1-4244-1468-7/07/$25.00 ©2007 IEEE 287

Linearization of Multichannel Amplifiers Close to Saturation with Improved Efficiency

Natasa Maleš-Ilić, Aleksandar Atanasković, Bratislav Milovanović

Abstract – In this paper an new linearization approach has been applied to the chain of three amplifiers connected in cascade. The second harmonics of the fundamental signals (IM2) together with the fourth-order nonlinear signals (IM4) are led to the output of third amplifier in cascade. The linearization scheme is arranged so that the IM2 signals are extracted at the output of the second amplifier whereas some additional nonlinear component such as MESFET is exploited as the source of IM2+IM4 signals. Generated nonlinear signals are combined, then adjusted in amplitude and phase and put at the third amplifier output. The third amplifier in cascade biased at class-A is harmonically controlled at input and output. This configuration enables high gain of class A amplifier combined with higher-drain efficiency. Consequently, power-aided efficiency is increased. Also, the third- and fifth-order intermodulation products of a complete amplifying system are reduced in a wide range of the input power going close to saturation.

Keywords – Multichannel amplifier, Intermodulation distortion, Linearization technique, Second harmonics, Saturation, Power-aided efficiency.

I. INTRODUCTION

One of the main challenges in wireless communications lies in the development of linear and efficient amplifiers. The influences of fundamental signals’ second harmonics (denoted as IM2 signals) to the third-order intermodulation products (IM3) in microwave power amplifiers have been investigated and applied in [1]-[4]. The basic concept of the linearization technique with the injection of IM2 signals gives good results in reduction of the IM3 products up to the certain power of the fundamental signals that depends on load impedance [3]. However, the linearization approach does not reduce the fifth-order intermodulation products (IM5), which are the results of microwave amplifier nonlinearity and should be considered as well. The linearization technique that uses the injection of IM2 signals has been extended in [5] by introducing the injection of the fourth-order nonlinear signals (IM4) at frequencies close to the IM2 signals in order to suppress the IM5 products of a single amplifier.

Nataša Maleš-Ilić is with the Faculty of Electronic Engineering, Aleksandra Medvedeva 14, 18000 Niš, Serbia, E-mail: natasam@elfak.ni.ac.yu

Aleksandar Atanasković is with the Faculty of Electronic Engineering, Aleksandra Medvedeva 14, 18000 Niš, Serbia, E-mail: beli@elfak.ni.ac.yu

Bratislav Milovanović is with the Faculty of Electronic Engineering, Aleksandra Medvedeva 14, 18000 Niš, Serbia, E-mail: bata@elfak.ni.ac.yu

In practice, the transmit path of microwave signals is usually composed of a chain of cascaded amplifiers to achieve sufficient output power and signal gain. The linearization concept considered in [6] investigates linearization of three amplifiers connected in cascade. In the concept, IM2 signals produced at the output of the first amplifier in cascade are combined with the IM2 and IM4 signals turning up at the output of the second amplifier that is biased at class B or AB to provide the sufficient power level of those signals. Adjusted in amplitude and phase resulting IM2+IM4 signals are put at the input of the third amplifier. The appropriate harmonic termination of the third amplifier biased at class-A corresponds to class-F amplifier [7] that is a harmonically controlled by the IM2+IM4 signals at the input.

In the linearization approach proposed in this paper the IM2+IM4 signals are driven to the third amplifier output. The second amplifier in cascade operates at class-A to produce a required power of IM2 signals retaining the power of IM4 signals sufficiently low. One additional nonlinear source is required in the linearization circuit to produce IM2+IM4 signals. The slight amplitude adjustment of the generated signals is needed before their combining in 180°-hybrid. Afterward, resulting IM2+IM4 signals are led to the amplifier output to suppress the intermodulation products and to provide higher efficiency of harmonically controlled amplifier [8] that is biased at class-A. Such a configuration gives the increase of drain efficiency accompanied with the high gain of class-A amplifier.

