High-efficiency class E/F3 power amplifiers with extended

High-efficiency class E/F3power amplifiers withextended maximumoperating frequency

Chang Liu1, Xiang-Dong Huang2a), and Qian-Fu Cheng11 School of Microelectronics, Tianjin University, Tianjin 300072, China2 School of Electrical and Information Engineering, Tianjin University,

Tianjin 300072, China

a) [email protected]

Abstract: This paper presents high-efficiency class-E/F3 power amplifiers

with extended maximum operating frequency ( fmax) using a novel method of

a transmission-line compensation circuit (TLCC). Theoretical analysis is

presented in order to obtain circuit component values, which compensate

the excess output capacitance Cx and satisfy the required impedances of the

class-E/F3 power amplifiers at the fundamental frequency and harmonics.

The proposed circuit, whose fmax is 4 times higher than the conventional

structure, has been designed, fabricated, and measured. Besides, high-per-

formance results with the output power of 40.3 dBm, drain efficiency of

82.9% have been achieved.

Keywords: class-E/F3, high-efficiency power amplifier (PA), maximum

operating frequency, transmission-line compensation circuit (TLCC)

Classification: Power devices and circuits

References

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© IEICE 2018DOI: 10.1587/elex.15.20180503Received May 17, 2018Accepted May 24, 2018Publicized June 12, 2018Copyedited June 25, 2018

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LETTER IEICE Electronics Express, Vol.15, No.12, 1–10

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1 Introduction

With the rapid development of RF transmission systems, it is gradually required

that power amplifiers (PAs) operate with high efficiency, high output power, good

linearity and so on. Among these requirements, high-efficiency is the most critical

one, especially in high power or battery-powered applications [1]. Therefore, it has

been a hot topic to develop high-efficiency PAs.

The class-E PA is one of the well-known high-efficiency PAs due to its

relatively simple realization and elimination of turn-on switching losses because

of a soft-switching operation mode [2, 3]. However, as far as the peak drain voltage

(Vmax) is concerned, the class-E approach is not a good choice for practical

applications because of the relatively large switch stresses to active devices,

especially in the integrated circuit [4]. Fortunately, differing from the class-E PA,

the class-F/F−1 PA has lower Vmax and higher attainable operating frequencies [5].

Whereas, due to the tuning requirements [6, 7] and the lack of a simple circuit

implementation, e.g., [8], the class-F/F−1 PA also has performance limitations.

Based on the advantages and disadvantages in class-E PA [2, 3, 4] and class-F/F−1

PA [5, 6, 7, 8], it is of great significance to combine the two high-efficiency PAs

and present a new PA mode of operation: class-E/F3 PA [9, 10, 12, 13, 14, 15],

which not only realizes a relatively simple structure, but also reduces the peak

voltage Vmax [9, 10]. However, in the class-E/F3 power amplifier, the optimum

shunt capacitance (C) decreases with the increase of the maximum operating

frequency (fmax, is defined as the maximum frequency at which the device output

capacitance Cout can provide the shunt susceptance Bopt required for optimum

operation [11]) for the prescribed output power P0 and DC supply voltage VDS

[12, 13]. In practical applications, C becomes smaller than Cout in the high fmax

[14], which results in excess output capacitance Cx (¼ Cout � C). Owing to this, the

class-E/F3 PA operates at a suboptimal condition and its efficiency consequently

decreases a lot [15]. In a word, the fmax of the conventional class-E/F3 PA is

limited to hundreds of MHz when keeping its optimal mode of operation, thus

representing a crucial issue.

In this paper, in order to further increase the fmax of a class-E/F3 power

amplifier to GHz when operating at an optimal condition, a novel method of a

transmission-line compensation circuit (TLCC) is proposed. This structure com-


3



















pensates Cx at both the fundamental and harmonic frequencies. Therefore, the

TLCC bypasses the limitations on fmax of the class-E/F3 PA. Besides, a high

performance PA, whose fmax is 4 times larger than the conventional structure, is

designed and fabricated to validate the theory. In brief, due to its extended fmax,

simple construction and low-loss implementation at high frequencies, the proposed

circuit is more suitable for use as a class-E/F3 amplifier operating in the microwave

band.

