THESIS FOR THE DEGREE OF LICENTIATE OF ENGINEERING
Optimum GaN HEMT Oscillator Design Targeting
Low Phase Noise
Mikael Hörberg
Microwave Electronics Laboratory
Department of Microtechnology and Nanoscience MC2
CHALMERS UNIVERSITY OF TECHNOLOGY
Gothenburg, Sweden, April 2015
Optimum GaN HEMT Oscillator Design Targeting Low Phase Noise
MIKAEL HÖRBERG
© Mikael Hörberg, 2015
ISSN 1652-0769
Technical Report MC2-304
Microwave Electronics Laboratory
Department of Microtechnology and Nanoscience - MC2
Chalmers University of Technology
SE-412 96 Gothenburg
Sweden
Phone: +46 (0)31 772 1000
Printed by Chalmers Reproservice
Gothenburg, Sweden, 2015
ii
iii
Abstract
The thesis considers design of low phase noise oscillators, given the boundary condition
of the used technology. Important conditions are the power handling of the active device,
device noise floor, the quality factor of the resonator, bias settings, and low frequency
noise. A particular focus in this study is optimization of the coupling factor between the
resonator and the active device, which is the factor that is most easy to influence for a
circuit designer. Resonators have to be well matched to the active device to ensure a good
performance. As a measure on oscillator design efficiency, the thesis uses an effective
noise figure that is compensated for the unloaded quality factor (Q0) of the resonator and
the power consumption of the active device.
The active device technology in this study is a 0.25 um GaN-HEMT process. All designs
are based on a device with 400 um gate periphery that is processed either as a single-die
HEMT assembled in a hybrid solution discrete on PCB, or in a MMIC-implementation
with the amplifying part, or the complete oscillator on chip. Low-frequency-noise (LFN)
measurements are performed and benchmarked versus other GaN HEMT devices as well
as InGaP HBT and GaAs HEMT. It is found that the used device presents relatively low
noise in comparison to other GaN HEMTs. It is also found that power-normalized far
carrier noise, e.g., @100 kHz is comparable to levels in InGaP HBT devices.
Three oscillators, based on similar reflection amplifiers but different resonators, are
designed. The three resonators are: an external discrete LC-resonator with Q0≈49, a quasilumped on-chip MMIC resonator, Q0≈40, and an external metal cavity, Q0≈3800. For each
resonator, the impedance level is chosen to match the active device. The fabricated
oscillator test beds are made flexible so that the small-signal open loop gain can be
experimentally tuned. It is demonstrated that the best phase noise is reached for a smallsignal open-loop gain close to unity. A too high gain margin is normally bad from a phase
noise perspective. The discrete hybrid oscillator presents a phase noise
of -123 dBc/Hz@100 kHz from a 1 GHz oscillation frequency; the MMIC oscillator
presents a phase noise of -106 dBc/Hz@100 kHz from a 15 GHz oscillation frequency;
and the cavity based oscillator presents an excellent phase noise of -145 dBc/Hz@100 kHz
from a 10 GHz oscillation frequency. Normalizing these results versus Q0 and DC-power,
results in effective noise figures of 16-22 dB. The effective noise figure is identified to
originate primarily in finite DC to RF power efficiency and up-converted flicker noise.
Keywords: GaN HEMT, MMIC, phase noise, low frequency noise, resonator coupling,
cavity resonator, reflection oscillator
v
List of publications
Appended papers
[A] M. Hörberg, S. Lai, T. N. T. Do, D. Kuylenstierna, “Phase noise analysis of a tunedinput/tuned-output oscillator based on a GaN HEMT device,” in 44th European
Microwave Conference Proceedings, 5-10 Oct. 2014, Rome, Italy, 2014 pp. 1118-1121.
[B] M. Hörberg, T. Emanuelsson, S. Lai, T. N. T. Do, H. Zirath, D. Kuylenstierna,
“Phase Noise Analysis of an X-Band Ultra-low Phase Noise GaN HEMT based Cavity
Oscillator,” submitted to IEEE Transactions on Microwave Theory and Techniques.
[C] M. Hörberg, D. Kuylenstierna, “Low phase noise power-efficient MMIC GaNHEMT Oscillator at 15 GHz based on a Quasi-lumped on-chip resonator,” in IEEE
MTT-S International Microwave Symposium Digest, 17-22 May, Phoenix, Arizona, 2015.
[D] T. N. T. Do, M. Hörberg, S. Lai, D. Kuylenstierna, “Low Frequency Noise Measurements - A Technology Benchmark with Target on Oscillator Applications,” in 44th European Microwave Conference Proceedings, 5-10 Oct. 2014, Rome, Italy, 2014 pp. 468471.
Other papers
[a] S. Lai, D. Kuylenstierna, M. Özen, M. Hörberg, N. Rorsman, I. Angelov, et al., “Low
Phase Noise GaN HEMT Oscillators With Excellent Figures of Merit,” IEEE Microw.
Compon. Lett., vol. 24, pp. 412-414, 2014.
[b] S. Lai, D. Kuylenstierna, M. Hörberg, N. Rorsman, I. Angelov, K. Andersson, et al.,
“Accurate Phase-Noise Prediction for a Balanced Colpitts GaN HEMT MMIC
Oscillator,” IEEE Trans. Microw. Theory Techn., vol. 61, pp. 3916-3926, 2013.
[c] T. N. T. Do, A. Malmros, M. Hörberg, N. Rorsman, P. Gamarra, C. Lacam, M-A. di
Forte-Poisson, M. Tordjman, R. Aubry, D. Kuylenstierna, “Effects of surface passivation
and deposition methods on the 1/f noise performance of AlInN/AlN/GaN HEMTs”, IEEE
Electron Device Lett.
vii
Notations and abbreviations
Notations
𝛽
C
𝑓1/𝑓3
fm
f0
F
Ic
Id
k
L
ℒ(𝑓𝑚 )
PAVO
PRF
Q0
QL
R
T
Vc
Vd
ω
𝛤𝑅 , 𝛤𝐴
q
𝑌𝑖𝑛
𝑍𝑖𝑛
Coupling factor
Capacitance
Flicker noise corner frequency
Offset frequency
Carrier center frequency
Noise Figure
Collector current
Drain current
Boltzmann’s constant
Inductance
Single sideband phase noise at offset fm
Available RF power
RF-power
Unloaded Quality-factor
Loaded Quality-factor
Resistance
Temperature in Kelvin
Collector voltage
Drain voltage
Angular frequency (rad/s)
Reflection coefficient to resonator, amplifier
Elementary charge
Input admittance
Input impedance
Abbreviations
ADC
AMPS
ATM
BJT
CW
DAC
DUT
DRO
FET
GaAs
GaN
GSM
HBT
HEMT
HSPA
InGaP
LFN
LTE
MPLS
NMT
PLL
QAM
SiGe
TACS
TDM
VCO
WCDMA
3GPP
Analogue to Digital Converter
Advanced Mobile Phone Services
Asynchronous Transfer Mode
Bipolar Junction Transistor
Continuous Wave
Digital to Analogue Converter
Design Under Test
Dielectric Resonator Oscillator
Field Effect Transistor
Gallium Arsenide
Gallium Nitride
Global System for Mobile Telecommunication
Heterojunction Bipolar Transistor
High Electron Mobility Transistor
High Speed Packet Access (Note: both uplink and downlink)
Indium Gallium Phosphide
Low Frequency noise
Long Term Evolution
Multiprotocol Label Switching
Nordic Mobile Telephone Group
Phase Locked Loop
Quadrature Amplitude Modulation
Silicon Germanium
Total Access Communication System
Time Division Multiplexing
Voltage Controlled Oscillator
Wideband Code Division Multiple Access
Third Generation Partnership Project
viii
Contents
LIST OF PUBLICATIONS.......................................................................................... V
APPENDED PAPERS ..................................................................................................................................... V
OTHER PAPERS ........................................................................................................................................... V
NOTATIONS AND ABBREVIATIONS ................................................................. VII
NOTATIONS..............................................................................................................................................VII
ABBREVIATIONS .....................................................................................................................................VIII
CHAPTER 1. .................................................................................................................. 1
INTRODUCTION .......................................................................................................... 1
EARLY EXPERIMENTS ON WIRELESS COMMUNICATION .............................................................................. 1
HISTORY OF THE MOBILE PHONE ................................................................................................................ 1
MOBILE DATA COMMUNICATION CONQUERS THE WORLD .......................................................................... 2
MOTIVATION AND CONTRIBUTION OF THIS WORK ...................................................................................... 4
CHAPTER 2. .................................................................................................................. 7
OSCILLATOR BACKGROUND ................................................................................. 7
OSCILLATOR REPRESENTATION ....................................................................................................... 7
Feedback oscillators ............................................................................................................................ 7
Negative resistance oscillators ............................................................................................................ 8
PHASE NOISE ................................................................................................................................... 8
RESONATORS ................................................................................................................................... 9
Quality factor ...................................................................................................................................... 9
Loaded Quality-factor ....................................................................................................................... 10
Resonator technologies ..................................................................................................................... 10
VARACTORS .................................................................................................................................. 11
NOISE SOURCES IN ACTIVE DEVICES .............................................................................................. 11
Thermal noise ................................................................................................................................... 12
Shot noise ......................................................................................................................................... 12
Flicker noise...................................................................................................................................... 12
Generation-Recombination (GR)-noise ............................................................................................ 12
SYSTEM ASPECTS ........................................................................................................................... 15
CHAPTER 3. ................................................................................................................ 17
MEASUREMENT SET-UPS FOR NOISE CHARACTERIZATION ................... 17
LOW FREQUENCY NOISE MEASUREMENTS ...................................................................................... 17
Current noise amplification............................................................................................................... 17
Voltage noise amplification .............................................................................................................. 18
Measurements of the test bed ............................................................................................................ 19
PHASE NOISE MEASUREMENT METHODS ........................................................................................ 20
Direct Spectrum method ................................................................................................................... 20
PLL-method ...................................................................................................................................... 21
Frequency Discriminator Method ..................................................................................................... 22
Two channel cross-correlation method ............................................................................................. 22
Mixer-based measurements of two oscillators .................................................................................. 23
CHAPTER 4. ................................................................................................................ 25
OSCILLATOR, PHASE NOISE AND BENCHMARK ........................................... 25
PHASE NOISE MODELS .................................................................................................................... 25
Leeson’s equation ............................................................................................................................. 25
Everard’s model ................................................................................................................................ 26
Hajimiri’s model ............................................................................................................................... 27
OPTIMIZATION OF RESONATOR COUPLING ..................................................................................... 28
Feedback oscillator ........................................................................................................................... 29
Negative resistance oscillator ........................................................................................................... 30
BENCH MARKING OSCILLATORS..................................................................................................... 31
Figures of merit................................................................................................................................. 32
Theoretical noise floor ...................................................................................................................... 32
RESULTS REPORTED IN OPEN LITERATURE ..................................................................................... 33
CHAPTER 5. ................................................................................................................ 35
CIRCUIT DESIGN ...................................................................................................... 35
LOW FREQUENCY NOISE MEASUREMENTS ...................................................................................... 35
FLEXIBLE HYBRID OSCILLATOR ..................................................................................................... 38
CAVITY OSCILLATOR ..................................................................................................................... 40
MMIC-DESIGN.............................................................................................................................. 43
CHAPTER 6. ................................................................................................................ 47
CONCLUSIONS AND FUTURE WORK ................................................................. 47
ACKNOWLEDGEMENTS......................................................................................... 49
REFERENCES ............................................................................................................. 51
Chapter 1.
Introduction
Early experiments on wireless communication
The history of long distance wireless communication started in the last decennium of the
19th century when Guglielmo Marconi carried out some experiments to transmit a message
using Hertzian waves [2]. His main achievements took place in a period from September
1894 to August 1895. The investigated technology was to transmit through a high voltage
spark discharge, using an inductive coil invented by Ruhmkorff. The electromagnetic
frequency emission covered in this way a broad spectrum, extended from DC to ultraviolet
light. This broad spectrum created distortion and selectivity problems, and for the
modulated Hertzian waves to be able to travel at even longer distance, they have to follow
the curvature of earth, overcoming hills and obstacles. Marconi tried to improve the
communication by limiting the radiated spectrum, by using the ground and a tuned elevated
aerial, for both the transmitter and the same for the receiver. In this case he was first to
transmit through a frequency selective circuit. At the time when Marconi carried out the
experiments, it was not obvious how to carry out a message with more efficient
modulation.
History of the mobile phone
One of the most revolutionary applications of wireless communication is the mobile
telephony. The history of the mobile telephony starts with experiments in the US in the
1920’s [3]. The first mobile phones were usually car-bound. The radiotelephony became
more and more crowded, and the network operators had to use waiting lists for customers
to wait for available radio channels. Therefore, it was a strong demand to offer a more
efficient use of the frequency spectrum, by considering two critical problems in a cell
structure, that is roaming and hand-over. Roaming is mandatory to keep track of a
subscriber, and hand-over enables subscribers to keep a telephone call when moving from
one cell to another.
In the US the first analogue system of cellular phone services, AMPS (Advanced Mobile
Phone Services) was launched in 1978 and came into operation one year later, commercial
operation was opened a few years later in 1983. In Europe, Sweden was early to enable an
automatic system service in 1956. Nevertheless, the standardization work for the analogue
cellular standard started first in 1969, by the Nordic Mobile Telephone Group, the NMTGroup. They should secure an automatic operation, and a roaming compatibility between
all Nordic countries. It took more than ten years to develop the NMT-standard, which was
first introduced in Saudi-Arabia 1981, then slightly afterwards launched in the
Scandinavian countries [4].
1
2
Chapter 1 Introduction
Different competing mobile telephone standards appeared in the early 1980s. Besides the
Nordic system NMT, US had the system AMPS, Japan had the analogue system from NTT
(Nippon Telephone & Telegraphs), and German had the system MATS-E, developed by
Alcatel and Philips. The US-system AMPS was modified to a system called TACS, Total
Access Communication System.
When the number of subscribers increased, cross boarder roaming and interoperability
required a new standardization with digital technology. In Europe a system named GSM
(Global System for Mobile telecommunication) was developed from an initiative from
both private and governance persons [5]. It was decided to introduce GSM in July 1, 1991.
The first specification of GSM phase I, was approved in 1989. Many patents were
registered, and main suppliers of the equipment were Motorola, Ericsson and Nokia, that
together with Siemens and Alcatel became important players on the mobile telephone
market.
The mobile communication has now changed from being of national and regional
concern to become a global task involving global standardization. An organization as
3GPP (The Third Generation Partnership Project), was formed. 3G was launched to be the
first mobile system handling broadband data, and the next step 4G, LTE (Long Term
Evolution), and LTE-advanced increased the available data speed even more [6].
Mobile data communication conquers the world
Today, mobile data traffic is increasing rapidly. A forecast is a tenfold increase from 2013
to 2019, meaning an annual increase of 45% during these years [1]. By the end of 2019,
the total number of mobile subscriptions is predicted to exceed nine billion. Out of this,
more than 80 % is expected to be supported by mobile broadband, and the remaining by
fixed broadband, mobile PC tablets, and router subscriptions, as is shown in Figure 1-1.
10
Mobile PCs, tablets
and mobile router
subscriptions
Fixed broadband
subscriptions
Number of subscriptions in billions
9
8
7
Mobile broadband
subscriptions
6
Mobile
subscriptions
5
4
3
2
1
0
2010
2012
2014
2016
2018
2020
Figure 1-1 Number of mobile subscriptions in billions, [1].
The demand of more high-speed data traffic forces the fast mobile networks to be rolled
out at an increased rate. Estimated usage of WCDMA/HSPA for the world’s population in
2019 is about 90%, and LTE of about 65%. Besides the increased number of connected
3
devices, the data rate will be intensified due to more advanced applications requiring highspeed data communication. The usage of mobile communication has already become a part
of the daily lives, all from sharing experiences by streaming HD-videos, or to conduct
high-security mobile banking.
The radio access networks are rolled out at higher rate. Simultaneously the cell-structure
is tightened to enable high-speed capacity to more users. The tightened cell-structure leads
inevitably to higher demand on the backhaul to transport the data between the radio base
stations. For high-speed mobile networks, the traffic demand on the backhaul between base
station sites is in the Gbps range per base station, illustrated in Figure 1-2.
2013
2016
2019
80% of sites
50 Mbps
180 Mbps
270 Mbps
20% of sites
180 Mbps
540 Mbps
900 Mbps
Few % of sites
360 Mbps
900 Mbps
1.8 Gbps
Figure 1-2 Backhaul traffic of subscribers that use LTE from 2013 and predicted
evolution to LTE-advanced, [1].
Figure 1-3 Illustration of backhaul network between the radio base station access-net with wired and
microwave based interface, [1].
To handle this increased demand on capacity in the microwave backhaul, an improved
spectral efficiency must be reached. The maximum number of symbols per second
transmitted on a microwave carrier is limited by the channel bandwidth. By coding each
symbol by a higher number of bits, the spectral efficiency can be improved.
4 QAM
1024 QAM
Figure 1-4 Example of Quadrature Amplitude Modulation (QAM). (a) 4-QAM. (b) 1024-QAM.
4
Chapter 1 Introduction
The more complex the modulation scheme, the more sensitive the system is to
imperfections in the radio transport, as rain, multi-path fading, etc. Furthermore, the
spectral purity is degraded due to imperfections such as noise in the receiver and nonlinarites in the transmitter. In particular, the phase noise in the frequency conversion in the
radio chain is crucial and the signal sources are not allowed to fluctuate in frequency over
time. The impact of phase noise to the available capacity, as function of constellation type
and channel bandwidth is illustrated in Figure 1-5.
Improved
Phase noise
needed
@100kHz
#bits QAM
Phase noise
req.
[dBc/Hz]
@100kHz offset
Capacity Mbit/s
2048 60
115
235 335 470
10 1024 55
512 50
105
100
215 305 430
195 280 390
-98
8 256 45
75
170 245 345
-92
128 35
64 30
32
70
65
155 225 325
140 200 290
4
16 20
8
45
95 135 180
2
4 10
20
45
65
80
7
14
28
40
56
Modulation
6
1000
-86
-80
250
Channel
Bandwidth [MHz]
Figure 1-5. Phase noise requirements and data rate as functions of channel bandwidth and modulation
format for a fixed signal-to-noise ratio, [7].
Figure 1-5 shows the capacity (Mbit/s) that can be reached for a given symbol rate
(channel bandwidth) and modulation scheme (4 QAM up to 2048 QAM). In reality, the
modulation that can be used for a certain bandwidth is limited by phase noise. Figure 1-5
presents limit lines indicating what modulation performance that can be used for a given
phase noise and signal bandwidth.
Motivation and contribution of this work
GaN High-Electron Mobility transistor (GaN-HEMT) has since some years been an
emerging technology for power electronics due to its high breakdown voltage, high power
capability and efficiency. These characteristics are very beneficial for oscillator design, as
high voltage swing across the resonator lowers the phase noise. Furthermore, there is
always demand on high drain efficiency for generating RF-power. GaN HEMTs usually
have a low RF-noise floor compared to bipolar transistors that are limited by shot noise.
The low noise floor is of importance when higher modulation bandwidth is used in a
communication system [8]. One drawback of GaN HEMTs is the high amount of flicker
noise that up-converts to phase noise close to the carrier. Flicker noise is dependent of bias
current which makes it difficult to use the high power capability in GaN compared to
technologies with lower power handling as CMOS and SiGe. However, the flat white noise
is improved by the high power capability in GaN.
The power handling in the active devices and the quality factors of the resonators
determines what phase noise performance that can be achieved in a certain technology. A
comparison of performance reported in different technologies is presented in Figure 1-6.
5
InGaP-HBT
1.[9]
2.[9]
3.[10]
CMOS
6.[13]
7.[14]
8.[15]
GaN-HEMT
9.[16]
10.[17]
11.[18]
12.[19]
13.[20]
SiGe-HBT
14.[10]
15.[21]
16.[22]
4.[11]
5.[12]
17.[23]
18.[23]
19.[23]
Figure 1-6 Published results of phase noise at 100 kHz in different technologies for MMIC-oscillators
are presented, together with calculated phase noise limit lines.
Figure 1-6 shows the phase noise at 100 kHz for different technologies versus oscillation
frequency for a number of published oscillators designed in MMIC technology. Phase
noise limit lines for each process technology are calculated from available quality-factors
and the power capability of a typical transistor size in the respective technologies.
Assumptions for this calculation are discussed in detail in section 4.3. For mature processes
like CMOS, the results are fairly well saturated at the phase noise limit line, but for GaNHEMT there is still a significant discrepancy between reported values and the theoretical
limit, which motivates this work.
The resonator coupling is essential for minimizing the phase noise [24]. Strong coupling
is needed for transferring power to the resonator, which lowers the phase noise, however
strong coupling will also lower the loaded quality-factor which has a negative effect on the
loaded phase noise. In this study, several technologies of resonators have been used, where
the impedance matching to the active device is discussed. The active devices are fabricated
in the same GaN-HEMT process, and the same transistor size is used, in some case used
as a discrete component, and in other case integrated in a MMIC. The first design, a hybrid
oscillator with lumped LC-resonator, connected to a single HEMT device, with a tuned
input and output net is showing a phase noise of -123 dBc/Hz@100 kHz from a 1 GHz
oscillation frequency. The second design is a flexible cavity oscillator test bed with
optimized resonator coupling, showing -145 dBc/Hz@100 kHz from a 10 GHz oscillation
frequency. Finally, an integrated MMIC oscillator with a quasi-lumped impedance
transformed resonator is showing state-of-the-art -106 dBc/Hz@100 kHz from a 15 GHz
oscillation frequency. If normalizing these results to the unloaded quality factor of the
resonator, and power consumption, it corresponds to effective noise figures of 16-22 dB,
according to Everard’s theory in [24], and a discussion in this thesis.
Modeling of low frequency noise is also discussed, and measurement methods for
characterization under different bias conditions are described in [25]. In simulations of upconverted flicker noise to phase noise, cyclostationary models have to be used for accurate
phase noise prediction which is shown in [26].
6
Chapter 1 Introduction
This thesis is organized as follows. Chapter 2 describes the background of the oscillator
theory, Chapter 3 describes the different measurement setups used in this study, and
Chapter 4 discusses different models for predicting phase noise, and methods for
benchmarking phase noise performance. Chapter 5 reports on oscillators designed in this
study, and finally the thesis is concluded in Chapter 6 that also includes a discussion about
future work.
Chapter 2.
Oscillator background
Oscillator representation
The purpose of an oscillator is to generate a periodic output signal, by converting DCpower to RF-power. Generally, the oscillator acts as an unstable amplifier, with a specific
feedback path, that at start up allows noise to grow and creates a wanted signal. The noise
is then shaped by a highly filtering and selective mechanism using positive feedback at the
particular wanted frequency, and it is then amplified until it reaches saturation. The gain
in the closed loop will saturate to unity at a steady state, and the active device will only
compensate for the losses in the feedback path. Signals not fulfilling the oscillation
condition will be suppressed. If the oscillator suffers a transient disturbance, as pulling
from a load variation, or as pushing from a change in bias supply, it will correct itself to
the frequency fulfilling the oscillation condition.
The oscillator can be seen as either as a positive feedback system, or as a reflection
(negative resistance) amplifier connected to a resonator. Generally, there are no strict
differences between the two representations; they can be used arbitrarily for representation
of an oscillator. In the following chapters, there are some general characteristics of each
type discussed.
Feedback oscillators
Figure 2-1 shows a positive feedback system.
X(s)
+
G(s)
Y(s)
H(s)
Figure 2-1. Block diagram of a feedback oscillator.
