Chinese Journal of Electronics
Vol.18, No.4, Oct. 2009
An Ultra Low-Power FCC-Compliant
5th-Derivative Gaussian Pulse Generator for
IR-UWB Transceiver∗
QIN Bo1 , CHEN Hongyi1 , WANG Xin2 , WANG Albert2 and HAO Yinghui3
(1.Institute of Microelectronics, Tsinghua University, Beijing 100084, China)
(2.Department of Electrical Engineering, University of California, Riverside, CA 92521, USA)
(3.Yantai Vocational College, Yantai 264670, China)
Abstract — A FCC-compliant ultra low-power lowcost 5th-derivative Gaussian Pulse generator (PG) for full
3.1-10.6GHz Impulse-radio (IR) carrier-free Ultra wideband (UWB) transceiver was designed and fabricated in
foundry 0.13µm CMOS. This PG integrates three cascade
stages to generate square wave, Gaussian pulse and 5thorder Gaussian derivative waveform, respectively. Measurement shows the lowest reported power consumption of
5.1pJ/pulse at 100MHz Pulse repeating frequency (PRF),
the smallest die area of only 0.02mm2 , short 5th-derivative
Gaussian pulse width of 770ps and peak to peak amplitude
of 66mV. The FCC-compliant IR-UWB pulse generator
potentially allows up to 1.3Gbps throughput for low-cost
low-power hi-QoS wireless multimedia and video streaming.
Key words — Ultra wideband (UWB), Pulse generator (PG), 5th-derivative Gaussian, FCC-compliant, Low
power.
I. Introduction
During the past several years after Federal communication
commission (FCC) permitted the commercial development of
Ultra wideband (UWB) technology from 3.1GHz to 10.6GHz
in 2002[1] , more and more momentums have been attracted on
this rising technology. While industrial development has been
focusing on DS-UWB and MB-OFDM UWB, it is commonly
agreed that they do not fully use the available UWB spectrum to eventually realize the highly desired multi-Gbps wireless streaming throughput. On the other hand, Impulse radio
(IR) UWB technology can transmit extremely short impulse
trains using the full 3.1-10.6GHz available spectrum and in a
carrier-free scheme. It hence allows a much simpler RF frontend, BPSK modulation and digital baseband, which make fullCMOS IR-UWB system a low-power low-cost hi-performance
wireless solution to eventually realize multi-Gbps hi-QoS multimedia and video wireless applications.
In order to completely comply with and take full use of
the Effective isotropic radiated power (EIRP) spectral mask
over 3.1–10.6GHz regulated by FCC, the pulse width and am∗ Manuscript
plitude of radiated UWB signals must follow very tight restriction, i.e., pulse width < 1ns and pulse amplitude < 1V.
It is hence extremely challenging to design UWB Pulse generator (PG) meeting such strict specifications while achieving
low-power for hi-throughput operation and enabling low-cost
simple CMOS IR-UWB systems. Early reported PG designs
used step recovery diode and microstrip technique for pulse
generation[2,3] , which do not meet the integration, low-power
and low-cost requirements. Recently, Ref.[4] reports 1.7ns
313pJ/pulse Gaussian pulse generated and up-converted to a
550MHz band at 5GHz using complicated analog topology.
Ref.[5] depicts a traditionally modulated 17ns PG for 7–9GHz
band with programmable carrier where the bandwidth and
pulse width greatly limit the wireless data throughput. Threeoptional channels concept is presented in Ref.[6] with 3ns pulse
width and 550MHz bandwidth, which requires a hi-pass filter
for FCC compliance and uses a very complex digital topology. Refs.[7] and [8] present 8-delay-cell type 5th-derivative
Gaussian pulse generator whose delay stages can be further
simplified for low-power low-cost operation. Ref.[9] reports a
2nd-derivative Gaussian PG requiring off-chip bandpass filters
to deliver FCC-compliant 1.5ns 63pJ/pulse pulses over 0.55GHz. A Gaussian PG with complex calibration to produce
accurate 1ns pulse is presented in Ref.[10], which however consumes high power of 1.8nJ/pulse and big size of 1.95mm2 .
This paper presents a new approximated methodology for
Gaussian pulse generation and novel 4-delay-cell all-digital
3.1–10.6GHz full-band 5th-derivative Gaussian PG circuit in
0.13µm CMOS with record low power of 5.1pJ/pulse and size
of 0.02mm2 . Section II discusses design of a 5th-derivative
Gaussian PG as the competitive candidate for IR-UWB. The
new FCC-compliant UWB pulse generator circuit is described
in Section III. Section IV presents the measurement results,
followed by the conclusions.
II. 5th-Derivative Gaussian Pulse
Practically, there are several different pulse generation
Received Nov. 2008; Accepted Feb. 2009. This work is supported by the National Natural Science Foundation of China
(No.60776025, No.90607021, No.60729308) and Foundation of Tsinghua University (No.SIST2027).
