Abstract—Envelope Tracking techniques are used to increasethe efficiency of modern radiofrequency transmitters. Thesetechniques are based on varying the supply voltage of theradiofrequency power amplifier according to the envelope ofthe signal to be transmitted. This paper presents an EnvelopeTracking system based on a multilevel topology that targetsrelatively low voltage systems (12-28 volt range) and medium tohigh power applications (> 50 W peak power). The proposedconverter achieves low output voltage ripple, high trackingbandwidths, high efficiency and high output power capabilities.An appropriate characterization of the load behavior of theradiofrequency power amplifier allows the system to work inan open loop manner. This paper shows that the envelopetracking system proposed is capable of increasing the efficiencyof linear, Class-A and Class-B commercial radiofrequency poweramplifiers between 10 and 15 %.
I. INTRODUCTION
Modern radiofrequency transmitters use linear radiofre-quecy power amplifiers (RFPA) to deliver the required outputpower to the antenna. Linear amplifiers are preferred overswitching amplifiers due to their inherent high linearity, thatallows modern communication systems to use non-constantenvelope transmission schemes, like Enhanced Data Rates forGlobal System Mobile Evolution (EDGE) or Wideband CodeDivision Multiplex Access (WCDMA). The major drawbackof such systems is that linear RFPAs have very low efficien-cies; for instance, the maximum theoretical efficiency of aclass A linear RFPA is 50 %, while in conventional operationwith amplitude modulated signals its average efficiency canbe in the 20 % range. Fig. 1a shows a conventional linearRFPA amplifying a non-constant envelope modulated signal.Fig. 1b shows the corresponding waveforms; a considerableamount of power, represented by the shaded area, is lost inthe amplifier. From these figures it can be deduced that thecloser the supply voltage is to the envelope of the signal, thehigher the efficiency will be.
Envelope Tracking (ET) is a technique based on varyingthe supply voltage of the amplifier according to the envelopeof the signal being transmitted; thus, the efficiency is alwaysvery close to the theoretical maximum. Fig. 1c shows aconventional ET system, and Fig. 1d shows its operatingwaveforms; in the ET system the supply voltage is alwaysvery close to the envelope of the signal, which allows us toobtain the maximum theoretical efficiency.
The DC-DC converter shown in Fig. 1c should have severalespecial features to be suitable for ET systems:
• High efficiency• Low output voltage ripple• High bandwidth• High output power capability
These requirements cause the design of an appropriate DC-DC converter to be a challenging task. Several topologieshave been used for this application [1]–[7], achieving differentresults in terms of the output signal bandwidth that can bereproduced, the power handling capability and other figuresof merit. The highest tracking bandwidth in high powerapplications has been reported using a SEPIC converter (nearly1.25 MHz) in [2], but the efficiency in this case was verylow (around 80 %). High tracking bandwidths compatible withhigh efficiencies were achieved in [3], and were in the rangeof 50 kHz.
This paper describes an ET system based in the MultipleInput Buck Converter (MIBuck) topology first proposed in[9]. Fig. 2 shows a block diagram of the system: an analog todigital converter acquires the envelope signal, and an FPGAgenerates the appropriate control signals for the multiple inputtopology, represented as a high frequency voltage selector plusa low-pass filter. As Fig. 2 shows, the system works in anopen loop manner. This is possible because in ET techniquesthe varying output voltage supply that has to be generateddoes not need to be very accurate: there is a supply voltagethat maximizes the RFPA efficiency, and the closer the supplyvoltage is to this value, the higher the efficiency will be (aslong as the supply voltage is higher than a certain minimumvalue that ensures appropriate RFPA operation). Thus, a smallmismatch between the output and the desired voltage simplylowers the overall transmitter efficiency. However, in order toensure the feasibility of the system, the load behavior of theRFPA has to be carefully analyzed.
This paper is organized as follows: in section II the mainfeatures of the proposed multilevel converter are summarized.Section III presents several results concerning the behavior ofClass A and Class B amplifiers as loads. Section IV showsthe experimental setup built using the proposed multilevelconverter and two different commercial RFPAs; a 200 W, 27MHz, Class B amplifier and a 300 W, 27 MHz, Class A push-
Fig. 1. (a) Diagram of a conventional transmitter without ET; (b) characteristic waveforms; (c) diagram of a transmitter that uses ET; (d) characteristicwaveforms.
Digital control
system
V0
Vn
Vi
High frequency
voltage selector Low pass
filter
Envelope
signal
1 V
20 VMultilevel
square
waveformFixed input
voltages
Fig. 2. General scheme of the proposed topology: a multilevel squarewaveform is filtered to obtain the desired envelope.
pull amplifier. Finally, the conclusions are presented in sectionV.
