IEEE Solid-State Circuits Magazine - Spring 2016 - 82

are that a rectangular response in
one domain corresponds to sin(x)/x
(sinc(x)) in the other and that the
Gaussian response is the crosspoint, the shape that is the same

signal to noise power ratio, which is
not equivalent to the individual bit
energy to noise power density ratio
(IBEND, also known as Eb/N 0). Elaborate signal processing algorithms,

Good engineering requires a mixture
of mathematical skills and physical
understanding.
in both domains. "Squaring up" a
Gaussian shape in one domain
always leads toward a sinc shape in
the other domain.
For amplifier applications, the FT
requires that, in the presence of any
nonlinearity, there will be harmonics
and intermodulation cross products
(distortion) among multiple signals
present in the amplifier. This is
why receivers must have extremely
linear circuitry until signal channelization is completed. It also
means that for any PA that is operating with multiple signals present
[e.g., orthogonal frequency division
modulation (OFDM) and long-term
evolution (LTE)], any transistor nonlinearity must incur intermodulation
distortion. This includes class-AB.
Successful PA designs for these signals must be at or very close to classA, as industry has learned.

Conservation of Energy
Energy is neither created nor
destroyed, but it can be transformed.
From the point of view of PA design,
this means that if energy efficiency
is lower than 100%, something is
"getting hot" from the energy that
is staying in the PA and being dissipated. We need to be able to point
to what is getting hot before we can
work toward improving energy efficiency of the PA.

Shannon's Capacity Limit
The key point here is that limits on
our ability to communicate more
bits per second in any allocated
bandwidth is dependent only on the

82

S P R I N G 2 0 16

including coding, only allow us to
approach this limit. Multi-input,
multi-output (MIMO) structures are
no exception.
Good engineering requires a mixture of mathematical skills and physical understanding. Emphasizing one
part of this mixture over the other
inevitably leads to problems. Both
cases are unfortunately prevalent
today: emphasizing mathematics
without tying models to physical circuit behavior and also running with
circuit measurements without paying
close attention to physical principles
for guidance. It is my hope that all of
our engineering can be balanced!

References

[1] E. McCune, "A technical foundation for
RF CMOS power amplifiers-Part 1," IEEE
Solid-State Circuits Mag., vol. 7, no. 3, pp.
81-85, 2015.
[2] J. B. Anderson, T. Aulin, and C. E. Sundberg, Digital Phase Modulation. New York:
Plenum, 1986, p. 24.
[3] J. G. Proakis, Digital Communications, 3rd
ed. New York: McGraw-Hill, 1995, p. 194.
[4] G. F. Montgomery, "A comparison of amplitude and angle modulation for narrowband communication of binary-coded
messages in fluctuation noise," Proc. IRE,
vol. 42, pp. 447-454, Feb. 1954.
[5] A. J. Viterbi, Principles of Coherent Communication, New York: McGraw-Hill,
1966.
[6] M. J. E. Golay, "The application of radio interferometry to extraterrestrial
metrology," IRE Trans. Space Electron.
Telemetry, vol. SET-5, no. 4, pp. 186-193,
Dec. 1959.
[7] M. Schwartz, Information Transmission,
Modulation, and Noise, 4th ed. New York:
McGraw-Hill, 1990.
[8] H. Taub and D. L. Schilling, Principles of
Communication Systems, 2nd ed. New
York: McGraw-Hill, 1986.
[9] E. McCune, "Solving the broken sequence," IEEE Microwave Mag., vol. 15, no.
4, pp. 40-50, June 2014.
[10] E. McCune, "Extended phase-shift keying,"
Ph.D. dissertation, Elec. Comp Eng. Dept.,
Univ. California, Davis, CA, Aug. 1998.

IEEE SOLID-STATE CIRCUITS MAGAZINE

[11] E. McCune, "pPSK for bandwidth and energy efficiency," in Proc. 43rd European
Microwave Conf., Nuremberg, Oct. 2013,
pp. 569-572.
[12] E. McCune, "Foundations of green communications," in Proc. IEEE Int. Commun.
Conf., London, U.K., June 7-12, 2015,
pp. 2744-2749.
[13] T.-S. Lee and C.-C. Liu, "Design techniques
for low-voltage VHF BiCMOS Gm-C filters
with automatic tuning," in Proc. 1st IEEE
Asia Pacific Conf. ASICs, Seoul, Aug. 1999,
pp. 59-62.
[14] T. W. Kim and B. Kim, "A 13-dB IIP3 improved low-power CMOS RF programmable gain amplifier using differential circuit transconductance linearization for
various terrestrial mobile D-TV applications," IEEE J. Solid-State Circuits, vol. 41,
no. 4, pp. 945-953, Apr. 2006.
[15] A. Niknejad and D. Chowdhury, "Transforming RF and mm-wave CMOS circuits,"
in Proc. Int. Symp. VLSI Design, Automation Test, Hsinchu, Apr. 2009, pp. 138-141.
[16] B. J. Thompson, "Graphical determination of performance of push-pull audio amplifiers," Proc. IRE, vol. 19, no. 4,
pp. 591-600, Apr. 1933.
[17] F. E. Terman, Radio Engineering Handbook. New York: McGraw-Hill, 1943.
[18] J. F. Toennies. (Mar. 1938). Differential amplifier. Rev. Sci. Instrum. vol. 9. [Online].
Available: scitation.aip.org/content/aip/
journal/rsi/9/3/10.1063/1.1752445
[19] L. M. Clement, F. M. Ryan, and D. L. K.
Martin, "The Avalon-Los Angeles radio toll circuit," Proc. IRE, vol. 9, no. 6,
pp. 469-505, Dec. 1921.
[20] D. H. Steinbrecher, "Optimum efficiency
of a cascade of low-gain amplifiers," IEEE
Trans. Microwave Theory Tech., vol. 18,
no. 11, pp. 951-956, Nov. 1970.
[21] E. Bedrosian, "The analytic signal representation of modulated waveforms," Proc.
IRE, vol. 50, pp. 2071-2076, Oct. 1962.
[22] J. W. Goodman, "A superposition property
of angle modulation," Proc. IRE, vol. 49, p.
1084, June 1961.

About the Author
Earl McCune (emc2@wireless and
highspeed.com) received his B.S. from
the University of California, Berkeley,
his M.S. from Stanford University, and
his Ph.D. from the University of California, Davis. His experience in RF circuits,
signals, and systems spans more than
40 years. He cofounded two Silicon
Valley startups: one doing direct digital synthesis beginning in 1986, which
merged with Proxim in 1991, and the
second, Tropian, doing switch-based
RF transmitters beginning in 1996,
which was acquired by Panasonic ten
years later. He has 74 issued patents in
the United States. He has authored two
books, Practical Digital Wireless Signals
and Dynamic Power Supply Transmitters. He has been an IEEE Microwave
Theory and Techniques Society Distinguished Lecturer since 2013.
http://scitation.aip.org/content/aip/ http://www.highspeed.com
Table of Contents for the Digital Edition of IEEE Solid-State Circuits Magazine - Spring 2016