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Chinese Journal of Electronics
schemes available for impulse UWB PG, such as rectangular,
sinusoidal and Gaussian methods. However, considering the
spectrum characteristics, Gaussian pulse and its nth-derivative
(n = 1, 2, 3 · · ·), especially 5th-order, are considered as the
best fit since their side lobes have the smallest energy, making them easier to meet the strict FCC EIRP spectrum mask
requirement[11] . Thus, in this work, Gaussian pulse and its
5th-derivative pulse generation scheme will be fully discussed.
The time sequence and Power spectrum density (PSD) for
Gaussian pulses can be respectively expressed as following
¶
µ
t2
1
(1)
exp − 2
G0 (t) = A √
2σ
2πσ
ε0 (f ) =
A2
exp[−(2πf σ)2 ]
Tf
(2)
where A is amplitude parameter, σ is time parameter also
called variance and Tf is pulse interval equaling to reciprocal
of Pulse repeating frequency (PRF). Apparently from Eq.(2),
the maximum PSD of Gaussian pulse is located at DC, making it not suitable for FCC-compliant UWB. However, when
applying derivation to Eq.(1), the corresponding PSD peak
after Laplace transformation will move toward to high frequency. Considering the characteristics of Laplace transformation where a jω item will be introduced once there is a
derivation occurring in time domain, hence combining Eqs.(1)
and (2), the expressions of 5th-derivative Gaussian pulse in
time and frequency domains can be derived as
µ
¶
−15σ 4 t + 10σ 2 t3 − t5
t2
√
G5 (t) = A
exp − 2
(3)
2σ
2πσ 11
A2
(2πf )10 exp[−(2πf σ)2 ]
(4)
ε5 (f ) =
Tf
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transmitted pulse width in a certain extent. Defined the pulse
width τ as the period across which the energy accumulated
achieves 99.9% of that over infinite time span, we can get
Z
τ /2
−τ /2
ÁZ
G2n (t)
∞
G2n (t) ≥ 99.9%
(6)
−∞
According to Eq.(6), we have τ = 8σ for 5th-derivative
Gaussian pulse. From Eqs.(5) and (6), we can illustrate the
relationships among the time parameter σ, pulse width τ
and the optimized frequency fopt as shown in Fig.1. Apparently, an optimized 5th-derivative Gaussian pulse shall feature
fopt = 6.85GHz and τ = 8σ ≈ 420ps, which is our design goal
in this work.
III. Circuit Design
1. Approximate algorithm for Gaussian pulse
Actually, it is infeasible to implement a 5th-derivative
Gaussian pulse generator directly based on Eq.(3) in CMOS,
since it implies a very complicated circuit topology. For example, Ref.[12] reports a 2nd-derivative Gaussian pulse generator
using MOSFET operating in sub-threshold region to generate
the waveform, which makes accurate control close to impossible in actual design under PVT variations. To realize low
power and low cost design, a new systematic approximation
method is proposed in this paper. The new Gaussian PG design method utilizes a simple CMOS inverter concept where
the exponential function associated with capacitive load charging and discharging serves to generate the required various
Gaussian pulses, which can be understood using the conceptual two CMOS inverter schematic and its equivalent circuit
as shown in Fig.2.
Clearly, Eq.(4) suggests an optimized frequency fopt where
PSD achieves the maximum. Careful design to locate the
maximum PSD at the center of UWB spectrum, i.e., fopt =
6.85GHz, can certainly utilize the FCC-allowed UWB bandwidth the most. In order to find the optimized frequency point
corresponding to the maximum PSD, by differentiating Eq.(4)
against frequency f and setting it to zero, we have
√
fopt = 5/2πσ
(5)
Fig. 2. Approximate concepts to generate Gaussian pulse and
comparison with ideal Gaussian waveform
Fig. 1. Relationships among time parameter, pulse width and
optimized frequency for 5th-derivative Gaussian pulse
Obviously, the optimized center frequency fopt is only related to the time constant σ. Meanwhile, σ also represents the
Inverter M1p -M1n generates a delayed square wave at
Vg , while inverter M2p -M2n produces a Gaussian pulse at
Vo by carefully sizing MOSFETs and tuning the charging/discharging procedure. M1p , M1n , M2p & M2n are modeled by R1p , R1n , R2p & R2n and switches K1p , K1n , K2p &
K2n . To understand it, assume input changes from low to
high, K1n turns on and M1n moves from saturation to linear
region. The charged C1 starts discharge via M1n and Vg drops
An Ultra Low-Power FCC-Compliant 5th-Derivative Gaussian Pulse Generator for IR-UWB Transceiver
gradually to zero, which progressively turns on K2p with M2p
transferring from sub-threshold to saturation for small Vo . Assume C1 being charged to VDD initially, neglecting transistor
high-order effects and using the I-V characteristics described
in Ref.[13], the Vg waveform can be derived as