The output signal in Figure 2-1 can be expressed:
𝑌(𝑆) = 𝑋(𝑆)
𝐺(𝑆)
1 − 𝐺(𝑆)𝐻(𝑆)
(2-1)
For the oscillation to occur, the denominator should equal zero, and following conditions
must be fulfilled, the so called Barkhausen criterion
7
8
Chapter 2 Oscillator background
|𝐺(𝑆)𝐻(𝑆)| > 1
(2-2)
∠𝐺(𝑆)𝐻(𝑆) = 𝑛360∘
(2-3)
Negative resistance oscillators
Figure 2-2 shows the case of a negative resistance oscillator. In this respect, the amplifying
active part is described as a one-port, with a reflection gain. The coupled resonator is
therefore also a one-port.
R(s)
G(s)
ΓR
ΓA
Figure 2-2. Block diagram of a negative resistance oscillator.
G(s) models the active part, and R(s) is the frequency response of the resonator. To fulfill
the oscillation conditions, following expressions must be fulfilled, equally to the feedback
system.
|𝛤𝑅 𝛤𝐴 | > 1
(2-4)
∠𝛤𝑅 𝛤𝐴 = 𝑛360∘
(2-5)
Phase noise
Ideally, oscillators are generating a pure sinusoidal waveform. In reality, due to
imperfections in material and outer disturbances as from load or supply net, the frequency
will fluctuate, and the phase and amplitude will vary with time. A behavioral model of the
oscillator can be described as
𝐴(𝑡) = 𝐴0 (1 + 𝐴𝑛 (𝑡))cos(2𝜋𝑓𝑡 + 𝛿Φ𝑛 (𝑡))
Oscillator
(2-6)
A(t)
where the sinusoidal waveform is modulated by two slowly varying noise functions, 𝐴𝑛 (𝑡),
amplitude noise, and 𝛿Φ𝑛 (𝑡), phase noise.
In practice the amplitude noise function, 𝐴𝑛 (𝑡), is suppressed in a system where the
oscillator’s amplitude is limited by the active devices going in compression. The phase
noise term is described as a cumulative phase error term, described by a Wiener process
9
(a)
(b)
Figure 2-3 (a) Cumulative phase error (deg) over time. (b) Spectrum (dBc/Hz) around carrier due to
phase noise.
where
𝛿Φ𝑛 = 𝛿Φ𝑛−1 + ΔΦ
(2-7)
Resonators
The resonator in the oscillator is crucial as it acts as the frequency selective part and
determines the frequency for the oscillation. The frequency response of the resonator
shapes the noise around the carrier as it transmits the wanted signal in the feedback path,
and suppresses signals or noise at unwanted frequencies. In case of a frequency
controllable oscillator the resonance frequency has to be changed. In this chapter, a generic
definition of the quality factor is stated, continued with some practical methods to calculate
the quality-factor of a resonator. Loading issues when connecting the resonator to the
active circuit are in detail investigated in further sections. The impact of a varactor is
briefly presented, however the oscillators in this study have been designed for fixed
frequencies.
Quality factor
Passive circuits forming the resonator in an oscillator are often characterized and
benchmarked in terms of a quality factor (Q-factor). In a resonator, the energy alternates
between electrically and magnetically stored energy. The Q-factor of a resonator can be
expressed as the ratio between stored energy and the energy loss per cycle, i.e., average
power loss,
Qdef = 2π
Stored energy
Stored energy
=ω
Energy dissipation per cycle
Average power loss
Magnetic energy, 𝑊𝑚 , is maximized when electrical energy, 𝑊𝑒 is zero, and vice versa,
i.e., 𝑊𝑠𝑡𝑜𝑟𝑒𝑑 = 𝑊𝑒,𝑝𝑒𝑎𝑘 = 𝑊𝑚,𝑝𝑒𝑎𝑘 . Measuring of the Q-factor according to the general
definition is quite impractical, and it is often necessary to use some of the following derived
methods. The first method is using the 3 dB bandwidth of the frequency response of the
power transmission, or the power reflection at center frequency, 𝜔0 .
10
Chapter 2 Oscillator background
𝑄=
𝜔0
∆𝜔3𝑑𝐵
(2-8)
Another relation is the phase slope of the input impedance, for a parallel resonator,
𝑄=−
𝜔0 𝜕∅(𝑍𝑝 )
|
2 𝜕𝜔 𝜔=𝜔0
(2-9)
or by using the phase slope of the input impedance for a serial resonator.
𝑄=
𝜔0 𝜕∅(𝑍𝑠 )
|
2 𝜕𝜔 𝜔=𝜔0
(2-10)
If an electrical model of the resonator is used, then the Q-factor of the resonator can be
calculated directly from the component values,
Cs
Ls
Lp
Rs
Cp
Rp
𝑄=
𝜔0 𝐿𝑠
1
=
𝑅𝑠
𝜔0 𝐶𝑠 𝑅𝑠
(a) Serial resonance
(2-11)
𝑄=
𝑅𝑃
= 𝜔0 𝐶𝑃 𝑅𝑃
𝜔0 𝐿𝑃
(2-12)
(b) Parallel resonance
Figure 2-4 (a) Schematics of a serial resonance circuit and (b) a parallel resonance circuit.
Loaded Quality-factor
When resonators are not connected to any load, they are characterized by the unloaded Qfactor, 𝑄0 . In reality, this metric is often impractical and useless, as resonators always have
to be connected to some device injecting power into it, or to couple out a wanted injecting
signal from it. In case of an oscillator, this means that it must connect to an active device,
thus loading it with its internal resistance. This load network can also be characterized by
an external Q-factor, 𝑄𝑒𝑥𝑡 . The total loaded Q-factor, 𝑄𝐿 , for the network is then calculated
as
1
1
1
(2-13)
=
+
𝑄𝐿 𝑄0 𝑄𝑒𝑥𝑡
Resonator technologies
The unloaded quality factor, 𝑄0 , of a resonator is of importance for effective filtering with
high frequency selectivity and shaping the noise around the carrier. Dependent on the
building practice, different types of resonators are used, example dielectric resonators
(used in DROs), metal cavities, lumped components, distributed transmission lines as
resonant stubs, and crystals. The technology choice is affected by the Q-factor needed,
power handling of the resonator, frequency tunability, etc.
11
Varactors
To enable tuning of the oscillation frequency, a tunable element, e.g., a varactor has to be
included in the resonator. This is normally done by implementing a voltage controllable
capacitor as a part of the resonator. For cavities or DROs, the connected varactors disturb
the electromagnetic field in relation to the applied tuning voltage. The Q-factor of the
varactor will lower the Q-factor of the whole resonator, as the varactor normally has a
lower Q-factor than the other components building up the resonator. This is due to internal
resistivity and current leakage inside the component. This effect depends on the strength
of the inclusion of the varactor to the resonator. Weak inclusion factor lowers the effect of
the varactor, which also means a lower tunability. Therefore, it is a tradeoff between the
inclusion factor of the varactor, and the Q-factor of the total resonator.
Besides lowering the Q-factor, the varactor also up-converts noise because it will pick
up noise from the tuning net, and force the frequency to fluctuate. The resonance frequency
is dependent on the capacitance and a typical voltage impact on the varactor capacitance
is expressed as
1
(2-14)
𝜔0 =
√𝐿𝐶(𝑉𝑚 )
where
1
(2-15)
𝐶(𝑉𝑚 ) = 𝐶0
𝜂
𝑉
(1 − 𝜓𝑚 )
0
where 𝜓0 is the built in potential in the junction, and 0.1 < 𝜂 < ~2, which is a factor
dependent of the doping gradient in the pn-junction. Example for an abrupt doping is
𝜂=0.5. This will make additional contribution to the phase noise as
𝐾02 𝑉𝑚2
ℒ(𝑓𝑚 )~10log [
]
8𝑓𝑚2
(2-16)
where ℒ(𝑓𝑚 ) is the added phase noise in (dBc/Hz) at offset frequency, 𝑓𝑚 , 𝐾0 is the tuning
sensitivity of the varactor calculated from the slope of C(Vm) and the varactor inclusion
factor to the resonator. 𝑉𝑚 is the tuning voltage.
Noise sources in active devices
The active device plays a central role for the phase noise around the carrier. The device
noise floor and the low frequency noise (LFN) will due to up-conversion in the oscillation
process create phase noise. Choosing a proper device technology is therefore very
important when minimizing the noise. The noise levels are different for different
technologies at various frequencies, and therefore compromising between different
technologies is often necessary. Normally field effect transistors (FETs), and high-electron
mobility transistors, (HEMTs), have lower high-frequency noise level, but higher noise at
low-frequencies.
Transistor technologies are from the two classes, bipolar transistors (BJTs), and FETs.
Examples of bipolar transistors are heterojunction bipolar transistors (HBTs), processed in
material as InGaP or SiGe. Examples of FETs are HEMTs processed in material as GaN,
or GaAs. Without going into details in the semiconductor physics, following chapters will
describe their impact on phase noise in the oscillator application. Most focus is on the
12
Chapter 2 Oscillator background
internal noise figures of the transistors. Other effects as the power capability for creating a
better signal-to-noise-ratio, the drain efficiency, and the linearity, are discussed for the
oscillator design in Chapter 5.
The noise sources with most impact on oscillator phase noise coming from the active
parts are thermal noise, shot noise, flicker noise, and generation-recombination (GR) noise.
Thermal noise
Thermal noise is white Gaussian noise, and has no bias dependence. It is determined by
the resistance of the circuit and its equivalent noise temperature. Thermal noise was
investigated by Nyquist and Johnson, [27], [28]. The noise is a distribution of voltages and
currents in a network due to the thermal electron agitation, called Brownian motion. It can
be modeled as
2
(2-17)
< 𝑖𝑛,𝑡ℎ
> 4𝑘𝑇
=
Δ𝑓
𝑅
where 𝑅 is the circuit resistance, and 𝑇 the physical temperature, or an equivalent noise
temperature.
Shot noise
Shot noise is associated with the discrete nature of charge flow, and arises because of the
emission of charge carriers across a potential barrier, and is therefore contributed in bipolar
devices. It is white and frequency independent noise which increases with the bias current.
It can be modeled as,
2
< 𝑖𝑛,𝑠
>
= 2𝑞𝐼𝐷𝐶
Δ𝑓
(2-18)
where 𝐼𝐷𝐶 is the current bias, and 𝑞 the elementary charge.
Flicker noise
Fluctuations in the conductance of semiconductors and metals produce this noise. A reason
for this is variation in the number of free electrons or their mobility in the presence of a
DC current. It is thus dependent on the bias current and the frequency. A model of the
flicker noise behavior is found in [29] and [30]. The flicker noise can be mathematically
expressed as
𝐴
2
(2-19)
< 𝑖𝑓𝑙
> 𝐾𝑓 𝐼𝐷𝐶𝑓
= 𝐹𝑓𝑒
Δ𝑓
𝑓
where the flicker noise coefficients Kf, Af, and Ffe, are used to curve fit measured data. 𝑓 is
the frequency.
Generation-Recombination (GR)-noise
Fluctuations in the number of free carriers, typical in a semiconductor where the carrier
concentration can vary over several orders of magnitude, causes this kind of noise. It may
appear in transitions between the conduction band and other energy levels in the energy
13
gap, in conduction band, or valence band etc. GR noise depends on bias current and
frequency as
𝐴
2
(2-20)
< 𝑖𝑛,𝑙
>
𝐾𝑏 𝐼𝐷𝐶𝑏
=
2
Δ𝑓
𝑓
1+( )
𝑓𝑏
where 𝐼𝐷𝐶 is the bias current, 𝐾𝑏 and 𝐴𝑏 are fitting parameters. Frequency 𝑓 is related to
frequency 𝑓𝑏 when GR-centres are activated [31]. This gives the characteristic frequency
shape, called Lorentzian.
The noise sources occur differently in a HEMT or in a BJT. Figure 2-5 shows a noise
model of a HEMT with a representation of their main noise sources. The gate resistance
and drain resistance contribute most to thermal noise. Flicker noise and GR-noise appear
across the channel, and they are represented as noise sources on the gate and on the drain.
<inRg2>
G
RG
Cgs
<ing2>
<inRgd2>
Cds Rds
Cgd
+
Rgd
Vgs
- gmVgs
Rgs
S
Thermal noise:
<
2
𝑖𝑛𝑔
<
2
𝑖𝑛𝑑
D
Rd
<ind2>
4𝑘𝑇
∆𝑓
𝑅𝐺
2
< 𝑖𝑛𝑅𝑔
>=
2
< 𝑖𝑛𝑅𝑔𝑑
>=
Flicker noise and GR-noise:
<inRd2>
4𝑘𝑇
∆𝑓
𝑅𝑔𝑑
>=
2
< 𝑖𝑛𝑅𝑑
>=
𝐴
𝐾1𝑓 𝐼𝐺 1𝑓
𝑓 𝐹1𝑓𝑒
𝐴
∆𝑓 +
𝐴
>=
𝐾2𝑓 𝐼𝐷 2𝑓
𝑓 𝐹2𝑓𝑒
4𝑘𝑇
∆𝑓
𝑅𝑑
𝐾1𝑏 𝐼𝐺 1𝑏
𝑓 2
1+( )
𝑓1𝑏
∆𝑓
𝐴
∆𝑓 +
𝐾2𝑏 𝐼𝐷 2𝑏
𝑓 2
1+( )
𝑓2𝑏
∆𝑓
Figure 2-5 Noise model of a HEMT with corresponding main noise sources [32].
For a BJT, thermal noise appears due to the base resistance. Shot noise appears due to
the junction on the collector and the base. Figure 2-6 shows a noise model of a BJT with
their corresponding main noise sources.
14
Chapter 2 Oscillator background
<inrb2>
Rπ
B
R0
RC
C
rb
Cπ
E
Thermal noise:
Cr
<iB2> ic
2
< 𝑖𝑛𝑟𝑏
>=
4𝑘𝑇
∆𝑓
𝑟𝑏
<iC2>
E
< 𝑖𝐶2 >= 2𝑞𝐼𝑐 ∆𝑓
Shot noise:
Shot noise, flicker noise
and GR noise:
𝐴
<
𝑖𝐵2
>= 2𝑞𝐼𝐵 ∆𝑓 +
𝐾1𝑓 𝐼𝐵 1𝑓
𝑓 𝐹1𝑓𝑒
𝐴
∆𝑓 +
𝐾1𝑏 𝐼𝐵 1𝑏
𝑓 2
1+( )
𝑓𝑏
∆𝑓
Figure 2-6 Noise model of a BJT with corresponding main noise sources.
Flicker noise and GR-noise have a dominant low frequency (LF) behavior. LFNmeasurement is important in device characterization as it can reveal imperfections in the
process. Some imperfections can cause traps and surface states for the electrons, which
lead to LFN. LFN-measurement is often used for benchmarking the technology. The phase
noise close to the carrier in oscillators, is dependent of the LF-noise, and will be upconverted in the oscillation.
The amount of LFN varies a lot with transistor technology. A commonly used parameter
is the LF corner frequency, 𝑓𝑐 , which defines the frequency where the LFN is the same as
the white noise floor. However, an uncertainty is to estimate the noise floor as the
measurement noise floor also contributes to this. Devices with high RF-noise figure can
also by this definition get a lower LF corner frequency. This argues to handle this
parameter carefully. The corner frequency is illustrated in Figure 2-7. Vertical structures
like HBTs generally have lower LF-noise, than FETs and HEMTs which are more exposed
in the surface. Traps and surface states for the electrons are more frequent in laterally
structured devices. For example InGaP/GaAs HBTs have LF corner frequency of about
20 kHz, while in the case of GaN HEMT it can be ~1 MHz. A detailed LF-noise
measurement comparing different transistor technologies is presented in [Paper D].
15
1/fslope
Power
[dBc]
White noise floor from,
device RF-noise figure and
measurement setup
fc
f [Hz], logscale
Figure 2-7. Low frequency noise. The white noise floor is difficult to determine, and often limited by
the noise floor of the measurement system.
System aspects
For an oscillator, the LFN, is of specific interest as it up-converts to phase noise close in
the carrier. LFN has impact on a communication system and distorts modulated signals as
creating a frequency error, adding error-vector-magnitude, (EVM) or degrading the
selectivity of a receiver. This occurs when the power of a local oscillator signal is
distributed in frequency, and a clean signal for mixing the wanted signal is not performed.
Close in noise to the oscillator is more difficult to filter out, although a phase locked loop,
(PLL) to some extent can suppress the very close in noise inside the regulation loop
bandwidth from an oscillator. Inside the regulation loop, the noise of the oscillator is
suppressed, and the noise is principally set by the noise floor of the phase detector, and the
up-converted reference. Achieving a good noise floor of a PLL is also a severe problem, if
you are limited by low comparison frequency in the PLL. This can be due to requirements
for changing channel frequencies with a certain resolution in a communication system. To
handle spurious in a more advanced fractional PLL may also limit the flexibility to set for
best phase noise frequencies.
Chapter 3.
Measurement set-ups for noise characterization
Two main setups are discussed in this chapter, a LFN measurement of a biased device, and
a phase noise measurement at the carrier frequency for a complete oscillator. An alternative
method to LFN measurement is to use RF-excitation and measure the residual phase noise
around the carrier. This operation equals more the real oscillation condition with a
waveform trajectory sweeping over several voltage and current states. A drawback is the
additional noise in the RF-signal source to take care of, and it is not as fundamental for
modeling as the static LFN measurement. Most LFN models in the simulators are
implemented as current noise sources for specific bias levels. The measurement method
with RF-excitation has not been investigated in this study.
The LFN measurement is useful when comparing different semiconductor technologies
and showing their potential usage in oscillator applications. From a design perspective, it
is essential to start to measure the fundamental noise figures of the transistor to find the
best operating condition, regarding bias points, load line, etc. The phase noise performance
is the result of all up-converted noise by the oscillation mechanism.
Low frequency noise measurements
Measuring the low frequency noise spectra will put some specific demands on the
instrumentation setup. The bias tee must have low cutoff frequency, and the input
impedance of the low noise amplifiers must be chosen carefully not to affect the DUT.
Two measurement methods have been studied and they are discussed in the following
sections.
Current noise amplification
This method is using a transimpedance preamplifier system, based on a commercial
amplifier (SR570), [33]. If a low bias level is used, <5 mA, the internal bias supply in
SR570 can be used with a good noise performance. If a higher bias level is needed, an
external bias tee must be added. This limits the lowest cutoff frequency, because of the
practical size of the inductors and capacitors. In addition, large capacitors are often of the
electrolyte type, which itself has a 1/f-noise, and therefore the system noise level must be
investigated carefully in the setup. This setup is illustrated in Figure 3-1, and described in
[25].
17
18
Chapter 3 Measurement set-ups for noise characterization
SR570
+150mH
22mF
Agilent
SMU
Agilent
35670A
DUT
+Low pass
filter
Figure 3-1. LF-noise setup with current noise amplification.
The transimpedance amplifier has low impedance, around ~1 Ω, and the biastee
components, 150 mH and 22 mF are parallel resonant at 3 Hz, not to short-circuit the
DUT’s LF-noise, and to make good conduction for the current noise to the low impedance
currentamplifier.
1
(3-1)
𝑓𝑟𝑒𝑠 =
= 3 Hz
2𝜋√0.15 ∙ 0.022
The output of the amplifier is connected to a dynamic signal analyzer, Agilent 35670,
which measures the voltage of the signal in time domain and calculates the FFT for
frequencies up to 100 kHz.
One disadvantage with the current amplifier method is the long time needed to charge
the large capacitor in the DC-block when changing bias, which makes these measurements
versus bias very time consuming.
Voltage noise amplification
This method is using a high-impedance voltage amplifier, SR560, [34]. The bias to the
device is injected through a load resistor, in this setup chosen to 100 Ω. This value is
suitable for the studied sizes of devices. As there is a lower cutoff frequency for the bias
components in the signal path, the noise can be measured almost down to DC. This makes
the method very attractive. The load resistor must be chosen carefully, preferable less than
the transistor channel resistance, Rds, to ensure that the total resistance is dominated by the
external load. However, when calculating the current noise and the load resistance, Rds will
be in parallel with the external load resistor, which is seen in Figure 3-2.
19
SR560
+Rload
Agilent
35670A
High Z
Ch_1
Ch_2
DUT
SR570
Low Z
+-
Figure 3-2. LFN setup with a voltage amplification on the drain, and with SR570 on the gate for
biasing purpose.
The SR560 measures the voltage noise terminated through the load resistor in parallel
with Rds. The calculated impedance is used to normalize the voltage noise to current noise.
The used voltage gain of the SR560 is about 40 dB (100 V/V), and its noise floor at input
is about 4n𝑉/√Hz. The transconductance amplifier SR570 can be used to measure the gate
noise simultaneously, but main reason in this measurement is to use its internal supply to
bias the gate.
< 𝐼𝑑𝑟𝑎𝑖𝑛 𝑛𝑜𝑖𝑠𝑒 >=
< 𝑉𝑚𝑒𝑎𝑠 𝑛𝑜𝑖𝑠𝑒 35670 >
(𝑅𝑑𝑠 //𝑅𝑙𝑜𝑎𝑑 ) ∙ 𝐺𝑣𝑜𝑙𝑡𝑎𝑔𝑒 𝑔𝑎𝑖𝑛 𝑆𝑅560
(3-2)
The same dynamic signal analyzer, Agilent 35670, is used to sample the output signal
from the low noise amplifiers. A description of this setup is found in [35].
Measurements of the test bed
To investigate the system noise level with the different setups, a BJT transistor 2N2222
was used because it has a relatively low LFN. Low bias (<8 mA, 3 V) was used to be able
to compare the different setups, and not to introduce too much LFN from the DUT itself.
The external bias supply for the voltage method has been both battery and a parameter
analyzer, Agilent 4156. The current method has used the internal supply in SR570.The
results are shown in Figure 3-3(a). In Figure 3-3(b) a GaN-HEMT device has been
measured with the two comparing methods.
20
Chapter 3 Measurement set-ups for noise characterization
(a)
(b)
Figure 3-3 (a). Noise floor characterization of the test bed. (b) Comparison between the setups, the
current-method (SR570), and the voltage method (SR560) measuring a GaN-HEMT, 4x75 in CTHprocess, biased at Vg/Vd=-2V/11V.
The thermal noise floor of the load resistor (100 Ω) used in the SR560-setup is calculated
as
4𝑘𝑇
(3-3)
2
< 𝑖𝑛,100
>=
= 1.6 ∙ 10−22 (A2 /Hz)
𝑅
This is about 10 dB lower than the lowest measured noise in Figure 3-3, and therefore it
has a negligible effect on the system noise floor in this studied frequency range.
A conclusion is that the noise from the power supply affects more than the measurement
method, and in the further LFN measurements in this study, the voltage noise amplification
has been used. The voltage noise method benefits LFN measurement almost down to DC,
which is shown in Figure 3-3 (b).
Phase noise measurement methods
For a complete oscillator, phase noise measurement is used to characterize the noise
performance. In this chapter, different phase noise measurement methods are discussed.
Direct Spectrum method
Phase noise measurement can be done by connecting the device to a spectrum analyzer
which is tuned to the oscillation frequency. This is the simplest and perhaps the oldest
method of phase noise measurement. The phase noise is directly measured as the power
spectral density in (dBc/Hz). As the measurement is applied with existence of the carrier,
the dynamic range of the spectrum analyzer can significantly limit the resolution in this
method. Important figures to consider are the resolution bandwidth (RBW) of the spectrum
analyzer and an accurate measurement of the carrier power. The inherent single side band
noise (SSB) at the offset of interest must be significantly less in the analyzer. Typically, a
suppression of about 10 dB is required. A spectrum analyzer normally only measures the
magnitude of the noise sidebands, and can therefore not differentiate the amplitude noise
from the phase noise. Typically, the amplitude noise from the measurement object should
21
as a rule of thumb be at least 10 dB lower than the phase noise, not to affect the phase noise
contribution. Other limitations and difficulties with this method are:

The spectrum resolution bandwidth (RBW), must be normalized to 1 Hz. The
RBW-filter is normally given as its 3-dB bandwidth, and the noise bandwidth might
be slightly greater than the 3-dB bandwidth. Example for Agilent instrument it is
1.0575 wider, which has to be taken into account in the normalizing.

