Chapter2
syphilisModulation Schemes Effect on RF Power
Amplifier Nonlinearity and RFPA Linearization Techniques
2.1Introduction
In this chapter,RF modulation schemes effects on RF power amplifier nonlinearities are prented.A review of various power amplifier RF linearization techniques are discusd.
2.2RF Modulation Scheme in Bandpass Radio
Communication Channel
In radio communications,modulation can be described as the process of conveying a message signal by superimposing an information bearing signal onto a carrier signal by varying the signal characteristic[31–33].Modulation is the process of changing a higher frequency signal in proportion to a lower frequency one or vi versa.The higher frequency signal is referred to as the carrier signal and the lower frequency signal is referred to as the information bearing message signal or modulating signa
l [31–33].The characteristics(amplitude,frequency or pha)of the carrier signal are varied in accordance with the information bearing signal.The high-frequency carrier signals can be transmitted over the air,overfiber or coax cable.The u of high frequency signals will make the amplifier and antenna design easier for effective radio design[32,33].
商务英语课程Figure2.1shows the up conversion of the complex-valued baband signal x’(t)to the passband then the transmission of the real-valued bandpass signal x(t) through the communication channel[31].After the bandpass signal goes through the channel,a down-conversion of the bandpass output Y(t)into a complex-valued baband signal Y’(t)occurs.The baband signal x’(t)is up-converted to the bandpass signal by amplitude,pha or frequency modulation in order to transmit it.The modulated bandpass signal x(t)can be described as
Z.El-Khatib et al.,Distributed CMOS Bidirectional Amplifiers:Broadbanding
7 and Linearization Techniques,Analog Circuits and Signal Processing,
DOI10.1007/978-1-4614-0272-52,©Springer Science+Business Media New York2012
82Modulation Schemes Effect on RF Power Amplifier Nonlinearity :::
Fig.2.1A general universal illustration of a bandpass communication channel system
x.t/D A.t/cos .2 f o t C .t//(2.1)
where f o is the carrier frequency,A(t)is the amplitude and (t)is the pha modulation.
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The bandpass signal x(t)has an envelope bandwidth lower then the carrier frequency f o .Using trigonometric identities,this signal can be re-written as
x.t/D I .t/cos .2 f c t/ Q.t/sin .2 f c t/
第二国际
(2.2)
where I(t)is the in-pha component and Q(t)is the quadrature component
I .t/D A.t/cos ŒÂ.t/
(2.3)Q.t/D A.t/sin ŒÂ.t/
(2.4)Conquently,the bandpass signal x(t)can be re-written in complex form as
x.t/D A.t/cos ŒÂ.t/ cos .2 f c t/ A.t/sin ŒÂ.t/ sin .2 f c t/(2.5)x.t/D A.t/cos Œ2 f c t C Â.t/ D Re A.t/e jÂ.t/e j 2 f c t
(2.6)x.t/D Re x 0.t/e j 2 f c t
(2.7)where x’(t)is the baband input signal and can be reprented as
x 0.t/D I .t/C jQ.t/
(2.8)x 0.t/D A.t/e jÂ.t/(2.9)Therefore,the real-valued bandpass input signal x(t)can be obtained from the complex valued baband input signal x’(t)as [31,33]
x.t/D Re ˚x 0.t/e j 2 f o t «(2.10)
2.2RF Modulation Scheme in Bandpass Radio Communication Channel9
Fig.2.2Ideal radio quadrature upconverter transmitter
where f o is the carrier frequency.Similarly,the baband output signal y’(t)can be obtained from the bandpass output signal y(t)through demodulation process 2e j2 f o t.
The communication channel can be linear or nonlinear.The choice of a modula-tion scheme depends on the physical characteristics of this channel,required levels of performance and hardware trade-offs[33].
2.2.1Ideal Radio Transmitter
As shown in Fig.2.2the baband processor converts the information we want to nd into data.The data can be either analog(continuously varying)or digital(in discrete states)in format[31,33,34].
An ideal radio quadrature upconverter transmitter generates a high-frequency carrier for the data information to ride on.To do this we u a component called an oscillator as shown in Fig.2.2.Ideal radio quadrature upconverter transmitter as shown in Fig.2.2has an oscillator that converts DC bias into a radio-frequency carrier.Then the carrier is combined with the data using a component called a modulator[32–34].The data adjusts or modulates the characteristics of the carrier(amplitude,frequency or pha)in a controlled manner.The third step is to increa the signal strength with a power amplifier so that it can be detected by the receiver.The output of the power amplifier feeds an antenna which broadcasts the information carrying signal into the air.It also can be transmitted through other communication mediums such asfiber or coax cable[32–34].
异乡人医生2.2.2RF Power Amplifier Linearity for Non-Modulated Signal Active MOSFET devices can be modeled by nonlinear current and charge sources that depend on the device voltages[12,13].The nonlinear sources will give ri
102Modulation Schemes Effect on RF Power Amplifier Nonlinearity::: to distortion when driven with a
modulated signal.The real MOSFET device output impedance is nonlinear and the mobility is not a constant but a function of the vertical and horizontal electricfield.We may bias the active MOSFET device where the device behavior is more exponential.And there is also an internal feedback so when the input signal driven into the amplifier is incread,the output is also incread until a point where distortion products can no longer be ignored[12,14].
No transistor is perfectly linear since the inherent nonlinearity of the diode junctions that compri many of the active devices found in most amplifiers.The harmonics of the output signal are generated by nonlinearities of the MOSFET devices.The major three nonlinear elements of the MOSFET devices are nonlinear transconductance g m,the device drain capacitance C d and gate capacitance C gs [12,15].The real MOSFET devices generate higher order distortion[12,16].Models are ud to characterize the nonlinear behavior of a miconductor device in order to predict the resultant signal properties[15,16].