II. MULTILEVEL CONVERTER MAIN CHARACTERISTICS
Figure 3 shows the proposed MIBuck converter. Twoswitches are turned on and off alternatively, in order togenerate a square voltage waveform at the input node ofthe low pass filter. Said waveform thus changes between thetwo input voltages that have been selected. Fig. 4 showsthe equivalent circuit in the aforementioned situation and thecorresponding waveforms.
The MIBuck topology has several advantages over otherpreviously proposed topologies for ET applications: the squarevoltage waveform shown in Fig. 4b is easy to filter, thusallowing low output voltage ripple. As smaller filter compo-nent values can be used in comparison with a conventional
buck topology, the tracking bandwidth can also be increased.Furthermore, the voltage stresses over the semiconductors aresmaller, thus diminishing switching losses, increasing the effi-ciency and allowing higher switching frequencies. Efficienciesabove 90 % were reported in [9], when the MIBuck washandling around 35 W of average output power and more than90 W of peak power, and the switching frequency was above3 MHz. More details regarding the operating principles of theMIBuck topology can also be found in [9].
III. LOAD BEHAVIOR OF LINEAR RFPAS
In Fig. 3 the MIBuck converter is loaded with a constantresistor. As the actual load is in fact the RFPA, its behaviorbecomes a major concern; for instance, knowledge of theload value allows us to select L and C in order to fulfillcertain bandwidth requirements and to ensure that the systemis appropriately damped. This section qualitatively analyzesthe load behavior of the linear RFPA depending on its classof operation.
Vn
Vn-1
V1
ViD0
D1
Di
Dn-1
L
C R
Mn
Mn-1
Mi
M1
Fig. 3. Multiple input buck converter topology.
716
L
C RVi
Vj
Dj
Mj
Mi
Vout
Di
Vfilter
(a)
Vi
Vj Vout
Vfilter
T
Ton
(b)
Fig. 4. (a) Equivalent circuit used to calculate the conversion ratio; (b)typical static waveforms when branches i and j are switching alternatively.The dashed line shows the average output voltage.
Fig. 5a shows a large signal simplified equivalent circuitof the system. Ideally, the reference envelope signal, venv (t),is amplified and then applied to the RFPA. L and C are theoutput filter of the converter. Fig. 5b shows a simplified linearamplifier using a single bipolar transistor and supplied bythe envelope tracking system: CL,RF is a bypass capacitanceand thus has a very low impedance at the RFPA operatingfrequency. CRF and LRF form a resonant circuit at theoperating frequency, ensuring a sinusoidal output voltage.
Considering the transistor as a two-port network and takinginto account that, at the beginning of an arbitrary RF cycle,CL,RF is charged to Gvvenv (t) (neglecting L and C), circuitin Fig. 6 can be obtained (only the output port is shown). Notethe explicit dependence of the parameter iscc (short circuitcolector current) with vin. As Co and go change within an RFcycle, due to the inherent large-signal operation of the RFPA,they should be considered non-linear impedances. However,in the calculations that follow, such non linearity will beneglected by calculating an average value for both impedances.
In the circuit of Fig. 6, LRF causes the average value ofthe voltage v1 to be zero over one RF cycle:
〈v1〉 =∫ TRF
0
v1dt = 0 , (1)
thus allowing us to obtain the equivalent circuit in Fig. 7,iscc being the averaged short circuit colector current, and Co
and go being averaged values of Co and go, respectively.Furthermore, Co will be typically much smaller than C,the output capacitance of the converter, and thus it can beneglected for practical purposes. At this moment, it is worthto remark that, due to the averaging procedure, the circuit inFig. 7 is valid for the relatively low frequency variations ofvenv (t).
L
CGv∙venv (t)
isupply (t)
vsupply (t)venv (t)
RFPA
(a)
Bias circuit
RL,RF
Gv∙venv (t)
vin (t)
ibvce
ic
LRFCRF
CL,RF
L
C
(b)
Fig. 5. (a) Equivalent simplified large signal model of the system: theenvelope signal venv is amplified and applied to the load; (b) simplifiedlinear RFPA using a single transistor. The bias circuit defines the class ofoperation of the amplifier.
RL,RF
Gv∙venv (t)
LRFCRF
L
C
Cogo
v1
iscc(vin)
Fig. 6. Equivalent circuit based on admittance parameters.
