NTIA Report 00-375 

Nonlinear Operation 

of a MMIC RF Power Amplifier 

and its Effects on Battery Current, 

Interference, and Link Margin

Roger A. Dalke 

Robert J. Achatz 

Yeh Lo 

U.S. DEPARTMENT OF COMMERCE 

William M. Daley, Secretary

Gregory L. Rohde, Assistant Secretary 

for Communications and Information 

January 2000 

PRODUCT DISCLAIMER 

Certain commercial companies, equipment, instruments, and materials are identified in this report to 

specify adequately the technical aspects of the reported results. In no case does such identification

imply recommendation or endorsement by the National Telecommunications and Information

Administration, nor does it imply that the material or equipment identified is necessarily the best 

available for the purpose. 

iii

CONTENTS

Page 

1. INTRODUCTION ............................................................................................................................. 1 

2. FACTORS AFFECTING PORTABLE TRANSCEIVER BATTERY CURRENT ......................... 2 

3. RF POWER AMPLIFIER CHARACTERIZATION ........................................................................ 4 

3.1 Typical Portable Transceiver Power Amplifier .................................................................. 4 

3.2 A General Mathematical Model for Nonlinear Narrowband 

 RF Power Amplifiers ..........................................................................................................7 

3.3 Determination of AM-AM and AM-PM Characteristics for a

Narrowband Portable Transceiver Power Amplifier......................................................... 10 

4. RF POWER AMPLIFIER MEASUREMENT DESCRIPTION ..................................................... 10 

4.1 Test Fixture........................................................................................................................ 10 

4.2 Amplitude and Phase Measurement .................................................................................. 12 

5. RF POWER AMPLIFIER MEASUREMENT RESULTS.............................................................. 13 

5.1 AM-AM and AM-PM Measurements............................................................................... 13 

5.2 Power Supply Current and Efficiency............................................................................... 15 

6. REQUIRED SIGNAL-TO-NOISE RATIO AND LINK MARGIN FOR π/4 DQPSK .................. 16 

7. POWER SPECTRAL DENSITY FOR π/4 DQPSK........................................................................ 19 

8. RESULTS ........................................................................................................................................ 23 

9. SUMMARY.................................................................................................................................... 25 

10. REFERENCES .............................................................................................................................. 26 

11. BIBLIOGRAPHY.......................................................................................................................... 27 

APPENDIX.......................................................................................................................................... 29 

v 

NONLINEAR OPERATION OF A MMIC RF POWER AMPLIFIER AND ITS EFFECTS ON 

BATTERY CURRENT, INTERFERENCE, AND LINK MARGIN 

Roger A. Dalke, Robert J. Achatz, and Yeh Lo1

This report describes measurement, modeling, and simulation methods that are used 

to analyze the relationship between nonlinear operation of a typical PCS portable 

transceiver power amplifier and battery current, out-of-band power, and link margin. 

First the nonlinear characteristics of the PCS amplifier and associated battery current 

were obtained from amplifier measurements at various bias voltages and RF output 

signal levels. A mathematical model of the power amplifier based on these 

measurements was then used to simulate the communications link for purposes of 

determining the power spectral density and symbol-error ratio for a variable envelope 

digitally modulated signal using π/4 DQPSK with 35% root raised cosine filtering. 

The out-of-band power and symbol-error ratio were computed to determine the link 

margin for a maximum symbol-error ratio of 10-3. 

Key words: MMIC RF power amplifier; PCS transceiver amplifier; nonlinear amplifier; out-of-band 

power; symbol-error ratio (SER); variable envelope digital modulation; adjacent channel interference 

1. INTRODUCTION 

Portable transceivers operating in microwave bands are ubiquitous due to the proliferation of 

2400-MHz wireless local area network modems, 1900-MHz Personal Communication Services 

(PCS) phones, 900-MHz PCS two-way pagers, and 800-MHz cellular phones. Each of these devices 

transmits information over a distance at a specified data rate and reliability while striving to provide 

the user with acceptable talk- and standby-time. The power amplifier consumes most of the battery 

current capacity during talk-time and therefore is the main impediment to longer talk-times. One 

method of increasing talk-time is to use power efficient nonlinear amplifiers. For variable envelope 

modulations, the use of nonlinear amplification distorts the signal, thereby reducing spectral 

efficiency and reliability. The system designer must balance these competing goals to obtain a 

reliable power- and spectrum-efficient system. 

Power amplifiers are designed so that battery current is conserved whenever possible. For example, 

during standby-time, battery current is conserved by shutting the power amplifier off. During talktime, battery current is a function of power amplifier bias voltage and input signal power. In this 

study we examined the implications of conserving talk-time battery current by varying the bias 

voltage and input signal power. Specifically, we evaluated the influence of bias voltage and input 

power on out-of-band power (OBP) and the radio link margin for a typical PCS portable transceiver 

power amplifier emitting a digitally modulated variable envelope signal. 