The detector in the spectrum analyzer may not be accurate enough to measure true
rms power.

The local oscillator might have stability issues, giving a residual FM, or noise sideband.
PLL-method
A phase detector can be used to separate phase noise and amplitude noise. The phase
detector generates a signal that is proportional to the phase difference between the two
signals. If the signals are 90 deg out of phase, the voltage is zero, and the small fluctuations
due to phase noise can be amplified with a high resolution without saturation. This method
is illustrated in Figure 3-4, [36].
Signal 1
∆Φin
Φ
∆Vout =K∆Φin
Signal 2
Figure 3-4 Two signals 90 deg out of phase cancel the DC-component, and the output AC voltage is
proportional to the phase fluctuations.
Normally the second signal is produced by an internal oscillator of the instrument itself,
as is illustrated in Figure 3-5, [36]
DUT
Low- pass-filter Low- noise
(LPF)
amplifier
Baseband
analyzer
90°
Reference
source
Phase lock
loop (PLL)
Figure 3-5 PLL-method with quadrature mixer with a phase locked secondary VCO.
Typically a double balanced mixer is used as a phase detector in this setup. The product of
2f is suppressed by a low pass filter, and the difference contains the low frequency AC-
22
Chapter 3 Measurement set-ups for noise characterization
signal of phase fluctuations proportional to the combined phase noise contributions of the
two sources. This is illustrated in Figure 3-6, [36].
Untuned
source
Phase
detector
inputs
Phase
detector
Low-pass
filter
Low- noise
amplifier
Phase
detector
output
Φ
VCO
source
Phase
lock loop
control
Tune
voltage
output
Figure 3-6 PLL-method with a phase detector with a locked secondary VCO.
This method requires a clean and tunable reference oscillator, and a large frequency drift
of the DUT, can cause tracking problems for the reference oscillator.
Frequency Discriminator Method
The signal from the DUT is divided in two paths where one is delayed, and the other one
is phase-adjusted. The two signals are then mixed together. The delay line converts
frequency fluctuations to phase fluctuations, and the phase shifter is set to the quadrature
phase of the two signals. An attenuator is used to adjust the amplitude. The mixer or the
phase detector converts the phase fluctuations to voltage fluctuations. This concept is
illustrated in Figure 3-7, [36].
Delay line
DUT
Low- pass-filter Low- noise
(LPF)
amplifier
Amp
Baseband
analyzer
Phase
Splitter
90°
detector
Φ
Tunable phase Att
shifter
Figure 3-7 Frequency discriminator with delay line.
Other concerns with this method are

The analogue delay line may degrade the sensitivity due to its loss.

Longer lines ideally improve the sensitivity, but the added loss can exceed the
available source power. A longer delay line also sets the maximum offset frequency that can be measured.
Two channel cross-correlation method
By using two identical channels, and if the system noise in each channel can be assumed
uncorrelated, the DUT noise can be correlated. Therefore, the system noise can be
suppressed according to the formulas in Figure 3-8, [36].
23
Internal system noise N1 Measured noise: Nmeas
CH1
Signal source
Under test
DSP
Nmeas
Cross-correlation
(Correlation#=M)
Splitter
Source noise, NDUT
CH2
Internal system noise N2
𝑁𝑚𝑒𝑎𝑠 = 𝑁𝐷𝑈𝑇 +
𝑁1 +𝑁2
√𝑀
, 𝑁1 and 𝑁2 are uncorrelated
M (Number of correlations)
Noise reduction on (𝑁1 + 𝑁2 )
10
-5 dB
100
-10 dB
1000
-15 dB
10000
-20 dB
Figure 3-8. Two channel cross correlation method.
Mixer-based measurements of two oscillators
The previous setups and phase noise measurement methods are mostly handled by the
instrument equipment itself, as in Figure 3-6. It is however important to know the different
methods to understand their limitations. The phase noise of a commercial signal source
analyzer, as for an FSUP50 from Rohde Schwarz, is at low offset frequency and high input
frequency often limited by its internal oscillator, and it degrades by the measured input
frequency as 𝑃𝑁𝑙𝑖𝑚𝑖𝑡 ~20 log 𝑓𝑖𝑛𝑝𝑢𝑡 . For lower input frequency, the performance is limited
by the flat noise floor in the instrument. Example of typical values of the sensitivity for an
FSUP50 is shown in TABLE I, [37].
TABLE I
FSUP50 PHASE NOISE SENSITIVITY VERSUS INPUT FREQUENCY AND OFFSET, [37]
Frequency
offset
1k
10k
100k
1M
10M
30M
Input frequency, values
dBc/Hz
R&S®FSUP50
10 MHz
-150
-155
-160
-165
100 MHz
-145
-150
-160
-165
-165
1 GHz
-134
-143
-158
-165
-172
-172
10 GHz
-116
-126
-138
-150
-167
-170
40 GHz
-106
-114
-126
-140
-155
-159
If the DUT phase noise is expected to be very good, it is necessary to provide a setup
containing two DUTs of assumed equal performance. Then phase noise can be measured
for the down-converted signal at a frequency where the instrumentation noise floor is
lower. A 3 dB noise contribution from the two equal DUTs shall be compensated.
24
Chapter 3 Measurement set-ups for noise characterization
SA
Meas IF-freq
Attenuator
(isolate for
pulling)
Isolator
F0
DUT Osc
F0+/-IF
Ref Osc
Figure 3-9. Measurement setup with two equally DUTs.
Figure 3-9 shows the dual oscillator configuration. An isolator is placed in the reference
path to prevent load pulling, and the measured device has a small attenuator for setting a
broadband load.
Chapter 4.
Oscillator, phase noise and benchmark
Phase noise models
Several different models have been developed for phase noise prediction. The models
differ in complexity, e.g., which noise sources that are included and in what way the noise
is processed in the simulation algorithm. In the most fundamental case, only the thermal
noise of the active device and resonator is considered. When that is up-converted, it will
be filtered by the half power bandwidth of the resonator, f0/2QL, that forms the noise shape
to this frequency. Above this frequency the phase noise slope versus offset frequency
reduces by 20 dB if not limited by the noisefloor. To enhance the model even more, a
frequency corner, f1/f3, can be included. It defines the frequency when flicker noise at the
low offset frequency increases over the thermal noise, as in the Leeson's model, [38]. Still
these models are fundamental, and only consider a stationary state of the noise sources.
A more advanced model considers the nonstationary behavior of the noise, as flicker
noise, that is essentially current dependent, and changes along the waveform trajectory
over the active device. This implies a cyclostationary effect of the noise, that is considered
in Hajimiri’s model [26].
Other models express the phase noise as a function of the power inside the resonator
explicitly and how that is coupled to the active device, affecting the loaded Q-factor. This
is handled in Everard’s models [24]. Following chapters describe these models more
detailed.
Leeson’s equation
Phase noise behavior in an oscillator was quantitatively described by Leeson [38]. His
model describes the phase noise behavior, which are assigned from following
interpretations,
(4-1)
𝑓1/𝑓3
𝐹𝑘𝑇
𝑓0 2
ℒ(𝑓𝑚 ) = 10log [
[1 + (
) ] [1 +
]]
2𝑃𝑠
2𝑄𝐿 𝑓𝑚
𝑓𝑚
where 𝑘 is Boltzmann’s constant, T is the temperature in Kelvin, Ps is the RF-power
dissipated in the resonator and QL is its loaded quality factor. F and f1/f3 are fitting
parameters used for setting the noise level dependent on active device noise as well as
nonlinear noise conversion. Outside fm=f0/(2QL), the phase noise is inversely proportional
to PS and independent of QL, but inside fm=f0/(2QL) it is inversely proportional to the
product PSQL2. The corner frequency, f1/f3, is called the flicker noise corner and determines
where the phase noise due to up-converted LF noise follows a steeper slope. Normally it
defines where a rise from -20 dB/decade to -30 dB/decade occurs close in to the carrier.
25
26
Chapter 4 Oscillator, phase noise and benchmark
This frequency corner, f1/f3, is not the same as fC-corner frequency as was defined in the
LF-noise characterization. A relation between them is derived in [26].
From (4-1) it is seen that dependent on the QL -factor of the resonator and the flicker
noise corner 𝑓1/𝑓3 , the phase noise function ℒ(𝑓𝑚 ), will according to Leeson’s model have
two possible orders of their corner frequencies down to the noise floor. This is illustrated
in Figure 4-1 and Figure 4-2.
Power
[dBc]
1/f3slope
1/fslope
FkT/
2Ps
f0/2QL
f1/f3
Freq [Hz], logscale
Figure 4-1. Phase noise behavior, where the resonator bandwidth due to the high Q falls inside the
flicker noise corner.
Power
[dBc]
1/f3slope
1/f2slope
FkT/
2Ps
f1/f3
f0/2QL
Freq [Hz], logscale
Figure 4-2. Phase noise behavior, where the bandwidth due to a low-Q-tank falls outside the flicker
noise corner.
Leeson’s model predicts well the phase noise, for devices and bias levels with low flicker
noise. For devices with high amount of bias dependent noise, cyclostationary effects
related to the nonlinear up-conversion must be considered.
Everard’s model
Feedback type oscillator
Everard [24] presents a phase noise model derived from a positive feedback view. The
phase noise is expressed as a function of the ratio 𝑄𝐿 ⁄𝑄0, which depends on the coupling
factor 𝛽 between the resonator and the active device as
𝐹𝑘𝑇
𝑓0 2
ℒ(𝑓𝑚 ) = 10log [𝐴
( ) ]
8(𝑄0 )2 (𝑄𝐿 ⁄𝑄0 )2 (1 − 𝑄𝐿 ⁄𝑄0 )𝑁 𝑃 𝑓𝑚
(4-2)
27
where the values of parameters A and N, respectively, depend on the definition of
RF-power and the value of the output resistance, ROUT, and input resistance, RIN. Following
bullets summarize the different cases.

N=1 and A=1 if P=PRF and ROUT=0

N=1 and A=2 if P=PRF and ROUT=RIN

N=2 and A=1 if P=PAVO and ROUT=RIN
In this model the ratio 𝑄𝐿 ⁄𝑄0 is used as a parameter, and the resonator coupling has an
optimum value, derived to 𝑄𝐿 ⁄𝑄0 = 1/2. A coupling factor 𝛽, can be defined as,
𝛽=
𝑄0
−1
𝑄𝐿
(4-3)
This coupling is in more detail described in section 4.2.
Negative resistance type oscillator
The negative resistance representation uses a one port active device, and therefore only
one internal resistance. Everard [24] gives an approximate model for the best phase noise
for a negative resistance at the optimum resonator coupling to:
𝑓0 2
ℒ(𝑓𝑚 ) = 10log [
( ) ]
2𝑄0 2 𝑃𝑟 𝑓𝑚
𝐹𝑘𝑇
(4-4)
It is worth mentioning that the power dissipated inside the resonator, 𝑃𝑟 , is only half in
the negative resistance type compared to the feedback oscillator type for a given phase
noise performance. This is seen if inserting P=PRF, ROUT=RIN, and the optimum resonator
coupling for feedback, QL/Q0=1/2, corresponding to Rr=RRF/2 in (4-2). This will evaluate
to that double as much power is needed in the tank to give the same ℒ(𝑓𝑚 ) as is described
for a negative resistance type in (4-4). This makes an advantage of negative resistance type
if the resonator has power limitations, example for crystal oscillators. Crystal oscillators
are often of reflection type oscillators.
Hajimiri’s model
Everard’s model presented above is a purely linear model that cannot treat time-varying
noise sources. Although useful for understanding oscillators, a time-invariant model is not
satisfactory to describe an oscillator under arbitrary operational conditions. Ali Hajimiri
has developed a rather simple and intuitive time-variant model where the noise sources are
treated cyclostationary. In his model he introduced an impulse sensitivity function (ISF),
[26]. The ISF-function models the responding phase change of the voltage in tank when a
current impulse is disturbing. The main idea is that the LF-noise is weighted in the upconversion dependent of the waveform of the voltage amplitude and the current swing in
the resonator. The resonator is most sensitive for disturbance at the zero crossing, which
causes a remaining phase error.
28
Chapter 4 Oscillator, phase noise and benchmark
Vout
Vout
∆V
∆V
t
i(t)
t
i(t)
t
t
(a)
(b)
Figure 4-3 (a) A current impulse occurs when the voltage over the capacitor in the resonator is at
maximum. The disturbed signal will still be in phase with the original signal. (b) A current impulse
occurs when the voltage over the capacitor in the resonator is at minimum (zero crossing). The
disturbed signal will be shifted in phase compared to the original signal.
The ISF-function is periodic, and can be expanded in a Fourier series as
∞
𝑐0
Γ(𝜔0 𝜏) = + ∑ 𝑐𝑛 cos(𝑛𝜔0 𝜏 + 𝜃𝑛 )
2
(4-5)
𝑛=1
where the weight factors of the up-converted flicker noise is related to the ratio of Fourier
coefficients.
𝜔1⁄𝑓3 = 𝜔1⁄𝑓
𝑐02
𝑐0
≈ 𝜔1⁄𝑓 ( )2
2
2Γ𝑟𝑚𝑠
𝑐1
(4-6)
This gives a closed form of the predicted phase noise as described in [39],
ℒ(𝑓𝑚 ) = 10log [
𝑐02
2
𝑖𝑛0
2
𝑞𝑚𝑎𝑥
2𝑓𝑚
2]
(4-7)
where 𝑖𝑛0 is the current amplitude of the waveform trajectory, and 𝑞𝑚𝑎𝑥 is the maximum
charge stored in the resonator, and 𝑐0 is the coefficient from the Fourier expansion in (4-5).
Optimization of resonator coupling
To achieve the best performance in a given technology, the coupling of a resonator is of
essential importance. High Q-factor, 𝑄𝐿 , of the resonator and high power, 𝑃𝑆 , have positive
impact of the phase noise. According to Leeson’s equation (4-1), it is the factor 𝑃𝑆 𝑄𝐿2 , that
has to be maximized to minimize the phase noise, for offset inside fm=f0/(2QL). To transfer
high power to the resonator for lowering the phase noise, it will require a strong coupling.
This is contradictory as a strong coupling will degrade 𝑄𝐿 , and thus make the phase noise
level worse.
29
Feedback oscillator
A model of a feedback type oscillator is depicted in Figure 4-4.
Rin
Vs
Ro ut
Resonator
C
Rlos s
L
Vr
Figure 4-4. Model of a feedback oscillator.
The amplifier is modeled with internal resistances at both input, 𝑅𝑖𝑛 , and at output, 𝑅𝑜𝑢𝑡 .
The resonator is a two-port transmission resonator that closes the feedback path. The tank
itself is a serial resonance circuit, modeled with 𝐿 and 𝐶, and the loss resistance 𝑅𝑙𝑜𝑠𝑠 ,
defining the unloaded Q0, according to (2-11). In the complete feedback path, the internal
serial resistances of the amplifier also act as loss resistances. In this discussion, they are
simplified to be the same, 𝑅𝑖𝑛 = 𝑅𝑜𝑢𝑡 = 𝑍0 and the complete loop loaded Q-factor can be
defined as
𝜔𝐿
𝜔𝐿
(4-8)
𝑄𝐿 =
=
𝑅𝐿𝑜𝑠𝑠 + 𝑅𝑖𝑛 + 𝑅𝑜𝑢𝑡 𝑅𝐿𝑜𝑠𝑠 + 2𝑍0
From this, a ratio of the unloaded and loaded Q-factor is often of interest to extract, and
with use of the defined coupling factor, 𝛽, from (4-3) gives
𝑄0 𝑅𝐿𝑜𝑠𝑠 + 2𝑍0
2𝑍0
=
=1+
= 1+𝛽
𝑄𝐿
𝑅𝐿𝑜𝑠𝑠
𝑅𝐿𝑜𝑠𝑠
(4-9)
The voltage across the tank can also be expressed as
𝑉𝑟 = 𝑉𝑠
𝑅𝐿𝑜𝑠𝑠
𝑄𝐿
= 𝑉𝑠
𝑅𝐿𝑜𝑠𝑠 + 2𝑍0
𝑄0
(4-10)
and if we assume the maximum available power from the amplifier to be
𝑃𝑎𝑣𝑜
𝑉𝑠 2
=
2 ∙ 2𝑍0
The dissipated power inside the resonator will be
(4-11)
30
Chapter 4 Oscillator, phase noise and benchmark
𝑃𝑟 =
𝑉𝑟 2
𝑉𝑠 2 𝑄𝐿 2
𝑃𝑎𝑣𝑜 4𝑍0 𝑄𝐿 2
𝑄0
𝑄𝐿 2
= 2
=
( ) = 2𝑃𝑎𝑣𝑜 ( − 1) ( )
𝑅𝐿𝑜𝑠𝑠 𝑄0 𝑅𝐿𝑜𝑠𝑠
𝑅𝐿𝑜𝑠𝑠 𝑄0
𝑄𝐿
𝑄0
𝑄𝐿
𝑄𝐿
= 2𝑃𝑎𝑣𝑜
(1 − )
𝑄0
𝑄0
(4-12)
To achieve the best phase noise performance, the power dissipated in the resonator
should be maximized, to create the best signal to noise ratio. This optimum in terms of
𝑄𝐿 ⁄𝑄0 quote is derived in [24] to be
𝑄𝐿 1
(4-13)
=
𝑄0 2
An interpretation of this is that half of the available power is dissipated in the resonator, ¼
is reflected, and ¼ is transmitted. For achieving the best phase noise according to Everard’s
equation (4-2), this is the best coupling of the resonator. In the feedback case with Rin=Rout,
that can be expressed as,
𝑓0 2
ℒ(𝑓𝑚 ) =
( )
𝑃𝑎𝑣𝑜 𝑄0 2 𝑓𝑚
2𝐹𝑘𝑇
(4-14)
If instead of the available power, the power dissipated in the tank is calculated
(4-15)
𝑉𝑟 2
𝑃𝑎𝑣𝑜
𝑃𝑟 =
=
𝑅𝐿𝑜𝑠𝑠
2
The optimum phase noise for a feedback oscillator is
𝐹𝑘𝑇 𝑓0 2
ℒ(𝑓𝑚 ) =
( )
𝑃𝑟 𝑄0 2 𝑓𝑚
Negative resistance oscillator
A model of a reflection type oscillator is depicted in Figure 4-5.
Resonator
Ri
Rs
Vs
L
C
ΓR
ΓA
Figure 4-5 Model of a reflection oscillator.
(4-16)
31
In the case of a reflection type oscillator, often called a negative resistance oscillator, the
active part, the amplifier, is a one-port device. It has a reflection coefficient, |𝛤𝐴 | > 1. The
connected resonator circuit is also a one port, with a reflection coefficient 𝛤𝑅 . In the same
manner as for the feedback oscillator, the unloaded Q-factor of the resonator can be written
as (2-11), and the loaded Q-factor as a function of the coupling factor as in (4-9).
Everard has shown in [24] that the single-side band phase noise spectrum for a reflection
type oscillator can be expressed as
(4-17)
𝐹𝑘𝑇
𝑓0 2
ℒ(𝑓𝑚 ) =
(
)
8(𝑄0 )2 (𝑄𝐿 /𝑄0 )2 (1 − 𝑄𝐿 /𝑄0 )𝑃𝑅𝐹 𝑓𝑚
Inserting (4-9) in (4-17), the phase noise can be expressed as
𝐹𝑘𝑇
𝑓0 2
ℒ(𝑓𝑚 ) =
( )
8(𝑄0 )2 𝛽/(1 + 𝛽)3 𝑃𝑅𝐹 𝑓𝑚
This equation will have its optimum value for
1
𝛽=
2
𝑄𝐿
or instead expressed with 𝑄
0
𝑄𝐿 2
=
𝑄0 3
(4-18)
(4-19)
(4-20)
2
The power dissipated in the resonator, 𝑃𝑟 = 3 𝑃𝑅𝐹 , and inserting this value in (4-18) gives
(4-21)
9𝐹𝑘𝑇 𝑓0 2
ℒ(𝑓𝑚 ) =
(
)
16𝑃𝑟 𝑄0 2 𝑓𝑚
This model is derived more accurately from the optimal coupling, and deviate slightly
from the approximately calculated formula for an optimized reflective oscillator given in
(4-4).
If we consider the power delivered from the amplifier, 𝑃𝑅𝐹 , use the optimum value of 𝛽,
and define a DC to RF power efficiency, 𝑃𝑅𝐹 = 𝜂𝑃𝐷𝐶 , then we get
ℒ(𝑓𝑚 ) =
𝐹𝑘𝑇
𝑓0 2
(
)
8(𝑄0 )2 𝛽/(1 + 𝛽)3 𝜂𝑃𝐷𝐶 𝑓𝑚
(4-22)
which at optimum resonator coupling from (4-19) simplifies to
27 𝐹𝑘𝑇
𝑓0 2
ℒ(𝑓𝑚 ) =
( )
32 𝜂𝑃𝐷𝐶 𝑄02 𝑓𝑚
(4-23)
The expression in (4-23) can be used to calculate bounds on phase noise, given available
𝑃𝐷𝐶 , and 𝑄0 from the given technology.
Bench marking oscillators
Benchmarking oscillators in literature are often a challenging task as several performance
parameters are used. Different process-technologies have different power capabilities,
32
Chapter 4 Oscillator, phase noise and benchmark
available Q-factors of the resonators and different noise performances for close in or far
out frequencies. The design topologies and features differ as different oscillation
frequency, tunability, bandwidth etc. A commonly used parameter for benchmarking is the
power normalized figure of merit, FOM, that was defined by Wagemans [40], and further
refined in [41]. It is defined as
𝑓0
(4-24)
𝐹𝑂𝑀 = −ℒmeas (𝑓𝑚 ) + 20 log ( ) − 10log(𝑃𝐷𝐶 )
𝑓𝑚
where ℒmeas (𝑓𝑚 ) is the measured phase noise at offset frequency 𝑓𝑚 , 𝑓0 is the oscillation
frequency and 𝑃𝐷𝐶 the DC-power consumption.
Figures of merit
To benchmark the oscillator performance versus different technologies, FOM, is calculated
under the assumption of no flicker noise. In the Leeson’s equation, this is used as a base
for scaling the effect of resonator power, and Q-factor. The fitting parameter, Feff, can there
be extracted as
𝑓0
27𝑘𝑇
(4-25)
𝐹eff = ℒmeas (𝑓𝑚 ) − 20 log ( ) − 10log
− 30 + 10log(𝑃𝐷𝐶 )
𝑓𝑚
32
+ 20log(𝑄0 ) = 174.6 + 20log(𝑄0 ) − 𝐹𝑂𝑀.
If assuming no flicker noise and no RF-noise from the active device, and 100 % DC to
RF power efficiency, meaning that 𝐹eff =0 dB in (4-25), FOMmax is found to be linearly
related to the unloaded Q-factor of the resonator. Normally 𝐹eff > 0 dB, and FOM will be
reduced. One obvious reason for 𝐹eff > 0 dB in (4-25) is the finite efficiency. The effect
of nonideal resonator coupling increases 𝐹eff also. If the effect of finite efficiency and nonideal resonator coupling are considered, an operating noise figure can be defined by using
the expression in (4-22) as
𝐹𝑜𝑝 = 173.9 + 10log
8𝜂𝛽
+ 20 log(𝑄0 ) − 𝐹𝑂𝑀
(1 + 𝛽)3
(4-26)
It is seen that 𝐹op = 𝐹eff in the ideal case 𝜂 = 100% and ideal coupling 𝛽 = 1/2.
