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带宽拓展的E/F3类射频功率放大器设计(2020.09 MTT)-从理论到ADS版图-ADS工程（2000个子文件）

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共 2000 条

3732 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 68, NO. 9, SEPTEMBER 2020

A Generalized High-Efﬁciency Broadband

Class-E/F

Power Ampliﬁer Based on Design

Space Expanding of Load Network

Zhenxing Yang , Mingyu Li , Member, IEEE, Zhijiang Dai , Member, IEEE, Changzhi Xu,

Yi Jin, Tian Li, and Fang Tang

, Senior Member, IEEE

Abstract— This article presents an analytical and coherent

design method for the generalized high-efﬁciency broadband

parallel-circuit (PC) Class-E/F

power ampliﬁer (PA). By import-

ing the initial phase shift of the third harmonic and adding series

reactive element to the load network, a free design parameter can

be deﬁned and the design space of the load network parameters

are expanded. The design equations of the idealized waveforms

and the optimum values of the load network components are

derived in detail, and the performance of the peak drain voltage,

maximum operating frequency, and power output capability can

be improved. In addition, with the expanding space of load

network, the generalized PC Class-E/F

structure exhibits broad-

band capability. A matching method with the real frequency

technique (RFT) and the de-embedding technique is presented

to design the optimal broadband matching network. To verify the

validity of the proposed method, a broadband high-efﬁciency PA

working from 1.7 to 2.6 GHz (fractional bandwidth of 42%) is

designed. The experimental results of the fabricated PA present

high-efﬁciency characteristics of 68.5%–81% drain efﬁciency and

62%–75.8% power-added efﬁciency with 38.8–40.5 dBm output

power over the whole operation bandwidth.

Index Terms— Broadband, Class-E/F3, high efﬁciency,

impedance, parallel-circuit (PC), power ampliﬁers (PAs).

I. INT RODUCTION

IGH-EFFICIENCY p ower ampliﬁers (PAs) with

extended bandwidth are important solutions to save the

energy consumption and transmitter costs in modern wireless

communication systems. To improve efﬁciency of the PA,

several k inds of conﬁgurations have been widely investigated,

such as Class-D [1], Class-E [2], Class-F/F

−1

[3], and Doherty

PA [4], [5]. Among them, Class-E PA is one of the most

popular switching-mode ampliﬁers due to its higher efﬁciency

and relatively simple circuit topology. Theoretically, Class-E

PA can reach 100% collector or drain efﬁciency (DE) with

nonoverlap of the transient voltage and current waveforms.

Manuscript receiv e d February 3, 2020; re vised April 7, 2020 and May 24,

2020; accepted June 17, 2020. Date of publication July 23, 2020; date of

current version September 2, 2020. This work was supported by the National

Natural Science Foundation of China under Grant 61801377. (Corresponding

author: Mingyu Li.)

Zhenxing Yang, Mingyu Li, Zhijiang Dai, Tian Li, and Fang Tang are with

the School of Microelectronics and Communication Engineering, Chongqing

Uni versity, Chongqing 400044, China (e-mail: myli@cqu.edu.cn).

Changzhi Xu and Yi Jin are with the Xi’an Branch, China Academy of

Space Technology, Xi’an 710100, China.

Color versions of one or more of the ﬁgures in this article are available

online at http://ieeexplore.ieee.org.

Digital Object Identiﬁer 10.1109/TMTT.2020.3009530

However, the obvious disadvantage of Class-E PA is its

typical narrow bandwidth performance. To overcome this

problem, various design approaches have been proposed to

extend the bandwidth of Class-E PA. For example, Class-E

mode PA with parallel-circuit (PC) can achieve the broadband

capability using reactance compensation technique in [6 ].