 

1

 The authors are with the Institute for Telecommunication Sciences, National Telecommunications and Information 

Administration, U.S. Department of Commerce, Boulder, CO 80303. 
When the bias voltage is adjusted to decrease the quiescent current, the nonlinear characteristics of 

the power amplifier become more pronounced. For variable envelope signals, the corresponding

nonlinear transformation of the output current waveform results in distortion of the transmitted

signal, ergo undesirable effects such as increased spectrum usage (i.e., OBP) and decreased reliability

(i.e., increased symbol errors) must be considered. Increased spectrum usage can also degrade signals 

in adjacent bands. These effects can be reduced by decreasing or “backing off” the input power; 

however, this is also undesirable because the corresponding decrease in output power also decreases

the link margin. 

In this study we evaluated the relationship between battery current, OBP, and link margin by 

measuring and modeling the nonlinear characteristics of a typical PCS portable transceiver power 

amplifier at various bias voltages and input signal powers. A nonlinear model of the power amplifier

was developed and used to predict the power spectral density (PSD) and required SNR of a π/4 

differential quadrature phase-shift keyed (DQPSK) signal filtered by a 35% excess bandwidth root

raised cosine (RRC) filter. The OBP was computed from the PSD while the allowable path loss was 

computed from the output power and required SNR. The approach presented in this paper provides 

quantitative methods for assessing the electromagnetic compatibility of mobile and fixed link 

services operating in adjacent bands. 

Section 2 describes a typical PCS portable transceiver and explains the relationships between battery

current, output power, and link margin. In Section 3, we describe a typical power amplifier and a 

commonly used circuit model that accounts for the nonlinear behavior of RF power amplifiers. Also,

we derive the mathematical model that was used to simulate the narrowband portable transceiver

described in this report. A description of the amplifier that was measured and modeled along with the 

measurement configuration and procedures is given in Section 4. The measurement results are

summarized in Section 5. In Section 6, we describe the simulation methods used to analyze the 

amplifier output signal and present the resulting PSD plots and OBP calculations. Section 7 describes 

the methods used to calculate system performance in terms of symbol-error ratio (SER) as a function

of SNR, and gives the results of these calculations. A summary and conclusions are given in Sections 

8 and 9. 

2. FACTORS AFFECTING PORTABLE TRANSCEIVER BATTERY CURRENT 

The portable transceiver considered in this study is typical of those used in cellular radio networks 

whose base stations are distributed throughout a city, campus, or building. Figure 1 shows a block

diagram of such a portable transceiver. The amplified signal passes through a transmit/receive 

diplexer or switch and a harmonic filter before exciting the antenna. 

2
Figure 1. Block diagram of a portable transceiver. 

When designing such a communication system, it is essential that the power required to operate the 

portable transceiver be minimized (i.e., talk-time is maximized). In general, talk-time is a function of 

the rms battery current IDC, and the battery current capacity C. 

Talk-time .

DC I

C =

The battery current capacity is limited by the battery technology while the battery current is 

determined by power amplifier operating parameters such as bias voltage and input power. Table 1

shows the battery current capacity of 4 rechargeable 6-V battery packs used to power portable 

transceivers [1].

Table 1. Voltage and Current Capacity of Portable Transceiver Battery Packs 

Electrical 

Characteristic 

Nickel 

Cadmium 

Nickel 

Metal 

Hydride 

Lithium 

Ion 

Lithium 

Metal 

Voltage (V) 6.0 6.0 7.2 6.0

Current Capacity 

(A-Hr) 

1.0 1.2 0.8 1.6

3
This table shows that talk-time can vary by as much as a factor of 2 for different battery technologies.

It should be noted that in addition to battery current capacity, other factors such as cost, volume, and

weight are considered in battery selection. 

As indicated above, talk-time can be increased by reducing battery current, which is a function of 

power amplifier operating parameters such as bias voltage and input power. As the bias voltage is 

decreased, the amplifier becomes more nonlinear since the input signal amplitude falls below the 

transistor's pinch off voltage for a larger portion of an RF carrier cycle. The class of amplifier

operation is defined by the percent of time the output current flows in one RF carrier cycle. Class A

operation output current flows 100% of the time, Class AB operation output current flows between

50% and 100% of the time, and Class B operation output current flows 50% of the time. Class AB 

amplifiers are commonly used in portable transceivers where minimizing the power required to

operate an amplifier is important [2].

While decreasing bias voltage, in general, reduces the battery current required to operate the 

amplifier, there are undesirable consequences due to nonlinear amplifier behavior. These nonlinear 

effects result in an increase in OBP and degradation of system performance. Each of these effects

must be carefully analyzed when designing a portable transceiver. In the following sections of this 

report we analyze these interrelated effects for a typical Class AB PCS RF power amplifier emitting

a digitally modulated variable envelope signal. 

3. RF POWER AMPLIFIER CHARACTERIZATION

3.1 Typical Portable Transceiver Power Amplifier 

A typical multistage power amplifier consists of two or three cascaded amplifier stages with 

associated bias and matching circuitry. These power amplifiers are made with discrete components 

mounted on a printed circuit board, microwave integrated circuits (MICS) whose components are 

integrated into more than one substrate, or as a monolithic microwave integrated circuit (MMIC) 

whose components are integrated onto a single monolithic substrate [3]. 

The amplifier stages are made with silicon or GaAs semiconductors. Silicon is used to build either

bipolar transistors or metal oxide semiconductor field effect transistors (MOSFET). GaAs is used to 

build metal epitaxial semiconductor field effect transistors (MESFET). GaAs MESFET’s are widely

used in portable transceiver power amplifiers because they have a higher frequency range, higher 

power efficiency, and higher drain to source breakdown voltage than silicon. Figure 2 shows a block 

diagram of a typical GaAs MESFET multistage power amplifier. 