In t

,
t ≤ t1 = Vthn C1 /In
 VDD −
C1
Vg =
(7)
t−t1

−

(VDD − Vthn )e Req C1 ,
t > t1
where Vthn is threshold voltage, In = Kn (VDD − Vthn )2 is
constant saturate current and Req = 1/Kn (VDD − Vthn ) is
equivalent linear region resistor for M1n . Next, assuming same
threshold voltage for NMOS and PMOS, i.e., Vthn = −Vthp =
Vth , M2p will operate at weak inversion for t < t1 while in
saturation when t > t1 . Using Kirchhoff law, we have

In t
 I0 e ζVT C1 ,
t ≤ t1 = Vth C1 /In
dVo
= Ip ≈
C2
t−t1 ´2
³
−

dt
Kp (VDD − Vth )2 1 − e Req C1 ,
t > t1
(8)
where I0 and ζ are process dependant parameters and VT =
kT /q is thermal voltage. Solving Eq.(8) by integration results
in the required output signal waveform as
´
 ³ t
η −1 ,

M
e
t ≤ t1 = Vth C1 /In




 ³ t1
´
Vo =
(9)
M e η − 1 + P (t − t1 )




2(t−t1 )
´
1

−
Q ³ − Rt−t

+
4e eq C1 − e Req C1 − 3 , t > t1
4
where η = ζVT C1 /In , M = I0 η/C2 , P = Kp (VDD − Vth )2 /C2
and Q = P · 2Req C1 . To validate the new approximate Gaussian generation method, the output pulse amplitude obtained
using our approximation algorithm for a 2-inverter circuit is
compared with that from accurate Gaussian simulation in time
domain as illustrated in Fig.2, which shows that the new design method matches ideal simulation very well. The minor
discontinuity point observed, marked with a dashed circle, is
attributed to adoption of simplified two-segment CMOS modeling for weak inversion to saturation transition used in this
approximation method, referring to Eqs.(7) to (9), which could
not occur in real transistor operation.
2. Circuit implementation
Fig.3 shows a block diagram for our novel 4-delay-cell 5thderivative Gaussian PG using the above 2-inverter Gaussian
approximation concept.
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In Fig.3, the 5th-derivative Gaussian pulse generator consists of three cascade stages: Square wave (SW) generation,
Gaussian pulse formation and 5th-derivative combination. A
square wave generator produces needed square waveforms from
a common sinusoid. Sharp rising/falling edges are critical to
extremely narrow pulse generation. A novel 4-delay-cell topology is used to generate four carefully delayed phases and the
delay time ∆t can be controlled by adjusting the delay cell.
Four 2-inverter units, each composed of a delay cell and a
Separate pulse generator (SPG), produce four phase-shifted
0th-order Gaussian pulses, which are combined by a multiplexing unit to generate the desired 5th-derivative Gaussian
pulse at the output.
The detailed schematic and timing diagram of the proposed 4-delay-cell 5th-derivative Gaussian pulse generator are
shown in Fig.4. Five square waveforms (SW1–SW5) are produced by four delay cells, which go through the NAND/NOR
gates (i.e., SPG) to generate the four phase-shifted 0th-order
Gaussian pulses. A final 5th-derivative Gaussian pulse is then
produced by M1 /M2 /M3 /M4 multiplexing. This greatly simplified 4-delay-cell PG topology leads to significantly reduced
power dissipation and circuit size.
Fig. 4. Schematic and timing diagram of the proposed 4delay-cell 5th-derivative Gaussian pulse generator
IV. Measurements
