401978-1-4799-5296-0/14/$31.00 © 2014 IEEE

PROC. 29th INTERNATIONAL CONFERENCE ON MICROELECTRONICS (MIEL 2014), BELGRADE, SERBIA, 12-14 MAY, 2014

A “Raised-Fractional-Power”

Wireless Transmitter Power Consumption ModelN. Zogovic, G. Dimic, and D. Bajic

Abstract—Wireless communications afford mobility and flex-ible network topologies of computer networks. However, theirenergy efficiency must keep improving. Since the major powerconsumer in a wireless transmitter is the power amplifier, energyefficiency can be improved by reducing transmit power dependingon the channel conditions and performance metrics. We proposea novel transceiver power consumption model for Class A, ABand B power amplifiers. It is a better fit than the existing affinemodel of the total transmitter power consumption, as a functionof the transmit power. In the model, we explicitly upper- andlower-bound transmit power.

I. INTRODUCTION

The energy efficiency (EE) of wireless communications

[bit/Joule] has become an important issue in wireless networks

[1], [2]. A major boost to EE can be achieved by adapting the

transmit power, i.e. power delivered to antenna, pt, to channel

attenuation change, because the dominant power consumer

in a transceiver is the transmitter power amplifier (PA) [2],

[3]. Since the control mechanism for pt is not clearly stated

in previous work [4]–[8], there is some ambiguous in EE

modeling from the perspective of communications protocols,

so we try to address the problem of modeling by considering

pt control mechanism focusing on component level, as defined

in [2].

The dominantly used wireless transmitter power consump-

tion model is an affine transformation pt → pTX, where pTX

is the total power consumption at transmitter [2], [9]. In other

models, it is typically assumed that pt is proportional to dn,

where d is the transmitter-to-receiver distance, and n ≥ 2, [9];

this comes from modeling the channel loss over a wireless link

L ∼ dn.

For most types of PAs, the PA efficiency increases with pt[7], [8]. In [8], it is proposed that pTX ∼ d−

n

m , where m is

the efficiency degradation factor. For simulated Class A and

C transmit PAs, m = 2.6 and 2.8 is obtained, respectively [8].

In [10], the model pTX ∼ √pt, with explicit bounds pt ∈

[pt,min, pt,max] and pt dependent on L, is proposed.

We reconsider the pt → pTX model, by analyzing possible

control of pt in the Class A, AB, and B, linear PAs. We

avoid using L and propose a transformation pTX (pt) ∼ ptwith

explicitly bound pt ∈ [pt,min, pt,max], where v ∈ [0, 1]. The

model verification using data of real transceivers shows that it

Nikola Zogovic and Goran Dimic are with the Institute Mihajlo Pupin,University of Belgrade, Belgrade, Serbia, e-mail: nikola.zogovic@pupin.rs,goran.dimic@pupin.rs.

Dragana Bajic is with the Faculty of Technical Sciences, University of NoviSad, Novi Sad, Serbia, e-mail: dragana.bajic@gmail.com.

This work was supported in part by grants TR32043 and III43002 of theMinistry of Education and Science of the Republic of Serbia.

Figure 1. Wireless transceiver block-scheme

approximates pTX (pt) more accurately than the affine model

does. Data fitting indicates that v > 1m

for m = 2.6 or 2.8. The

adapted model applies to any topology and any deterministic

or probabilistic model of L.

II. POWER AND ENERGY CONSUMPTION MODEL

A. Transceiver Power Consumption Components

Wireless transceiver consists of transmitter (TX) and re-

ceiver (RX) sections. Typical transmitter and receiver block

schemes are given in [11], reproduced here for convenience in

Fig. 1.

The following blocks make a transceiver: digital-to-analog

converter (DAC), radio frequency synthesizer (RFS), upcon-

version/downconversion mixer (mix), power amplifier (PA);

low-noise amplifier (LNA), baseband amplifier (BA), base-

band anti-aliasing filter (AAF), and analog-to-digital converter

(ADC). In equations below, p denotes power and suffixes de-

note the transceiver blocks. The total transmitter and receiver

power consumptions, pTX and pRX, are [11]

pTX = pDAC + pRFS + pmix + pPA (1)

pRX = pLNA + pRFS + pmix + pBA + pAAF + pADC.(2)

The purpose of transmitter PA is to amplify the signal to the

specified power level, pt, and feed it to the antenna. Hence, PA

power consumption, pPA, depends on the desired level of pt,

e.g. [12], and so does pTX, c.f. (1). The PA is the dominant

power consumer with a wide range of power consumption,

whereas power consumption of every other block is constant.