Theoretical noise floor
The best performance that can be achieved for given process parameters as 𝑄0 , and power
capability, PDC (mW), occurs if 𝐹eff =0 dB in (4-25). This equation can be used to show
phase noise limit lines for the phase noise performance for a technology.
𝑓0
ℒ𝑚𝑖𝑛 (𝑓𝑚 ) = −174.6 − 10log10 (𝑃𝐷𝐶 ) − 20log10 (𝑄0 ) + 20log10 ( )
𝑓𝑚
(4-27)
TABLE II presents process parameters as 𝑄0 and practical power capability. Calculated
bounds of the phase noise at 100 kHz for a 10 GHz oscillation frequency are shown. The
power capability values are calculated from an averaged DC-consumption of the
considered MMIC-designs among those from [9]-[23]. Using reported result on DCconsumption in this calculation will then consider the practical issues also, for example the
33
common choice of transistor size and bias condition to achieve the needed cooling etc.
Typical Q-factors for the respectively process technology are found in textbooks as [42].
Phase noise limit lines and published results together with designs from this work are
shown in Figure 4-6. The phase noise limit lines are based on calculations from (4-27).
InGaP-HBT
1.[9]
4.[11]
2.[9]
5.[12]
3.[10]
CMOS
6.[13]
7.[14]
8.[15]
GaN-HEMT
9.[16]
10.[17]
11.[18]
12.[19]
13.[20]
SiGe-HBT
14.[10]
17.[23]
15.[21]
18.[23]
16.[22]
19.[23]
GaN-This work
20. LC-tank [Paper A]
21. Cavity [Paper B]
22. MMIC [Paper C]
Figure 4-6 Published results from MMIC processes for phase noise at 100 kHz and phase noise limits
are illustrated, together with the results of the designs from this work.
TABLE II
PHASE NOISE LIMIT AT 100 KHZ FOR A 10 GHZ OSCILLATION FREQUENCY, CALCULATED
FROM PROCESS PARAMETERS FOR MMICS.
Vc, / Vd (V)
Ic / Id (mA)
Q0
Phase noise@100k
[dBc/Hz], fcenter=10 GHz
GaN
HEMT
30
120
InGaP
HBT
5
90
CMOS
90 nm
1
9
SiGe HBT
3
25
40
40
10
10
-142
-133
-104
-113
Results reported in open literature
This study has considered an oscillator with external cavity resonator. TABLE III is
showing state-of-the-art oscillators with external resonators of different technology. The
phase noise at 100 kHz offset, L(100k), and oscillation frequency, f0, are shown, together
with DC-power dissipation, and power normalized figure-of-merit value, FOM.
34
Chapter 4 Oscillator, phase noise and benchmark
TABLE III
BENCHMARK OF LOW PHASE NOISE OSCILLATORS BASED ON EXTERNAL RESONATORS
Ref.
L(100k) (dBc/Hz) f0 (GHz)
Pdc [mW] FOM@100k Active device
Technology
Resonator
Technology
[43]
-140
8.2
700(**)
209
N/A
DRO
[44] fig 9
-132(*)
9.2
N/A
N/A
GaAs pHEMT
Silver coated cavity
[45]
-137
10.2
N/A
N/A
N/A
DRO
(***)
[46]
-118
10.6
54
201
GaN HEMT
DRO
[46]
-123
10.6
46(***)
207
GaAs pHEMT
DRO
[46]
-135
10.6
N/A
N/A
SiGe HBT
DRO
[47]
-149
7.61
400
221
GaAs InGaP HBT
DRO
[47]
-142
7.61
100
220
GaAs InGaP HBT
DRO
Cavity
oscillator
[Paper B]
-144
9.9
200
220
GaN HEMT
Aluminum cavity
(*)
The plot in [44] is used to estimate the phase noise. (**) A buffer amplifier is included, but output power is
comparable with other output power in this work. (***) calculated from power density and transistor size.
FOM(fm)=-L(fm)+20log(f0/fm)-10log(Pdc). Pdc is dissipated power in [mW].
The work demonstrated in [Paper B] has one of the best FOM reported.
Chapter 5.
Circuit design
This section describes the design and optimization of three oscillators in GaN-technology
targeting low phase noise. Important preconditions from the process technology are the
available Q-factor for the passives in the resonator, the power capability of the active
device, the low frequency noise and the RF noise figure. Most of these parameters set the
boundary condition for the optimization. Critical design issues to consider are the resonator
matching and the choice of the bias point. These effects are discussed in detail in this
section.
The impact of the Q-factor of the resonator is shown for different resonator topologies.
Investigated resonators are an external resonator with surface mount components, a metal
cavity in aluminum, and an integrated quasi-lumped resonator integrated on III-V
substrate. The active device in all variants has been a GaN-HEMT device, for its good
power handling, despite its disadvantage of high flicker noise. Due to the large amount of
flicker noise and its current dependency, the optimum bias point has been limited to quite
a low bias level, and the benefit of GaN’s high power capability is not obviously shown.
Different test circuits and an investigation of LFN measurements on different devices are
presented, and the contribution of this work to publication is summarized as
1. External resonators

A flexible hybrid oscillator with a lumped LC-resonator, [Paper A,
EuMW, 2014]

A cavity oscillator, [Paper B, submitted to MTT]
2. MMIC integrated resonator

Reflection type with quasi-lumped LC-resonator, [Paper C, MTT-S,
2015].
3. LF noise measurements

Low Frequency Noise Measurements - A Technology Benchmark with
Target on Oscillator Applications, [Paper D, EuMW, 2014]
Low frequency noise measurements
Knowledge of the active device is a necessity before a good VCO-design can be done.
Characterization of the active device regarding LFN is useful for indicating noise behavior
35
36
Chapter 5 Circuit design
versus bias points and offset frequency. Hooge [48], was first in 1969 to describe the LFN
connected to a physical model. This model has later on been refined due to the complex
structure of modern transistors, and is today implemented in modern simulators as ADS
[49]. In this model, the LFN is usually modeled as a bias dependent current source, and
has a frequency slope as ~1/fn as described in (2-19).
A LFN measurement of a GaN-HEMT device of the same size and from the same process
as the oscillators designed in this study is shown in Figure 5-1.
(a)
(b)
Figure 5-1 Measured LFN of a GaN HEMT, 8x50 um. (a) LFN versus frequency with Id.as parameter
and Vd=10 V. (b) Measured LFN@100 kHz versus Vd and Id.
Parameter extraction from the measurement on an 8x50 um GaN-HEMT fabricated at the
−10
TriQuint Semiconductor in Figure 5-1(a) according to (2-19), give 𝐾𝑓 = 6.4 ∗ 10 ,
𝐴𝑓 = 0.87, 𝐹𝑓𝑒 = 1.38
The plot in Figure 5-1(a) at this relatively high bias does not show a clear 1/f-slope. A
theory explaining this behavior is that different G-R, generation-recombination, centers
activate at different bias voltages. All these may superpose to a 1/f slope, described by
[31], [50]. In Figure 5-1(b), LFN is showing a strong dependency in the drain current, but
also a dependency in drain voltage.
LFN at 1 kHz, 10 kHz and 100 kHz normalized to DC power is a relevant benchmark
parameter for oscillator applications. In TABLE IV, LFN for GaN-HEMTs compared to
other III-V material (InGaP HBT and GaAs pHEMT) are presented.
Device
GaN
HEMT 1
GaN
HEMT 2
GaN
HEMT 3
GaN
HEMT 4
GaN
HEMT 5
GaN
HEMT 6
GaN
HEMT 7
InGaP
HBT 1
InGaP
HBT 2
GaAs
pHEMT 1
GaAs
pHEMT 2
GaAs
pHEMT 3
GaAs
pHEMT 4
GaAs
pHEMT 5
GaAs
pHEMT 6
1.3
1.5
1.5
250
250
250
250
250
250
1000
1000
150
150
100
100
100
100
4x75
2x50
4x50
8x50
4x50
(G2)
8x50
(G3)
4x20
2x20
2x20
4x20
2x20
4x20
2x40
4x40
1
1
1
1
1
1
1.2
1.2
1.3
1.3
1.3
1.5
250
2x75
𝑭𝒇𝒆
Lg/Wb
(nm)
Size
(μm)
24,9
11,5
11,2
5,55
24,8
12,6
9
9
52,6
4,73
81,0
38,9
20,0
27,4
19,3
Id (mA)
3
3
3
3
3
3
3
3
10
10
10
10
10
10
10
2,65E-16
1,83E-16
1,81E-16
1,43E-16
1,87E-16
1,42E-16
4,095E-18
7,00E-18
2,79E-15
4,50E-16
3,10E-15
1,53E-15
6,75E-16
2,27E-16
4,26E-16
LFN@1kHz
Vd(V)
(A2/Hz)
3,55E-15
5,32E-15
5,35E-15
8,61E-15
2,51E-15
3,75E-15
1,52E-16
3,89E-16
5,31E-15
9,51E-15
3,83E-15
3,92E-15
3,37E-15
8,31E-16
2,21E-15
(A/Hz•V)
3,88E-17
2,76E-17
3,35E-17
2,00E-17
4,40E-17
3,00E-17
4,54E-19
5,30E-19
6,66E-17
1,71E-17
1,45E-16
6,66E-17
2,56E-17
3,26E-17
2,41E-17
LFN@10kHz
(A2/Hz)
5,19E-16
8,015E-16
9,92E-16
1,20E-15
5,91E-16
7,92E-16
1,68E-17
1,96E-17
1,27E-16
3,618E-16
1,78E-16
1,71E-16
1,28E-16
1,19E-16
1,25E-16
(A/Hz•V)
4,71E-18
4,06E-18
3,85E-18
2,64E-18
4,98E-18
2,59E-18
1,32E-19
1,10E-19
6,55E-19
1,43E-19
3,48E-18
1,75E-18
8,63E-19
2,67E-18
1,76E-18
LFN@
100kHz
(A2/Hz)
TABLE IV
MEASURED DEVICES WITH VOLTAGE AMPLIFICATION METHOD REPORTED IN [PAPER D].
6,31E-17
1,18E-16
1,14E-16
1,59E-16
6,682E-17
6,85E-17
4,90E-18
4,07E-18
1,24E-18
3,03E-18
4,30E-18
4,50E-18
4,31E-18
9,76E-18
9,13E-18
(A/Hz•V)
37
38
Chapter 5 Circuit design
where Lg is the gate length, Wb base width, Ffe is the frequency slope (1/f Ffe), and LFN
(A2/Hz)@ 1 kHz, @10 kHz, and @100 kHz, resp. the measured LFN for the offset
frequencies. It is obvious that the flicker noise at <100 kHz is higher for GaN-HEMTs than
for InGaP HBTs. GaN HEMTs are however better if the power normalized noise is
considered. The active devices for all designed oscillators in this study are based on the
GaN HEMT 8x50 (G3), which is shaded in TABLE IV.
Flexible hybrid oscillator
A flexible oscillator implemented on a hybrid solution with lumped and distributed
elements on Rogers’s substrate was designed and manufactured. The active device, as was
earlier described to be from the same process and with the same size of transistor, was in
this case a bare die of a standalone HEMT in a common source configuration. This HEMT
configuration was used in the previous LFN characterization, and therefore the study of
up-converted phase noise in this oscillator can be compared to the LFN behavior. The
mechanism of the noise up-conversion from LFN is however complex, and this study is
limited to compare the behavior versus the bias level, and an investigation of the impact of
the oscillator’s open loop gain.
The oscillation frequency was designed to 1 GHz. The termination net on the gate side
is realized by an inductive piece of a transmission line, in serial with a capacitor. The
effective inductance value can be adjusted by changing the capacitor. The drain side is
connected to the resonator where an in-phase tuning is performed by connecting different
pieces of transmission lines. The resonator itself is a serial LC-network, parallel to a
50 ohm resistor to secure a good load outside the resonance frequency. At serial resonance,
the impedance will be much less, and the load resistor will have a negligible effect.
The oscillator is assembled with two separate PCBs, for gate and drain separately, with
the active device mounted on a cooling shelf in between. In this way, the resonator and the
amplifier can be characterized separately. In Figure 5-2 (a) a photo is shown, and in (b) a
schematic is depicted.
Vg
DC
λ/4 bias
feed
λ/4 bias
feed
Vd
DC
Vout
Γamp Γres
Coupling Vout
Ø-co mp
Lterm
DUT
Rtank
DCblock
Cterm
Ltank
Rstab
Ctank
Reso nato r
(a)
(b)
Figure 5-2 (a) Assembly of the hybrid oscillator. (b) Schematic
Figure 5-3 (a) shows the measured reflection coefficients of the two different discrete
LC-resonators. The resonator with the best Q-factor (TankA) was calculated to 𝑄0 = 49,
39
and the corresponding 𝑅𝑠 = 11 Ω, which has been used in the further measurements.
Figure 5-3 (b) shows the reflection gain of the active device with different capacitors in
the termination net. The resonator determines the oscillation frequency to 1 GHz, and the
gain at this fixed frequency is thus adjustable.
Tank A and Tank B
Amplifier
0
25
TankA
amp [dB]
res [dB]
X: 1.021e+009
F=1.03GHz
Y: -3.877
G=-3.8dB
-4
Cterm=100pF
Cterm=10pF
Cterm=6.8pF
Cterm=5pF
20
TankB
-2
-6
-8
15
10
5
0
-10
0.5
1
Freq [Hz]
-5
0.5
1.5
1
Freq [Hz]
9
x 10
(a)
1.5
9
x 10
(b)
Figure 5-3(a) Reflection coefficient into the resonator for two different LC-resonators with two
different impedance levels, Rs, and Q0-factors. (b) Reflection gain into the amplifier where the peak
has been shifted by changing the capacitors in the termination net.
Measuring the complete oscillator showed that high margin in small signal loop gain is
not beneficial. The high gain forces the oscillator into higher compression resulting in more
up-converted flicker noise. The best termination net for the amplifier that matches the gain
of the resonator with the best Q-factor, was to use capacitance value Cterm=6.8 pF. Figure
5-4 (a,b) show the magnitude and phase of the loop gain versus off-set frequency.
Mag open loop, [dB] C
1
5
2
2
3
-2.2
-2
3
3.5
3.5
-1.8
Vg [V]
(a)
7
-1.6
0
1
0
0
-1
-1
-1
6
2.5
3
5
2
2.
2.5
2
0
1
1.
1
1
2
1.5
Vd [V]
0
0 .5
1.5
2
8
1
2
2
3
9
=6.8pF, (f=1034MHz)
term
1
1
1.5
Vd [V]
4
0.5
0 .5
8
5
0.5
5
4
-1
-0.5
0
9
6
Phase open loop, [Deg] C
10
10
7
=6.8pF, (f=1034MHz)
term
-2.2
-2
-3
-4
-5
-6
-2
-3
-4
-2
-1.8
-2
-3
-4
-5
-6
-7
-1.6
Vg [V]
(b)
Figure 5-4 (a) Magnitude of the open loop gain (dB), Cterm=6.8 pF. (b) Phase of the open loop gain
(deg), Cterm=6.8 pF.
In Figure 5-5 (a,b) the phase noise at 100 kHz and at 1 MHz are shown versus bias point.
40
Chapter 5 Circuit design
PN@1M, vs Vg and Vd
PN@100k, vs Vg and Vd
-2.1
-2
-110
(a)
-147
-14
6
9.5
-14
-149
6
4
-121
-120
-119
-117
-115
-1.9
-1.8
Vg [V]
-147
-123
Vd [V]
-1-12
23 3.4
.2
Vd [V]
-2.2
12201
--11
-1 79
-1
-1115 0
-11
22
-1
-1.6
-2.2
-148
-148
-147
-147
-146
-145
-144
-142
-140
-135
-145
-144
2
2 -14
-140
-1.7
0
-15
-121
-120
2 -119
-1175
-11
-123
-122
8
-1
49
.5
-148
4
2
-12 3 .2
3
--1122
-123
-122
2
-12
--112233.2
-122
-147
46
-1
15
-1
17
6 -1
19
-1120
- 21
-1
-123.2
17
-1
9
-1120
-1 21
-1
8
19
-1 0
-1221
-1
9
-14
5
-11
10
-148
10
-2.1
-2
-1465
-1444
-1
-142
-140
-135
-12-5130
-1.9
-1.8
Vg [V]
-135
-1.7
-135
-1.6
(b)
Figure 5-5. (a) Phase noise at 100 kHz vs. Vg and Vd. (b) Phase noise at 1 MHz vs. Vg and Vd.
At frequency offset 100 kHz the optimum phase noise is constant in a “valley” for an
increased power dissipation. More power in the resonator lowers the phase noise but
increased drain currents and drain voltages increase the up-converted flicker noise. This
counterbalances the improvement. At higher frequency offset, 1 MHz where the flicker
noise is less pronounced, the optimum bias point occurs at a higher bias level, due to the
higher power level in the resonator. Another aspect is that the region with the best phase
noise matches the in-phase condition (phase=0), as is shown in Figure 5-4 (b). However,
deviation in bias points from the optimum in-phase region has a minor impact, due to
relatively small phase changes. A phase change will force the oscillator to another
oscillation frequency, but due to the rather low Q-factor of this resonator makes this effect
negligible and the main reason for the optimum bias is related to the waveform and phase
noise conversion.
In Figure 5-5 (b), the best phase noise is measured to -150 dBc/Hz@1 MHz, and with
Q0=49 in the resonator, and a DC power consumption of 250 mW, (4-24) evaluates to
FOM=186 and (4-25) to Feff=22 dB. Simulated RF-efficiency is about 65%, which explains
about 2 dB of Feff.
Cavity oscillator
Another test oscillator in this study was built with a MMIC-reflection amplifier as the
active device, connected to an external metal cavity. The amplifier is based on the same
active HEMT as in the previous design, and it is designed for 10-15 GHz. To make the
transistor unstable, a source inductor is placed in serial with a small resistor of 15 Ω to
ground. The resistor maintains a stable bias over temperature and process. In parallel to the
resistor, a capacitor is used for peaking the reflection gain to the desired frequency. The
bias net for gate includes a resistor of 1 k, and on drain an inductor acts as an RF-choke.
Close to the pads, decoupling capacitors with small feeding resistors are added. The RF
port with reflection gain is on the gate side, which connects to the external tank. Figure 5-6
(a) shows a chip photo, and Figure 5-6 (b) shows a schematic of the reflection amplifier.
41
Vgg
Vdd
Zterm
Connection
to tank
Source
feedback
(a)
(b)
Figure 5-6(a) Chip photo of the active device, size 1.0x1.0mm (b) Schematic of the active device.
The resonator is made of a metal cavity, placed on top of a brass plate. On the brass plate,
a piece of a micro strip line on Rogers’s PCB is mounted in a 1 mm deep and 4 mm wide
trench. This strip couples to the cavity. On one side this connects to the amplifier PCB, and
on the other side an attenuator of 3 dB is mounted, which makes a broadband load outside
resonance frequencies. The RF-signal is for practical reasons extracted through this
attenuator. The cavity is designed for the TE101-mode, and is pressed by a clamp to the
brass plate. It can be flexibly positioned along the line for the best in-phase tuning, and can
be adjusted perpendicularly to the line to change the coupling-factor.
(a)
(b)
Figure 5-7 (a) A picture of the metal cavity, with hole size 21.7x21.7x10.8 mm. (b) HFSS-model of
the micro strip coupling to the cavity.
In Figure 5-8 (a), a picture of the assembly is shown, and in Figure 5-8 (b) a block
diagram of it is depicted.
42
Chapter 5 Circuit design
Cavity
Microstrip
Coupling to
cavity
f
Load
termination
RF
out
Transmission
length
inphasing
(a)
(b)
Figure 5-8 (a) Cavity oscillator assembly. (b) Block diagram of the cavity oscillator.
Figure 5-9 shows the measured reflection at phase tuned reflection to the cavity board
for the different cavity offset positions, with their equivalent serial loss resistance, Rs
calculated. The Q0 is measured to 3800. Figure 5-9 (b) shows the magnitude of the
reflection gain.
(a)
(b)
Figure 5-9 (a) shows measured reflection coefficient of the cavity at different offset positions. The
frequency sweep is, f=9.9 GHz to 10.0 GHz, Figure (b) shows measured reflection gain (dB) of the
amplifier at oscillation frequency versus Vg and Vd.
Phase noise measurement was done by using two equal oscillators in a mixed
measurement, as was described in section 3.2. One of the two oscillators (reference
oscillator) has been fixed at its best operating condition while the other test oscillator has
been swept for different test conditions. The measured phase noise has afterwards been
compensated (in linear terms) for the noise power generated from the reference oscillator.
The best phase noise was seen at a cavity offset giving a loop gain of about 0.5 dB (at a
cavity offset position of 5.9 mm and an equivalent Rs=20 ohm). Figure 5-10 (a) shows the
phase noise versus offset frequency for this position over all bias states, and Figure 5-10
(b) shows a contour plot of the phase noise at 100 kHz offset versus bias levels for this
position. The best phase noise, -144.5 dBc/Hz@100 kHz offset was measured at the bias
levels Vd=4-5 V, and Vg=-1.9 V to -1.6 V. The flat optimum region in gate voltage may be
explained by the fact that higher RF-power is counterbalanced by the increase of upconverted flicker noise due to higher bias currents. Higher drain voltages will also increase
43
the loop gain, compared to Figure 5-9 (b), which forces the oscillator in hard compression,
and result in even more up-converted LF-noise.
(a)
(b)
Figure 5-10 (a) Measurement in phase noise vs offset frequency for all bias states. Dots are
simulations. (b) Phase noise contours at 100 kHz for different bias states.
A summary of the optimum phase noise performance versus bias and cavity positions is
shown in TABLE V. Due to the high amount of flicker noise, the optimum bias is at quite
a low bias level, and at a loop gain 0.5 dB.
TABLE V
SUMMARY OF OPTIMUM PERFORMANCE FOR DIFFERENT CAVITY POSITIONS AT OFFSET
FREQUENCY 100 KHZ AND 400 KHZ
Cavity
Rs/loss
position (ohm)/(dB)
offset (mm)
0.6
3.4
3.9
5.9
8.1/2.8
14/5
19.2/7
20/7.4
Optimum phase
noise performance
@100k (dBc/Hz) @
bias level (Vd/Vg)
-139 @4/-1.9
-141@4/-1.8
-141.5@5/-1.6
-144.5@5/-1.8
Phase noise FOM @
@ 400k
400k (dB)
(dBc/Hz)
-152.5
-155.5
-156
-160
219
223
221
227
Fop @
Gain [dB] Reflection |𝑅𝑁 |
400k
Amp @ opt for 100k. (ohm)
(dB)
bias (Vg/Vd)
15
10
9
7
6.8
7.0
8
7.9
18.7
19.1
21.6
21.3
Open
loop gain
(dB)
4
2
1
0.5
It is seen in TABLE V that the best FOM=227 dB@400 kHz offset, and with Q0=3800,
(4-25) evaluates to an Feff=20 dB. Simulated RF efficiency is about 7% and explains about
12 dB of it.
MMIC-Design
In this setion a designed MMIC-oscillator is presented. It is a negative resistance oscillator
with an internal on-chip resonator. The resonator is implemented with quasi lumped
elements, and transformed by a quarter-wave transformer to match the impedance of the
active device.
The active device is the same reflection amplifier used for the cavity oscillator in 5.3.