II. AMPLIFIER DESIGN

The design of the amplifying system with the linearization circuit, which is represented in Fig. 1, has been carried out by the program Advance Design System (ADS). The Amp I has been designed as distributed amplifier in configuration of three cascaded single-stage amplifier. MESFET used for amplifier design is Mitsubishi MGFC2407 modeled by Curtice nonlinear model given by the manufacturer. The Amp II is a single stage narrowband amplifier operating at 2.5 GHz with NEC NE71000 transistor which nonlinear model is EEFET3 assigned by the manufacturer. The nonlinear amplifier denoted as Amp III has been designed as a broadband single-stage amplifier where MESFET nonlinearity is modeled by Curtice-cubic model. The third amplifier harmonically controlled at the input and output [8], which is characterized by the high drain efficiency, is biased at class-A. Input circuit is designed to shorten IM2 signals whereas the output circuit is initially set as in class-F amplifier (shorten IM2 signals and open the third harmonics), then optimized to provide the required termination for IM2 signals retaining

288

high drain efficiency. The designed amplifying system amplifies the fundamental signal at 2.5 GHz by 25 dB in reference to the input. It should be stressed that Harmonic balance analysis has been carried out in simulation.

Fig. 1. Amplifier with the circuit for linearization

The fundamental signals from the first amplifier in cascade are led to the inputs of the second amplifier and a nonlinear source. The second amplifier in cascade operates at class-A to produce a required power of IM2 signals retaining the power of IM4 signals sufficiently low. The nonlinear source is composed of MESFET transistor operating at adjustable bias conditions to enable simultaneously an enough power of both IM2 and IM4 signals.

The linearization procedure proposes that the IM2 signals from the second amplifier output are combined with IM2+IM4 signals through 180-hybrid to attain a suitable power levels of both IM2 and IM4 signals that should be additionally adjusted in amplitude and phase and guided to the drain of the third amplifier. The term ‘feedforwarded’ will be used for latter operation in the following text. Since the nonlinear source and second amplifier in cascade are driven by the signal of the same power they generate nonlinear IM2 signals that have nearly equal power levels. The power of IM4 signals differs remarkably that is caused by distinct bias points.

It should be stressed that in the new proposed linearization approach there is one nonlinear source more than in the concept described in [6]. The main reason for that is a need to avoid the significant attenuation of IM2+IM4 signals generated at the output of the second amplifying stage before their combining with IM2 signals from the first stage which are at the substantially lower power levels. Moreover, the resulting signals should be amplified significantly to reach the appropriate power levels for linearization. In new concept, the second amplifier can be biased in more linear region, that is accompanied with higher gain, giving the adequate IM2 signals at its output. Moreover, in dependence on bias point, an additional nonlinear source yields IM2+IM4 signals of power levels that are slightly higher or nearly equal to the IM2 signals from the second amplifier. Therefore, the mixing of IM2 and IM2+IM4 signals does not acquire great attenuation keeping power level of resulting signals on more suitable

level, that should be additionally amplified incomparably less than in concept [6].

The ideal elements from ADS have been used for components such as bandpass filters, phase shifters, variable attenuators, amplifier, power combiners and dividers.

III. ANALYSIS

The expression for the nonlinearity of MESFET in amplifier circuit, under the assumption of neglecting the memory effect, is represented by eleven terms as given by Eq.(1), [9], [10]. The drain-source current is dependent upon two control voltages: vgs–voltage between gate and source and vds-voltage between drain and source of the transistor. The Eq.(1) connects the nonlinearity of the drain-source current ids, in reference to voltage vgs that is represented by the

coefficients )(10

iK to )(50iK ,where index i, i=1,2,3, marks the

order of amplifier in cascade. The nonlinearity of drain-source current in terms of vds is

expressed by the coefficients )(01iK to )(

03iK . Also, the equation

encompasses “mixing” terms )(11

iK , )(12

iK and )(21iK .

( ) ( ) ( ) ( ) ( ) ( ) ( )( ) ( ) ( ) ( )( ) ( ) ( ) ( ) ( ) ( )( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ... t

,

212

22111

303

20201

550

440

330

22010

++++

++++

+++

+++=

tvtvKtvtvKvtvK

tvKtvKtvK

tvKtvK

tvKtvKtvKvvi

dsgsi

dsgsi

dsgsi

dsi

dsi

dsi

gsi

gsi

gsi

gsi

gsi

dsgsds

(1)

A carrier supplemented with a baseband spectrum VB(jω) can represent the spectrum of a digitally modulated fundamental signal, Vinfund(jω), as given below:

( ) ( ) ( )021

ω±ωδ⊗ω=ω jVjV Binfund. (2)

If IM2+IM4 signals from the nonlinear source combined with the IM2 signals from the output of second are led to the drain of the third amplifier the drain-source voltage v’ds can be written by Eq.(3), where vds is the drain-source voltage before putting the IM2 and IM4 signals to the amplifier output.