Although Class-E PA can achieve good performances with

a simple load network, it still suffers from its high peak switch

voltage (V

MAX

) stress of 3.56 times of the DC supply voltage

), which will limit the practical circuit im plementation

even for moderate output power level. Recently, some new

Class-E ampliﬁer conﬁgurations were constantly studied to

improve the PA performance, where V

MAX

, maximal operating

frequency ( f

MAX

), and output power capability (c

) of the PA

should be taken into account together [7]–[25].

Among them, the harmonic tuning method can effectively

improve the ampliﬁer performance by adopting the resonance

network, which is widely used in conventional Class-F or

inverse Class-F PAs [12]–[19]. Correspondingly, the combined

mixed Class EF or E/F operation modes can be provided. It is

obvious that Class-EF is a hybrid of Class-E and Class-F, and

Class-E/F is a hybrid of Class-E and inverse Class-F. These

mixed modes lead to a tradeoff between circuit simplicity of

Class-E and beneﬁts of Class-F or inverse Class-F by reducing

the peak voltage at the device output. The mixed Class-EF

and its variants have been reported in [12]–[14]. For example,

the performance of Class-EF

circuit is analyzed in terms of

its duty cycle in [12], which can offer a V

MAX

of 3.46 V

at a duty cycle of 0.5. The Class-FE PA presented in [13]

offers a low V

MAX

of only 2V

for duty cycles less than

50% as in Class-F. In [14], two new variants of Class-EF

PA with harmonic-peaking structure are proposed to enhance

the maximal operating frequency. In [15]–[19], the mixed

Class-E/F family is deﬁned and analyzed, which have the

hybrid features of Class-E and inverse Class-F. In these modes,

the zero-voltage and zero-voltage-derivative Class-E switching

conditions can be obtained and some number of harmonics can

be tuned in the fashion of inverse Class-F, and the desirable

voltage and current waveforms can be achieved for improved

circuit performance. Generally, tuning the second harmonic

tends to increase the drain peak voltage even higher than

in Class-E mode, while tuning the third harmonic tends to

reduce the peak voltage [15]. For example, the Class-E/F

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Authorized licensed use limited to: University of Electronic Science and Tech of China. Downloaded on March 27,2024 at 05:14:43 UTC from IEEE Xplore. Restrictions apply.

YANG et al.: GENERALIZED HIGH-EFFICIENCY BROADBAND CLASS-E/F

PA 3733

proposed in [15] can offer a V

MAX

of 3.67V

, while the Class-

E/F

PA can offer a V

MAX

of 3.14V

. The performance of

Class-E/F

3,5

is further analyzed in [16], which can offer a

MAX

of 3.20 V

. Therefore, Class-E/F

PA, as an attractive

solution for considering circuit simplicity, high performance,

and sufﬁciently low drain peak voltage, has been comprehen-

sively researched [16]–[19].

On the other hand, to further improve the performance

of the Class-E ampliﬁer, such as f

MAX

and c

of the PA,

the PC Class-E PA structure with the ﬁnite DC feed inductor

have been developed in [20]–[24]. The value o f the maximum

operation frequency of the PC Class-E PA can be increased

to 1.4 times than that of the optimum Class-E PA w ith

shunt capacitance. The value of the output power capabil-

ity can be increased to 1.06 times [20]. However, a larger

MAX

of 3.65V

will be offered by the PC Class-E PA

compared with the conventional Class-E PA with a V

MAX

of 3.56 V

. A similar situation can also be obtained in [22].

These char acteristics will limit its applications in practical

system. To reduce the peak drain voltage, a combination of

PC structure with the m ixed Class-E/F mode was proposed

in [25], which can achieve better performance in V

MAX

, f

MAX

and c

without signiﬁcantly increasing the circuit complexity

and is suitable for designing high-frequency PA.

In this article, an extended and generalized PC Class-

E/F

PA is proposed and analyzed. Different from the design

procedure of [25], by importing the initial phase shift of the

third harmonic and adding a series reactive element to the load

network, the free parameter can be deﬁned correspondingly.