4
Figure 2. Block diagram of a GaAs multistage power amplifier. 

The class of amplifier operation depends upon the bias voltage, input power, battery voltage, and 

load impedance. In a multistage power amplifier each amplifier stage may have a different class of 

operation to improve overall power efficiency or linearity. The input matching network impedance is 

the complex conjugate of the device input impedance for maximum power transfer. Interstage and 

output matching networks transform input impedance of the next stage to a load resistance that 

maximizes output power at the fundamental frequency [4, 5]. Harmonic frequencies resulting from 

nonlinear amplification are commonly shunted to ground. 

Table 2 shows the output power required at the antenna input for some typical portable transceiver 

applications [6]. Power amplifier output power is found by adding 1-2 dB to these values to

compensate for the losses between the power amplifier output and the antenna. 

5
Table 2. Typical Output Power Used in Portable Transceiver Applications 

Portable Transceiver Application Output power (dBm) 

2400-MHz WLAN modem 20.0 

1900-MHz TAG-5 DCS-based TDMA PCS phone 30.0 

1900-MHz TAG-4 IS-136-based TDMA PCS phone 27.8 

1900-MHz TAG-2 CDMA PCS phone 23.0 

1900-MHz TAG-3 TDMA PCS phone 20.0 

900-MHz PCS two-way paging 30.0 

800-MHz cellular phone 27.8 

Figure 3 depicts the location of the gate, drain, and source components of a typical GaAS MESFET

integrated onto a substrate [7]. Figure 4 illustrates the (large signal) equivalent circuit of the same

GaAS MESFET [8]. RS, RD, RG, and LS, LD, LG are the parasitic resistances and inductances for the 

source, drain, and gate respectively. CDS is the drain-to-source capacitance. CG and CD are the gate--

to-channel capacitances while Ri is the gate-to-channel resistance. ID is the internal drain current

source. The most significant sources of nonlinear behavior are CG, CD, and ID. Each is a function of 

VG and VD as shown in Figure 4. 

Figure 3. Integrated GaAS MESFET.

6
Figure 4. Equivalent circuit of GaAs MESFET. 

3.2 A General Mathematical Model for Nonlinear Narrowband RF Power Amplifiers

In this subsection we derive a mathematical model that characterizes a narrowband nonlinear power 

amplifier. The primary purpose of what follows is to show that this particular model is valid for a 

fairly general class of narrowband nonlinear systems. Essentially the amplifier is treated as a generic 

nonlinear system that operates on a narrowband RF input such as may be used in a digital 

communications system. It is shown that for a sufficiently narrow bandwidth, the nonlinear amplifier 

can be characterized by two functions of the input signal envelope voltage. These functions can be 

determined empirically from direct measurements of the amplifier or from the analysis of amplifier

circuit models such as that shown in Figure 4. This model is commonly used for the analysis of

narrowband nonlinear power amplifiers [9].

Suppose we have an electronic device where the output y0 at a particular time t depends in a 

nonlinear way on the input x0 at all times prior to t or x0(t-ξ) for all ξ, ξ≥0. The input can be

considered as a function of ξ and a parameter t, i.e. u(ξ;t). Assuming that the system is stationary, 

u(ξ)∈L2

 (i.e., u is square-integrable), and y0(t)∈L2, then we can write the nonlinear response in terms

of a functional series [10]

[ ] ( ) [ ( ; ), !

1 ( ) ;

0

0 F u t

n

y t G u t n

n

ξ ∑ ξ

∞

=

= = ] (3-1)

7
where Fn[u] is a regular homogenous functional of the form

[ ] ( ) ( ) ( ) ( ) n n n n n F u ξ;t ... k ξ 1,

...,ξ u ξ 1;t ...u ξ ;t dξ 1...dξ ∫ ∫

∞

−∞

∞

−∞

= (3-2)

and where the kernel functions kn (ξl,...,ξn)∈L2 are symmetric with respect to their arguments (ξn) as

defined in [11]. The kernel functions are determined independently of the variable function u. If the

function u(ξ;t) is an analytic function of t then the functional G[u(ξ;t)]=y0(t) is also an analytic

function of t. 

The Volterra Series [12] given by Equation 3-1 is applicable to a substantial number of electronic

systems encountered in communication problems and is commonly used to calculate distortion in

various types of amplifiers. For our purposes it is assumed that the input signal to such a device has

the form

( ) Re{ } cos(2 ) 2

0 π ψ π = = − − x t xe A ft i ft (3-3)

where the complex amplitude is x = A eiψ and x (and hence both A and ψ) might vary with time so as 

to modulate a carrier at the frequency f. If the variation is slow, we will assume that a steady-state 

analysis is appropriate for our purposes. 