2 Class-E/F3 PAs

2.1 Standard idealized class-E/F3 PAs

The circuit schematic of the idealized class-E/F3 PA is depicted in Fig. 1. The

transistor must be driven sufficiently hard such that it operates like a switch rather

than a current source. The series-tuned resonator L0C0 and the series resonant LnCn

circuit are tuned at the fundamental and the third harmonic, respectively. Mean-

while, the quality factors of them are sufficiently high. The optimal load impe-

dances at the fundamental frequency and higher harmonics seen by the transistor,

Zopt, are given in (1). The loading network presents R in series with L at f0, an

open circuit at all harmonics except the third harmonic, and a short circuit at the

third harmonic. For the prescribed output power P0, DC supply voltage VDS, and

operating frequency f0, the optimal load resistance R, series inductance L and shunt

capacitance C can be calculated using (2), (3) and (4). Besides, the expression for

fmax can be obtained like (5).

Zopt ¼R þ j!0L; at f0

0; at 3f0

1; at nf0; n ¼ 2; 4; 5 . . .

8><>:

ð1Þ

R ¼ 0:657V2DS

P0

ð2Þ!0L

R¼ 0:961 ð3Þ

!0CR ¼ 0:209 ð4Þfmax ¼ 0:0506

P0

CV 2DS

: ð5Þ

Fig. 1. The circuit schematic of the idealized class-E/F3 PA.


4


Ideally, the shunt capacitance C can entirely furnish the device output capaci-

tance Cout. By substituting C ¼ Cout, fmax can be rewritten as

fmax ¼ 0:0506P0

CoutV 2DS

: ð6Þ

2.2 Class-E/F3 PA with extended fmax

From (5), it follows that C decreases with the increase of fmax for the prescribed

P0 and VDS. In practical applications, C becomes smaller than the device output

capacitance Cout in the high fmax, which results in excess output capacitance Cx

(¼ Cout � C). The enhancement of fmax is achieved by compensating Cx. This

translates into higher fmax expressed in (7) as follows, where Cx is defined as KC

(K > 0):

fmax ¼ 0:0506P0

ðCout � CXÞV 2DS

¼ 0:0506ð1 þ KÞ P0

CoutV 2DS

ð7Þ

Compared with the original result given in (6), fmax is increased by 1 þ K

times. which can be realized by the proposed TLCC given in Section 3.

3 TL compensation circuit for class-E/F3 PA

Some methods including a lumped-element equivalent circuit [16], and TLCC [17]

have been presented to compensate Cx and extend fmax in other high-efficiency

switch-mode PAs. However, the method in [16] has been restricted by the lumped-

element model and large parasitic losses at high frequencies [17]. Therefore, as

described in Fig. 2, a new class-E/F3 PA circuit topology with TLCC is proposed

in this paper. Due to the advantage of the proposed TLCC, it is convenient to satisfy

the impedance conditions for both the fundamental and harmonics without any

other redundant circuits.

In order to simplify the problem, three reference points (A, B, C) are placed in

Fig. 2. The characteristic impedances and electrical lengths of the cross-junction

TL1–TL4 are Z1, Z1, Z2, Z2 and 45°, 75°, 45°, 45°, respectively. At second harmonic

Fig. 2. A new class-E/F3 PA circuit topology with TLCC.


5


frequency, the cross-junction can provide an open termination at the point B. At the

third harmonic, TL1 resonates with TL2 in order to provide an open-circuit at the

point A. Therefore, the cross-junction seen by the point B at the third harmonic can

be simplified as a 3�=4 transmission-line, which can provide a short termination so

as to satisfy the condition of the harmonic impedance like (1).