The equivalent load seen by the converter can then beexpressed as:
Zeq =vsupply (t)isupply (t)
=vsupply (t)
vsupply (t) go + isc
. (2)
Neglecting the dynamic effect of the low pass filter, (2) canbe rewritten as:
Zeq =Gvvenv (t)isupply (t)
=Gvvenv (t)
Gvvenv (t) go + iscc
. (3)
The following sections are dedicated to draw more specific
717
Co goGv∙venv (t)
L
Ciscc
Fig. 7. Final equivalent circuit for the load behavior analysis of the RFPAwith the averaged admittance parameters.
expressions from (3), depending on the class of operation ofthe RFPA.
A. Class-A RFPAs
In Class-A amplifiers, the bias circuit keeps the transistorin its active region even in absence of the input signal. Fig. 8shows a set of typical transistor ic−vce curves, along with itscolector current. It is assumed that iscc can be approximatedby the point where the actual ic − vce curve defined by thebias circuit intersects the ic axis. Thus, it depends only on thebias current of the transistor:
iscc,A = k · Ibias , (4)
where the dependence on vin has been eliminated. The averageoutput conductance, go, is now approximated by the slope ofthe actual ic − vce curve defined by the bias current:
go,A =ic,t1 − ic,t2
vsupply (t1)− vsupply (t2)= tanα . (5)
It is apparent that the equivalent load in Class-A operation isfinally given by a conductance, go,A, and by a constant currentsource, iscc,A. Thereby, the main factor that determines thedynamic response and the damping factor of the LC outputfilter of the converter is go,A.
Fig. 9 shows actual measured curves of a Class-A commer-cial amplifier whose main characteristics will be described indetail in the experimental results section. The figure showsseveral ic − vce curves. The noticeably high values found for
go,A (i.e. low values for the resistance1go,A
) show that an
appropriate damping of the output filter will be possible. It is
Ibias,1
Ibias,2
Ibias,3
vsupply(t1)vsupply(t2)
vce
ic,t1
ic,t2
ic
α
tColector current
vin(t1)
iscc
vsupply(t2)vsupply(t1)
vin(t2)
Fig. 8. Typical RF power bipolar transistor ic − vce curves and basicoperating waveforms in Class-A.
1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 60
1
2
3
4
5
6
7
Vce
(Volts)
i c (A
mp
s)
ib = 200 mA
ib = 250 mA
ib = 300 mA
ib = 400 mA
1 / go,A
= 3.3
1 / go,A
= 5 - 3.3
1 / go,A
= 10
1 / go,A
= 20 - 50
Fig. 9. Measured ic − vce curves in an actual Class-A RFPA (model KL-300). The relatively constant slope of the curves for each bias current can beclearly appreciated.
also worth to remark that, for a fixed bias current, the slopeof each ic − vce, i.e. go,A, remains approximately constant.
B. Class-B RFPAs
In Class-B RFPAs the bias circuit keeps the transistor at theboundary between its active region and cut-off, being driveninto the active region by the input signal. Fig. 10 shows a setof typical transistor ic − vce curves, along with its colectorcurrent.
It can be easily shown that the peak and the average colectorcurrents are related as follows [10]:
iscc =iscc,peak
π. (6)
Assuming perfect linear operation of the RFPA, the colectorcurrent and the input voltage can be related as follows:
iscc (t) = gm · vin (t) , (7)
gm being the transconductance of the RFPA. Equation (7) canbe rewritten in terms of the peak values:
iscc,peak = gm · vin,peak (t) . (8)
Ibias= 0
Ibias,2
Ibias,3
vsupply(t1)vsupply(t2)
vce
ic
tColector current
vin(t1)
iscc,t2
vsupply(t2)vsupply(t1)
vin(t2)
iscc,t1
Ibias,1
Fig. 10. Typical RF power bipolar transistor ic − vce curves and basicoperating waveforms in Class-B.
718
go,AGv∙venv (t)
L
Ck∙Ibias
(a)
go,B Gv∙venv (t)
L
Cm
v
g
G
(b)
Fig. 11. (a) Final equivalent circuit of the RFPA in Class-A operation; (b)final equivalent circuit of the RFPA in Class-B operation.
Taking into account that the peak of the input voltage is bydefinition venv (t), the following relationship can be written:
gm being the averaged value of gm. Combining (6) and (10),the short circuit average colector current can be obtained:
iscc,B =gm · venv (t)
π. (11)
Substituting (11) into (3), the equivalent impedance in Class-B
operation is obtained:
Zeq,B =Gvvenv (t)
Gvvenv (t) go,B +gmvenv (t)
π
=
=1
go,B +gm
Gvπ
.
(12)
As can be deduced from (12), the final equivalent circuit is
made up of two resistances situated in parallel,1go,B
and
Gvπ
gm. Fig. 11 summarizes the previous results for each class
of operation.