Power amplifiers can be classified in to two categories,linear and nonlinear.Lin-ear power amplifiers prerve amplitude and pha information where as nonlinear power amplifiers only prerve pha information[32,33].Linear power amplifiers employ transistors as current sources with high impedance.Nonlinear power am-plifiers employ transistors as switches with low impedance.Linear p
ower amplifiers can drive both broadband and narrowband loads.Nonlinear power amplifiers usually drive a tuned circuit narrowband load.Models are ud to characterize the nonlinear behavior of a miconductor device in order to predict the resultant signal properties. The simple polynomial approximation is a nonlinear transfer function bad upon the Taylor ries expansion.Typically thefirst-order(gain),cond-order(squaring) and third-order(cubing)terms are considered[15,16].
Power amplifier device nonlinearity can be modeled by a polynomial[14,35]
v o.t/D f.v i.t//D a1v i.t/C a2v2
i .t/C a3v3
i
.t/C a N v N
i
.t/D
N
X
n D1
a N v N
i
.t/
(2.11)
Applying a single-tone RF signal to the power amplifier transistor
v i.t/D A1cos.!o t C 1/(2.12)
v o.t/D a1A1cos.!o t C 1/C a2A2
1cos2.!o t C 1/C C a n A n
desktop是什么意思1
cos n.!o t C 1/
(2.13)
Writing out the respon v o.t/by performing trigonometric expansion[36,37]
v o.t/D a1A1cos.!o t C 1/C a2A2
1
2
a2
A2
1
环保材料英文2
cos2.2!o t C2 1/
C a3A3
1
4
cos2.3!o t C3 1/C a3
3A3homework什么意思
1
4
cos2.!o t C 1/(2.14)
2.2RF Modulation Scheme in Bandpass Radio Communication Channel
11Table 2.1One tone signal
generated harmonics a 1A 1cos .!o t C 1/
Linear gain a 2A 21DC offt (lf-bias)a 2A 212cos 2.2!o t C 2 1/
Second harmonic distortion a 3A 314cos 2.3!o t C 3 1/
Third harmonic distortion a 33A 314cos 2.!o t C 1/(AM AM and AM PM)
Pin RF PA Pout [Hz]R F I n p u t P o w e r R F O u t p u t P o w e r Fundamental Zone Fundamental Harmonics Sum of Intermods
Spectrum of Fundamental Tones, Harmonics and Intermodulation Products [Hz]
Second Harmonic Zone DC Zone D P D P Third Harmonic Zone f 1f 2f 1f 2f 2-f 12f 2-2f 12f 1-f 2
demos2f 2-f 12f 12f 23f 13f 2
f 1+f 22f 1+f 22f 2+f 13f 1-2f 23f 2-2f 1Compression region Linear region
Fig.2.3Output spectrum of a power amplifier that includes the desired fundamental signals as well as the spurious products created by intermodulation distortion
Another method of testing power amplifier linearity is the two-tone method with two cloly spaced fu
ndamental signals tones applied to the test amplifier (Table 2.1).The amplitude is incread until the third-order cross-product produces a signal above the noi floor [32–34].
As shown in Fig.2.3the result of applying two tones to amplifiers that exhibit a degree of nonlinearity is intermodulation distortion (IMD)and third-order har-monics grouped in harmonic zones.As can be depicted from Fig.2.4that the third order intermodulation products (2f 1 f 2)and (2f 2 f 1)are the main contributor to distortion in that they are very near the fundamental tones and are not filtered out as is the ca of the cond order intermodulation products (f 1 f 2;2f 1;f 1C f 2and 2f 2)[32–34].
Typically the third-order intermodulation distortion product (IM3)are of most concern since distortion products which are far away in frequency from the desired output can be removed by filtering as shown in Fig.2.4[32–34].
Applying a two-tone RF signal to the power amplifier
v i .t/D v cos .!1t/C v cos .!2t/(2.15)
The two-tone signal covers the complete dynamic range of the amplifier (Table 2.2).The amplifier output is a power ries expansion up to the fifth-order is given by Rogers and Plett [32]
v o D a 1v i C a 2v 2i C a 3v 3i C a 4v 4i C a 5v 5i (2.16)
The output voltage with two-tone signal
122Modulation Schemes Effect on RF Power Amplifier Nonlinearity:::
Fig.2.4Intermodulation products falling in-band
v o.t/D a1vŒcos.!1t/C cos.!2t/ C a2v2Œcos.!1t/C cos.!2t/ 2
心理学专业排名C a3v3Œcos.!1t/C cos.!2t/ 3C a4v4Œcos.!1t/C cos.!2t/ 4
C a5v5Œcos.!1t/C cos.!2t/ 5(2.17)
Figure2.5shows a plot of IM3versus P i n and P o u t versus P i n.If the1:1slope line of the fundamental Pout and the1:3slope line of the third order intermodulation product are extended,they will interct at a point called IP3,the third-order intercept point.IP3is an approximation becau the slope assumption is not truly valid outside the linear region.The higher the IP3point the less distortion at higher power levels.In the linear part of Fig.2.5,the Pout versus Pin curve has a slope of 1:1.The P1dB point which is the power where the gain drops by1dB compared to the linear gain was another way to characterize power amplifiers[32–34].
In the nonlinear region in Fig.2.5higher efficiency is gained over50%,however distortion is incread significantly.Constant amplitude modulation schemes like AMPS or FM radio u saturated power amplifiers that are more efficient than linear ones[32–34].