The resonator in this case is on chip and designed for 15 GHz. As was seen in the analysis
for the cavity oscillator, the open loop gain should be kept low to avoid high compression
and thus up-conversion of noise. If a serial resonator is connected directly to the amplifier,
44
Chapter 5 Circuit design
the Rs will often be too low to match the reflection gain in the amplifier to a corresponding
Rneg. This is due to the practical usable values of microstrips or lumped components used
in MMIC-technologies. For this amplifier 𝑅𝑁 = −14 Ω and a reasonable 𝑅𝑠 = 10 Ω to
match this. This assumption is based on some margin for the loss in the resonator, and to
secure a proper startup oscillation behavior. The loss resistance of the microstrip /4resonator can be calculated as
(5-1)
𝑐0
𝜋𝜇0
𝑅𝑆 ≈
√
4𝑊 𝜎𝜀𝑟 𝑓
It will end up with a width as small as 𝑊 = 5 µm. This width will also result in a low Qfactor. Instead, in this resonator, a parallel resonator is created with a capacitor and a piece
of microstripline in parallel, then transformed by a /4-transformer, to a serial resonator.
This implementation enables higher 𝑅𝑠 without degrading the Q-factor. Eqn (5-2) and (5-3)
show more realistic values for the parallel resonator with lumped values L and C, given
desired 𝑅𝑠 = 10 Ω and Q about 40 for the process. 𝑍𝑐 is the characteristic impedance for
the /4-transformer, and chosen to 80 Ω. This solves to L=1.7 nH and C=0.6 pF which are
suitable for a MMIC-process.
(5-2)
𝑍𝐶2
𝐿=
𝑅𝑠 𝜔0 𝑄
𝐶=
𝑅𝑠 𝑄
𝑍𝐶2 𝜔0
(5-3)
Figure 5-11 (a) shows a chip photo of the oscillator, and Figure 5-11 (b) shows a schematic
of it. The resonant circuit is marked with a circle.
Vgg
/4transmission
line
Vdd
50W
Stab
resistor
Osc
Output
(a)
Zterm
Source
feedback
(b)
Figure 5-11 (a). A chip photo of the reflection type oscillator with a chip resonator. Size 2.0x1.0 mm.
(b) Schematic. The resonant circuit is indicated with a circle.
The phase noise for 15 GHz oscillation frequency versus offset for all bias states is shown
in Figure 5-12 (a). Figure 5-12 (b) shows a contour plot of the phase noise at 100 kHz
offset vs bias points.
45
(a)
(b)
Figure 5-12(a) Phase noise versus offset frequency for all bias states (guide lines for -30 dB/dec resp.
-20 dB/dec are added). (b) Phase noise at 100 kHz offset for all bias states.
The best phase noise -106 dBc/Hz@100 kHz offset for 15 GHz oscillation frequency is
reached for quite a low bias, Vd/Vg=3 V/-1.8 V. For increased Vd/Vg phase noise increases
due to a higher amount of flicker noise that is up-converted. The higher bias level is
therefore not beneficial. In Figure 5-12 (a), it is shown that this offset gives a -30 dB/dec
slope due to the flicker noise. The flicker noise corner corresponding to the change to
a -20 dB/slope is shown at offsets above 1 MHz.
The best phase noise at 100 kHz, gives FOM=191 dB, and with Q0≈40, corresponds
according to (4-25) to Feff=16 dB.
Chapter 6.
Conclusions and future work
This thesis has presented issues in optimization of oscillators targeting low phase noise.
The choice of technology is important as the process parameters set boundaries for the
achievable performance. Important figures are LFN, device noise floor, power handling,
and the Q-factor of the resonator. Bounds on minimum phase noise calculated from the Qfactor and the power capability of the active device have been derived to show the
performance under optimized conditions.
GaN HEMT technology is attractive for oscillator design due to its high power capability.
However, immaturities of today’s GaN-HEMT-technology, e.g., high flicker noise,
prevents full utilization of the power swing. Nevertheless, it is demonstrated in this thesis
that very good power-normalized figure of merit can be reached. For low bias levels the
GaN-HEMT shows better figures than competitive technologies like InGaP-HBT.
On design-level, the parameter that affects oscillator phase noise the most is the match
between the resonator and the active device. The matching issue of the resonator is
particularly investigated in this thesis. High margin in small-signal open loop gain is
seldom beneficial, as it will results in oscillators running in deep compression, which
causes nonlinear up-conversion noise, e.g., flicker noise. Even in the linear region,
assuming no flicker noise, optimizing the coupling factor is critical as the active device
loads the resonator and hence degrades its Q-factor. On the other hand, high coupling
ensures a high signal power in the resonator. Optimum coupling factors were theoretically
derived by Everard. For the feedback oscillator type, the optimum coupling was evaluated
to be β=1 and for the negative resistance type the optimum coupling was evaluated to
β=1/2. In our study where flicker noise contributes to the up-conversion of phase noise,
the best phase noise achieved is detected at small-signal open loop gain close to 0 dB,
corresponding to β=1.
In this study we have used active devices from the same GaN-process and with the same
transistor size. The transistor has been a separate bare die HEMT or the same commonsource GaN HEMT integrated in an MMIC-based reflection amplifier. Three different
resonators are investigated: an external discrete LC-resonator with Q0≈49, a quasi-lumped
on-chip MMIC resonator, Q0≈40, and an external metal cavity, Q0≈3800. For each
resonator, the impedance level is chosen to match the active device. The discrete hybrid
oscillator presents a phase noise of -123 dBc/Hz@100 kHz from a 1 GHz oscillation
frequency; the MMIC oscillator presents a phase noise of -106 dBc/Hz@100 kHz from a
15 GHz oscillation frequency; and the cavity based oscillator presents an excellent phase
noise of -145 dBc/Hz@100 kHz from a 10 GHz oscillation frequency. If these results are
normalized with respect to Q0 and PDC, they correspond to effective noise figures of
16-22 dB. Main contribution to the effective noise figures are the finite DC to RF
47
48
Chapter 6 Conclusions and future work
efficiency, which for the cavity oscillator was around 10 %, and thus explaining 10 dB on
its effective noise figure. Other contributors are the up-converted flicker noise and RFnoise figure. Calculated FOM for these three oscillators are: for the hybrid oscillator
186 dB@100 kHz, for the MMIC-oscillator 191 dB@100 kHz, and for the cavity oscillator
227 dB@400 kHz.
As the open-loop-gain was seen as a critical parameter, reflection amplifiers with
electrically controllable gain and constant low noise figures have been designed. A future
work is to evaluate these amplifiers and see if improved performance can be reached with
a better control of the open-loop gain.
The future work involves design of new cavity resonators with MEMS and varactors
used for rough tuning, and analogue fine-tuning, respectively. The varactor must be weakly
coupled in order to maintain a high Q in the resonator.
49
Acknowledgements
This work would never be done for me without some remarkable great persons that
supported me in the daily work.
First, I would like to express my gratitude to my examiner and head of the Microwave
Electronics Laboratory, Prof. Herbert Zirath, and Prof. Jan Grahn as head of the GigaHertz
Center who let me in to this wonderful academic world again, and for providing a
stimulating and pleasant research environment.
Extremely gratitude I would like to express to my supervisor, Dr. Dan Kuylenstierna,
who guided me through the academic work and gave me daily advice and continuous
encouragement, and for helping me in the writing and with practical things as wire
bonding, or in other words for being the best supervisor!
I would like to thank my co-supervisor Dr. Mattias Thorsell, and Dr. Mattias Ferndahl
who helped me in the laboratory work.
Special thanks I would like to bring to Dr. Szhau Lai for introducing me in the research
field, and for being a discussion colleague throughout the work. Special thanks also to Klas
Eriksson, Andreas Westlund, Dr. Mustafa Özen, Dr. Rumen Kozhuharov, and Dr. Vessen
Vassilev for giving much advice through my work. Thanks Thanh Ngoc Thi Do and
Mingquan Bao for many fruitful discussions within the GaNOsc project.
I would like to thank all other colleagues at the Microwave Electronics Laboratory who
have done the daily work being lovely.
Special thanks I would bring to my colleagues, managers, mentors and sponsors at
Ericsson AB, in particular to Dr. Peter Olanders, Dr. Hannes Medelius, and Annika
Engblom who have sponsored my work, and Thomas Emanuelsson for bringing interesting
research topics and valuing my research work for Ericsson AB.
Finally, I would like to thank my family, my wife Karin, my daughters Annie and Emelie
for supporting me and making me feel loved all the time. I love you so much!
This work was supported by the GigaHertz Center in a joint research project financed by
the Swedish Governmental Agency for Innovation Systems, (VINNOVA), Chalmers
University of Technology, Ericsson AB and Ruag Space AB.
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54
Paper A
Phase noise analysis of a tuned-input/tuned-output oscillator based on
a GaN HEMT device
M. Hörberg, S. Lai, T. N. T. Do, D. Kuylenstierna
44th European Microwave Conference Proceedings, 5-10 Oct. 2014,
Rome, Italy, 2014 pp. 1118-1121.
Phase noise analysis of a tuned-input/tuned-output
oscillator based on a GaN HEMT device
Mikael Hörberg*#, Lai Szhau#, Thanh Ngoc Thi Do#, Dan Kuylenstierna#
*
Ericsson AB
Lindholmspiren 11, SE-417 56, Gothenburg, Sweden
#
Microwave Electronics Laboratory, Department of Microtechnology and Nanoscience
Chalmers University of Technology
Gothenburg, Sweden
mikhor@chalmers.se
Abstract—This paper reports on an experimental analysis of
phase noise in a tuned-input/tuned-output oscillator based on a
bare-die GaN HEMT device. To investigate phase noise
dependency on resonator coupling factor (β ), the circuit is
designed with flexibility to modify the resonant tank, in terms of
unloaded quality factor (Q0) and impedance level. The reflection
coefficient (Γamp) from the reflection amplifier can also be varied.
With exception for very high values of Γamp, the circuit is robust
to variations in β. It is more important to choose a bias point
where the flicker noise is low and the power reasonably high. A
minimum phase noise of -150dBc/Hz @ 1MHz off-set from a
1GHz oscillation frequency and a power normalized figure of
merit (FOM) of 186 are reached.
An interesting analytical result is also presented; power
normalized figure of merit, commonly used for benchmark of
oscillators is bound by Q0 and can be related to the theoretical
noise floor limit.
open-loop gain. It is investigated under what conditions the
oscillator performs the best, with the least up-conversion of
low-frequency noise. The unloaded-quality factor (Q0) of the
resonator is also measured individually and phase noise
measurements
compared
to
low-frequency
noise
measurements of the GaN HEMT device. The measured phase
noise is compared to the theoretical phase noise limit that
would be achieved if the active device acts as a noise free
energy restorer, optimally coupled to the resonator. It is also
analytically shown that the theoretical phase noise limit can be
related to power-normalized oscillator figure of merit [6].
II.
THEORY
Oscillator phase noise can be quantitatively modeled by
Leeson’s equation, [1].
Keywords—LF-noise, phase noise, oscillator, GaN HEMT.
Δ
L
I.
INTRODUCTION
OW phase noise oscillators are critical components in
wireless communication systems. For a given resonator
quality factor, the phase noise performance at room
temperature is fundamentally limited by the RF power [1].
From this perspective Gallium Nitride (GaN) high electron
mobility transistor (HEMT) technology is attractive. The
drawback with GaN HEMT and other field-effect-transistor
(FET) technologies is relatively high flicker noise limiting
near-carrier phase noise performance. A couple of GaN
HEMT oscillators have been published and most have a 1/f3
slope all the way down into noise floor, clearly indicating
influence from flicker noise [2]-[5]. There is a need to study in
more detail how the phase noise of GaN HEMT oscillators
depend on bias conditions, in particular how the effect of
signal power and flicker noise are best traded versus each
other.
In this paper we present a tuned-input/tuned-output
oscillator based on a GaN HEMT device. The circuit is
designed with flexibility to change magnitude and phase of
10
2
1
2
Δ
1
Δ
/
Δ
(1)
where Ps is RF power swing and QL is the loaded quality
factor of the resonator. To reach a good phase noise, Ps and QL
must be simultaneously high which is contradictory as QL is
reduced due to loading when more power is coupled to the
resonator. The principle can be easily understood from a
simple reflection-type oscillator model as in. Fig. 1.
Fig. 1 Schematic of negative resistance oscillator.
In Fig. 1, the reflection amplifier is moodeled as a signal
source with internal resistance Rneg. At
A the oscillation
frequency ω0, the source injects energy into the resonator; the
power coupled to the resonator can be expresssed
| |
2 neg 1
(2)
1
where β=Rneg/Rs is the coupling coefficient between
b
the source
and the resonator and η is the DC to RF convversion efficiency.
Also QL can be expressed in terms of β as
1
(3)
1
where Q0 is the unloaded quality factor of thee resonator.
Combining (1)-(3) and focusing on the 1/f2 reegion, where
flicker noise has no influence, the single-sidee band phase noise
in logarithmic scale can be expressed
Δ
10log
1
(4)
Δ
8
The finite efficiency η is merged into F. Based on (4)
minimization of phase noise is a matter of
o optimizing the
coupling coefficient β. Differentiation revveals an optimum
β=1/3 which inserted into (4) shows thaat the theoretical
minimum phase noise that can be reached is
are shown in Fig. 2(a) and (b), respectively. The resonant tank,
placed at the drain-side, is based on surface-mount
components while the gate is terminated in a piece of
transmission line in series with
w
a capacitance Cterm, which
determines the reflection-gaiin (Γamp) seen at the drain
terminal. The gate terminaation and the resonator are
implemented on separate PCBss with the transistor in-between,
so that Γres and Γamp can be measured
m
individually to ensure
satisfaction of small-signal opeen-loop gain.
Γres depends on the equivaleent series resistance Rtank of the
resonator. For a given Q0, Rtank can be changed by the
impedance level Zc=(L/C)1/2. Note
N
that Rtank is not a physical
element but represents the parasitic loss of the surface
mounted L and C. |Γamp| can be increased or decreased by
changing Cterm. Fig. 3(a) show
ws Γres for two resonators with
different Zc. Fig. 3 (b) shows how Γamp changes with Cterm. If
Cterm =5pF, Γamp is too low andd the oscillator will not oscillate.
In the case of Cterm =100pF, Γam
mp is very high and the oscillator
goes easily into compression with
w negative consequences for
phase noise and difficulty to coontrol oscillator with bias. Fig. 4
shows how |Γamp| varies withh Vd/Vg for Cterm=6.8pF and
Cterm=10pF. The absolute gain is higher for Cterm=10pF and the
variation with bias larger. The rest of this paper will focus on
Cterm=6.8pF for which |Γamp| haas a smooth and relatively small
variation with Vg/Vd.
Vg
DC
λ/4 bias
feed
λ/4 biass
feed
Vd
DC
Vout
Γamp Γres
Coupling Vout
Ø
Ø‐comp
Lterm
DUT
min
Δ
173.1
20log
10log
.
Rtank
(5)
DC‐
block
Cterm
Ltank
Rstab
In (5), F is set equal to unity which is the theoretical
t
limit in
the case where the reflection amplifier acts
a
as a lossless
energy restorer. The discrepancy betweenn minimum phase
noise in (5) and a measured phase noise meas Δ can be
defined as a figure of merit on how welll an oscillator is
designed, i.e.,
meas
Δ
10log
173.1
173.1
20log
Ctank
Resonator
(a)
(6)
20log
where FOM is commonly used power norrmalized-oscillator
figure of merit [6]. Equation (6) is an interresting result as it
shows that FOM is linearly proportional to the theoretical
minimum phase noise, and also that minnimum achievable
FOM depends on the resonator’s Q0 as only input
i
parameter.
(bb)
III.
DESIGN OF EXPERIMEN
NT
A 1 GHz tuned-input/tuned-output oscillattor is implemented
on gold-coated PCB with a bare-die GaN
aN HEMT device
connected by bond wires. Schematic and phhoto of the circuit
Fig. 2 a) Schematic and b) Photo of thee oscillator.
The possibility to adjust ZC and Cterm can ensure that the
magnitude of the open loop-gain is sufficiently high.
-6
15
10
5
-8
0
-10
0.5
-5
0.5
1
Freq [Hz]
1.5
1
Freq [Hz]
9
x 10
(a)
1.5
x 10
9
(b)
Fig. 3 Measured S parameters. (a) Resonator. (b) Reflection amplifier at
Vg=-2V, Vd=10V.
Reflection gain vs. bias level. C
term
=6.8pF
Reflection gain vs. bias level. C
=10pF
term
20
8
15
[dB]
[dB]
6
4
10
5
10
2
10
4 -2.5
Vd [V]
-2
6
-2
6
-1.5
8
-1.5
8
4 -2.5
Vd [V]
Vg [V]
Vg [V]
(a)
(b)
Fig. 4 Reflection gain versus bias level for different termination.
Mag open loop, [dB] C
1
1
1.5
1.5
9
2
1.5
-2.2
2
2
2.5
2
3
3.5
3.5
-2
-1.8
Vg [V]
(a)
-1.6
-1
1
0
0
-1
-1
4
-2.2
-2
-3
-4
-5
-6
-2
-3
-4
-2
6
7
10
10
MEASUREMENT AND ANALYSIS
PN@100k, vs Vg and Vd
10
5
-11
17
-1
9
-1120
- 1 21
-1
8
2
5
5
10
Freq [Hz]
Fig. 6 shows measured phase noise versus off-set frequency
under different bias conditions for the case of Cterm=6.8pF
connected to TankA (Qres=49 and Rtank=11ohm, calculated
from small-signal S parameter measurements of resonator). It
is seen that the slope depends on bias condition. To better
illustrate the bias dependency, Fig. 7 shows contour plots of
L(Δf) at 100kHz and 1MHz, respectively. At Δf =1MHz phase
noise improves with increased drain voltage and current, a
minimum of -150dBc/Hz is achieved at Vd/Id=10V/70mA.
This is good as the motivation to use GaN HEMT for
oscillators is that phase noise should improve with increased
power. On the other hand, phase noise at 100 kHz stays
essentially invariant along the same valley of increased
Vd/Vg. The reason is that the increased power is counteracted
by flicker noise which increases with Id. Fig. 8 shows
measured flicker noise for the 8x50um GaN HEMT device
used in the oscillator, the measured data can be fit with a
standard flicker noise model with kF=6×10-10 and AF=0.87. If
flicker noise would be only current dependent and unaffected
by bias the phase noise would be invariant with Id for AF=1.
1
0
6
2.5
3
5
2.
3
IV.
2
1
7
0
5
1.
Vd [V]
0 .5
1
0
6
4
10
1
8
1
7
2
3
0.5
3
10
=6.8pF, (f=1034MHz)
2
-1
-0.5
0.5
term
-160
-1.8
Vg [V]
(b)
-2
-3
-4
-5
-6
-7
-1.6
15
-1
17
6 -1
19
-1120
- 21
1
4 -121
Fig. 5 Measured open-loop gain (ΓresΓamp). (a) Magnitude. (b) Phase.
2
-12 3 .2
3
--1122
-123
-122
-120
2 -119
-1175
-11
-2.2
-2.1
19
-1 0
-1221
-1
2
- 12
--112233.2
-123
-122
121
--120
-119
-1
15
-117
-110
-2
-1.9
Vg [V]
(a)
-122
-123.2
Vd [V]
Phase open loop, [Deg] C
0.5
8
4
=6.8pF, (f=1034MHz)
0
9
5
term
10
10
-140
-123
-4
Γamp [dB]
Γres [dB]
X: 1.021e+009
F=1.03GHz
Y: -3.877
G=-3.8dB
Cterm=100pF
Cterm=10pF
Cterm=6.8pF
Cterm=5pF
20
TankB
-120
Vd [V]
TankA
-80
-100
-1-123
23 .4
.2
25
0
-2
-30dB slope
-20dB slope
PN
-60
Fig. 6 Phase noise vs. offset frequency for all bias. With fluctuation line, 30dB/dec, -20dB/dec. Spurious is removed.
Amplifier
Tank A and Tank B
Phase noise over all bias
-40
[dBc/Hz]
However, any effort would be in vain if the phase condition
cannot be guaranteed. To cope with the phase, the layout
shown in Fig. 2 (b) includes five alternative microstrip paths
that can be interchanged with bond-wires. Before the resonator
and reflection amplifier are connected together, the bondwires are connected to the path that ensures∠ Γ Γ
0. Fig. 5 shows contour plots of phase and magnitude of the
open loop-gain versus Vd/Vg for a reflection amplifier with
Cterm=6.8pF connected to tank A.
-1
22
-121
-120
-119
-117
-115
- 110
-1.8
-1.7
-1.6
PN@1M, vs Vg and Vd
9. 5
- 14
-147
-148
Vd [V]
8
-14
6
-147
.5
0
-15
-1
49
9
-14
-147
-148
10
-149
6
-147
-147
-1
-146
-145
-144
-142
-140
-135
46
4
-148
-148
-145
-144
-142
2 -140
-2.2
-2.1
-2
-1465
-1444
-1
-142
-140
-135
-12-5130
-1.9
-1.8
Vg [V]
V.
-135
-135
-1.7
-1.6
(b)
Fig. 7 Contour plots of L(∆f). (a) 100 kHz. (b) 1MHz.
It is interesting to compare Fig. 7 to Fig. 5, the valley of
minimum phase noise agrees pretty well with fulfillment of
the phase condition at the resonant frequency of the resonator.
0, the circuit will not oscillate where Q0 is
If ∠ Γ Γ
the best which would have negative consequences for phase
noise.
Focusing on 1MHz which is essentially in the 1/f2 region
(6) can be used to calculate FOM and discrepancy compared
to theoretical noise floor. Along the gradient of minimum
phase noise FOM=186-183 for F=21-24, out-of-which 2-3dB
can be explained due to a coupling that deviates slightly from
optimum =1/3 and a finite internal oscillator efficiency
which is about 65%, calculated from simulated wave-forms.
LF noise compared to simulation
[A 2 /H z ]
10
10
10
Id=0.2mA
Id=7.0mA
Id=26mA
Id=53mA
-12
A GaN HEMT based tuned-input/tuned-output oscillator
with possibility to control magnitude and phase of open-loop
gain has been built. The circuit is used to draw conclusions
about phase noise in a GaN HEMT based oscillator. In the
1/f2 slope-region, phase noise scales approximately with DC
power, a minimum of -150dBc/Hz@1MHz offset from 1GHz
is achieved. Normalized to DC power, a figure of merit of
186dB, among the best reported for GaN HEMT based
oscillators is reached.
It is found that at 100kHz off-set, the performance is limited
by flicker noise and stays essentially constant if power is
increased and the phase match condition is maintained. On the
other hand at 1MHz off-set, the phase noise is power limited
and it improves with power if the phase match condition is
maintained.
Other configurations, like common gate or common drain
may give other result on figure of merit, and are topics for
further work.
ACKNOWLEDGMENT
Triquit Semiconductors are acknowledged for support of
this work, for processing of GaN device.
REFERENCES
[1]
[2]
-16
-20
10
0
1
10
2
10
10
3
4
10
CONCLUSIONS
5
10
[3]
Freq [Hz]
Fig. 8 Measurement vs. simulation of LF-noise, (8x50um GaN), Vd=10V.
Table I compares this work to GaN oscillators in open
literature. To calculate F for oscillators in literature, Q0=40 is
assumed which is a reasonable value for MMIC resonators.
[4]
[5]
[6]
J. Everard, Fundamentals of RF Circuit Design with Low Noise
Oscillators. New York: Wiley, 2001, reprinted 2002. 2003.