IV. EXPERIMENTAL RESULTS
A block diagram of the experimental setup used to testthe performance of the proposed envelope tracking systemis shown in Fig. 12. An Agilent 33210A function generatorgenerated the envelope reference signal, that was sampledby a 12 bit Analog to Digital Converter (TI THS1230) andfeed to the digital control system, implemented in a Virtex4 FPGA. The Mibuck prototype was supplied using threeseparate voltage sources of 12 V, 8 V and 4 V, and its switchingfrequency was set to 1.6 MHz. The inductance of the low passfilter was 5.6 µH , and the capacitance was 500 nF, yieldinga tracking bandwidth of 95 kHz.
A. ET system performance using a Class-A RFPA
A commercial Class-A amplifier (model KL-300 from RMItaly [12]) was used to test the proposed ET system. Theamplifier operated at 27 MHz, and was capable of providing300 W of peak RF power to a 50 Ω load. It used two SD1446RF power bipolar transistors in push-pull configuration. As itwas intended to operate in Class-B, an appropriate bias circuitwas incorporated. Fig. 13 shows the experimental setup.
Fig. 14 shows several results when the ET system wastracking different envelope waveforms. Figs. 14a and 14b show10 kHz and 50 kHz sinusoids, respectively. Fig. 14c shows an
Multiple input
converter
Envelope signal
generatorModulator
27.125 MHzLinear RFPAEnvelope
signal
1 V
12 V
Modulated signal
(carrier + information)
“Amplified”
envelope signal
50 Ω
load
12 V8 V 4 V
12 V
Fig. 12. Experimental setup used to test the proposed envelope tracking system.
719
Fig. 13. Experimental setup used for Class-A measurements.
EDGE envelope signal. It is apparent that the ET system iscapable of appropriately supplying the RFPA, performing anaccurate envelope tracking in open loop conditions. A slight
(a)
(b)
(c)
Fig. 14. Experimental results obtained with the setup shown in Fig. 13.The output RF signal and the supply voltage are shown: (a) 10 kHz sinusoidenvelope signal; (b) 50 kHz sinusoid envelope signal; (c) EDGE envelopesignal.
distortion can be observed in the supply signal, probably dueto the poor performance of the modulator and also to theactual non-linear behavior of the parameters derived in sectionIII-A. However, such distortion does not noticeably affect theoutput RF signal. Table I shows the efficiency of the RFPAsupplied with a constant voltage and the added efficiency ofthe converter and the RFPA while ET was being carried out.The average efficiency improvement achieved was around 10% when the peak output RF power was around 60 W.
Fig. 15 shows the supply voltage waveform under a stepreference in the envelope signal. As the output filter wasdesigned with no overshoot, it is apparent that in Class-Aoperation go,A provides enough damping.
B. ET system performance using a Class-B RFPA
A commercial Class-B amplifier (model KL-200 from RMItaly [12]) was also used to test the proposed ET system. Theamplifier operated at 27 MHz, and was capable of providing200 W of peak RF power to a 50 Ω load. It used one SD1446RF power bipolar transistor. Fig. 16 shows the experimentalsetup.
Fig. 17 shows the results when the ET system was supplyingthe amplifier with the same envelope waveforms shown in Fig.14. Once again, the ET system is capable of appropriately sup-plying the RFPA, and some distortion can also be appreciated.The ET system performs as expected in open loop conditions.Table II shows efficiency measurements with and without theET system. The average efficiency improvement achieved wasaround 15 % when the peak output RF power was around 75W.
According to section III-B, the equivalent load seen by theconverter in Class-B operation is made up of two terms, iscc,B
and go,B . In Fig. 18a a step reference was set as the inputto the ET system, while in Fig. 18b the step reference was
TABLE IOVERALL EFFICIENCY WITHOUT AND WITH ET: CLASS-A RFPA.
Without ET 13.3 % 14.2 % 12.7 %With ET 24.2 % 25.5 % 22.1 %
Fig. 15. Supply voltage of the Class-A RFPA under a step change in theenvelope signal.
720
Fig. 16. Experimental setup used for Class-B measurements.
only applied to the supply of the RFPA, but not to its input.Thereby, in the latter situation iscc,B will become constant andonly go,B will remain; the system will become less damped.
(a)
(b)
(c)
Fig. 17. Experimental results obtained with the setup shown in Fig. 16.The output RF signal and the supply voltage are shown: (a) 10 kHz sinusoidenvelope signal; (b) 50 kHz sinusoid envelope signal; (c) EDGE envelopesignal.