For this harmonic input, we have [11] 

( ) 2 !( )! ( ) ,

( 2 )(2 )

1 0

0 K f k n k

A e

y t k n k

i f i k n n

n k

−

∞ − + −

=

∞

= − ⎟

⎠

⎞ ⎜

⎝

⎛ = ∑ ∑ π ψ

(3-4)

where 

( ) ( ,... , ,..., ) k ,n k n 1 k k 1 n K f K f f f f − = +

⎩

⎨

⎧

− + ≤ ≤

≤ = f k m nf m k

f m 1 (3-5)

and Kn(f1,...,fn) is the n-fold Fourier transform of kn(ξ1,...,ξn). 

The system response is required to be a causal real function of time, hence 

( ,..., ) ( ,..., ) 1

*

n 1 n n n K f f = K − f − f (3-6)

8
where the asterisk superscript denotes the complex conjugate. In addition, if h(t) is the system

response then causality requires that 

h(t) = s(t) h(t) (3-8)

where s(t) is the unit step function. If the Fourier transform of the system response is H(f), the 

causality requirement can be written as 

. 1 ( ) ( ) 2

1 ( ) ⎥

⎦

⎤ ⎢

⎣

⎡

− = + ℘∫

∞

−∞

dx

f x

H x

i

H f H f

π

(3-9)

Hence, the real and imaginary parts of the Fourier transform form a Hilbert transform pair, explicitly

{ } { }

dx

f x

H x H f ∫

∞

−∞ −

I R = ℘1 ( ) ( )

π

(3-10) 

{ } { }

dx

f x

H x H f ∫

∞

−∞ −

R I = − ℘1 ( ) ( )

π

where ℘ denotes the principal value of the integral, I the imaginary part of the function, and R the

real part of the function. 

For a narrowband power amplifier, the harmonics are suppressed resulting in the series: 

⎥

⎦

⎤ ⎢

⎣

⎡ = + − + − + ( , , ) ... 16 ( ) 2 ( ) 3

3

1

2 K f f f A K f A

y t e i πft iψ

(3-11) 

( , , ) ... , 16 ( ) 2

*

3

3

*

1

2

⎥

⎦

⎤ ⎢

⎣

⎡

+ + − + − K f f f A K f A

ei πft iψ

which is a real function of time as required. From the causality requirement, in general, the functions

Kn(•) are complex. For a single frequency we have a series of complex numbers scaled by increasing 

powers of the input signal amplitude that can be written in polar form where clearly both the output 

amplitude and phase are functions of the input amplitude A 

{ 2 ( )

1

2 ( ) ( ) i ft i i A

n

n

i ft i n y t e A z e A e π ψ π ψ φ ρ − + ∞

=

− + = R

⎭

⎬

⎫

⎩

⎨

⎧ = R ∑ } (3-12)

9
This expression leads directly to a fairly general characterization of the baseband transfer function 

for a narrowband nonlinear power amplifier 

e x g A x

A

A

y t A ei A i i A ( ) ( ) ˆ( ) ( ) ( ) ( ) = = = φ − ψ ρ φ ρ (3-13)

where g(A) is the complex gain function. It is interesting to note that when the Kn(•) are pure real, the

system is memoryless and the output only depends on the present value of the input (i.e., the kn(•) are

weighted Dirac delta functions). It should also be recalled that when Equation 3-12 is used to analyze 

communications devices, it is assumed that the bandwidth is sufficiently narrow that the steady-state

approximation is reasonable. 

3.3 Determination of AM-AM and AM-PM Characteristics for a 

Narrowband Portable Transceiver Power Amplifier 

The previous analysis shows that two functions are required to characterize the output of a 

narrowband nonlinear power amplifier. The function ρ(A) describes the amplitude-pushing 

characteristics (AM-AM) of the device. The function φ(A) describes the phase-pushing 

characteristics (AM-PM) of the device. Once these functions are determined, Equation 3-12 can be 

used to simulate the signal emitted by a portable transceiver power amplifier. The output of such a 

simulation can be used to calculate the power spectral density or SER for an amplified digitally 

modulated variable envelope signal. The results of such an analysis are given in Sections 6 and 7. 

In general, the nonlinear functions can be determined either by creating and analyzing a device 

model (e.g., an equivalent circuit) or direct RF measurements. Nonlinearities of field effect 

transistors commonly used in power amplifiers can be accounted for in equivalent circuit models by

introducing appropriate variations in the circuit elements as functions of instantaneous drain and gate 

voltages such as that shown in Figure 4. For our purposes, the two nonlinear functions were obtained 

from RF measurements described in the following section. 

4. RF POWER AMPLIFIER MEASUREMENT DESCRIPTION 

4.1 Test Fixture 

A power amplifier targeted for portable transceivers transmitting in the 2-GHz PCS band was used to

evaluate the relationship between battery current, OBP, and link margin for a commercially available

power amplifier. The nonlinear characteristics of this particular amplifier were determined from the 

measurements described in this section. The nonlinear model developed from these measurements 

was then used in simulations to obtain PSD and SER curves as described in the following sections. 

10
The power amplifier contains three amplifier stages in a 16-pin case. It has a maximum gain in 

excess of 30 dB and can transmit more than 2 W of power. It is mounted on a printed circuit board

with a power amplifier support integrated circuit (IC), drain current control, input and output 

matching networks, and bias voltage divider network. The test fixture is powered by an adjustable 

power supply set to 4.8 V capable of supplying 3 A of drain current. A block diagram of the test 

fixture is shown in Figure 5. 