( ) ( )

( ) ( )[ ]

( ) ( ) ( ) ( )[ ]} ( )( )241

'

0

4323

)3(42

)3(

4323

ω±ωδ⊗ω⊗ω⊗ω⊗ω

ρ+⎩⎨⎧ ω⊗ωρ−

+ω=ω

ϕ−ϕ−

+

jVjVjVjV

ejVjVe

jVjV

BBBB

jFBB

jF

dsIMIMds

FF(3)

To approach the optimum power level of IM2 and IM4 signals for the linearization they should be set on adequate amplitude and phase. Parameters F

23ρ and F23ϕ represent amplitudes and

phases of the IM2 signal driven at the drain of the third amplifier, whereas F

43ρ and F43ϕ relate to the same parameters

when IM4 signal is considered.

289

The drain-source current of the third amplifier at frequencies of IM3 and IM5 products is given by Eqs.(4) and (5), respectively where the coefficients )2,1(

10K to )2,1(50K are

treated as dominant nonlinerities of the chain of the first and second amplifier in cascade. The coefficients )3(

10K to )3(50K ,

)3(11K , )3(

12K and )3(21K characterize the third amplifier.

In (4) the first term relates to the IM3 products of the first and second amplifiers linearly transmitted by the third amplifier. The second term exists due to the cubic nonlinearity of the third amplifier that mingles fundamental signals. The third term (mixing term )3(

11K ) is generated between gate-source voltage of the fundamental signal and drain-source voltage of the feedforwarded IM2 signal.

( )

( ) ( ) ( ) ( )0

2311)3(

30)2,1(

10

)3(10

)2,1(303

21

41

43

43

23

ω±ωδ⊗ω⊗ω⊗ω

⎪⎭

⎪⎬⎫⎥⎦

⎤⎢⎣

⎡ρ−+

⎩⎨⎧ +≈ω

ϕ−

jVjVjV

eKKK

KKjI

BBB

jF

IMds

F (4)

According to this, it is possible to reduce spectral re-growth caused by the third-order distortion of fundamental signal by choosing the appropriate amplitude and phase of feedforwarded IM2 signal ( F

23ρ , F23ϕ ).

The nonlinearity of the drain-source conductance expressed by coefficients )3(

01K , )3(02K and )3(

03K is assumed to have a negligible contribution to the IM3 power levels according to [9] and [10]. The mixing terms between drain and gate, )3(

12K and )3(

21K produce drain-source current at IM3 frequencies with the opposite phase, so that they cancel each other [9].

( ) ( )

( )

( ) ( ) ( ) ( ) ( )

( )0

2223

)3(12

433

11)3(

30)2,1(

30)3(

50)2,1(

10

310

)2,1(505

21

81

41

169

85

85

23

43

ω±ωδ⊗

ω⊗ω⊗ω⊗ω⊗ω⎭⎬⎫⎥⎦

⎤ρ+

⎢⎣

⎡+ρ−++

⎩⎨⎧ +≈ω

ϕ−

ϕ−

jVjVjVjVjV

eK

eKKKKK

KKjI

BBBBB

jF

jF

IMds

F

F

(5)

The first term in Eq.(5) represents IM5 products of the chained first and second amplifiers, that are linearly amplified by the third amplifier in cascade. The second term expresses the drain-source current of the IM5 products that is formed due to the existence of fundamental signals and amplifier nonlinearity of the fifth-order, )3(

50K . The first and second amplifiers generate IM3 products that interact over the third-order nonlinear term )3(

30K with fundamental signal run to the

third amplifier input (third term in Eq.(5)). Also, IM5 products are formed by )3(

11K term that stirs IM4 signals led at the output of the third amplifier and fundamental input signal. Mixing term which stands by )3(

12K coefficient in Eq.(5) is generated due to reaction between fundamental signal at the amplifier input and two IM2 signals observed at its output.

Therefore, it arises from Eq.(5) that a proper selection of the amplitude and phase of the IM4 signals in the fourth term reduces IM5 products.

IV. SIMULATED RESULTS

The designed amplifying system with the additional circuit for linearization has been tested for three sinusoidal fundamental signals at frequencies 2.5 GHz, 2.51 GHz and 2.522 GHz when the power of fundamental signals at the input is –19 dBm that is 3 dB below 1-dB compression point.