A fully integrated FCC-compliant 4-delay-cell 5thderivative Gaussian pulse generator for impulse-based carrierfree IR-UWB transceiver is designed and fabricated in a
foundry 0.13µm CMOS. The die photo is shown in Fig.5 and
the occupied area without testing pads is merely 0.02mm2 .
Fig. 5. Die photo of the proposed 5th-derivative Gaussian PG
Fig. 3. Topology of the proposed 5th-derivative Gaussian
pulse generator
Fig.6 shows the measured 5th-derivative Gaussian pulse
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Chinese Journal of Electronics
train and one single zoomed in pulse in time domain with
100MHz PRF. The measured pulse width is τ ∼ 770ps and signal amplitude is Vpp ∼ 66mV, which somewhat deviate from
the preferred values from circuit analysis as mentioned in Section II. This discrepancy is mainly attributed to inaccuracy in
the foundry provided PDK models because the 0.13µm CMOS
process used was still in its early qualification phase at the time
of this design. Although the maximum PSD does not locate
at the proposed optimum frequency of 6.85GHz and the whole
spectrum does not fully occupy the FCC EIRP mask room,
the relationship between the pulse width and fopt still meets
Eq.(5). In future work, revision will be applied to improve the
5th-derivative PG performance by further narrowing the pulse
width.
Since the measured 5th-derivative Gaussian pulse still has
fairly narrow width, the proposed PG circuit can be used and
embedded in the IR-UWB single-chip transmitter with simple BPSK modulation, which is favorable to avoid complicated
baseband modulation topology and capable of potentially support up to 1.3Gbps wireless data throughput with low cost and
low power.
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dissipation at 1.2V supply measured at 100MHz PRF.
Table 1 is the performance summary and comparison with
other published papers, indicating that this design achieves
the record lowest power consumption, the smallest die area
and the second narrowest pulse width.
Table 1. Performance summary and comparison
with other reported papers
f -Band
Vpp
Power
Size
τ (ns)
Tech.
Refs.
(GHz)
(mV) (pJ/pulse) (mm2 )
[4] 5.1–5.6 1.7
250
313
2.38 0.18µm BiCMOS
[5]
7–9
17
200
40
0.066
90nm CMOS
[6] 2.9–5.2
3
700
47
0.08
90nm CMOS
[7] 3.1–10.6 2.4
148
58
0.18
0.5µm CMOS
[8]
0–10
0.42
51
36
0.13
0.18µm CMOS
[9]
0.5–5
0.8
330
63
1.56
0.13µm CMOS
[10]
1
600
1800
1.95
0.35µm CMOS
[14] 3.1–8
1.75 1280
825
0.4
0.18µm CMOS
This
3.1–10.6 0.77
66
5.1
0.02
0.13µm CMOS
work
V. Conclusions
We demonstrated a new FCC-compliant ultra low-power
fully integrated 5th-derivative Gaussian PG circuit designed
in 0.13µm CMOS for full-band IR-UWB transceiver, which
features novel approximated algorithm and new all-digital 4delay-cell topology and reasonably complies with FCC UWB
power mask. Measurement shows the lowest reported power
dissipation of 5.1pJ/pulse at 100MHz PRF, a very short pulse
width of 770ps and a very small die area of less than 0.02mm2 .
It can potentially support a very high data rate up to 1.3Gbps
for hi-quality wireless video streaming.
References
Fig. 6. Measured pulse train and waveform of the 5thderivative Gaussian pulse generator (100MHz PRF)
Fig. 7. Measured PSD of the proposed 5th-derivative Gaussian PG