The drain current controller is used to conserve battery current when not transmitting. In our tests the 

VRAMP and VIDLE pins of the power amplifier support IC were set so that drain current control was 

disabled. This forced the power amplifier to operate continuously at a power level determined by the 

bias voltage and input power. Additional heat sinking was added to insure that the power amplifier

did not overheat. Input, interstage, and output matching was tuned for the 1850- to 1910-MHz band.

The test fixture had 50 Ω input and output impedance that matched interfacing RF test equipment. 

The biasing of all three amplifier stages was controlled by a common pin on the case; thus variation 

of individual amplifier stage bias voltages was not possible. Bias voltage control was adjustable, as 

shown in Figure 5. The power amplifier support IC generated -4.0 V for the bias voltage. An

adjustable voltage divider was used to vary the bias voltage to any value from -4.0 to 0 V. The lower

voltage corresponded to a negligible quiescent current, whereas the higher voltage corresponded to a

relatively large quiescent current. 

Figure 5. Block diagram of power amplifier test fixture. 

11
4.2 Amplitude and Phase Measurement 

The AM-AM and AM-PM measurements were obtained with the equipment depicted in Figure 6. 

The continuous wave signal out of the signal generator was amplified and split into test and reference 

channels. The test channel was power amplified by the test fixture whereas the reference channel was 

not. A spectrum analyzer was used to measure the amplitude of the test channel for the AM-AM 

function. The phase measurement circuit, shown in Figure 7, was used to measure the phase 

difference between the test and reference signals for the AM-PM function. Battery current was 

measured with an ammeter placed between the adjustable power supply and the test fixture as shown 

in Figure 6. The current measurements included all power normally required to operate the power 

amplifier. This included the relatively small currents required for the power amplifier support IC and 

drain current control. 

Figure 6. Block diagram of AM-AM, AM-PM, and battery current measurement setup. 

12
Figure 7. Block diagram of phase measurement setup. 

5. RF POWER AMPLIFIER MEASUREMENT RESULTS 

In this section we present the results of the RF power amplifier measurements described in Section 4. 

Measurements of the narrowband nonlinear functions (i.e., AM-AM and AM-PM) and associated

power supply current were acquired for various bias voltages. The results presented in this section 

are for bias voltages of -2 V, -2.25 V, and -2.5 V. 

5.1 AM-AM and AM-PM Measurements 

Least-square fitting routines were used to fit rational functions to the measured AM-AM and AMPM data. Typically, the data were divided into sections and fit with low-order polynomials or rational 

functions. These functions were used to characterize the nonlinear amplifier behavior in the 

simulations described in Sections 6 and 7. The measured data and approximations are given in the 

Appendix. 

Figure 8 shows the curves that were fit to the measured AM-AM and AM-PM functions for the 

various bias voltages. Figure 9 shows the gain as a function of the input power. It should be noted 

that as the bias voltage decreases, the gain decreases and significant nonlinear behavior occurs at 

relatively larger inputs. 

13
Figure 8. AM-AM and AM-PM for three bias voltages. 

Figure 9. Gain for three bias voltages.

14
5.2 Power Supply Current and Efficiency 

The measured average power supply current for bias voltages of -2.0 V, -2.25 V, and -2.5 V are 

shown in Figure 10 as a function of the input power Pin. Note that the power supply current increases 

(nonlinearly) as both Pin and bias voltage increase. Clearly, reducing the bias voltage for a fixed Pin

reduces the required power supply current. As indicated in Figure 9, decreasing the bias voltage for a 

fixed Pin also decreases the power gain. Hence, to maintain a fixed output power, Pin must be 

increased when bias voltage is decreased. If a significant increase in Pin is required, the savings in

power supply current may be fairly small, as noted in Figure 10, for bias levels of -2.0 V and -2.25 V. 

Figure 10. Power supply current for three bias voltages. 

Two related power amplifier quantities of interest in communications engineering are the output 

power Pout and the power supply current. In general, Pout must be sufficient to yield the minimum 

SER for a given communications link and signal modulation. A commonly used measure that relates 

the power supply voltage and current and Pout for power amplifiers is the power-added efficiency,

defined as 

.

DC DC

out in

V I

P − P

η =

where VDC and IDC are the power supply voltage and current. 

15
In Figure 11 we have plotted η as a function of Pout for the three bias voltages. It is clear from this

figure that for an output power of less than 31 dBm, decreasing the bias voltage increases the 

efficiency (i.e., decreases the power supply current). Of course merely decreasing the bias to

decrease power supply current may not be appropriate since decreasing the bias voltage will result in

increased signal distortion that can have a deleterious effect on the OBP and SER (as will be shown 

in Sections 6 and 7). 

Figure 11. Power-added efficiency for three bias voltages. 

6. REQUIRED SIGNAL-TO-NOISE RATIO AND LINK MARGIN FOR π/4 DQPSK 

The reliability of a radio link can be measured by the symbol error rate (SER). In this study, the radio 

link SER is determined using simulation methods. The simulated link corresponds to the physical 

channel defined by the cellular and PCS IS 136/54 mobile radio standard. The standard uses π/4 

differential quadrature phase-shift keying (DQPSK) modulation filtered with a 35% excess

bandwidth root raised cosine (RRC) pulse-shaping filter. The transmission rate is 24,300 symbols/s 

or 48,600 bits/s and the channel spacing is 30 kHz. Multiple access and duplexing features of IS 

136/54 were omitted. 