TABLE IIOVERALL EFFICIENCY WITHOUT AND WITH ET: CLASS-B RFPA.
Without ET 38.7 % 37.4 % 13 %With ET 57.5 % 55.3 % 27 %
Such effect can be clearly appreciated in Fig. 18b.
V. CONCLUSION
This paper presents an Envelope Tracking system based ona Multiple Input Buck converter topology. On one hand, thistopology is specially suitable for this application, as it achieveslow output voltage ripple, high efficiency and high trackingbandwidth. On the other hand, it requires several input voltagesources and a more complex control system.
As the proposed system is intended to work in an openloop manner, the load behavior of the RFPA has to be takeninto account. A simple, average qualitative model was derivedusing admittance parameters, showing that the output filterof the converter was damped, disregarding the actual classof operation of the RFPA. Experimental measurements ofthe amplifier ic − vce curves showed an appropriate dampingdue to the go,A parameter. Ideally, in Class-B the dampingis guaranteed by the completely resistive behavior derived insection III-B.
Section IV showed several experimental results of the ETsystem in open loop conditions and using two different com-mercial amplifiers. As Figs. 14 and 17 show, the ET systemwas capable of tracking different envelope signals, increasingthe efficiency of the system between 10 and 15 %.
Future work will be focused on determining the equivalentload model parameters from RFPA datasheet, as long as onaccurately characterizing the distortion introduced by the ETsystem, in order to evaluate the limits of open loop operation.
ACKNOWLEDGMENT
This work has been funded by the Spanish Ministry ofScience and Education under FPU program (refs. AP2006-04777 and AP2008-03380), and by project TEC-2007-66917.
REFERENCES
[1] F. Wang, A. Yang, D.Y.C. Lie, D. Kimball, L. Larson, P. Asbeck,”Design of Wide-Bandwidth Envelope Tracking Power Amplifiers forOFDM Applications”. IEEE Transactions on Microwave Theory andTechniques, vol. 53, no. 4, pp. 1244–1255, 2005.
[2] D. Anderson, W. Cantrell, ”High-Efficiency High-Level Modulator forUse in Dynamic Envelope Tracking CDMA RF Power Amplifiers”.IEEE MTT-S International Microwave Symposium Digest, vol. 3, pp.1509–1512, 2001.
[3] M. Hoyerby, M. Andersen, “Self-Oscillating Soft Switching EnvelopeTracking Power Supply for Tetra2 Base Station”. 29th InternationalTelecommunications Energy Conference (INTELEC), pp. 53–60, 2007.
[4] A. Soto, J.A. Oliver, J.A. Cobos, J. Cezon, F. Arevalo, “Power supplyfor a radio transmitter with modulated supply voltage”. IEEE AppliedPower Electronics Conference (APEC) 2004, pp. 392-398.
721
(a)
(b)
Fig. 18. (a) Supply voltage and output RF voltage when a step referencesignal is given to the ET system; (b) supply voltage when the step referenceis applied only to the supply of the RFPA. The increase of the overshootsuggests a decrease of the damping factor.
[5] M. Hoyerby, M. Andersen,, “High-Bandwidth, High-Efficiency EnvelopeTracking Power Supply for 40W RF Power Amplifier Using ParalleledBandpass Current Sources”. IEEE Power Electronics Specialist Confer-ence (PESC 2005), pp. 2804-2809.
[6] V. Yousefzadeh, E. Alarcon, D. Maksimovic, “Three-level buck con-verter for Envelope Tracking Applications”. IEEE Transactions onPower Electronics, vol. 21, no. 2, march 2006.
[7] M. Vasic, O. Garcıa, J.A. Oliver, P. Alou, D. Dıaz, J.A. Cobos, “Multi-level power supply for high efficiency RF amplifiers”. IEEE AppliedPower Electronics Conference (APEC 09), pp. 1233-1238, February2009.
[8] J. Sebastian, P. Villegas, F. Nuno, M. Hernando, “High-Efficiencyand Wide-Bandwidth Performance Obtainable from a Two-Input BuckConverter”. IEEE Transactions on Power Electronics, vol. 13, no. 4, pp.706–717, july 1998.
[9] M. Rodrıguez, P. Fernandez, A. Rodrıguez, J. Sebastian, “Multilevelconverter for Envelope Tracking in RF power amplifiers”. IEEE EnergyConversion Congress and Exposition 2009 (ECCE 2009), pp. 503-510,September 2009.
[10] Steve C. Cripps, “RF Power amplifiers for wireless communications”.Artech House, Inc., 2nd edition, 2006, Chap. 3.
