ClassF3poweramp

8/6/2019 ClassF3poweramp

1/4

Maximum Drain Efficiency Class F3RF Power Amplifier

Marian K. KazimierczukDepartment of Electrical Engineering

Wright State University

Dayton, Ohio 45435, USA.

Email: [email protected]

Rafal P. WojdaDepartment of Electrical Engineering

Wright State University

Dayton, Ohio 45435, USA.

Email: [email protected]

AbstractThis paper presents a design procedure for theclass F3 RF power amplifier. The required range of the draincurrent conduction angle for the class F3 power amplifier isspecified. Additionally, an equation for the resistance of thethird harmonic resonant circuit is given. Class F3, AB, and C

power amplifiers were designed and simulated to compare theirrespective performance in terms of efficiency.

I. INTRODUCTION

Class F RF power amplifiers (PAs) utilize multiple-

harmonic resonators in the output network to shape the active

device output voltage, such that the power loss in the device

is reduced and the efficiency is improved [1]-[7]. The main

concept of the class F power amplifier is to increase the

overall efficiency with respect to class A, B, AB, and C

power amplifiers. In the MOSFET class F RF power amplifier,

the drain current flows when the drain-to-source voltage is

low, and is zero when the drain-to-source voltage is high.

Therefore, the product of the drain current and the drain-to-source voltage waveforms is low, and the power dissipated

in the active device is significantly reduced. Class F power

amplifiers can be categorized as having either maximally flat

drain-to-source voltage or maximum drain efficiency [4], [5],

[7].

Present literature claims that the 3rd harmonic resonant

circuit does not consist of any parallel resistance [1]-[7].

However, the presence of this resistance is essential in shaping

the MOSFET drain-to-source voltage vDS waveform becausethe third harmonic of the voltage across R3 is generated. Upto now, all literature has lacked a design procedure for the 3rd

harmonic resonant circuit.The objectives of this paper are to:

introduce a design procedure for the third harmonic

resonant circuit in the class F3 power amplifier, determine the resistance of the resonant circuit for the

third harmonic, and

establish the drain current conduction angle.

II . CLASS F RF POWER AMPLIFIER WITH THIRD

HARMONIC

The circuit of the class F RF power amplifier with a third

harmonic resonator, called F3, is shown in Fig. 1. The circuitconsists of a transistor, load network, and RF choke (RFC).

Fig. 1. Class F3 power amplifier with third harmonic resonator.

The load network is composed of two parallel-resonant RLC

circuits connected in series. The first resonant circuit is tuned

to the third harmonic 3fo. The second resonant circuit is tunedto the operating frequency fo and the ac power is delivered tothe load resistance R.

The drain current waveform for any conduction angle is

expressed as

iD =

IDM

cos tcos 1cos for < t

0 for 2 , (1)

where IDM is the peak value of the drain current. The cosineof the conduction angle of the drain current is given by

cos =Vt VGS

Vgsm, (2)

where Vt is the threshold voltage, VGS is the dc component ofthe gate-to-source voltage, and Vgsm is the amplitude of theac component of gate-to-source voltage. The drain-to-source

voltage is given by [7] as

vDS = VI+vds1+vds3 = VIVm cos t+Vm3 cos 3t, (3)

where Vm3 is the voltage drop across the resistor R3 due tothe 3rd harmonic and Vm is the voltage drop across the resistorR due to the fundamental component of the output voltage.The third harmonic waveform vds3 is 180

out of phase with

respect to the fundamental frequency voltage vds1.

978-1-4244-9474-3/11/$26.00 2011 IEEE 2785


2/4

Fig. 2. Fourier coefficients n of the drain current iD as a function ofconduction angle .