A block diagram of the transmitter and receiver used in the simulation is shown in Figure 12. A 

uniform random number generator produces a random sequence of 2-bit symbols to be transmitted.

These symbols are mapped to their corresponding QPSK symbols. The differential encoder adds the 

16
phase of the current symbol to the sum of the phases of all preceding symbols. The symbols are then

up-sampled to 16 samples/symbol (N-1 zeros are appended to the sequence after each symbol where

N is the number of samples per symbol) and filtered by a finite impulse response RRC pulse-shaping 

filter to yield the digitally modulated signal. 

The amplifier model, based on the narrowband nonlinear model derived in Section 3 and using the

nonlinear functions described in Section 5, multiplies the undistorted digitally modulated signal by a 

complex gain that is a function of signal amplitude. The normalized complex gain (see Equation 

3-13) is computed as follows: 

, ( )

( ( )) ( ) 0

g Aop

g A t

g t =

where A2

(t) is the instantaneous input signal power and is the mean input signal power. 2 Aop

Figure 12a. Block diagram of simulated π/4 DQPSK with RRC filtering transmitter. 

Figure 12b. Block diagram of simulated π/4 DQPSK with RRC filtering receiver. 

White Gaussian noise was added prior to the receiver's RRC matched filter. The output of the

matched filter was sampled once per symbol. The symbols were detected by subtracting the phase of

the previous symbol from the present one. The decision block (slicer) decided which symbol was 

sent. This symbol was compared to the transmitted symbol to determine the number of received 

symbol errors. 

17
Figure 13 shows the SER curves for Pout = 28 and 31 dBm in combination with biases of -2.0 and

-2.5 V, respectively, compared to the theoretical performance for a linear amplifier. These results 

correspond to the most linear and the worst-case nonlinear operation of the amplifier based on the 

measurements presented in this report. Figure 13 contains error bars corresponding to a standard

deviation in computed SER. 

Figure 13. SER in an AWGN channel for a portable transceiver communications link. 

The received signal power is a function of the radio link loss; this along with effective isotropic

radiated power and required SER (and hence SNR) determines the link margin of the transceiver. 

In order to compare the results for various amplifier operating conditions, the link margin for the 

transceiver operating at the 3 bias voltages and Pout = 28, 29, 30, and 31 dBm were calculated relative 

to a reference link margin where the transceiver is operated at Pout = 28 dBm and -2.0 V bias. When

the propagation path is assumed to be the same for all cases, the relative link margin (RLM) is given

by: 

RLM P SNR [P SNR ] (dB) = out − req − out − req reference

where SNRreq is that required to achieve an SER of 10-3. Assuming the reference link margin is the 

desired link margin, the additional power given by the RLM corresponds to an allowable increase in

effective range over the reference case. For example assuming only free space loss, each additional 

6 dB in RLM corresponds to doubling the effective range relative to the reference case. 

18
Table 3 shows the SNR and RLM for each of the cases described above. The required SNR for a 

linearly amplified signal is 12.9 dB which for each output power would increase the RLM by a

fraction of a dB. Assuming only free space loss, the 2.9 dB RLM at Pout =31 dBm and -2.0 V Pout

corresponds to an increase in effective range of about 40%. 

Table 3. Required SNR and RLM as a Function of Bias Voltage and Output Power 

Pout Bias (V) SNR 

@ 10-3 SER 

(dB) 

RLM 

(dB) 

-2.50 13.6 2.6

-2.25 13.6 2.6 31 dBm

-2.00 13.3 2.9

-2.50 13.1 2.1

-2.25 13.2 2.0 30 dBm

-2.00 13.1 2.1

-2.50 13.1 1.1

-2.25 13.1 1.1 29 dBm

-2.00 13.2 1.0

-2.50 13.1 0.1

-2.25 13.1 0.1 28 dBm

-2.00 13.2 0.0

7. POWER SPECTRAL DENSITY FOR π/4 DQPSK 

The spectral efficiency of a communication system using a variable envelope modulation scheme

depends on the symbol rate, the transmitter filter, and the nonlinear characteristics of the power 

amplifier. In this section, we give estimates of the PSD for a radio link that utilizes a digitally

modulated signal based on the IS 136/54 standard described in Section 6. The PSD was calculated

using simulation methods incorporating the narrowband nonlinear models from Section 3.

19
Baseband digital simulation of the amplified signal was accomplished by creating a filtered π/4 

DQPSK symbol stream digitized with 13 samples per symbol and applying the nonlinear functions 

that represent the power amplifier behavior. The filtered symbol stream (weighted impulses) was 

generated using a pseudorandom noise code that was convolved with a finite impulse response filter 

based on the RRC pulse shape. The PSD of the distorted transmitted signal was obtained by using

the Welsch method for averaging modified periodograms [13]. In this method, a Hanning window is 

applied to a simulated output data segment consisting of 4096 samples. The PSD was estimated by 

performing a Fourier transform of each data segment and averaging the square of the magnitude of

several hundred transformed data segments. 