Then, the design equations of Class-E/F

PA are derived in

terms of the free parameter whose value can be chosen within

a certain range, which will lead to an inﬁnite number of

solutions for the load network parameters. It can also be

shown that the generalized PC Class-E/F

PA proposed in this

article can pr ovide higher f

MAX

than that of [12] and [25]

through detailed theoretical analysis. Furthermore, the broad-

band capability of the proposed generalized PC Class-E/F

PA is analyzed in detail and the optimal broadband matching

network is designed. In summary, the contributions of this

article are summarized as follows. First, the design space of the

PC Class-E/F

PA introduced in [25] is reﬁned and expanded

through importing the initial phase shift of the third harmonic

and the free parameter. Second, profound insights about the

design tradeoffs among V

MAX

, f

MAX

,andc

of Class-E/F

PA are provided through different circuit parameters; Third,

a transmission-line (TL) load network design approach is

presented, which not only fulﬁlls the operational conditions of

the proposed generalized PC Class-E/F

PA but also extends its

bandwidth. Therefore, the proposed generalized PC Class-E/F

PA can provide a good choice for high-efﬁciency broadband

microwave power ampliﬁcation.

This article is organized as follows. In Section II, the

generalized PC Class-E/F

load network along with the free

parameter are given, and the circuit analysis along with the

design equations about the voltage and current waveforms

are derived in detail. Section III introduces the TL load

network design approach for the b roadban d capability of

the proposed generalized PC Class-E/F

PA. The simulation

Fig. 1. Basic circuit of a generalized PC Class-E/F

PA.

Fig. 2. Equi valent circuit of the generalized PC Class-E/F

PA.

and measurement results are presented in Section IV. Then,

Section V provides the conclusion.

II. C

IRCUIT ANALYS I S

The basic circuit of a generalized PC Class-E/F

PA is

shown in Fig. 1. It is composed of an ideal device, a shunt

capacitor C, a shunt inductor L, a series resonant L

tuned

at the fundamental frequency, and a parallel series resonant

tuned at the third harmonic, a series reactive element X,

and a load resistance R. The derivation processes of the design

equations are carried out under the following assumptions.

1) All the circuit elements have no parasitic parameters.

2) The transistor works as an ideal switch. Namely,

the switch-

ON resistor is 0, the switch-OFF resistor is

inﬁnite, and its switching is instantaneous.

3) The quality factors of the series resonant and parallel

series resonant are sufﬁciency high so that the current

through the resonant can be considered as a sinusoidal

wave.

4) The shunt capacitance C is assumed to be linear and

consists of a shunt capacitance C

ext

and the transistor

output capacitance C

out

,whereC

out

is independent of

the drain voltage.

To further simplify the analysis o f the basic circuit structure,

Fig. 2 presents the equivalent circuit. Through analyzing the

voltage and current waveforms, the characteristics of the gen-

eralized PC Class-E/F

can be determined. Meanwhile, the

generalized PC Class-E/F

PA works with zero-voltage switch-

ing (ZVS), and the zero-voltage-der ivative switching (ZVDS)

conditions can be written as follows:

(

)

θ=2π

= 0(1)

(

)

dθ



θ=2π

= 0(2)

where v

(θ) is the voltage across the switch, θ = ωt,andω

is the angular frequency.

Authorized licensed use limited to: University of Electronic Science and Tech of China. Downloaded on March 27,2024 at 05:14:43 UTC from IEEE Xplore. Restrictions apply.

3734 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 68, NO. 9, SEPTEMBER 2020

The output current i

(θ) ﬂowing through the resistor and the

nth-harmonic current i

(θ) ﬂowing through the L

parallel

series resonant are all sinusoidal and can be deﬁned as follows:

(

)

= I

sin

(

θ + ϕ

)

(3)

(

)

= I

sin

(

nθ + ϕ

)

(4)

where I

is the fundamental frequency current amplitude and

is the initial phase shift. I

is the nth-harmonic current

amplitude and ϕ

is the nth-harmonic initial phase shift.