Fig.7 shows measured pulse spectrum that reasonably complies with FCC mask, yet centers at 4GHz, lower than the expected fopt = 6.85GHz due to the same reasons above. The
simplified topology results in a record low 5.1pJ/pulse power
[1] FCC, First Report and Order, FCC 02-48, February 14, 2002.
[2] J. Han and C. Nguyen, “A new ultra-wideband ultra-short
monocycle pulse generator with reduced ringing”, IEEE Microwave and Wireless Components Letters, Vol.12, No.6,
pp.206–208, 2002.
[3] S. Yilmaz and I. Tekin, “Ultra-wideband N-bit digitally tunable pulse generator”, Proc. IEEE International Conference
on Ultra-Wideband, Zurich, Switzerland, pp.438–441, 2005.
[4] D. Wentzloff and A. Chandrakasan, “Gaussian pulse generators for subbanded ultra-wideband transmitters”, IEEE Transactions on Microwave Theory and Techniques, Vol.54, No.4,
pp.1647–1655, 2006.
[5] J. Ryckaert, G. Van der Plas, V. De Heyn, C. Desset, B. Van
Poucke and J. Craninckx, “A 0.65-to-1.4nJ/Burst 3-to-10 GHz
UWB All-Digital TX in 90nm CMOS for IEEE 802.15.4a”,
IEEE Journal of Solid-State Circuits, Vol.42, No.12, pp.2860–
2869, 2007.
[6] D. Wentzloff and A. Chandrakasan, “A 47pJ/pulse 3.1-to-5GHz
all-digital UWB transmitter in 90nm CMOS”, IEEE International Solid-State Circuits Conference Digest, San Francisco,
California, USA, pp.118–591, 2007.
[7] H. Kim and Y. Joo, “Fifth-derivative Gaussian pulse generator for UWB system”, Proc. IEEE Radio Frequency Integrated
Circuits Symposium, Long Beach, California, USA, pp.671–674,
2005.
[8] H. Xie, X. Wang, A. Wang, B. Zhao, Y. Zhou, B. Qin, H. Chen
and Z. Wang, “A Varying pulse width 5th-derivative Gaus-
An Ultra Low-Power FCC-Compliant 5th-Derivative Gaussian Pulse Generator for IR-UWB Transceiver
sian pulse generator for UWB transceivers in CMOS”, Proc.
IEEE Radio and Wireless Symposium, Orlando, Florida, USA,
pp.171–174, 2008.
[9] L. Smaini, C. Tinella, D. Helal, C. Stoecklin, L. Chabert, C.
Devaucelle, R. Cattenoz, N. Rinaldi and D. Belot, “Single-chip
CMOS pulse generator for UWB systems”, IEEE Journal of
Solid-State Circuits, Vol.41, No.7, pp.1551–1561, 2006.
[10] C.F. Liang, S.T. Liu and S.I. Liu, “A calibrated pulse generator
for impulse-radio UWB applications”, IEEE Journal of SolidState Circuits, Vol.41, No.11, pp.2401–2407, 2006.
[11] H. Sheng, P. Orlik, A.M. Haimovich, L.J. Cimini, Jr. and J.
Zhang, “On the spectral and power requirements for ultrawideband transmission”, Proc. IEEE International Conference on Communications, Anchorage, Alaska, USA, pp.738–
742, 2003.
[12] Y.J. Zheng, H. Dong and Y.P. Xu, “A novel CMOS/BiCMOS
UWB pulse generator and modulator”, IEEE Microwave Symposium Digests, Fort Worth, Texas, USA, pp.1269–1272, 2004.
[13] T.H. Lee, The Design of CMOS Radio-Frequency Integrated
Circuits, First Edition, Cambridge University Press, New York,
USA, pp.53–55, 1998.
[14] T. Norimatsu, R. Fujiwara, M. Kokubo, M. Miyazaki, A. Maeki,
Y. Ogata, S. Kobayashi, N. Koshizuka and K. Sakamura, “A
UWB-IR transmitter with digitally controlled pulse generator”,
IEEE Journal of Solid-State Circuits, Vol.42, No.6, pp.1300–
1309, 2007.
QIN Bo
received B.S. degree in
electrical engineering from Xi’an Jiaotong University, China, in 2004.