Mishra, R.A. York, "Low phase-noise 5 GHz AlGaN/GaN HEMT
oscillator integrated with BaxSr1-xTiO3 thin films," Microwave
Symposium Digest, 2004 IEEE MTT-S International , vol.3, no.,
pp.1509,1512 Vol.3, 6-11 June 2004
G. Soubercaze-Pun, J. G. Tartarin, L. Bary, J. Rayssac, E. Morvan, B.
Grimbert, S-L Delage, J.-C. De Jaeger, J. Graffeuil, "Design of a X-band
GaN oscillator: from the low frequency noise device characterization
and large signal modeling to circuit design," Microwave Symposium
Digest, 2006. IEEE MTT-S International , vol., no., pp.747,750, 11-16
June 2006
S. V. Danylyuk, S. A. Vitusevich, V. Kaper, V. Tilak, N. Klein, L. F.
Eastman, and J. R. Shealy, "Phase noise study of AlGaN/GaN HEMT Xband oscillator" phys. stat. sol. (c), 2: 2615–2618, 2005
S H. Liu, X. Zhu, C. C. Boon, X. Yi, M. Mao, and W. Yang, "Design of
Ultra-Low Phase Noise and High Power Integrated Oscillator in GaNon-SiC HEMT Technology",IEEE Microwave and Wireless
Components Lett., accepted
A. Wagemans, P. Ballus, R. Dekker, A. Hoogstraate, H. Maas, A.
Tombeur, and J. Van Sinderen, “A 3.5mW 2.5GHz Diversity Receiver
and a 1.2mW 3.6GHz VCO in Silicon-On-Anything,” ser. IEEE SolidState Circuits Conference, 1998. Digest of Technical Papers. 1998 IEEE
International, 1998, pp. 250–251.
Paper B
Phase Noise Analysis of an X-Band Ultra-low Phase Noise GaN
HEMT based Cavity Oscillator
M. Hörberg, T. Emanuelsson, S. Lai, T. N. T. Do, H. Zirath,
D. Kuylenstierna
Submitted to IEEE Transactions on Microwave Theory and
Techniques, Dec. 2015.
1
Phase Noise Analysis of an X-Band Ultra-low
Phase Noise GaN HEMT based Cavity
Oscillator
Mikael Hörberg, Thomas Emanuelsson, Szhau Lai, Thanh Ngoc Thi Do, Herbert Zirath, Fellow,
IEEE, Dan Kuylenstierna
Abstract—This paper reports on an ultra-low phase noise
oscillator based on a GaN HEMT MMIC reflection amplifier and
an aluminum cavity resonator. It is experimentally investigated
how the oscillator’s phase noise depends on cavity coupling factor,
phase matching, and bias condition of the reflection amplifier.
For the optimum bias and cavity position phase noise of -144
dBc/Hz and -160 dBc/Hz at offsets of 100 kHz and 400 kHz,
respectively, from a 9.9 GHz carrier frequency is reached. This is
to the best of the authors’ knowledge a record in reported
performance for any oscillator based on a GaN HEMT device. The
optimum performance at 400 kHz offset corresponds to a power
normalized figure of merit (FOM) of 227 and compensating for
finite efficiency in the reflection amplifier, the achieved result is
within 7 dB from the theoretical noise floor, assuming a linear
theory. The paper also presents an interesting theoretical result;
the power normalized the FOM is theoretically limited only by the
unloaded Q factor of the resonator.
Keywords—Phase noise, oscillator, cavity, GaN HEMT.
L
INTRODUCTION
ow phase noise is required in a communication system to
handle advanced modulation schemes such as higher order
QAM and OFDM. In modern systems with high data rates, far
carrier phase noise is of increased importance [1]. Far-carrier
phase noise performance, e.g., white phase noise, is determined
primarily by the noise figure of the active device and the power
swing over the resonator [2], [3]. In this perspective, GaN
HEMT technology, with its high breakdown voltage, is a ggood
choice for the active device. Beside high breakdown voltage,
GaN HEMT has better noise figure compared to bipolar
technologies such as SiGe HBT and InGaP HBT, and thus
better capability for good far-carrier phase noise performance.
A few GaN HEMT oscillators have been reported in open
literature and some of them show promising far carrier phase
noise performance [4-6]. However, near carrier phase noise is
not as good as required in many application, due to significant
flicker noise. To meet the near carrier phase noise
specifications, despite the higher flicker noise, a GaN HEMT
oscillator based on a high-Q cavity resonator has been designed
and is reported in this paper.
Manuscript received Nov xx, 2014.
The authors are with the Microwave Electronics Laboratory, Department of
Microtechnology and Nanoscience, Chalmers University of Technology,
Gothenburg, Sweden.
The designed oscillator is based on a GaN HEMT MMIC
reflection amplifier and a rectangular aluminum cavity. It
oscillates at 9.9 GHz with an excellent phase noise of -160
dBc/Hz @400 kHz and -144 dBc/Hz at 100 kHz. To the best of
the authors’ knowledge this is by far the best performance
reported for any oscillator based on a GaN HEMT device. It is
also, regardless of active device technology, better than many
microwave oscillator based on high-Q resonators, e.g., metal
cavity or dielectric resonators.
The performance of the cavity-based GaN HEMT oscillator
is also benchmarked versus the theoretical noise floor
according to Everard’s theory [7]. The circuit is designed with
flexibility to adjust the coupling factor between the cavity and
the amplifier, by shifting the offset between the cavity and a
microstrip line coupling to the amplifier. For optimum coupling
factor and bias point, the measured phase noise is 7 dB above
the theoretical noise floor, after compensation for finite
efficiency of the amplifier.
The theoretical part of this paper presents an interesting
relation; the power normalized phase noise figure of merit
(FOM) [8] commonly used to benchmark oscillators is linearly
related to the theoretical phase noise floor. It is shown that
FOM in theory is bound only by the unloaded quality factor
(Q0) of the resonator, under the assumption that the active
device acts as a noise free energy restorer with 100%
efficiency.
THEORY AND BACKGROUND
Oscillator phase noise at offset frequency ݂௠ from an
oscillation frequency ݂଴ can be quantitatively modeled by
Leeson’s equation [2],
ࣦሺ݂௠ ሻ ൌ ͳͲŽ‘‰ ቎
݂ଵȀ௙య
‫ܶ݇ܨ‬
݂଴ ଶ
ቈͳ ൅ ൬
൰ ቉ ቈͳ ൅
቉቏
ʹܲ௦
ʹܳ௅ ݂௠
݂௠
(1)
where ݇ is Boltzman’s constant, ܶ is the temperature in Kelvin,
ܲ௦ is the RF-power dissipated in the resonator and QL is its
loaded quality factor. F and ݂ଵȀ௙య are fitting parameters used
for fitting the noise level depending on active device noise as
well as nonlinear noise conversion [9].
Mikael Hörberg (e-mail: mikhor@chalmers.se), Thomas Emanuelsson and
Herbert Zirath are also employed at Ericsson AB, Lindholmspiren 11, SE41756, Gothenburg, Sweden.
2
Equation (1) shows that far carrier phase noise, greater than
݂௠ ൌ ݂଴ Ȁሺʹܳ௅ ሻ, is inversely proportional to ܲ௦ , and
independent of ܳ௅ . Below ݂௠ ൌ ݂଴ Ȁሺʹܳ௅ ሻ phase noise is
inversely proportional to the product ܲ௦ ܳ௅ଶ . Very near carrier
phase noise depends also on the nonlinear conversion of flicker
noise. Thus optimization of far-carrier phase noise is done by
maximizing the power coupled to the resonator while
optimizing the near carrier phase noise is about finding an
optimum coupling factor (E) that represents the best trade-off
between coupled power and loaded Q factor.
Fig. 1 shows a schematic of a negative resistance-type
oscillator based on a series resonator and a reflection amplifier
modeled as a negative resistance and a noise source. Fig. 1 may
also be seen as a high-efficiency feed-back oscillator with zero
output impedance [10].
-RN
Rs
L
eNR
C
ΓR
(6)
where ܲ஽஼ is the DC power in mW. Equation (6) presents the
minimum phase noise that may be achieved if a resonator with
unloaded quality factor ܳ଴ is optimally coupled to an active
device fed with DC power ܲ஽஼ . In reality, the measured phase
noise is generally higher due to deficiencies in design and
technology, e.g., finite K, noise from the active device F>1,
and non-optimum coupling E≠1/2. In many cases it is difficult
to spot exactly what is the reason why ࣦ୫୧୬ ሺ݂௠ ሻ has not been
reached. However, the difference between measured SSB phase
noise ࣦ୫ୣୟୱ ሺ݂௠ ሻ and ࣦ୫୧୬ ሺ݂௠ ሻ can be used as a figure of merit
for the oscillator, i.e., design efficiency as proposed in [11]. In
this work we call the difference, the effective noise figure (Feff)
that can be expressed
where ܳ଴ is the unloaded quality factor of the resonator and ܲோி
is the total RF power inside the oscillator, i.e., DC
power×efficiency. ܳ଴ and ܳ௅ may be related through the
coupling coefficient E
ܳ଴
ܳ௅ ൌ
(3)
ͳ൅ߚ
(4)
Equation (4) can then be differentiated to show that the
minimum phase noise occurs for an optimum coupling of ߚ ൌ
ͳȀʹ which inserted back into (4) yields a minimum ͳȀ݂ ଶ phase
noise of
ʹ͹ ‫ܶ݇ܨ‬
݂଴ ଶ
൬
൰
͵ʹ ߟܲ஽஼ ܳ଴ଶ ݂௠
(5)
(7)
where in the last step the widely used power-normalized
oscillator phase noise figure of merit (FOM) [8] has been used
to simplify the equation.
It should be pointed out that Feff as defined in (7) is the
effective noise figure compared to an optimally coupled
resonator with 100 % efficiency, i.e., according to (6). If K and
E are known, the effect of these parameters may be inserted into
(7) to calculate an operating noise figure (Fop) including the
active device noise and its nonlinear conversion in the
oscillator.
‫ܨ‬௢௣ ൌ ͳ͹͵Ǥͻ ൅ ʹͲ Ž‘‰ሺܳ଴ ሻ െ ‫ܯܱܨ‬
ͺߟߚ
൅ ͳͲŽ‘‰ ൬
൰Ǥ
ሺͳ ൅ ߚሻଷ
Inserting (3) into (2), the phase noise can be expressed
‫ܶ݇ܨ‬
݂଴ ଶ
൬
൰
ͺሺܳ଴ ሻଶ ߚȀሺͳ ൅ ߚሻଷ ܲோி ݂௠
݂଴
൰ ൅ ͳ͹ͶǤ͸
݂௠
൅ ͳͲŽ‘‰ሺܲ஽஼ ሻ ൅ ʹͲŽ‘‰ሺܳ଴ ሻ
ൌ ͳ͹ͶǤ͸ ൅ ʹͲŽ‘‰ሺܳ଴ ሻ െ ‫ܯܱܨ‬Ǥ
‫ܨ‬ୣ୤୤ ൌ ࣦ୫ୣୟୱ ሺ݂௠ ሻ െ ʹͲŽ‘‰ ൬
Ignoring the transposed flicker noise and the noise floor region,
Everard [7] has shown that the single-side band phase noise
spectrum of a high-efficiency oscillator can be expressed
‫ܶ݇ܨ‬
݂଴ ଶ
ࣦሺ݂௠ ሻ ൌ
൬
൰
(2)
ͺሺܳ଴ ሻଶ ሺܳ௅ Ȁܳ଴ ሻଶ ሺͳ െ ܳ௅ Ȁܳ଴ ሻܲோி ݂௠
ࣦሺ݂௠ ሻ ൌ
ʹ͹ ݇ܶ
݂଴
ቇ ൅ ʹͲŽ‘‰ ൬ ൰
ଶ
͵ʹ ܳ଴ ܲ஽஼
݂௠
ൌ െͳ͹ͶǤ͸ െ ͳͲŽ‘‰ሺܲ஽஼ ሻ െ ʹͲŽ‘‰ሺܳ଴ ሻ
݂଴
൅ ʹͲŽ‘‰ ൬ ൰
݂௠
ࣦ௠௜௡ ሺ݂௠ ሻ ൌ ͳͲŽ‘‰ ቆ
Γamp
Fig. 1 Schematic picture of the reflection oscillator
ࣦሺ݂௠ ሻ ൌ
where K is the oscillator efficiency, ܲ஽஼ is the DC power and F
is the transistor noise factor. Assuming K=100% and F=1, the
minimum achievable single-side-band phase noise expressed in
dBc/Hz becomes
(8)
If the oscillator operates fairly linear, Fop will be similar to the
active device microwave noise figure, while if there is strong
nonlinear noise conversion it will be higher, compare
Hajimiri’s impulse sensitivity theory [9].
Before ending this discussion about how to benchmark
oscillators with figures of merit and relative to absolute noise
floor, it is worth to point out that the conventionally used FOM
does not relate oscillator phase noise to absolute noise floor and
further it does not normalize versus Q0 of the resonator. In fact
a high-Q oscillator may have comparatively good FOM without
being particularly well designed, i.e., not well utilized Q factor.
3
Setting Feff=0 dB in (7), it is found that the maximum
achievable FOM turns out to be bound only by the unloaded Q
factor of the resonator, i.e.,
‫ܯܱܨ‬ெ௔௫ ൌ ͳ͹ͶǤ͸ ൅ ʹͲŽ‘‰ሺܳ଴ ሻǤ
(9)
Equation (9) puts oscillator figures of merit in new
perspectives. Often it is claimed about figures of merit that they
are mixing up different factors and makes it more difficult to
distinguish pure technical performances. Such claims are true
in many cases. However, (9) presents a clear bound on FOM.
As far as Q0 is known, it can be directly related to the effective
noise figure (7)
DESIGN AND EXPERIMENTS
A. MMIC technology and device
The amplifier is manufactured in a 0.25 um GaN HEMT
process, TriQuint 3MI process. The model used for design is
Chalmers’ own model [12] based on in house measurements.
To compare measured and simulated results, the low
frequency noise model parameters of the transistor has been
extracted from measurements. Fig. 2 (a) shows the measured
LF-noise vs. frequency for different drain currents at fixed Vd,
and Fig. 2 (b) shows the measured LF noise at 100 kHz offset
for different Vd/Id setting. The IV-plots for the used transistor,
from the same wafer batch as the reflection amplifier, is
simulated and measured, see Fig. 3 (a,b). The transistor is based
on a common source grounded configuration, however in the
MMIC-amplifier a 15 : resistance is connected to the source
which will cause difference in the DC I/V characteristics, c.f.
Fig. 3 to Fig. 7. The noise current density is modelled with the
standard flicker noise model
(a)
(b)
Fig. 3 IV-plots simulated (red square) and measured (blue circle) for
the FET 8x50 um used in the design. (a) Id vs Vd, (b) Id vs Vg.
B. Reflection amplifier
To simplify the building practice and minimize the number
of interconnects associated with model uncertainties, the
reflection amplifier is integrated on a MMIC. Fig. 4 shows the
MMIC reflection amplifier based on a GaN HEMT with 400
μm gate periphery. To assure oscillation condition, the GaN
HEMT has an inductive termination at the drain and a parallel
LC network connected to the source, to peak gain at about 1012 GHz. A 15 : resistor is connected in series with the
inductance, partly for shaping the gain, but mostly for bias
stabilization.
Vgg
Vdd
Zterm
Connection
to tank
Source
feedback
஺
൏ ଓഥଶ௡ ൐ൌ ‫ܭ‬௙௘
‫ܫ‬ௗ ೑೐
(10)
݂ி೑೐೐
where the involved parameters extracted from measurements
shown in Fig. 2 are ‫ ݂݁ܭ‬ൌ ͸ǤͶ ‫Ͳͳ כ‬െͳͲ ǡ ‫ ݂݁ܣ‬ൌ ͲǤͺ͹ǡ ‫ ݂݁݁ܨ‬ൌ
ͳǤ͵ͺ. Id is the drain bias current, and ݂ the frequency.
(a)
(b)
Fig. 4 Reflection amplifier. (a) Chip photo, size 1.0x1.0mm,
(b) Schematics.
Fig. 5 shows the gain magnitude versus frequency for the
reflection amplifier described in Fig. 4. The gain is shaped to
peak in the desired resonance band, and roll off outside to
suppress undesired out-of-band oscillations. Fig. 6 (a,b) show
the gain and phase of the amplifier, respectively. At frequency
10 GHz, the measured reflection gain at Vd/Id 5V/40 mA,
ห߁௔௠௣ ห ൌ ͺ dB, corresponding to a ܴே ൌ െʹͳǤ͸ :, when
imaginary part is tuned out.
(a)
(b)
Fig. 2 (a) LF noise measurement of transistor [A2/Hz], for different Id.
Vd=10V is used in this comparison. (b) Contours of measured LFnoise [A2/Hz] vs Id and Vd @100 kHz.
4
݂௠௡௟ ൌ
Fig. 5 Measured reflection gain of amplifier vs frequency with bias
condition as parameter.
ܿ଴
݊ߨ ଶ
݈ߨ ଶ
݉ߨ ଶ
ඨቀ ቁ ൅ ቀ ቁ ൅ ൬ ൰
ܾ
݀
ܽ
ʹߨξߤ௥ ߳௥
(11)
where a, b, and d are the width, depth, and length of the cavity.
For the TE101-mode this means that a=d=O/2=21.7 mm while
b=ߣȀͶ to assure maximum margin to other resonant modes. For
practical reasons the corners of the cavity are rounded which
affects the resonant frequency slightly but has no negative
effect on the Q factor. Fig. 8 (b) shows an HFSS setup of the
metal cavity coupled to a microstrip line. The coupling to the
resonator is accomplished by a microstrip line recessed in a
brass plate acting as ground wall for the aluminum cavity. The
end of the microstrip line is terminated in ͷͲ: which
effectively suppresses unwanted resonances.
The coupling factor can be controlled by varying the
perpendicular offset position between the microstrip line and
the center of the cavity, changing the offset from 0 to 9 mm, Rs
changes from about ͹: to ʹͷ:. The highest possible Rs for a
weakly coupled cavity is determined by the load termination at
the end of the microstrip line.
(a)
(b)
Fig. 6 Measured (a) Gain [dB] and (b) phase [Deg] vs. bias at the
reference plane of the cavity position, for the reflection amplifier at 10
GHz.
In Fig. 6 (a), higher gain forces the oscillator to run in higher
compression. There is risk that the phase is changed by bias,
and the oscillation frequency will not appear for highest Q in
all bias points when tank is set for a fixed position. Fig. 6 (b)
shows this is a minor effect, and can be neglected
Bias points for the amplifier compared to simulated results
are shown in Fig. 7. The small source resistance in the bias
network contributes to additional slope in the IVcharacteristics.
(a)
(b)
Fig. 8 (a) Photo of the cavity. (b) HFSS-model of the cavity with offset
direction indicated.
Small reflection coefficient (*of the designed cavity was
measured with an E8361A 67 GHz VNA from Agilent. Fig. 9
(a, b) show the measured and simulated * from the cavity
board at different cavity positions.
(a)
(b)
Fig. 7 Bias points for the amplifier, measured (blue dots) compared to
simulated (red dots). (a) Id vs. Vd, (b) Id vs. Vg.
C. Cavity
The metal cavity is made of aluminum suitable for
industrial implementation. It is designed to resonate at 9.9 GHz
in the TE101-mode. The frequencies for different modes are
given by
(a)
(b)
Fig. 9 (a) Measured cavity reflection at different offset positions
deembedded in phase to reference plane for serial resonance. (b)
HFSS-simulations. Narrow sweep 9.9 to 10.0 GHz. The remaining
serial resistance Rs at resonance is calculated.
5
The measured * was converted to input impedance, and Q0
of the cavity was calculated from the phase slope of the input
impedance
߱଴ ߲߶ሺܼ௜௡ ሻ
ܳ଴ ൌ
ȁఠୀఠబ
(12)
߲߱
ʹ
The measurements show that Q0 is marginally affected by
the offset position while the impedance level is strongly
affected. The measured ܳ଴ ൌ ͵ͺͲͲ, and when cavity is
positioned for maximum coupling (microstrip line exciting in
the middle), measured ȁ߁௧௔௡௞ ȁ ൌ െʹǤ͸dB, corresponding to
ܴ௦ ൌ ͹Ǥͷ :.
D. Oscillator test bench
After characterization of the individual building blocks, i.e.
the reflection amplifier and the cavity, the two parts are merged
together to form a complete oscillator. The amplifier is soldered
on a brass plate, with a PCB for biasing. This plate is attached
to the cavity plate. A clamp presses the cavity in place, see Fig.
10 (a). The output power is extracted through an SMA
connector at the end of the microstrip line on opposite side of
the cavity. A 3 dB attenuator, connected between the microstrip
line and the source analyzer, ensures a good 50 : termination
suppressing potential spurious resonances.
(a)
(b)
Fig. 11 Measured open loop gain of assembled oscillator for different
cavity positions, bias setting Vd/Id=5V/30mA. (a). Magnitude vs.
frequency. (b) Narrow band polar plot around the resonant peak (9.910 GHz).
Fig. 11 shows that the maximum cavity offset position that can
maintain oscillation, under the given amplifier bias condition,
is 6.8 mm. The loop gain variation with bias is illustrated in
Fig. 12 that presents open loop gain versus Vd and Vg for the
cavity positioned at 5.9 mm off-set. It is seen that the gain of
the reflection amplifier is pretty invariant with Vg while it
increases about 4 dB when Vd is increased from 4 to 15 V. The
gain variation has implications on the phase noise as it will
affect the device compression level, this effect will be further
discussed in Section IV.
(a)
Cavity
Fig. 12 Open Loop gain [dB] vs. bias for cavity offset 5.9 mm, (offset
giving best phase noise)
Microstrip
Coupling to
cavity
I
Load
termination
RF
out
Transmission
length
inphasing
Fig. 13(a) shows the measured output power versus bias
for a cavity centered at 5.9 mm offset from the microstrip line.
Fig. 13 (b) shows the simulated efficiency [%] versus bias for
the same cavity position.
(b)
Fig. 10 Assembled oscillator. (a) Photo of complete module,
dimension of air cavity 21.7x10.9x21.7 mm. (b) Equivalent circuit
including reflection amplifier, metal cavity and attenuator at RF
output.
Fig. 11 shows open loop gain derived from measurements
of the reflection coefficients, ‫ܩ‬௟௢௢௣ ൌ ߁௔௠௣ ߁௧௔௡௞ , of the
reflection amplifier for different cavity positions. Fig. 11(a)
shows the magnitude of the open loop gain in dB and Fig. 11(b)
shows the open loop gain around resonant peak in polar form.
(a)
(b)
Fig. 13 (a) Measured power [dBm] at fundamental frequency, (b)
simulated efficiency [%].
6
The cavity oscillator is characterized with a Rhode &
Schwarz Signal Source Analyzer (FSUP50). A direct
measurement with the FSUP reveals that the oscillator is
capable of a phase noise comparable to or below the noise floor
of the measurement system, which is specified to a typical
value of -138 dBc/Hz @100 kHz for a 10 GHz signal [13].
Therefore a setup based on two almost identical cavity
oscillators was built and the outputs were down-converted to a
much lower measurement frequency, see Fig. 14 (a), where the
noise floor of the system is better. The IF frequency is 30 MHz
due to slightly different dimensions of the otherwise nearly
identical cavities. On one of the oscillators (the reference
oscillator) an isolator is placed to prevent load pulling, and on
the other oscillator (the DUT), a small attenuator (0-6 dB) is
placed to form a broadband load.
SSA
Meas IF-freq ~30MHz
Fig. 15 Mixer based PN-measurement [dBc/Hz]@100kHz at best
cavity position of the two cavity oscillators at 30 MHz for different
bias setting on the DUT-oscillator.
Isolator
Attenuator
(0-6dB)
noise measurements are linearly corrected for the contribution
from the reference oscillator, i.e., -144 dBc/Hz is subtracted.
The output power from the reference oscillator is about +10
dBm which is capable as the LO to the mixer.