Figures 14-17 show the calculated normalized PSD’s for output powers of 28, 29, 30, and 31 dBm;

bias voltages of -2.0 V, -2.25 V, and -2.5 V; and 24,300 symbols/s (30 kHz channel spacing). The 

OBP for each case is given in Table 4 below. For the purposes of this report, OBP is the ratio of 

power contained outside of a specified channel to the total power and is obtained by integrating the 

PSD as follows: 

∫ ∫

∞

− −∞

W = S f df W = S f df

B

B

c T ( ) , ( )

/ 2

/ 2

T

c

W

W OBP = 1−

where S (f) is the power spectral density and B is the channel spacing. 

Figures 14-17 show that for a fixed Pout, the OBP increases with decreasing bias voltage. For the bias 

voltages used in this study, this change is not dramatic as shown by the small variations in OBP. For 

a fixed bias voltage, the OBP increases with increasing Pout and the corresponding OBP varies 

significantly.

20
Figure 14. PSD at 31 dBm output power for three bias voltages. 

Figure 15. PSD at 30 dBm output power for three bias voltages. 

21
Figure 16. PSD at 29 dBm output for three bias voltages. 

Figure 17. PSD at 28 dBm output power for three bias voltages. 

22
Table 4. OBP as a Function of Bias Voltage and Output Power 

Pout DC bias 

(V) 

OBP (dB) 

-2.50 -19.6

31 -2.25 -19.6

dBm -2.00 -21.5

-2.50 -21.9

30 -2.25 -22.4

dBm -2.00 -23.3

-2.50 -23.5

29 -2.25 -23.9

dBm -2.00 -24.6

-2.50 -24.7

28 -2.25 -25.2

dBm -2.00 -25.3

8. RESULTS 

For the operating parameters considered in this study, we found that the power amplifier was most 

linear at 28 dBm mean output power and -2.0 V bias. In Table 5 we have summarized the significant 

results of this study: the relationship between amplifier nonlinearity (a function of bias and output

power), the battery current, the OBP, and maximum allowable radio link loss. The tabulated values

for OBP and maximum allowable radio link loss are relative to those obtained when the amplifier is

operating at -2.0 V bias and 28 dBm mean output power. 

The results presented show that the battery current varies by about 20-35% as a function of bias 

voltage for a fixed output power. Hence, decreasing the bias voltage can have a significant effect on 

battery current (i.e., talk-time). For the operating parameters under study, the most significant 

changes in OBP occurred when the output power was reduced. Varying the bias voltage had only a 

small effect on the OBP when compared to reducing the mean output power by 3 dB. Decreasing 

battery current by decreasing bias voltage is less effective for the higher output powers. For example, 

23
at 28 dBm, the battery current varied by 360 mA and at 31 dBm it only varied by 190 mA. Thus the 

results indicate that when operating at the relatively lower output power (i.e., 28 dBm) a significant

reduction in battery current is achieved by decreasing the bias voltage with only a small increase in

undesirable effects such as OBP and minimal reduction in effective range. At higher input powers, 

the increase in OBP was somewhat larger and the reduction in current was not as dramatic. 

As may be expected, increasing the output power also increased the RLM. The increase in RLM of 

2.6 dB is about the same as the 3 dB increase that would be obtained by increasing the output power 

of a linear amplifier from 28 to 31 dBm.

Table 5. Summary of Results 

Pout Bias (V) Current 

(mA) 

RLM (dB) Relative 

OBP 

(dBc) 

-2.50 810 2.6 5.7

31 dBm -2.25 1000 2.6 5.7

-2.00 1000 2.9 3.8

-2.50 740 2.1 3.4

30 dBm -2.25 910 2.0 2.9

-2.00 1000 2.1 2.0

-2.50 710 1.1 2.2

29 dBm -2.25 840 1.1 2.6

-2.00 960 1.0 1.3

-2.50 640 0.1 0.6

28 dBm -2.25 800 0.1 0.1

-2.00 1000 0 0

To the extent that link margins will allow, the most significant reductions in battery current were 

obtained at lower amplifier output power and bias voltage. For the amplifier under study, a reduction

in output signal power of 3 dB at a bias of -2.5 V corresponded to a reduction in RLM of about 2.5

dB, a decrease in OBP of about 5 dB, and a reduction of 170 mA in required battery current (about 

24
a 20% increase in talk-time). Thus if the additional 2.5 dB in RLM is not really necessary for a given 

system, a definite improvement in both talk-time and spectrum utilization can be obtained by backing 

off from the maximum rated power for this amplifier. 

9. SUMMARY 

In this report we have described a measurement, modeling, and simulation effort that analyzed the

relationship between battery current, OBP, and link margin for a typical PCS portable transceiver

power amplifier. The nonlinear amplifier characteristics and associated battery current were obtained 

from measurements of the PCS amplifier. The measurements were performed for various amplifier

bias voltages and input powers in the range of ±10 dBm. A mathematical model of the power 

amplifier based on these measurements was used to simulate the communications link in order to 

determine the PSD and SER for a digitally modulated signal using π/4 DQPSK with 35% RRC 

filtering. For this study, the simulations were limited to nonlinear amplifier transfer functions 

corresponding to bias voltages of -2.0 V, -2.25 V, and -2.5 V; and mean output signal powers of 28,

29, 30, and 31 dBm. The OBP was computed from the simulated PSD’s and the SER was used to

determine the RLM for a maximum SER of 10-3. 