The relationship b etween the voltage and the current on the

inductor and the capacitance can be described as follows:

(

)

= ωL

(

)

dθ

(5)

(

)

= ωC

(

)

dθ

(6)

where v

(θ) and v

(θ) are the voltages on the inductor L

and the capacitor C, respectively, and i

(θ) and i

(θ) are the

current ﬂowing through the inductor L and the capacitor C,

respectively.

When the switch is

ON,thatis,forθ [0, π], the voltage

on the switch is

(

)

= V

− v

(

)

= 0. (7)

The current ﬂowing through the shunt capacitance C is 0

according to (6). Consequently, the current ﬂowing through

the switch is

(

)

= i

(

)

+ i

(

)

+ i

(

)

. (8)

According to (3)–(5), i

(θ) can be rewritten as follows:

(

)

ωL

θ +i

(

)

+ I

sin

(

θ + ϕ

)

+ I

sin

(

nθ + ϕ

)

(9)

Since the initial

ON-state condition is i

(0) = 0, the initial

value for current i

(θ) at θ = 0 can be obtained as follows:

(

)

=−I

sin

(

)

− I

sin

(

)

. (10)

As a result, the switch current i

(θ) is

(

)

ωL

θ + I

[sin

(

θ + ϕ

)

− sin

(

)

]

+ I

[sin

(

nθ + ϕ

)

− sin

(

)

]. (11)

The amplitude of the nth-harmonic components can be

calculated using the Fourier series expansion



2π

(

)

sin

(

nθ + ϕ

)

dθ. (12)

Then I

can be calculated as follows when n is odd:

−2sin(ϕ

) cos(ϕ

)

−

2sin(ϕ

)−nπ cos(ϕ

)

sin(2ϕ

)

(13)

where

p =

ωLI

. (14)

When the switch is turn

OFF,thatis,forθ[π,2π ],

the current ﬂowing through the switch is 0 and then

(

)

= i

(

)

+ i

(

)

+ i

(

)

. (15)

Then the following initial

OFF-state conditions can be

obtained:

(

)

= 0,

(

)

ωL

− 2I

sin

(

)

− 2I

sin

(

)

. (16)

Rearranging (15) with (5) and (6) under the initial condi-

tions, the following relationship can be obtained:

ωC

(

)

dθ

ωL



− v

(

)

]dθ + i

(

)

+ I

sin

(

θ + ϕ

)

+ I

sin

(

nθ + ϕ

)

. (17)

The above equation can be simpliﬁed as a linear nonhomo-

geneous second-order differential equation

(

)

dθ

+ v

(

)

− ωLI

cos

(

θ + ϕ

)

−nωLI

cos

(

nθ + ϕ

)

− V

= 0. (18)

The general solution fo r this differential equation can be

obtained in the following normalized form:

(

)

= C

cos

(

qθ

)

+ C

sin

(

qθ

)

+ 1 −

1 − q

cos

(

θ + ϕ

)

npq

− n

cos

(

nθ + ϕ

)

(19)

where the parameter q is deﬁned as follows:

q =

√

. (20)

It is worth noting here that parameter q in (20) has the same

physical meaning from q in [21], where it is caused by the

freedom of the ﬁnite DC-feed inductor L value. C

and C

can be obtained from the initial OFF-state conditions of (16),

which can be given as follows:

=−

(

cos

(

qπ

)

+ qπ sin

(

qπ

))

−

1 − q



q cos

(

)

cos

(

qπ

)

−



1−2q



sin

(

)

sin

(

qπ

)



− n



nq cos

(

qπ

)

cos

(

)

−



− 2q



sin

(

qπ

)

sin

(

)



(21)

=−(sin(qπ) − qπ cos(qπ))

−

1−q



q cos(ϕ

) sin(qπ)+



1−2q



sin(ϕ

) cos(qπ)



− n



nq sin(qπ)cos(ϕ

)



− 2q



cos(qπ)sin(ϕ

)



. (22)

For an idealized DE of 100%, the consumed DC power is

equal to the output power P

delivered to the load R,thatis,

= I

· V

. (23)

Authorized licensed use limited to: University of Electronic Science and Tech of China. Downloaded on March 27,2024 at 05:14:43 UTC from IEEE Xplore. Restrictions apply.