F0=9.9GHz+ ~
30MHz
Cav osc 2
Used as reference at
Fixed setting
Slightly offset in frequency
F0=9.9GHz
Cav osc 1
DUT
(a)
Attenuator
Isolator
DUT oscillator
Reference
oscillator
Bias
Mixer
To SSA
(b)
Fig. 14 Mixer based experimental phase noise characterization
me setup. (b)
including two oscillators. (a) Schematic of measurement
Picture of the setup.
Components used:
Isolator
Attenuator
Mixer
0/3/6 dB
HMXR-5001
7-12 GHz
0-26 GHz
2-12.4 GHz
The two reflection amplifiers are identical, using the same
batch of active device. In the first phase noise measurement
both oscillators were tuned regarding cavity position and bias
in the same way, until an optimum phase noise of -141
dBc/Hz@100 kHz was measured for the down-converted
signal. The best value was found at Vg/Vd=-2/5V. Subtracting
3 dB from this value, due to the mixing process, it is found that
the minimum phase noise of a single oscillator is -144
dBc/Hz@100 kHz offset for optimum cavity position and
optimum bias see Fig. 15. In Fig. 16 the phase noise versus
offset frequency for best bias is shown.
In the further measurements, presented in Section IV, the
reference oscillator is kept fixed while the DUT is varied to
investigate variations with cavity position and bias. All phase
Fig. 16 Optimum phase noise performance achieved for cavity offset
5.9 mm and bias condition Vg/Vd=-1.7/5. This is the best result that
can be achieved in this study, and also sets the limit in the mixer based
measurement setup.
RESULTS AND MEASUREMENTS OF OSCILLATOR
A. Measurements of oscillator
The optimum phase noise performance was presented in
Fig. 15 and Fig. 16. Comparing to the gain variation presented
in Fig. 12, it is realized that increased loop gain quickly results
in the penalty of increased phase noise at 100 kHz offset. The
best phase noise performance is seen for low Vd, where the loop
gain is small. At increased Vd, and associated loop gain, the
100 kHz phase noise quickly increases, as is expected due to
nonlinear noise conversion as the device goes harder in
compression [9].
The gain compression can be controlled either by adjusting
the coupling factor to the cavity by changing the distance of the
cavity perpendicular to the exciting microstrip line, or by
limiting the gain of the amplifier by choosing lower Vd. TABLE
I presents optimum oscillator performance for four different
cavity coupling factors. In summary, the lower the loop gain,
the better the phase noise performance.
To further illustrate how the phase noise performance varies
with bias condition, Fig. 17 and Fig. 18 present phase noise
7
versus bias condition at offset frequency 100 kHz and 400 kHz,
respectively, for two different cavity couplings, i.e., the
weakest coupling (0.6 mm) and the strongest coupling (5.9
mm).
Fig. 17 shows that 100 kHz phase noise quickly degrades
with Vd while very little variation in phase noise is detected for
a change in Vg. The phase noise degradation with Vd can be
understood as an effect of the increased nonlinear noise
conversion associated with the increase in open loop gain, c.f.
Fig. 12. Similarly, the invariant phase noise seen for increased
Vg can be interpreted as the balancing of three effects: i)
increased flicker noise degrading phase noise, ii) increased
power improving phase noise, and iii) increased efficiency, c.f.
Fig. 13(b), improving phase noise.
dB difference compared to the theoretical noise floor, where it
is assumed that the noise of the active device is 0 dB, and 100%
efficiency (Ps=PDC), by setting Feff=0 in (7). Out of this, 12 dB
can be deduced to finite efficiency of the reflection amplifier.
Fig. 20 shows Fop according to (8)1. After compensation for
finite efficiency, a minimum Fop of 7 dB is reached for
Vd/Vg=5V/-2.1V. Note that the optimum phase noise, FOM and
Fop are reached for an open loop gain near unity, i.e., a coupling
factor near E=1, and not E=1/2 as deduced in the theory. The
reason is likely effects of nonlinear noise conversion that are
not taken into account in the theory.
(a)
(a)
(b)
(b)
Fig. 18 Measured phase noise@400 kHz vs bias. (a) The cavity at
offset 0.6 mm to the center coupling line. (b) The cavity at offset 5.9
mm to the center coupling line.
Fig. 17 Measured phase noise@100 kHz vs bias. (a) The cavity at
offset 0.6 mm from the center coupling line. (b) The cavity at offset
5.9 mm from the center coupling line.
Fig. 18, presenting phase noise at 400 kHz, shows also that
phase noise is invariant to a change in Vg. However, in contrast
to Fig. 17, little variation is seen for a change in Vd. A reason is
that 400 kHz, in contrast to 100 kHz is primarily in the ͳȀ݂ ଶ
region. As 400 kHz is in the ͳȀ݂ ଶ region, it is in accordance to
the theory in Section II a reasonable frequency for calculating
figures of merit. Fig. 19 shows power normalized FOM for
cavity offsets if 0.6 mm and 5.9 mm, respectively. At 5.9 mm
off-set, an excellent FOM of 227 is reached. Like phase noise,
FOM is invariant with Vg but decreases with Vd.
It is interesting to compare measured FOM to the
fundamental limit that can be calculated from (9). Given the
measured Q0=3800, FOMMax=246 according to (9). Thus, a 19
(a)
(b)
Fig. 19 Calculated FOM@400 kHz vs bias. (a)The cavity at offset 0.6
mm to the center coupling line. (b)The cavity at offset 5.9 mm to the
center coupling line.
TABLE I
SUMMARY OF OPTIMUM PERFORMANCE FOR DIFFERENT CAVITY PLACING AT OFFSET FREQUENCY 100KHZ AND 400 KHZ
Cavity
Rs/loss
Optimum phase noise Phase noise FOM @
position [ohm]/[dB] performance @100k
@ 400k
400k [dB]
offset [mm]
[dBc/Hz] @ bias level [dBc/Hz]
(Vd/Vg)
0.6
8.1/2.8
-139 @4/-1.9
-152.5
219
3.4
14/5
-141@4/-1.8
-155.5
223
3.9
19.2/7
-141.5@5/-1.6
-156
221
5.9
20/7.4
-144.5@5/-1.8
-160
227
1
It should be mentioned that the coupling coefficient for simplicity is kept
constant E =1, regardless of gain variation with bias, in generation of Fig. 20.
In reality, the coupling factor changes from E=1/3 to E=1 as the gain of the
Fop @
400k
[dB]
Gain [dB] Reflection
Amp @ opt for 100k.
bias (Vg/Vd)
ȁܴே ȁ
[ohm]
Open loop
gain
[dB]
15
10
9
7
6.8
7.0
8
7.9
18.7
19.1
21.6
21.3
4
2
1
0.5
reflection amplifier varies, however, the effect on the phase noise is only about
0.5 dB, according to (8).
8
(a)
(a)
(b)
Fig. 20 Calculated Fop@400 kHz. (a) The cavity at offset 0.6 mm to
the center coupling line. (b) The cavity at offset 5.9 mm to the center
coupling line.
B. Measurements compared to simulations
Fig. 21 compares measured phase noise versus offset
frequency, with bias condition as parameter, to simulations
using ADS Harmonic Balance with LF-noise parameters
according to (10) extracted from FET characterization. A pretty
good agreement is seen for the -20dB/dec region, while there is
significant discrepancy in the -30dB/dec region due to nonaccurate representation of the nonlinear noise conversion.
Fig. 22 (a,b) present phase noise versus off-set frequency at
100 kHz and 400 kHz, respectively, with Vg as parameter. The
figure shows simulations both with and without flicker noise
model. At 100 kHz offset the discrepancy between
measurements and simulations including flicker noise is about
5-7 dB while it is about 2-3 dB at 400 kHz offset. The larger
discrepancy at 100 kHz offset is due to nonlinear conversion of
flicker noise being more important near carrier. The reason for
showing the simulations without flicker noise is that it makes it
easy to compare to the fundamental noise limit and figures of
merit derived in Section II.
Fig. 23(a) and Fig. 23(b), respectively, show simulated and
measured Fop and FOM, extracted at 400 kHz. The simulations
without flicker noise give Fop=0.8-2.1 dB which agrees well
with the linear noise figure of the active device, as expected for
a well-designed oscillator. Measured NFmin for a GaN-HEMT
in this process is found to be ~0.8 dB@10 GHz. Considering
FOM presented in Fig. 23(b), the simulated FOM is about 234,
i.e., 12 dB lower compared to the FOMMax, a difference that is
explained by the finite efficiency of the reflection amplifier.
(b)
Fig. 22 (a) Simulated phase noise at 100 kHz, (b) simulated phase
noise at 400 kHz, with and without model considering LF-noise,
compared to measurement.
(a)
(b)
Fig. 23(a) Simulated Fop and (b) FOM compared to measurement.
Vd=4 V has been used.
TABLE II
BENCHMARK OF LOW PHASE NOISE OSCILLATORS BASED ON EXTERNAL
RESONATORS
Ref.
Pdc [mW]
L(100k) f0
(dBc/Hz) (GHz)
FOM@100k
Active device
Technology
Resonator
Technology
[14]
-140
8.2
700(**)
209
N/A
DRO
[15],
fig 9
-132(*)
9.2
N/A
N/A
GaAs pHEMT
Silver coated
cavity
[16]
-137
10.2
N/A
N/A
N/A
DRO
[17]
-118
10.6
54(***)
201
GaN HEMT
DRO
(***)
[17]
-123
10.6
207
GaAs pHEMT
DRO
[17]
-135
10.6
46
N/A
N/A
SiGe HBT
DRO
[18]
-149
7.61
400
221
GaAs InGaP HBT
DRO
[18]
-142
7.61
100
220
GaAs InGaP HBT
DRO
This
work
-144
9.9
200
220
GaN HEMT
Aluminum
cavity
(*)The
plot in [15] is used to estimate the phase noise. (**) A buffer
amplifier is included, but output power is comparable with other
output power in this work. (***) calculated from power density and
transistor size.
Fig. 21 Measurements compared to simulations. Dots are the
simulated data for the same bias range, Vd=3 to 13V, Vg=-2.2 to -1.6V.
Guideline for -20 dB/dec resp. -30 dB/dec slope are added in graph.
The result of the cavity oscillator reported in this paper has
been benchmarked versus performance of DROs and metal
cavity based oscillators in open literature. TABLE II presents a
summary of the benchmark, with focus on phase noise and
FOM at offset frequency 100 kHz. It is found that the oscillator
of this work performs very well in the comparison. In fact only
one oscillator with comparable or better figure of merit has
been found, it is a DRO based on an InGaP HBT [18], which
has slightly better FOM below 100 kHz off-set. However, it
should be mentioned that the oscillator in this work is based on
9
a resonator with lower Q factor, Q0=3800, compared to
Q0=8800 for the dielectric resonator in [18]. Compensating for
the Q factor, the oscillator of this work presents an effective
noise figure that is 7 dB closer to the theoretical noise floor.
CONCLUSIONS
A GaN HEMT oscillator based on a MMIC reflection
amplifier and an aluminum cavity has been designed,
manufactured and characterized. Excellent phase noise of -144
dBc/Hz@100 kHz and -160 dBc/Hz@400 kHz from a 9.9 GHz
oscillation frequency is experimentally demonstrated. At 400
kHz offset the power normalized figure of merit is 227. To the
authors’ best knowledge this is the best phase noise and figure
of merit reported for any oscillator based on a GaN HEMT
device. It is also state-of-the art for cavity based oscillators,
regardless of active device technology.
Beside, demonstrating excellent phase noise the work also
investigates experimentally how the phase noise depends on
coupling factor and bias conditions. It is found that near carrier
phase noise has minimum for relatively low drain voltage
(Vd=3-4V), moderate current, and the open loop gain as low as
possible. Compensating for finite efficiency in the reflection
amplifier, the measured phase noise is within 7 dB from the
theoretical noise floor.
This work demonstrates that oscillators with excellent
phase noise performance can be designed in GaN HEMT
technology, provided that coupling factor and bias levels are
well controlled in order to avoid nonlinear conversion of flicker
noise.
REFERENCES
[1]
[2]
[3]
[4]
[5]
[6]
[7]
[8]
[9]
M. R. Khanzadi, D. Kuylenstierna, A. Panahi, T. Eriksson, and H.
Zirath, "Calculation of the Performance of Communication Systems
From Measured Oscillator Phase Noise," IEEE Trans. Circuits
Syst.I,Reg.Papers, vol. 61, pp. 1553-1565, 2014.
D. B. Leeson, "A simple model of feedback oscillator noise
spectrum," Proc. IEEE, vol. 54, pp. 329-330, Feb 1966.
J. Everard, "Fundamentals of RF Circuit Design with Low Noise
Oscillators. New York, NY: Wiley " 2001.
L. Szhau, D. Kuylenstierna, x, M. zen, M. Horberg, N. Rorsman, et
al., "Low Phase Noise GaN HEMT Oscillators With Excellent
Figures of Merit," Microwave and Wireless Components Letters,
IEEE, vol. 24, pp. 412-414, 2014.
G. Soubercaze-Pun, J. G. Tartarin, L. Bary, J. Rayssac, E. Morvan,
B. Grimbert, et al., "Design of a X-band GaN oscillator: From the
low frequency noise device characterization and large signal
modeling to circuit design," in IEEE MTT-S Int. Dig,, Jun. 11–16,
2006, pp. 747-750.
S. Lai, D. Kuylenstierna, M. Horberg, N. Rorsman, I. Angelov, K.
Andersson, et al., "Accurate Phase-Noise Prediction for a Balanced
Colpitts GaN HEMT MMIC Oscillator," IEEE Trans. on MTT, vol.
PP, pp. 1-11, 2013.
J. Everard, X. Min, and S. Bale, "Simplified phase noise model for
negative-resistance oscillators and a comparison with feedback
oscillator models," IEEE Trans. Ultrason., Ferroelectr., Freq.
Contr., vol. 59, no.3, pp. 382-390, Mar 2012.
A. Wagemans, P. Ballus, R. Dekker, A. Hoogstraate, H. Maas, A.
Tombeur, et al., "A 3.5 mW 2.5 GHz diversity receiver and a 1.2
mW 3.6 GHz VCO in silicon-on-anything," in IEEE Int. Solid-State
Circuits Conf. Tech. Dig., 1998, pp. 250-251.
A. Hajimiri and T. H. Lee, "A general theory of phase noise in
electrical oscillators," IEEE J. Solid-State Circuits, vol. 33 no. 2,
pp. 179-194, Feb 1998.
[10]
[11]
[12]
[13]
[14]
[15]
[16]
[17]
[18]
J. K. A. Everard, "Low Noise Power Efficient Oscillators: Theory
and Design," Proc. IEEE Part G, vol. 133, pp. 172-180, Aug 1986.
J. van der Tang and D. Kasperkovitz, "Oscillator design efficiency:
A new figure of merit for oscillator benchmarking,," in Proc. IEEE
ISCAS, 2000, pp. 533-536.
I. Angelov, H. Zirath, and N. Rosman, "A new empirical nonlinear
model for HEMT and MESFET devices," IEEE Trans. on MTT, vol.
40, pp. 2258-2266, 1992.
"R&S FSUP Signal Source Analyzer Specifications," Version
06.02, Feb 2009.
"HMC-C200, Dielectric resonator oscillator module 8.0-8.3GHz,"
Datasheet Hittite Microwave corporation, v06.0612.
J. Maree, J. B. de Swardt, and P. W. van der Walt, "Low phase noise
cylindrical cavity oscillator," in IEEE AFRICON 2013, 2013, pp. 15.
"PSI DRO-10.600-FR," Datasheet Poseidon Scientific Instruments,
Rev 05/03 2003.
P. Rice, M. Moore, A. R. Barnes, M. J. Uren, N. Malbert, N. Labat,
et al., "A 10 GHz dielectric resonator oscillator using GaN
technology," in 2004 IEEE MTT-S Int. Dig., Fort Worth, TX, 2004,
pp. 1497-1500.
C. Florian, P. A. Traverso, G. Vannini, and F. Filicori, "Design of
Low Phase Noise Dielectric Resonator Oscillators with GaInP HBT
devices exploiting a Non-Linear Noise Model," in 2007 IEEE MTTS Int. Dig., Honolulu, HI, 2007, pp. 1525-1528.
Paper C
Low phase noise power-efficient MMIC GaN-HEMT Oscillator at
15 GHz based on a Quasi-lumped on-chip resonator
M. Hörberg, D. Kuylenstierna
IEEE MTT-S International Microwave Symposium Digest, Phoenix,
Arizona, 17-22 May 2015.
Low phase noise power-efficient MMIC GaN-HEMT Oscillator at
15 GHz based on a Quasi-lumped on-chip resonator
Mikael Hörberg*#, Dan Kuylenstierna#
*
Ericsson AB
Lindholmspiren 11, SE-417 56, Gothenburg, Sweden
#
Microwave Electronics Laboratory, Department of Microtechnology and Nanoscience
Chalmers University of Technology
Gothenburg, Sweden
mikhor@chalmers.se
Abstract—This paper reports on a negative resistance 15 GHz
GaN HEMT oscillator using a quasi-lumped integrated
resonator. The resonator is based on a lumped element parallel
LC resonator and a piece of transmission line acting as
impedance transformer and phase compensation. The main
advantage of this type of resonator is that it gives good flexibility
in choice of impedance level so that it is easy to control the
coupling factor between the active device and the resonator
which is mandatory to reach good phase noise. An excellent
phase noise of -106 dBc/Hz@100 kHz from a 15 GHz carrier is
experimentally demonstrated. The oscillator is also very power
efficient with a power normalized figure of merit (FOM) of 191
dB, extracted at 100 kHz offset. To the authors’ best knowledge
this is the highest FOM reported for a GaN HEMT MMIC
oscillator.
Index Terms—LF-noise, phase noise, oscillator, GaN HEMT.
I. INTRODUCTION
L
OW phase noise oscillators are critical components in a
communication system to handle advanced modulation
schemes such as higher order QAM and OFDM. In modern
systems with high data rates, far carrier phase noise is of
increased importance [1]. Far-carrier phase noise performance,
i.e., white phase noise, is determined primarily by noise figure
of the active device and the power swing over the resonator
[2]. In this perspective GaN HEMT technology, with its high
breakdown voltage, is a good choice for the active device.
Beside high breakdown voltage, GaN HEMT has better noise
figure compared to bipolar technologies such as SiGe HBT
and InGaP HBT.
MMIC design provide high integration level, is very
repeatable against process variations, and are cost effective in
volume production. To minimize phase noise, the resonator
must be well matched to the active device in order to trade off
power over the resonator and loaded Q factor. This is
particularly important in MMIC technology, where the
unloaded Q factor is relatively low. A common approach for
impedance transformation is to use tapped resonator
topologies, e.g., Colpitts or Hartley [3], with reactive
impedance transformation that provides flexibility in
impedance level. The Colpitts and Hartley topologies have
also been shown to support wave-forms resulting in low upconversion of flicker noise [4]. Excellent phase noise has been
demonstrated for balanced Colpitts and Hartley MMIC
oscillators [5] [6].
Recently, it was demonstrated that simple reflection type
oscillators can reach good phase noise and figures of merit
(FOM), provided that the waveforms are controlled [7], which
requires careful design of the resonator. A challenge in MMIC
technology is to design resonators yielding reasonable
impedance levels. In [7] a coupled distributed resonator was
used, but that is too space consuming for MMIC integration.
This paper demonstrates a low phase noise power efficient
15 GHz GaN HEMT MMIC oscillator using a quasi-lumped
integrated resonator that can be made fairly compact. The
resonator is based on a lumped element parallel LC resonator
and a piece of transmission line acting as impedance
transformer and phase compensation. It gives good flexibility
in choice of impedance level so that it is easy to control the
coupling factor between the active device and the resonator
with component values maximizing quality factor in MMIC
technology.
II. THEORY
Oscillator phase noise can be quantitatively modeled by
Leeson’s equation, [8].
ࣦሺȟ݂ሻ ൌ ͳͲŽ‘‰ ቎
ଶ
ȟ݂ଵȀ௙య
݂଴
‫ܶ݇ܨ‬
ቈͳ ൅ ൬
൰ ቉ ቈͳ ൅
቉቏
ʹܲ௦
ʹܳ௅ ȟ݂
ȟ݂
(1)
where Ps is RF power swing and QL is the loaded quality
factor of the resonator. To reach a good phase noise, Ps and QL
must be simultaneously high which is contradictory as QL is
reduced due to loading when more power is coupled to the
resonator. The principle can be easily understood from a
simple reflection-type oscillator model as in Fig. 1.
-RN
Rs
L
eNR
C
ȳR
ȳamp
Fig. 1 Schematic picture of the reflection oscillator
Inside the resonator bandwidth, ȟ݂ ൏ ݂଴ Τʹܳ௅ , ࣦሺȟ݂ሻ is
minimized for an optimum coupling between the resonator to
the active device. If the coupling coefficient is expressed
ߚ ൌ ܴ௦ Τܴே , see Fig. 1 [2], ࣦሺȟ݂ሻ in the ͳΤ݂ ଶ can be
expressed
‫ܶ݇ܨ‬
݂଴ ଶ
ࣦሺȟ݂ሻ ൌ
൬
൰
ͺሺܳ଴ ሻଶ ߚȀሺͳ ൅ ߚሻଷ ܲோி ȟ݂
(2)
By differentiation of (2), it can be shown that the optimum
phase noise is reached for β=1/2.
Designing for a certain β is about finding appropriate RS and
RN. Beside considering the ratio between RS and RN, the
absolute values of RS and RN are also important. A higher
value of RS would make the circuit less sensitive to gain
variations in the amplifier. It may seem contradictory to
design for high RS in a series resonator as the unloaded quality
factor Q0 of the resonator decreases with RS as
߱଴ ‫ܮ‬
ͳ
ൌ
ܴ௦ ߱଴ ‫ܥ‬
ܴ௦
where ω0 is the angular center frequency.
ܳ଴ ൌ
(3)
A detailed look at (3) shows that it is possible to reach high
Q0 simultaneous with relatively high RS under the condition
that the impedance level of the resonator is increased
accordingly, i.e. increasing L and reducing C. However, RS
cannot be scaled arbitrarily for two reasons. Firstly, a too high
RS would result in a loadline not maximizing the power swing.
Further, it is not practically possible to scale the impedance
level to maintain high Q0 for very high RS. In MMIC
technology, a reasonable RS is about 10 Ω which results in
Γin
Ζin
λ/4−
Open stub
Γin
Ζin
good coupling factor to an amplifier with a gain about 5-10
dB, corresponding to RS =-14 to -26 Ÿ.
The challenge is to find a resonator topology providing the
desired impedance level with a simultaneously high Q-factor.
The first and most obvious choice is a lumped-element series
resonator and another choice is an open quarter-wave (λ/4)
microstrip resonator. Since, lumped-element inductors in
MMIC technology are based on microstrips, the quality factor
and impedance of a microstrip resonator is considered first,
(a). With some approximations the series resistance of a λ/4
resonator can be expressed
ܴௌ ൎ
ܿ଴
ߨߤ଴
ඨ
Ͷܹ ߪߝ௥ ݂
where c0, is the free space velocity of, εr relative permittivity,
μ0 permeability of free space, σ metal conductivity, f the
frequency and W the width of the microstrip line. According
to (4) the strip width has to be reduced below 5μm in order to
reach reasonable RS which would also result in poor Q-factor.
As an open stub cannot reach RS high enough with decent Q0,
the same applies to a lumped series LC resonator.
Instead resonators for reflection-type oscillators are often
implemented with some kind of impedance transformation,
e.g., the coupled-line half-wave resonator shown in (b). This
type of resonator can easily achieve the right impedance level
with reasonable Q factor and be adjusted by the coupling
factor that is controlled with separation of the lines in the
coupler. A drawback although is relatively large dimensions
for the λ/2 long wide strips required in the on-chip coupler.
