7...

0,n

0,1

·100 (22.11)

Based on these equations, the analysis and design of the

current-fed resonant inverter can be performed. Normally, the

circuit operates close to the natural frequency ω

and the effect

of the high frequency harmonics can be neglected. To probe

this, Fig. 22.19a illustrates the THD of the output voltage as

a function of the normalized load and frequency, obtained by

plotting Eq. (22.11). As can be seen, for values of Q higher than

1 and for operation close to the natural frequency ( = 1), the

THD is low, which means that the output voltage is nearly a

sinusoidal waveform. However, for low values of Q, the out-

put voltage tends to be a square waveform and the THD tends

to the value of about 48%, corresponding to the THD of

a square waveform. Figure 22.19b illustrates the normalized

output voltage for the fundamental component.

As stated previously, when used as lamp ballast, the current-

fed parallel resonant inverter operates at the natural frequency

of the resonant tank to both ignite the lamp and limit the

current at normal running. Neglecting the effect of high-order

harmonics, the rms output voltage is given by the fundamental

component, and can be obtained using  = 1 in Eq. (22.9) as

follows:

0(rms)

≈ V

0,1(rms)

= I

S,1(rms)

Q =

√

(22.12)

In a current-fed resonant inverter, the DC input current I

is supplied from a DC voltage source V

with a series choke, as

stated previously. Then, the DC input current can be obtained,

assuming 100% efﬁciency, by equaling input and output power

as follows:

= V

0(rms)

(22.13)

580 J. M. Alonso

0.6 0.8 1 1.2 1.4 1.6 1.8 2

0.2

0.5

Ω

Q=0.01

THD(%)

0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

0.6

1.2

1.8

2.4

0.2

0.5

Q=3

Ω

0,1

S,1

(b)(a)

FIGURE 22.19 Characteristics of the current-fed parallel resonant inverter: (a) THD and (b) fundamental output voltage.

and then:

0(rms)

(22.14)

using Eq. (22.14) in Eq. (22.12) and solving for the output

voltage:

0(rms)

√

= 1.1V

(22.15)

As can be seen, when operating at the natural frequency,

the rms output voltage is independent of the resonant tank

load. The peak output voltage is equal to πV

/2. This value is

directly related to the peak voltage stress in the switches. For

a full-bridge topology, as shown in Fig. 22.11c, this value is

equal to the switch voltage stress. However, for the current-

fed push–pull inverter, the voltage stress is twice this value,

this is πV

, due to the presence of the transformer. This gives

a very high voltage stress for the switches in this topology, this

is the reason why the current-fed push–pull is mainly used to

implement low input voltage ballasts.

On the other hand, lamp starting voltage can vary from 5

to 10 times the lamp voltage in normal discharge mode. This

makes difﬁcult the use of the current-fed parallel resonant

inverter at constant frequency to both ignite the lamp and

supply it at steady state, since the output voltage is independent

of the resonant tank load.

One solution to this problem is to ignite the lamp at the res-

onant tank natural frequency and then change the frequency

to decrease the output voltage and output current to the nor-

mal running values of the lamp. This solution makes necessary

the use of extra circuitry to control the frequency, normally in

closed loop to avoid lamp instabilities, which increases the

ballast cost.

Another solution, very often used in low cost ballasts, is to

design the parallel resonant tank to ignite the lamp, and limit

the lamp current in discharge mode by using an additional

reactive element in series with the lamp. Normally a capacitor

is used to limit the lamp current in order to minimize the

cost of the ballast. This solution is used in combination with

the self-oscillating technique, which assures the operation at

a constant frequency equal to the natural frequency of the

resonant tank. Figure 22.20a illustrates this circuit. Normally

the effect of the series capacitor is neglected and the resonant

tank is assumed to behave as a sinusoidal voltage source during

both ignition and normal operation, as shown in Fig. 22.20b.

The high lamp starting voltage is obtained by means of a step-

up transformer, this is why typically a push–pull topology is

used. If V

is the DC input voltage and V

is the lamp ignition

voltage, then the necessary transformer turn ratio is given by

the following expression:

πV

(22.16)

(a)

RRC

(b)

1.1 V

FIGURE 22.20 (a) Typical parallel resonant circuit used to supply

discharge lamps and (b) equivalent circuit.