Thus, pRX in (2) is constant for any received signal power,

pr, e.g. [12]

402

Figure 2. A general scheme of power amplifier

pRX = const. (3)

B. A Simple Power Amplifier Power Consumption Model

Definition 1. The PA efficiency, ηPA, is

ηPA =pt

pPA(4)

It is desirable to have as large PA efficiency as possible, i.e.

ηPA → 1, with preserved linearity of the PA. The challenge

is that increased ηPAcomes at the expense of compromised

linearity of the amplifier. The PA efficiency vs. linearity trade-

off has led to evolution of several classes of power amplifiers,

such as A, AB, B, C, D, E and F, e.g. [13]. In Classes A, AB

and B, the output stage transistor of the PA operates in linear

regime thereby preserving input signal envelope (e.g. [13]).

We consider linear power amplifiers in Class A, AB and B,

with transmit power within range, pt ∈ [pt,min, pt,max].For a general scheme of PA see e.g. Fig. 15.1 in [13],

reproduced here for convenience in Fig. .

We describe a PA power consumption model using the

following simplifying assumptions, where VDD is the power

supply voltage:

1) PA output stage transistor conducts from 0 to VDD

output voltage.

2) The output stage transistor drain (or collector) volt-

age and current are vDS = VDS+IrfRL sin (ω0t) and

iD = ID + Irf sin (ω0t), respectively, where ω0 = 2πf0,

f0 is the signal carrier frequency, and T is the symbol

duration, T ≪ 1f0

. VDS, ID are bias voltage and current.

RL is the output resistance. Irf is the amplitude of the

current fed to the antenna.

The output transistor conducts if vDS (t) > 0 and iD (t) > 0.

The portion of an RF cycle that the output transistor conducts

is called conduction angle, 2φ. We show how setting of

VDS, ID, and VDD, shapes pPA (pt) and ηPA (pt).Class A PA (2φ = 2π) output voltage is vout =

−IrfRL sin (ω0t) and the power delivered to the antenna,

averaged over T , is pt =12I2rfRL. Hence,

pPA = VDDID, Irf =

√

2ptRL

. (5)

For Class A PA with variable output power:

Irf,min ≤ Irf ≤ Irf,max⇒ ηPA ∈ (0, 0.5). At the PA output

stage, pt is adapted by 3 approaches [13]–[15]:

1) Fix bias and supply voltage,

(VDS, ID) = (Irf,maxRL, Irf,max), VDD = Irf,maxRL.

(5) ⇒ pPA = const, so that (4) ⇒ ηPA ∼ pt.

2) Adapt bias, but fix supply voltage,

(VDS, ID) = (IrfRL, Irf), VDD = Irf,maxRL. (5)

⇒ pPA ∼ √pt, so that (4) ⇒ ηPA ∼ √

pt.

3) Adapt both bias, and supply voltage,

(VDS, ID) = (IrfRL, Irf), VDD = IrfRL. (5)

⇒ pPA ∼ pt, so that (4) ⇒ ηPA = const.

Class B PA (2φ = π) output stage consists of a turns-ratio-

n transformer and two push-pull configured transistors [13],

[14]. Averaging over T

pPA =2

πVDDIrf , pt =

n2

2I2rfRL, (6)

[13], [14]. In Class B ηPA ∈(

0, π4

)

, for Irf ∈(

0, VDD

n2RL

)

.

There are two approaches to adapt pt at the PA output stage

[13], [14]:

1) Fix supply voltage, VDD = Irf,maxn2RL. (6) ⇒ pPA ∼√

pt, so that (4) ⇒ ηPA ∼ √pt.

2) Adapt supply voltage, VDD = Irfn2RL, by varying Irf .

(6) ⇒ pPA ∼ pt, so that (4) ⇒ ηPA = const.

Class AB PA (π ≤ 2φ ≤ 2π) is a hybrid of Class A and Class

B PAs. There are two approaches to adapt pt at the PA output

stage [13]–[15]:

1) Adapt bias, but fix conduction angle and supply

voltage, (VDS, ID) = (−IrfRL cosφ,−Irf cosφ),VDD = 1

2πRLIrf,max (2φ− sin 2φ). Then

pPA = VDDID ⇒ pPA ∼ √pt, so that (4)

⇒ ηPA ∼ √pt.