In summary, these results indicate that battery current is strongly dependent on both the bias voltage 

and the output (or input) power. The results of this study show that power amplifier operating 

parameters that are selected to improve the quality and convenience of a communication system (e.g., 

extend battery life and link margin) have a direct consequence in terms of spectrum utilization. Such 

factors need to be considered in terms of spectrum utilization and allocation when nonlinear 

amplification of variable envelope modulations are implemented. Although the conclusions are

derived from the measurement, modeling, and simulation of a single MMIC power amplifier, the 

methodology described should be useful for both communication system design and spectrum 

management. The amplifier studied is used for power amplifying constant and variable envelope 

modulations in the PCS band. Its main disadvantage, for our purposes, was the inability to control the 

bias voltage of each of the three amplifier stages. Further work should include this capability.

Amplifier operating characteristics such as output power, OBP, and SER can also be controlled via 

the drain voltage. Such a study was beyond the scope of this effort, but should be considered in

future work.

25
10. REFERENCES 

[1] P. Dan, “Make the right battery choice for portables,” Electronic Design, pp. 115-120, Apr. 1,

 1996. 

[2] J. Staudinger, “Multiharmonic load termination effects of GaAs MESFET power amplifiers,”

 Microwave Journal, pp. 60-77, Apr. 1996. 

[3] C. Huang, “GaAs MMIC power amplifiers drive cellular systems,” Microwaves and RF, pp. 85-

86, Oct. 1994. 

[4] L. J. Kushner, “Output performance of idealized microwave power amplifiers,” Microwave

 Journal, pp. 103-116, Oct. 1989. 

[5] L. J. Kushner, “Estimating power amplifier large signal gain,” Microwave Journal, pp. 87-102,

 Jun. 1990. 

[6] L. Goldberg, “PCS: Technology with fractured standards,” Electronic Design, pp. 65-78, Feb. 

 6, 1995. 

[7] J. Millman, Microelectronics, New York, NY: McGraw Hill, 1979. 

[8] S.A. Maas, “MESFET power amplifiers,” In ch. 9 of Nonlinear Microwave Circuits, Norwood, 

MA: Artech House, 1988, pp. 359-396.

[9] A.A.M. Saleh, “Frequency-independent and frequency-dependent nonlinear models of TWT

 amplifiers,” IEEE Trans. Comm., vol. COM-29, no. 11, pp. 1715-1720, 1981. 

[10] N. Wiener, Nonlinear Problems in Random Theory, New York, NY: John Wiley & Sons, Inc., 

 1958, pp. 28-48. 

[11] E. Bedrosian and S. O. Rice, “The output properties of Volterra systems (nonlinear systems with 

memory) driven by harmonic and Gaussian inputs,” Proceedings of the IEEE, vol. 59, no. 12, 

pp. 1688-1707, Dec. 1971.

[12] V. Volterrra, Theory of Functionals and of Integral and Integro-differential Equations, New

York, NY: Dover Publications, Inc., 1959, pp. 21. 

[13] A.V. Oppenheim, Digital Signal Processing, Englewood Cliffs, NJ: Prentice Hall Inc., 1975,

 pp. 553-554.

26
11. BIBLIOGRAPHY

Power Spectral Density and Adjacent Channel Interference: 

J.F. Sevic and J. Staudinger, “Simulation of adjacent-channel power for digital wireless 

communication systems,” Microwave Journal, pp. 66-80, Oct. 1996. 

S. Aritlyavisitakul and T. Liu, “Characterizing the effects of nonlinear amplifiers on linear 

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J. S. Kenney and A. Leke, “Power amplifier spectral regrowth for digital cellular and PCS

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J.K. Cavers, “The effect of data modulation format on intermodulation power in nonlinear 

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M. Heutmaker, J.R. Welch, and E. Wu, “Using digital modulation to measure and model RF 

amplifier distortion,” in Proc. of the Wireless Comm. Conf, pp. 78-81, Aug. 1996. 

GaAs FET modeling: 

H. State, P. Newman, I. R. Smith, R. A. Pucel, and H. A. Haus, “GaAs FET device and circuit 

simulation in SPICE,” IEEE Trans. on Electron Devices, pp. 160-169, Feb. 1987. 

J. Staudinger, M. Golio, C. Woodin, and M. C. deBaca, “Considerations for improving the 

accuracy of large-signal GaAS MESFET models to predict power amplifier circuit 

performance,” IEEE Jour. of Solid-State Circuits, pp. 366-373, Mar. 1994. 

R. Howald, “Understanding distortion in GaAs MESFETS,” RF Design, pp. 71-80, Jun. 1997. 

State of the Art Power Amplifiers: 

F. A. Olson, “Microwave solid-state power amplifier performance: Present and future,” 

Microwave Journal, pp. 24-46, Feb. 1995. 

B. Stengel and V. Nair, “RF power amplifiers for portable communications applications,” 1994

IEEE MTT-S International Microwave Symposium Digest, pp. 1623-1626, May 1994. 

Improvements: 

J. Sheinwald, “MMIC compatible bandpass filter design: A survey of applicable techniques,” 

Microwave Journal, pp. 26-42, Mar. 1994. 

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