He
is currently working toward the Ph.D.
degree in Institute of Microelectronics,
Tsinghua University, China.
His research interests include ultra wideband system and circuit design, RF circuit design and mixed-signal IC design. (Email:
[email protected])
CHEN Hongyi Professor of Institute of Microelectronics in Tsinghua University (IMETU), Senior member of Chinese Institute of Electronics (CIE), Senior
member of Institute of Electric and Electronic Engineers (IEEE). His research accesses semiconductor device structures and
integrated circuit design. He is currently
working on ASIC and SOC (system on a
chip) design methodology, library development technology, algorithm mapping to hardware architecture and
realization, VLSI-DSP and applications in multimedia signal (e.g.
609
speech, audio, image and video) processing and information security fields, etc. He has published more than 230 academic articles,
co-published two books and co-translated two textbooks, claimed
21 items of US innovation patents (among which 13 items have
been awarded) with his colleagues and students. He has been advising 28 M.S. students with 22 receiving M.S./M.E. degrees and
27 Ph.D. candidates with 20 receiving Ph.D. degree. (Email: [email protected])
WANG Xin
received the B.S. degree from Beijing University of Posts and
Telecommunications, Beijing, China in
2005 and the MSEE degree from Illinois
Institute of Technology, Chicago, USA in
2007.
He is currently working toward
Ph.D. degree in Department of Electrical Engineering, University of California,
Riverside, USA. His research interests are
Ultra wideband (UWB) SoC design, RF
circuit design and Electrostatic discharge (ESD) design and applications. (Email: [email protected])
WANG Albert
IEEE Fellow, received the B.S. degree from Tsinghua University, China, and the Ph.D. degree from
The State University of New York at Buffalo in 1985 and 1996, respectively. From
1995 to 1998, he was a Staff Engineer
at National Semiconductor Corporation.
From 1998 to 2007, he was a Professor
of Electrical and Computer Engineering
in Illinois Institute of Technology, USA,
where he directed the Integrated Electronics Laboratory. He is currently a Professor of Electrical and Computer Engineering and Director for the Laboratory of Integrated Circuits and Systems at the
University of California, Riverside, USA. His research interests focus
on Analog/Mixed-Signal/RF ICs, Advanced on-Chip ESD Protection, IC CAD and Modeling, SoC, and Nano Devices, etc. He received the CAREER Award from the National Science Foundation
in 2002. He is the author of the book “On-Chip ESD Protection
for Integrated Circuits” (Kluwer, 2002) and 130+ peer-reviewed papers in the field, and holds several U.S. patents. Dr. Wang is Editor
for the IEEE Electron Device Letters and Guest Editor for IEEE
Transactions on Microwave Theory and Techniques. He was an Associate Editor for the IEEE Transactions on Circuits and Systems
I, Associate Editor for the IEEE Transactions on Circuits and Systems II, Guest Editor for the IEEE Journal of Solid-State Circuits
and Guest Editor-in-Chief for the IEEE Transactions on Electron
Devices. (Email: [email protected])