YANG et al.: GENERALIZED HIGH-EFFICIENCY BROADBAND CLASS-E/F

PA 3735

Fig. 3. Equivalent PC Class-E/F

load network at the fundamental frequency.

The DC current I

normalized to I

can be determined by

applying the Fourier series expansion to (11) as

2π



2π

(

)

dθ =

2π

[2 cos

(

)

− π sin

(

)

2 p

−



π sin

(

)

−

cos

(

)





. (24)

Using the Fourier series expansion to (19) and rearranging

(23), the following relationship can be obtained:

=−



2π

(

)

sin

(

θ + ϕ

)

dθ =

. (25)

Once the parameter q is set to be free parameter,

the unknown parameters p, ϕ

,andϕ

can be solved with

the three system equations of (1), (2), and (25).

The equivalent load network at the fundamental frequency is

given in Fig. 3. As shown in Fig. 3, the fundamental frequency

voltage V

consists of the two quadrature components V

and V

, which is fundamental frequency voltage through the

load R andreactance X, r espectively. A positive V

means

the reactance X is an inductor, while a negative V

means

the reactance X is a capacitor.

In th is case, the sinusoidal voltage v

(θ) can be expressed

as follows:

(

)

= v

(

)

+ v

(

)

=−V

sin

(

θ + ϕ

)

− V

cos

(

θ + ϕ

)

= V

sin

(

θ + δ

)

(26)

where δ is the phase shift of v

(θ). Correspondingly, according

to the amplitude and phase relationships of (26), the following

two equations can be derived:













(27)

δ = ϕ

− π + arctan





. (28)

Here, the normalized amplitude of V

can be calculated

using the Fourier series expansion:

=−



2π

(

)

cos

(

θ + ϕ

)

dθ. (29)

Commonly, the output power P

and the DC voltage V

are given as design parameters for most practical PA design.

The other design parameters can be described as the function

of P

and V

Rearranging (23), the optimum load resistance R can be

calculated as follows:

R =





= 2





. (30)

Combining (14) and (23), the series inductor L can be

expressed as follows:

ωL = p

. (31)

Subsequently, the shunt capacitor C can be derived from

(20)

ωC =

ωL

. (32)

The series reactance X can be expressed as follows:

. (33)

The maximum operating frequency f

MAX

in generalized PC

Class-E/F

mode is limited by the device output (collector or

drain–source) capacitance C

out

. If the shunt capacitance C is

equal to the device output capacitance (i.e., C = C

out

), f

MAX

can be expressed as follows:

MAX

= k

out

. (34)

As a result, the p arameter k can be derived from

(32) and (34)

k =

f · V

2π pq

. (35)

Another very important characteristic of Class-E/F PA, that

is, the output p ower capability c

, which is deﬁned as the ratio

of the DC supply power and the transistor maximum power,

can be given as follows:

MAX

(36)

where V

MAX

and I

MAX

are the peak switch voltage and current,

respectively.

As shown in Fig. 3, the optimum fundamental load

impedance for generalized PC Class-E/F

operation seen from

the switch can be determined through the load network para-

meters as

opt,E

(

R + jX

)

jωC

//jωL

−ωLX + j ωLR



1 − ω



+ j



ωL + X − ω

LC X



(37)

and the phase angle ζ of Z

opt,E

ζ = tan

−1



−R



− tan

−1



ωL + X − ω

LC X



1 − ω





. (38)

The phase diagram of the fundamental frequency com-

ponents of the normalized voltages and currents is shown

in Fig. 4. Table I lists the detailed values of the corresponding

voltages, currents and load network parameters of the phase

diagram in Fig. 4. It should be pointed out that all the results

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