Instead, the oscillator in this work is based on a lumped
parallel resonator that is transformed to a series resonator
through a high-impedance λ/4 line, (c). The component values
of the transformed parallel resonator can be expressed
ܼ஼ଶ
(5)
ܴ௦ ߱଴ ܳ
ܴ௦ ܳ
‫ܥ‬ൌ ଶ
(6)
ܼ஼ ߱଴
where RS is the desired effective series resistance and Zc is the
characteristic impedance of the λ/4 transformer.
‫ܮ‬ൌ
Parallel
resonator
Coupler
λ/2−
resonator
(4)
Γin
Ζin
λ/4−
transformer
Microstrip
piece
(a)
(b)
(c)
Fig. 2 Three resonator topologies (a) Quarter-wave line resonator. (b) Coupled-line half-wave resonator. (c) Quasi-lumped
transformed parallel resonator.
III. DESIGN
A reflection type oscillator, demonstrating the concept of
the quasi-lumped resonator, is implemented in a 0.25 um GaN
HEMT process from Triquint. Fig. 3(a) and Fig. 3(b),
respectively show chip photo and schematic of the designed
amplifier with the resonator indicated. The reflection amplifier
is built with a 400 um (8x50 um) gate periphery. The source is
grounded through an inductor with a small resistance (15 Ÿ),
in parallel with a capacitor for increased gain. The source
resistance is mostly used for bias stabilization. On the drain
side, an inductive termination is used, creating a reflective
gain on the gate side, where the resonator is placed. The
resonator has Q0=38 and Rs=10Ω, extracted from EM
simulations in ADS Momentum.
Vgg
λ/4−
transmission
line
Vdd
50Ω
Stab
resistor
Osc
Output
(a)
Zterm
Source
feedback
(b)
Fig. 3. a) Chip photo of the oscillator, size 2.0x1.0 mm and b)
Schematic.
The measured reflection gain of the amplifier is ห߁௔௠௣ ห ൌ
ͷ†, corresponding to ܴே ൌ െͳͶȳ at serial resonance.
Thus, the coupling factor is ߚ ൌ ܴ௦ Τȁܴே ȁ ൌ ͲǤ͹ǡ which is
slightly different from the ideal theoretical coupling ߚ ൌ ͳΤʹ
[9]. To suppress unwanted resonances out-of-band, a 50 Ÿ
load is added in parallel with the resonator. The 50 Ÿ load has
negligible influence at the fundamental oscillation frequency.
IV. RESULTS
The MMIC oscillator was measured with an FSUP-50
signal source analyzer from Rohde Schwarz. The oscillation
frequency is varying from 15.01 GHz to 15.12 GHz over the
measured bias range, mostly dependent on Vd. The output
power is coupled out from the resonator by a small capacitor
of 0.5 pF, and is varying from -10dBm to +2dBm for all swept
bias points.
Measured phase noise is shown in Fig. 4. Fig. 4(a) shows
phase noise versus offset frequency for various bias points
and. Fig. 4(b) shows a contour plot of 100 kHz phase noise as
a function of Vg and Vd.
(a)
(b)
Fig. 4 Measured phase noise [dBc/Hz] alternatively, (a) Versus offset
frequency. Guide lines for -30dB/dec resp -20dB/dec are added. (b)
offset 100 kHz.
It is seen from Fig. 4 that the minimum phase noise is -106
dBc/Hz and -133dBc/Hz, respectively at 100 kHz and 1 MHz
offsets, both achieved at low Vd/Vg. For increased Vd/Vg, phase
noise increases due to higher amount of flicker-noise that is
up-converted to phase noise. Increasing RF-power in resonator
by increasing bias is not beneficial at this low offset
frequency. The designed oscillator is very power efficient with
a power normalized figure of merit (FOM) [10] of 191 dB and
198 dB, respectively measured at 100 kHz and 1 MHz offset
frequencies. TABLE I presents a comparison versus other
GaN HEMT oscillators reported in open literature. There are
some oscillators with comparable phase noise, [7], [11], but
the power normalized figure of merit is better for the oscillator
reported in this work. In fact the FOM reached in this work is
higher than for any MMIC oscillator based on a GaN HEMT
device. The 1MHz FOM is also better than for any CMOS
oscillator and most InGaP HBT [5] [6] oscillators published.
TABLE I
COMPARISON TO STATE OF THE ART GAN HEMT BASED OSCILLATORS
Freq Power Pout Phase noise FOM* Phase noise FOM*
(GHz) (mW)/ (dBm) (dBc/Hz @100k (dBc/Hz @1MHz
@100k)
Vdc(V)
@1MHz)
Ref
1.95
400/4
19
-119
179
-149
189
[7]
7.9
1456/28
21
-112
178
-135
181
[11]
9.1
600/15
6
-101
172
-130
181
[12]
9.556 10625/30 32.3
-87
146
-115
154
[13]
9.9
600/10
17
-105
177
-135#
187
[14]
9.92
180/6
-6
-109
186
-136
193
[7]
15.05
63/3
-6
-106
191
-133
198
This
work
*
FOM=-L(fm)+20log10(f0/fm)-10log10(Pdc) where L(fm) is the phase noise at
offset frequency. 100kHz resp. 1MHz offset are used in the calculation, f0 is
the oscillation frequency, Pdc is the DC power measured in mW,[10]. #phase
noise scaled to 1MHz offset by 30dB/decade.
V. CONCLUSIONS
A low phase noise power-efficient GaN HEMT MMIC
oscillator based on a quasi-lumped MMIC resonator is
reported. The quasi-lumped resonator topology, incorporating
a parallel LC resonator and a piece of microstrip, offers good
flexibility in impedance level with good Q factor, which is
important in order to match the resonator and the active device
in reflection type oscillators. The prototype oscillator based on
the proposed resonator demonstrates an excellent phase noise
of -106 dBc/Hz at 100 kHz offset from a 15 GHz carrier
frequency.
[4]
[5]
[6]
[7]
[8]
[9]
ACKNOWLEDGMENT
This work was supported by the GigaHertz Center in a joint
research project financed by the Swedish Governmental
Agency of Innovation Systems (VINNOVA), Chalmers
University of Technology, Ruag Space AB, and Ericsson AB.
[10]
REFERENCES
[12]
[1]
[2]
[3]
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Zirath, "Calculation of the Performance of Communication
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D. Kuylenstierna, S. Lai, B. Mingquan, and H. Zirath, "Design of
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spectrum," Proc. IEEE, vol. 54, pp. 329-330, Feb 1966.
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Tombeur, et al., "A 3.5 mW 2.5 GHz diversity receiver and a 1.2
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Thompson, T. R. Prunty, et al., "High-power monolithic
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low frequency noise device characterization and large signal
modeling to circuit design," in IEEE MTT-S Int. Dig,, Jun. 11–16,
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pp.
747-750.
Paper D
Low Frequency Noise Measurements - A Technology Benchmark
with Target on Oscillator Applications
T. N. T. Do, M. Hörberg, S. Lai, D. Kuylenstierna
44th European Microwave Conference Proceedings, 5-10 Oct. 2014,
Rome, Italy, 2014 pp. 468-471.
Low Frequency Noise Measurements - A Technology
Benchmark with Target on Oscillator Applications
Thanh Ngoc Thi Do, Mikael Hörberg, Szhau Lai, Dan Kuylenstierna
Microwave Electronics Laboratory, Department of Microtechnology and Nanoscience
Chalmers University of Technology
Gothenburg, Sweden
tngoc@chalmers.se
Abstract—This paper presents low frequency noise (LFN)
measurements of some commonly used microwave transistor
technologies, e.g., GaAs-InGaP HBT, GaAs pHEMT, and GaN
HEMT. It investigates how the flicker noise scales with current
and voltage in the different technologies. The target application is
low-phase noise oscillators. From this perspective, low-frequency
noise at given frequency normalized to DC power is used as benchmark parameter. A comparison between different measurement
set-ups is also included. The problem of measuring low-frequency
noise at high drain voltages and currents is considered. It is found
that the flicker noise of GaN HEMT technology is in about the
same level as of GaAs pHEMT, but when normalized with the DC
power, GaN HEMT offers a better performance. For this reason,
GaN HEMT is considered to have better potential in oscillator
applications. Concerning InGaP HBT, when measured at 10 kHz
it provides better performance in term of both absolute noise level
and normalized values. Higher frequencies are in favor for GaN
HEMT technology.
Keywords—Low frequency noise, flicker noise, baseband noise,
oscillators
I.
INTRODUCTION
Flicker noise is a physical property of all active electronic
components [1]. It has large impact on circuits like power
detectors, oscillators, and baseband low-noise amplifiers.
Although the exact origin of flicker noise is unclear, the level is
known to differ between technologies. It is well known that the
levels of flicker noise are lower in bipolar junction transistors
(BJTs) compared to field-effect transistor (FETs). It is also clear
that the levels depend on the semiconductor lattice quality. The
level is generally higher in a material with more defects. Further,
in a material with high density of defects, the low-frequency
noise has less clear 1/f slope. Defects act as generationrecombination (G-R) centers resulting in a Lorentzian type of
noise [2]. It has also been shown that the level and characteristics
of the flicker noise is related to device reliability [3].
Hence, there are several reasons to study the flicker noise.
The purpose of this paper is to benchmark different technologies
for oscillator applications. In an oscillator, the flicker noise is
up-converted to phase noise around the microwave signal [4].
Therefore, LFN measurement is very important for the
characterization of devices. In this perspective, a device with
low flicker noise should be used. On the other hand, the phase
noise is directly proportional to signal-to-noise ratio [5], which
favors devices that can deliver high power. To weight both
flicker noise and power, this paper benchmarks devices versus
low-frequency noise, measured at a certain frequency,
e.g.10kHz and normalized with DC power. Three different
technologies InGaP HBT, GaAs pHEMT, and GaN HEMT are
compared in this paper.
II.
MEASUREMENT SETUP
The LFN measurements of devices in this paper are based on
two different setups.
A. Current-Voltage Amplifier based setup
This LFN measurement setup, called setup A and proposed
by Franz Sischka, Agilent Technologies [6], uses a current to
voltage preamplifier from Standford Research (SR570). An
internal voltage supply of the SR570 is used for collector/drain
biasing while the base current/gate voltage is biased through a
parameter analyzer for accurate current /voltage control and a
1Hz low-pass filter for the noise leakage elimination. A dual
channel dynamic signal analyzer (DSA) is used for FFT
calculation. Due to limitations of the DSA, the LFN
measurement range is limited from 1 Hz to 105.7 kHz. Thanks
to the good noise floor achieved with internal bias from the
SR570, this setup is perfect for LFN measurement of low noise
devices, e.g. HBTs, at low current/voltage biasing.
Fig. 1. Franz Sischka’s setup with external bias tee.
A limitation is that the internal voltage supply of the SR570
cannot support a voltage larger than 4V and a current larger than
6 mA. To improve the voltage/current handling capability, an
external bias tee is added, as shown in Fig.1. The additional bias
tee has a cut-off frequency of 3 Hz, leading to a discontinuity in
the LFN spectrum. Further, the big electrolyte capacitors used in
the bias tee are noisy which limits the noise floor. Besides being
noisy, the big capacitors also require long time for
charging/discharging at every collector/drain bias point. The
long time constants leads to difficulties in automatic control of
the setup.
B. Voltage-Voltage Amplifier based setup
An alternative to set up A completed with external bias tee is
to use a voltage to voltage preamplifier from Stanford Research
(SR560). Fig. 2 shows such a set-up based on the SR560, we
call this set-up B. An internal voltage supply of the SR570 is
used for gate biasing. At the drain side, the SR 560 is connected
to the device and the drain voltage is biased from a parameter
analyzer through a constant load resistor RL of 110Ω. The DC
I-V measurement is done before the LFN measurement to
calculate the compensation for the voltage drop across RL. In
every measurement, the channel resistance Rds also needs to be
determined from the measured I-V curve (Rds = ∆V/∆I). Finally,
the measured drain noise current is calculated by normalizing
the measured drain noise voltage (which is performed in DSA
and multiplied to the sensitivity of the SR560) to the parallel
combination of resistances of Rds and RL. This method also
allows LFN measurement at the gate side. The accuracy of this
method is very good in the forward-active region of the IV
curve where RL is dominating resistance over Rds. Our
experiments are carried out for a minimum measured drain
voltage of 2V for GaN HEMTs and 0.5V for GaAs pHEMT.
All measurements are controlled automatically by Matlab.
measure LFN below this level the parameter analyzer can be
replaced by a battery, but then it is difficult to control the bias
automatically. Despite having a noise floor limited by the
parameter analyzer, setup B is still preferred for measurements
of devices having 1/f noise levels higher than the noise floor of
the parameter analyzer.
Fig.3. LFN measurements of 4x125μm pHEMT device versus the frequency
with different measurement methods at Vd=3V, Vg=-1.2V and Id=0.04 mA.
III.
MEASUREMENT RESULTS AND DISCUSSION
In this part, the LFN results of some commonly used MMIC
transistor technologies are presented, e.g., GaAs-InGaP HBT,
GaAs pHEMT, and GaN HEMT. GaAs InGaP HBTs require a
low noise floor and are measured with set-up A, while GaAs
pHEMT and GaN HEMTs are measured with setup B. Figs. 4-6
show chosen LFN spectra of InGaP HBTs, GaAs pHEMT and
GaN HEMTs, respectively. Data from all measured devices are
summarized in Table I.
Fig. 2. LFN measurement setup based on voltage-voltage amplifier (SR560).
C. Setup Verification
The two set-ups are verified based on a 4x125μm GaAs
pHEMT with 220nm gate length. Its LFN is measured with the
different measurement setups (setup A, setup B and setup B
complemented with battery) for both low current biasing and
high current biasing. The results agree very well at high current
biasing. However, at low current biasing setup B is limited by
the noise floor of the parameter analyzer as seen in Fig.3. To
Fig.4. LFN measurements of 4x20μm GaAs-InGaP HBT device versus the
frequency at Vcc=3V and different base current biases.
Fig. 4 shows LFN spectrum of a 4x20μm GaAs-InGaP HBT
with a collector voltage Vcc=3V and a base current biased from
20µA to 60µA, corresponding to a collector current of 3mA to
9mA. LFN increases with collector current and saturates when
the device is saturated. It is also found that an increase of
collector voltage will increase LFN although less pronounced
than the current.
Fig. 5 shows LFN spectrum of a 150nm GaAs pHEMT
device with 80µm gate-periphery. It is found that the level of
noise is higher compared to InGaP HBT, and the shape of the
noise is very near the ideal 1/f which indicates the crystal quality
of the material is good with low density of localized traps which
would result in Lorentzian GR-type noise [2]. GaAs pHEMT
devices with 100nm gate-length have also been measured, their
spectrum is similar to the 150nm gate-length devices but the
level of noise is higher. An assumption is that the higher noise
in devices with shorter gate-length is due to more defects along
the gate.
1/fγ. Some previous works have shown that the slope of GaN
HEMT, γ, varies from 1 to 1.3 [7]. Our experiment shows an
even deeper slope, from 1.3 to 1.5. For Vgs>-2.2V, a Lorentzian
can also be spotted which is a sign of GR-type noise that can be
related to defects acting as traps. >1 and GR-noise is likely a
sign of non-perfect crystal quality. As crystal quality improves,
it is expected that the GR noise disappears and the slope of
flicker noise approaches unity.
Table I and Figs. 4-6 clearly verifies the well-known fact that
bipolar devices have lower flicker noise compared to fieldeffect-transistors. Although there are differences between the
different samples it is clearly seen that GaAs pHEMT and GaN
HEMT devices have noise in the same order of magnitude, while
the noise of InGaP HBTs is considerably lower. However, the
measurements of different devices are taken for quite different
bias points. In a fair comparison, the measured noise level
should be normalized versus power. With focus on oscillator
applications, we may initiate from Leeson’s equation [5] in
which the oscillator’s single-side-band phase noise spectrum is
defined as follows [4].
∆
10
.
1
∆
1
∆
/
(1)
∆
where f0 is the output frequency, Δf is the offset from the output
frequency, F is the noise factor, k is Boltzmann’s constant, Q is
the loaded quality factor, Ps is the power swing over the
resonator, and Δf1/f3 is the 1/f3 corner frequency.
Fig.5. LFN measurements of a 4x20μm pHEMT with 150nm gate length versus
the frequency at Vd =3V and different gate bias points. Right up corner is the DC
I-V characteristic of the device.
Equation (1) shows that in the 1/f3 region, oscillator phase
noise is proportional to (flicker noise)/Ps [5]. Assuming a
constant conversion efficiency, a fair benchmark for oscillator
applications is LFN/Pdc, where Pdc=Vd*Id. Table I shows that
when LFN is normalized with dc power, GaN HEMT has a
better performance compared to GaAs pHEMT. For example, at
10 kHz the best GaN HEMT device demonstrates a benchmark
parameter approximately five times better than the best GaAs
pHEMT one, corresponding to an improvement of 7dB in the
phase noise. At 100 kHz, the best GaN HEMT device has better
flicker noise normalized power than the InGaP HBTs measured
in this study.
-15
Fig.6. LFN measurements of a 2x75μm GaN HEMT with 250nm gate length
versus the frequency at Vd =10V and different gate bias points. Right up corner
is the DC I-V characteristic of the device.
Several GaN HEMT devices from different processes such
as UMS, TRIQUINT, and Chalmers have also been measured.
These devices all have different gate widths and number of
fingers. For GaN HEMT devices, the drain voltages are held
constant at 2V, 6V and 10V while the gate bias is swept. A
typical LFN spectrum of a 2x75μm GaN HEMT with 250nm
gate length at 10V drain voltage is shown in Fig.6. It is observed
that the slope is somewhat steeper than 1/f. It can be written as
Drain noise current@10kHz/(Id*Vd) (A/Hz.V)
1.2
x 10
GaN HEMT 2x50um
GaN HEMT 4x50um
1
GaN HEMT 8x50um
0.8
0.6
0.4
0.2
0
-3.8
-3.6
-3.4
-3.2
-3
-2.8
-2.6
Vg (V)
Fig.7. Benchmark parameters at 10 kHz of 250nm GaN HEMT devices with
different sizes versus the gate bias points
It should be mentioned that the measurements listed in Table
I are taken in the forward active region, where the flicker noise
normalized versus power has its lowest value. Fig. 7 shows
LFN(10 kHz)/Pdc versus gate voltage for 250nm GaN HEMT
devices with different gate-periphery length. The flicker noise
increases with current until the device is saturated. For low Vgs,
large devices have better performance, while for larger currents,
there is no distinct difference in performance between devices
with different gate periphery length.
IV.
in particular if phase noise at large off-set frequencies is of
concern.
REFERENCES
[1]
[2]
CONCLUSION
Low-frequency noise of GaAs-InGaP HBTs, GaAs pHEMT
and GaN HEMT devices have been compared. The work is
carried out with target on oscillator applications. From this
aspect, LFN at given frequency scaled with DC power is a
relevant benchmark parameter according to Leeson’s equation.
It is found that the best performance in terms of absolute flicker
noise levels is obtained for GaAs-InGaP HBTs. However, at
larger frequencies where shot noise may limit HBTs, GaN
HEMTs have potential for better performance. Thus for
oscillator design, GaN HEMT may be an attractive technology,
[3]
[4]
[5]
[6]
[7]
F. N. Hooge, “1/f Noise Sources”, IEEE Trans. Electron Devices, vol. 41,
no. 11, pp. 1926-1935, Nov.1994.
S. Rumyantsev, M. E. Levinshtein, R. Gaska, M. S. Shur, A. Khan, J. W.
Yang, G. Simin, A. Ping, T. Adesida, “Low 1/f Noise in AlGaN/GaN
HFETs on SiC Subtrates”, in Proc. 3rd International Conference on Nitride
Semiconductors (ICNS3), vol.176, Montpellier, France, July 1999,
phys.stat.sol. (a), pp. 201-204.
S. Mohammadi, D. Pavlidis, B. Bayraktaroglu, “Relation Between LowFrequency Noise and Long-Term Reliability of Single AlGaAs/GaAs
Power HBT’s”, IEEE Trans. Electron Devices, Vol. 47, No.4, pp. 677686, April 2000.
A. Hajimiri, T. Lee, “The Design of Low Noise Oscillators”, Boston:
Kluwer Acedemic Publishers, 1999.
D. B. Leeson, “A simple model of feedback oscillator noise spectrum”, in
Proceedings of the IEEE 54(2), pp. 329-330, 1996.
F. Sischka, “1/f noise measurements and modeling”, Agilent
Technologies Company, 2002.
C. Sanabria, “Noise of AlGaN/GaN HEMTs and Oscillators”, PhD
dissertation, University of California Santa Barbara, pp. 102, June 2006.
TABLE I.
COMPARISON OF BENCHMARK PARAMETERS OF DIFFERENT DEVICES
@
Vd (V)
LFN@1kHz
(A2/Hz)
@
.
(A/Hz.V)
LFN@10kHz
(A2/Hz)
.
(A/Hz.V)
LFN@100kHz
(A2/Hz)
.
(A/Hz.V)
19.252
10
4.26E-16
2.2143E-15
2.41E-17
1.253E-16
1.76E-18
9.1315E-18
1.3
27.376
10
2.27E-16
8.3065E-16
3.26E-17
1.19E-16
2.67E-18
9.7604E-18
250
1.3
20.037
10
6.75E-16
3.3678E-15
2.56E-17
1.275E-16
8.63E-19
4.305E-18
4x50
250
1.3
38.964
10
1.53E-15
3.9216E-15
6.66E-17
1.71E-16
1.75E-18
4.4965E-18
GaN HEMT 5
8x50
250
1.3
81.034
10
3.10E-15
3.828E-15
1.45E-16
1.784E-16
3.48E-18
4.2957E-18
GaN HEMT 6
4x50
250
1.5
4.732
10
4.50E-16
9.5139E-15
1.71E-17
3.618E-16
1.43E-19
3.0283E-18
GaN HEMT 7
8x50
250
1.5
52.604
10
2.79E-15
5.3114E-15
6.66E-17
1.265E-16
6.55E-19
1.2446E-18
InGaP HBT 1
4x20
1000
1.2
9
3
7.00E-18
3.8889E-16
5.30E-19
1.963E-17
1.10E-19
4.074E-18
InGaP HBT 2
2x20
1000
1.2
9
3
4.095E-18
1.5167E-16
4.538E-19
1.681E-17
1.324E-19
4.904E-18
GaAs pHEMT 1
2x20
150
1
12.611
3
1.42E-16
3.7507E-15
3.00E-17
7.924E-16
2.59E-18
6.8512E-17
GaAs pHEMT 2
4x20
150
1
24.833
3
1.87E-16
2.5101E-15
4.40E-17
5.911E-16
4.98E-18
6.682E-17
GaAs pHEMT 3
2x20
100
1
5.547
3
1.43E-16
8.6113E-15
2.00E-17
1.199E-15
2.64E-18
1.5852E-16
GaAs pHEMT 4
4x20
100
1
11.251
3
1.81E-16
5.3536E-15
3.35E-17
9.919E-16
3.85E-18
1.1412E-16
GaAs pHEMT 5
2x40
100
1
11.491
3
1.83E-16
5.3201E-15
2.76E-17
8.015E-16
4.06E-18
1.1786E-16
GaAs pHEMT 6
4x40
100
1
24.883
3
2.65E-16
3.5499E-15
3.88E-17
5.191E-16
4.71E-18
6.3055E-17
Device
Size
(μm)
Lg/We
(nm)
ɣ
Id (mA)
GaN HEMT 1
2x75
250
1.5
GaN HEMT 2
4x75
250
GaN HEMT 3
2x50
GaN HEMT 4
@