Expanding the drain current given by (1) into a Fourier

series

iD(t) = IDM

0 +

n=1

n cos nt

, (4)

one obtains the dc component of the drain current

II =1

2

iDd(t) =sin cos

(1 cos ) IDM = 0IDM,(5)

the amplitude of the fundamental component of the drain

current

Im =1

iD cos td(t) = sin cos

(1 cos ) IDM

= 1IDM, (6)

and the amplitude of the n-th harmonic of the drain current

Imn =1

iD cos ntd(t)

=2

sin n cos n cos n sin n(n2

1)(1

cos )

IDM = nIDM. (7)

Fig. 2 shows Fourier coefficients n of the drain current iDas a function of conduction angle . It can be seen that theconduction angle of the drain current must be in the range

90 < < 180 (8)

to satisfy the phase relation between first and third harmonic

voltage as shown in (3). Only in this range of , 1 ispositive and 3 is negative. Adding the third harmonic to thefundamental component reduces the drain-to-source voltage

amplitude Vpk. Hence, the voltage waveform vDS changes asthe ratio Vm3/Vm increases.

In the class F3 amplifier, the relation between the amplitudeof third harmonic Vm3 and the amplitude of the fundamentalcomponent Vm is expressed by

Vm3Vm

=Im3R3

ImR=

3IDMR31IDMR

=3R31R

= 112

sin 3 cos 3cos 3 sin ( sin cos )

R3R

. (9)

The ratio of the amplitude of the third harmonic Vm3 to theamplitude of the fundamental component Vm is equal to 1/9for maximally flat drain-to-source voltage vDS [4], [7] and isequal to 1/6 for maximum drain efficiency [5], [7]. Therefore,

the required resistance R3 for the class F3 amplifier withmaximally flat drain-to-source voltage vDS is

R3(maxflat) =R19|3| (10)

and for maximum drain efficiency is

R3(maxeff) =R16|3| . (11)

III. RESULTS

In the subsequent analysis, the class F3, AB, and C RFpower amplifiers are designed, simulated, and compared. The

output power of each amplifier is assumed to be 10 W, theoperating frequency is f = 800 MHz, and the input voltageis VI = 1 2 V. The following simulations are carried outusing Saber with an ideal MOSFET model excluding parasitic

capacitance and with the threshold voltage Vt = 1 V.

A. Class F3 Power Amplifier

From Fig. 2 and (8) it can be seen that the conduction

angle should be within the range: 90 < < 180. Forthe conduction angle = 110 and the dc component of thegate-to-source voltage VGS = 1.5 V, the required amplitudeof the ac component of the gate-to-source voltage from (2) is

Vgsm = 1.462 V. The saturation drain-to-source voltage is

vDSsat = vGS Vt = VGS + Vgsm Vt= 1.5 + 1.462 1 = 1.962 V. (12)

Selecting the minimum drain-to-source voltage vDSmin =2.4 V, the maximum voltage amplitude of the fundamental

component for the maximum drain efficiency class F3 poweramplifier is [7]

Vm =2

3(VI vDSmin) = 1.1547(12 2.4) = 11.085 V

(13)

and the amplitude of the third harmonic to achieve the max-

imum drain efficiency is Vm3 =Vm6

= 1.848 V. The loadresistance of the amplifier is

R =V2m2Po

=11.0852

2 10 = 6.14 . (14)

The Fourier coefficients of the drain current of the class F3PA for the conduction angle = 110 are 1 = 0.5315 and

2786


3/4

Fig. 3. The magnitude of input impedance Zi of the load network as afunction of frequency f for the class F3 power amplifier with maximumdrain efficiency.

3 = 0.04487. Hence, the resistance connected in parallelwith the resonant circuit tuned to the third harmonic is

R3 =1

6|3|R =0.5315

6| 0.04487| 6.14 = 12.13 . (15)

Assuming the loaded quality factor of the resonant circuit

for the fundamental frequency is QL = 8 and the loadedquality factor of the resonant circuit for the third harmonic

is QL3 = 20, the components are L =R

QL= 152.7 pH,

C = QLR

= 259 pF, L3 =R3

3QL3= 40.2 pH, and

C3 =QL33R3

= 109.3 pF. The magnitude of input impedance

of the designed load network Zi as a function of frequency fis presented in Fig. 3.

To ensure the constant input current II, the inductance of theRF choke (RFC) was selected as Lf = 1.23 H. To block thedc voltage on the load network, the output coupling capacitor

was chosen to be CB = 324 nF.The designed circuit for maximum drain efficiency was

simulated using Saber Sketch. In preliminary simulation, the

amplitude of the 3rd harmonic was greater than the amplitude

of that in the amplifier with maximum drain efficiency mode.