The output spectra consisting of the fundamental signals, IM3 and IM5 products are compared in Fig. 2 for the cases before and after linearization. Various results are gained for different input power levels and kinds of IM3 and IM5 signals. For example, all IM3 products at frequencies 2ωi-ωj (the first kind) and ωi+ωj-ωk (the second kind) i≠j≠k ∈(1,2,3) are approximately reduced by 18 dB. If the IM5 products at frequencies (2ωi+ωj-2ωk) and (3ωi-ωj-ωk) are concerned then the results become better for approximately 10 dB in reference to the case before linearization while IM5 products at frequencies (3ωi-2ωj) are decreased by 4 dB. Analyzing the results obtained when linearization approach proposed in [6] is applied it follows that the suppression of IM3 and IM5 products are only a few decibels for -19 dBm power of input signals.

Additionally, the amplifier has been simulated for OQPSK digitally modulated signals with 1.25 MHz spectrum width, carrier at frequency 2.5 GHz within a range of input power -17 to -11 dBm. The result that relates to the case when input power of fundamental signal is -15 dBm can be seen from Fig. 3. which compares the output spectra before and after linearization. The input power level corresponds to the output power into saturation region taking into consideration 6 dB pick to average ratio. The adjacent channel power ratio (ACPR) for ±900 kHz offset from carrier frequency over 30 kHz bandwidth becomes better for 17 dB. Also, the figure represents ACPR for 2.1-2.13 MHz offset, the range that belongs to the spectrum of IM5 products. The ACPR is improved by approximately 9 dB at this offset by applying the procedure proposed in this paper. Table 1. compares ACPR before and after linearization for the whole power range observed. It follows from the table that improvement in ACPR for both offsets is satisfactory at each power point. In addition, the Table 1 gives a raise of drain efficiency of the third amplifier in cascade when IM2+IM4 signals are feedforwarded in reference to the case before proposed procedure ((DA-DAbefore)%.

The class-A amplifier in the third stage provides the higher gain and output power in comparison with the case when the

290

TABLE I SIMULATED PARAMETERS OF OUTPUT SIGNAL FOR OQPSK DIGITALLY MODULATED SIGNAL FOR THE RANGE OF CARRIER INPUT POWER

Power [dBm] -17 -15 -13 -11 (DA-DAbefore)% 1.1 5.2 13.3 27.0 (PAEa-PAEb)% 4.4 11.8 23.2 38.7

Pout [dBm] 14.8 14.9 16.1 16.8 17.1 18.6 17.7 20.0 ACPRlow [dBm]

(-915 to -885kHz) -43.7 -58.1 -37.8 -55.7 -33.9 -47.8 -31.6 -41.7

ACPRhigh [dBm] (885 to 915kHz)

-39.6 -57.6 -35.9 -51.7 -33.7 -42.6 -32.6 -37.8

ACPR1low [dBm] (-2.13 to-2.1MHz)

-61.5 -65.6 -62.8 -72.8 -52.4 -66.8 -46.3 -62.0

ACPR1high [dBm] (2.1 to 2.13MHz)

-62.7 -67.9 -68.4 -77.4 -56.9 -68.3 -48.9 -65.5

third stage is class-F amplifier; therefore, the power-aided efficiency (PAE) is improved in reference to the class-F case as given in Table 1 (PAEa-PAEb)%.

Fig. 2. Output spectrum for -19 dBm input power of fundamental

signals; before (dashed line) and after linearization (solid line)

Fig. 3. Simulated spectrum of the output voltage for OQPSK

digitally modulated signal before (gray line) and after linearization (black line) for -15 dBm carrier input power

V. CONCLUSION

The linearization approach proposed in this paper uses the IM2 signals generated at the output of the second amplifier in cascade and IM2+IM4 signals appearing as the output of a high-order nonlinear component. Those signals are combined, adjusted and led to the amplifier output. The proposed technique gives good results in reduction of the IM3 and IM5

products for a wide range of the input power going to saturation. Additionally, IM2 and IM4 signals are adjusted not only to lower the IM3 and IM5 products but also to reach the high power-aided efficiency Quite the most important fact is that the linearization is enabled at high power levels that was not possible to achieve by the injection of IM2+IM4 signals at the third amplifier input.

REFERENCES

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