2) Adapt bias and supply voltage, but fix conduc-

tion angle, (VDS, ID) =(−IrfRL cosφ,−Irf cosφ),VDD = 1

2πRLIrf (2φ− sin 2φ). Then pPA = VDDID ⇒

pPA ∼ pt, so that (4) ⇒ ηPA = const.

a) A simple pPA model: Taking into account power

consumption of PA and the approaches to adapt PA output

power, we propose

pPA = pPA +∆pPA

(

pt

pt,max

)v

;

v ∈ {0, 0.5, 1} , pt ∈ [pt,min, pt,max] , (7)

where pPA and ∆pPA are constants with unit of measurement

[W]. pPA accounts for minimum fixed PA power consump-

tion and ∆pPA accounts for variation of total PA power

consumption from minimum to maximum. v depends on the

approach to adapt PA output power. Ratio pt

pt,maxnormalizes

the argument of the (.)v

operation to the range[

pt,min

pt,max, 1]

,

while the normalized argument is a number with no unit

of measurement. In practice, pt power levels are discrete.

However, we assume that pt can be adjusted continuously,

which facilitates the analysis below.

403

C. Transmitter Power Consumption Model

Starting from (7) and taking into account (1), we develop a

transmitter power consumption model:

1) Total constant power consumption at the transmitter is

accounted for by the minimum total transmitter power,

pTX,min. It is analogous to pPA from (7) and corresponds

to the minimum transmit power, pt,min.

2) Total variation in the transmitter power consumption

is modeled by the difference between its maximum,

pTX,max, and minimum, pTX,min. It is analogous to

∆pPA from (7), and accounts for changes in pTX due

to changes in output power level, pt ∈ [pt,min, pt,max].3) Exponent v is in the range v ∈ [0, 1], rather than having

discrete values as in (7). This facilitates modeling of

the influence of various PA properties, which were not

accounted for in the simple model (7).

Definition 2. Transmitter power consumption, pTX, is the best

fit, in the least squares sense, of the curve between the points

of minimum and maximum total transmitter power, pTX,min

and pTX,max, respectively, depending on the transmit power,

pt ∈ [pt,min, pt,max]:

pTX (pt) =

pTX,min + (pTX,max − pTX,min)

(

pt − pt,min

pt,max − pt,min

)v

, (8)

where v ∈ [0, 1] is the fitting parameter. Alternatively,

pTX (pt) = p0 + ρx (pt)v,

p0 = pTX,min,

ρ = pTX,max − pTX,min, (9)

x (pt) =pt − pt,min

pt,max − pt,min

.

The definition of x (pt) in (9) enables existence of a

fixed point (pt, pTX) = (pt,min, pTX,min), irrespective of the

value of v. Ratiopt,max

pt,minis typically at least 20dB. Thus, the

difference pt

pt,max− x (pt) =

pt,min

pt,max· pt,max−pt

pt,max−pt,minis negligible

relative to pt

pt,max. Finally, pt ∈ [pt,min, pt,max] ⇒ x ∈ [0, 1].

D. Model Fitting for Real Transceivers

Table I provides transceiver power settings1. The first six

transceivers are suitable for low-power communications in

personal area networks (PAN) and WSN. The following two

transceivers conform to the IEEE 802.11 standard (WiFi). The

last two rows show power settings for two power amplifiers

for WiMAX transmitters.

The model (9) is fitted using nonlinear least squares, for

power law, to evaluate optimal v, using data provided in

manufacturers data sheets. Fig. 3 shows pTX (pt) curve fitting

for CC1101 transceiver and affine approximation (v = 1).

1Data sheets are available at the following URLs: for transceivers no. 1, 2,5, and 6 at www.ti.com; no. 3 at www.semtech.com; no. 4 at www.atmel.com;no. 7 and 8 at http://para.maxim-ic.com; and for power amplifiers 9 and 10at www.analog.com.

Table ITRANSCEIVER MODEL SETTINGS (FIXED)

Power in [mW].