Therefore, a slight modification of the third harmonic resonant

circuit was made by decreasing the resistance R3 to 10 ,

which decreases the amplitude of third harmonic voltage.The waveforms of the voltage drops and currents through the

resistors R3 and R are presented in Fig. 4.It can be seen that the third harmonic was 180 out of phase

with respect to the fundamental frequency. Moreover, it can be

seen that the third harmonic waveform was attenuated after the

beginning of each period of the fundamental frequency. This

is because the resonant circuit for the third harmonic behaves

like a frequency multiplier. The amplitude of the fundamental

component was Vm = 11.365 V, the amplitude of the thirdharmonic was Vm3 = 1.91 V, the amplitude of the currentthrough resistor R was Im = 1.9 A, and the amplitude of thecurrent through resistor R3 was Im3 = 0.192 A. Hence, the

Fig. 4. Waveforms of the current io through resistor R (upper trace), currenti3 through resistor R3 (second trace from the top), fundamental componentof the output voltage vds1 (second trace from the bottom), and third harmonic

voltage vds3 (bottom trace).

power loss in 3rd harmonic resonant circuit due to resistance

R3 was

PR3 =1

2I2m3R3 =

1

2 (192 103)2 10.5 = 193.5 mW.

(16)

Fig. 5 presents the waveforms of the drain current iD anddrain-to-source voltage vDS . The conduction angle of thedrain current iD was 110

. The maximum drain current was

IDM = 3.4008 A, the maximum drain-to-source voltagevDS(max) = 22.2 V, and the minimum drain-to-source voltagevDS(min) = 2.0016 V, which is higher than the MOSFETdrain-to-source saturation voltage vDSsat, but is lower than theassumed minimum drain- to-source vlotage vDSmin = 2.4 V.

Fig. 6 shows waveforms of power dissipation in the transis-

tor, voltage vDS , and drain current iD. The overall efficiencyof the designed class F3 power amplifier with a conductionangle = 110 was = 71.66 %.

Using the same design procedure as shown above, the class

F3 power amplifier with the drain current conduction angle

Fig. 5. Waveforms of the drain current iD (upper trace) and drain-to-sourcevoltage vDS (bottom trace).

2787


4/4

Fig. 6. Waveform of power dissipation in the transistor (upper trace) andcombined waveforms of voltage vDS and drain current iD (bottom trace).

= 60 was designed. The waveforms of the drain current,

drain-to-source voltage, fundamental component of the outputvoltage, and the third harmonic voltage are shown in Fig. 7.

It can be seen that the third harmonic voltage is in phase

with the fundamental component of the output voltage and

that the drain-to-source voltage vDS has triangular shape.The waveforms shown in Fig. 7 are in contradiction to the

waveforms of the class F3 power amplifier, which proves thatthe class F3 PA should have the drain current conduction anglegiven by (8).

B. Class AB Power Amplifier

The parameters of the designed and simulated class AB

PA were: dc component of the gate-to-source voltage VGS =1.5 V, RF choke (RFC) inductance Lf = 1.23 H, couplingcapacitor CB = 324 n F, conduction angle = 110,loaded quality factor of fundamental frequency resonant circuit

QL = 8 with ideal passive components. The simulated overallefficiency of the designed class AB PA was = 54.36%.

C. Class C Power Amplifier

The parameters of the designed and simulated class C PA

were: dc component of the gate-to-source voltage was VGS =0 V, RF choke (RFC) inductance Lf = 1.23 H, couplingcapacitor CB = 324 nF, conduction angle = 60, loadedquality factor of fundamental frequency resonant circuit QL =

8 with an ideal passive components. The simulated overallefficiency of the designed class C PA was = 74.41%.

From the comparison of the designed amplifiers, it can be

seen that the efficiency of class F3 PA was higher than thatof class AB by 17%. However, the class C amplifier was

more efficient by 2.75%. Hence, the efficiency of the class C

power amplifier was the highest among all the three designed

amplifiers.

IV. CONCLUSIONS

This paper has presented the design procedure for the class

F3 RF power amplifier. The required conduction angle range for the class F3 amplifier has been established to be: 90

Documents

ClassF3poweramp