Furthermore, the electrical length of the drain biasing TL6 in Fig. 2 is 90° and it

consequently provides a short-circuit termination at 2!0. Thus, the shorted series

line TL5 behaves like an inductance La at the second harmonic

jZ3 tanð2�3Þ ¼ j2!0La: ð8Þwhere, �3 and Z3 are the electrical length and characteristic impedance of TL5,

respectively. This inductance La must be resonated with Cx at the point C, in order

to compensate Cx and provide the required open circuit for the second harmonic

like (1), and hence

j2!0CX þ 1

j2!0La¼ 0: ð9Þ

Note that there are two degrees of freedom ð�3; Z3Þ. Taking the fourth harmonic

into consideration, it is better to select 22.5° as the electrical length of TL5 because

of its open-circuit termination for the fourth harmonic at the point C. Thus, the

characteristic impedance of TL5 can be determined by (8)–(9).

At 4!0, since TL1 and TL3 represent the open-circuited terminations at the

point A, the cross-junction at the point B can be simplified as an inductance Lb:

Z1j tanð75 � 4Þ ¼ j4!0Lb: ð10Þ

Then, like the compensation for the second harmonic, the inductance Lb must

be resonated with Cx at the point C, in order to compensate Cx and provide the

required open circuit for the fourth harmonic like (1), and hence

j4!0CX þ 1

j4!0Lb¼ 0: ð11Þ

The characteristic impedance Z1 of TL1–TL2 can be determined by (10)–(11).

It should be noted that the electrical length of TL2 is 75° rather than 15° at the

fundamental. Although TL2 with electrical length of 15° can also resonate with TL1

at the third harmonic and its physical size is shorter, TL2 with electrical length of

75° has been employed because of its wider tuning space for characteristic

impedance Z2, so as to compensate Cx at 5!0 as far as possible.

Finally, at !0, an output match network (OMN) is created in order to

compensate Cx and match the 50Ω load to optimal load reactance like (1).

4 Design and verification

A design example of the class-E/F3 PA with TLCC is presented in order to better

understand the theoretical analysis described in the previous sections.

The design objectives are set as follows: VDS ¼ 28V and Pout ¼ 10W. The

transistor used in implementation is a CGH40010F GaN HEMT from Wolfspeed

with Cout ¼ 1:2 pF. Substituting these values into (6) yields fmax ¼ 0:54GHz.

According to (5), if the operation frequency is increased to 2.14GHz, whose fmax


6


is 4 times larger than that of the conventional circuit, the value of the shunt

capacitance C is decreased to 0.3 pF. Since Cout ¼ 1:2 pF, the excess capacitance Cx

required is 0.9 pF, implying K ¼ 3. Based on the theoretical analysis in the previous

section, the schematic of TLCC for class-E/F3 is presented in Fig. 3. The proposed

class-E/F3 PA with TLCC contains the loading network, input matching network

(IMN), biasing, and stabilizing circuits. The transmission-line parameters for

loading network in Fig. 3 can be calculated by (1)–(4) and (8)–(11). Here, the

simulated load impedances for the fundamental and harmonics are plotted in Fig. 4.

In accordance with (1), the class-E/F3 PA mode requirements for short-circuit and

open-circuit terminations at harmonics ð2!0; 3!0; 4!0Þ are met concurrently, as is

the optimal impedance at !0. Furthermore, by tuning the characteristic impedance

Z2, the impedance of the fifth harmonic is adjusted as high as possible. Therefore,

the proposed TLCC can effectively compensate the excess output capacitance Cx at

both the fundamental and harmonic frequencies.

For a practical transistor, the parasitic network formed by bonding wires and

package lead does not match the required exact values of proposed class-E/F3 PA

with TLCC in Fig. 3. Hence, the loading network is slightly modified by optimiz-

ing the parameters of the series and shunt transmission-lines. A 28Ω resistor

connected in parallel with a 3.9 pF capacitance is used to make the PA stable.

Fig. 3. Circuit schematic of the proposed TLCC for Class-E/F3.

Fig. 4. Simulated load impedances of the TLCC for class-E/F3 PA atfundamental and harmonic frequencies.