No. Transceiver pt,min pt,max pTX,min pTX,max pRX

1 CC1000 0.010 3.16 25.8 76.2 28.8

2 CC1101 0.001 10.00 36.3 97.2 46.8

3 SX1211 0.079 10.00 39.6 84.8 9.9

4 AT86RF212 0.079 10.00 31.5 74.4 27.6

5 CC2420 0.003 1.00 25.5 52.2 56.4

6 CC2500 0.001 1.26 29.7 64.5 39.9

7 MAX2830 1.170 165.96 642.0 1335.6 173.6

8 MAX2831 1.000 237.14 588.0 1062.6 173.6

9 ADL5570 5.250 426.30 672.0 2310.0 -

10 ADL5571 25.000 741.31 1085.0 3650.0 -

0 2 4 6 8 100

10

20

30

40

50

60

70

80

90

100

pt [mW]

pT

X [m

W]

data

vopt

v = 1

Figure 3. CC1101 pTX (pt) curve fitting: vopt = 0.58

The relative fitting error on sample i is

epTX,rel (i) =pTX (i)− pTX (i)

pTX (i)100%,

where pTX is the true value (from data sheet), and pTX is

the value obtained by fitting the model (9). The mean and

root mean square of relative fitting error, on the set of NS

samples, are µpTX,e and σpTX,e, respectively

µpTX,e =1

NS

NS∑

i=1

epTX,rel (i) , σpTX,e =

√

√

√

√

1

NS

NS∑

i=1

e2pTX,rel (i).

Fig. 4 shows epTX,rel versus pt for CC2420, AT86RF212 and

MAX2831 transceivers for vopt and v = 1.

Table II shows vopt; as well as µpTX,e [%] and σpTX,e [%]

for vopt and v = 1. The rightmost column of Table II showspt,max

pt,minin [dB]. Ratio

pt,max

pt,minis at least 20dB for transceivers,

as claimed in justification of (9).

The presented results indicate the merit of the model (9). It

better fits real transceivers than the affine model (v = 1). The

proposed model is valid for a wide range of transmit power,

from PANs via WiFi to WiMAX.

Fig. 3 indicates that the curvature of pTX (pt) has non-

negligible influence on power consumption or performance.

For pTX (v = vopt) = pTX (v = 1), fixed at some value, the

404

0 50 100 150 200 250−20

0

20MAX2831

pt [mW]

0 2 4 6 8 10 12−20

0

20AT86RF212

ep

TX,r

el

[%]

0 0.2 0.4 0.6 0.8 1 1.2−20

0

20CC2420

vopt

v = 1

vopt

v = 1

vopt

v = 1

Figure 4. pTX (pt) curve fitting residuals for vopt and v = 1

Table IIFITTED AND DERIVED TRANSCEIVER MODEL PARAMETERS

vopt, err [%] v = 1, err [%]pt,max

pt,min

Transceiver vopt µpTX,e σpTX,e µpTX,e σpTX,e [dB]

CC1000 0.64 - 0.56 4.69 9.84 12.62 25.0

CC1101 0.58 1.06 4.68 9.87 11.67 40.0

SX1211 0.60 - 0.25 1.12 7.96 9.76 21.0

AT86RF212 0.77 - 0.36 3.36 4.67 6.92 21.0

CC2420 0.48 - 0.04 1.48 10.65 12.89 25.0

CC2500 0.55 - 0.55 4.23 7.82 10.54 31.0

MAX2830 0.80 - 0.14 0.73 3.37 4.10 21.5

MAX2831 0.67 - 0.30 1.95 4.34 5.64 23.8

ADL5570 0.72 - 1.01 3.04 7.96 9.95 19.1

ADL5571 0.69 - 0.78 3.47 10.46 12.16 14.7

curvature causes pt (v = vopt) ≤ pt (v = 1) because

pt (v = vopt)− pt,min

pt (v = 1)− pt,min

=

(

pt (v = 1)− pt,min

pt,max − pt,min

)1

v−1

≤ 1,

where equality holds at pt = pt,min or pt = pt,max. This

motivates analysis of the influence of v on energy efficiency

of wireless links, with adaptable pt.

III. CONCLUSION

We have proposed a novel transceiver power consumption

model, pTX (pt), suitable for adaptive transmission power

control. The model is obtained from an analysis of the

electronics of the power amplifier, as the dominant power

consumer in a transceiver. We have shown that the proposed

model is a tighter approximation of a real transceiver power

consumption than the affine model. The model explicitly

bounds pt ∈ [pt,min, pt,max].

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