7


Furthermore, the input matching network provides the optimum input impedance of

the transistor, obtained by the source-pull simulation, to a 50Ω source.

The final photograph of the proposed class-E/F3 PAwith TLCC is illustrated in

Fig. 5. The circuit is fabricated on Rogers 5880 substrate with a thickness of 31mil

and dielectric permittivity of 2.2. The total size of the module is 8:2 cm � 5:8 cm.

The active device is biased with a drain voltage of 28V, gate bias voltage of −3Vand drain quiescent current of 68.1mA.

The proposed class-E/F3 PAwith TLCC is characterized under different driving

powers to evaluate its dynamic performance. The measured and simulated results

for output power, gain, drain efficiency (DE) and power-added efficiency (PAE)

versus RF input power are illustrated in Fig. 6. As shown in Fig. 6, The perform-

Fig. 5. Photograph of the fabricated class-E/F3 PA with TLCC.

Fig. 6. Simulated and measured output power, gain, DE and PAEversus RF input power on the condition that f0 ¼ 2:14GHz,VGS ¼ �3V, VDS ¼ 28V.


8


ance of a peak PAE of 78.0% and DE of 82.9% is obtained at an output power of

40.3 dBm.

Fig. 7 shows the measured PA performance of output power, gain, DE and PAE

from 1.9GHz to 2.4GHz with a constant input power of 30 dBm. A DE of larger

than 60% can be maintained from 2.0 to 2.36GHz.

As summarized in Table I, a performance comparison of the recently reported

high-efficiency microwave PAs is presented. A frequency-weighted average effi-

ciency (FE) is introduced here to evaluate the PA efficiency together with frequency

Fig. 7. Measured output power, gain, DE and PAE in terms offrequency.

Table I. Performance comparison of recently various high-efficiencymicrowave PAs

Ref. Classf0

(GHz)�

(%)PAE(%)

Gain(dB)

Pout,sat

(dBm)FE2

(%)

[10] E/F3 2.14 76.0 73.1 14.3 40.0 88.4

[17] PC1 E 2.80 76.0 70.8 10.7 40.1 91.6

[18] E 2.14 73.7 70.0 12.0 43.0 84.7

[19] E 2.90 77.5 72.2 12.2 40.2 94.2

[20] E 3.10 - 63.4 - - 84.1

[21] E−1 1.00 79.7 78.8 19.0 41.0 78.8

[22] F 2.40 82.2 74.0 10.0 20.0 92.1

[23] F 1.88 75.8 70.7 11.7 39.7 82.8

[24] F−1 1.00 83.1 81.3 15.9 39.7 81.3

[25] F−1 2.35 - 63.8 - 32.2 79.0

[26] EF 1.50 85.0 81.0 13.1 41.9 89.6

[27] EF3 3.00 - 63.4 - - 83.4

This work E/F3 2.14 82.9 78.0 12.3 40.3 94.3

1PC: parallel circuit.2FE: frequency weighted efficiency (GHz)0.25�PAE.


9


[28]. It is evident that the proposed PA products the highest FE among the

mentioned PAs because of its extended operating frequency and high efficiency.

5 Conclusion

In this paper, a transmission-line compensation circuit has been developed in order

to compensate the excess output capacitance and consequently extend the max-

imum operating frequency fmax of a class-E/F3 PA mode when keeping its optimal

mode of operation. Theoretical analysis has been presented so as to determine the

values of the required circuit elements in detail. Based on the methodology

developed in this paper, the proposed class-E/F3 PA has been designed, fabricated,

and measured. The high-performance results of the fabricated class-E/F3 PA have

been realized with the output power of 40.3 dBm, drain efficiency of 82.9% at the

operating frequency of 2.14GHz. In brief, due to its extended fmax, simple

construction and high performance, the class-E/F3 PA with TLCC is suitable for

use as a high efficiency PA operating in the microwave band.

Acknowledgments

This work was supported by the National Natural Science Foundation of China

under Grant 61501322.nts.


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High-efficiency class E/F3 power amplifiers with extended