Terahertz Source and Imager
MASCHUSETTS INSTITUTESSOF TECHNOLOGY
OCT 26 2017
ARCHIVES Submitted to the Department of Electrical Engineering and Computer
Science in partial fulfillment of the requirements for the degree of
Master of Science in Electrical Engineering and Computer Science
at the
A uthor ... ................. Department of Electrical Engineering and Computer Science
August 23, 2017
Assistant Professor of Electrical Engineering and Computer Science Thesis Supervisor
Accepted by....... Signature redacted ' / UU Leslie A. Kolodziejski
Professor of Electrical Engineering and Computer Science Chair, Department Committee on Graduate Students
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Source and Imager
Zhi Hu
Submitted to the Department of Electrical Engineering and Computer Science on August 23, 2017, in partial fulfillment of the
requirements for the degree of Master of Science in Electrical Engineering and Computer Science
Abstract
In this thesis, two chip designs using the scalable array architecture are introduced. Firstly, we introduce a scalable architecture of coherent harmonic oscillator array for high-power and collimated radiation beam at mid-THz band. The array is 2D- coupled, and each element achieves these functions: (i) maximize oscillation at funda- mental frequency fo= 2 50 GHz; (ii) synchronize phase of fo and its harmonics among elements; (iii) cancel near-field radiation of fo, 2fo and 3fo, and (iv) efficiently radiate at 4fo and combine power in free space. The resultant compact design fits into the optimal radiator pitch of A/2 (half wavelength) for side-lobe suppression and enables high density implementation of THz arrays. An array prototype of 42 coherent radi- ators, or 91 resonant antennas, at 1 THz is also presented using IHP S13G2 130-nm SiGe process. The chip occupies 1-mm 2 area and consumes 1.1 W of DC power. The measured total radiated power and effective isotropically-radiated power (EIRP) are 80 pW and 13 dBm, respectively. Secondly, we introduce a scalable architecture of coherent receiver array for beam-steerable imaging. The array is also 2D-coupled, and each element achieves theses functions: (i) maximize oscillation at fo=120 GHz; (ii) synchronize phase of fo and its harmonics among elements; (iii) cancel radiation of fo and 2fo; and (iv) receive and down-convert RF signal near 2fo=240 GHz and output baseband signal for digital beam-forming. Chip is fabricated using TSMC 65nm LP CMOS technology.
Thesis Supervisor: Ruonan Han Title: Assistant Professor of Electrical Engineering and Computer Science
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Acknowledgments
I'd like to thank Prof. Ruonan Han for his strong support and very effective guidance
throughout the past two years, especially during tough times. Also, I'd like to thank
my fellow labmates for many constructive discussions. Finally, I'd like to thank my
parents for their continuous encouragement and wholehearted support.
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Contents
2.1 Overview of the Array Architecture . . . . . . . . . . . . . . . . . . . 24
2.2 Design of 1-THz Oscillator . . . . . . . . . . . . . . . . . . . . . . . . 26
2.2.1 250-GHz Oscillator Core . . . . . . . . . . . . . . . . . . . . . 26
2.2.2 Branched Resonator . . . . . . . . . . . . . . . . . . . . . . . 29
2.2.3 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . 30
2.3.1 Inter-Element Frequency/Phase Synchronization . . . . . . . . 32
2.3.2 Quantitative analysis of transmission-line-based coupling . . . 35
2.3.3 Selective 4fo radiation using branched resonator . . . . . . . . 41
2.3.4 Routing of DC bias . . . . . . . . . . . . . . . . . . . . . . . . 44
2.3.5 Boundary of the entire array . . . . . . . . . . . . . . . . . . . 44
2.4 Prototype and Experimental Results . . . . . . . . . . . . . . . . . . 49
2.4.1 Measurement of the Oscillation/Output Frequencies . . . . . . 49
2.4.2 Characterizations of the 1-THz Radiation . . . . . . . . . . . 52
3 240-GHz 16-Element Heterodyne Imager 57
3.1 Array Architecture . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
3.2.1 Design of Standalone 120-GHz Oscillator . . . . . . . . . . . . 67
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3.3 Design of PLL . . . . . . . . . . . . . . . . . . . . . .
List of Figures
2-1 Comparison of output power and architecture of sub- and mid-THz
radiators from some representative works [10][11][9][14][13][6][5][8][7]. 20
2-2 Estimation of number of coherent radiators integrated on a 10mm2
area and the corresponding beam width across the spectrum from RF
to visible light. Works shown are [15][9][10][16]. . . . . . . . . . . . . 21
2-3 (a) Conventional 4th-harmonic oscillator and (b) the compact 4h -harmonic
oscillator presented in this paper using a multi-functional electromag-
netic structure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2-4 A 3x3-element array: (a) basic conceptual diagram, and (b) physical
implementation, including the DC bias connections. . . . . . . . . . . 25
2-5 Structure of a single element. Left inset shows the 1-THz oscillator, and
the right inset shows the branched resonator. For clarity, the signal
trace of microstrip, which in the actual layout is implemented using
stacked metal 2-4 (as is illustrated in the upper half figure) is drawn in
the left inset to be above the ground plane, which in the actual layout
is implemented using top-metal 1. . . . . . . . . . . . . . . . . . . . . 27
2-6 Transformation of the half-circuit equivalent of Fig. 2-5b to a standard
self-feeding oscillator topology (in which ZG=oo). . . . . . . . . . . . 28
2-7 HFSS simulation of resonance tank impedance looking into two collector-
slotline interfaces. In (a) excitations are out-of-phase, and in (b) exci-
tations are in-phase. . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
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2-8 Array forming from a single element. Field distribution of fo is shown
in 1 x 1, 1 x 2, and 2 x 1 case to show coupling between horizontal and
vertical elements. Field distribution of 4fo is shown in 2 x 2 case to
demonstrate coherent radiation as the result of coupling. . . . . . . . 32
2-9 Simulated waveforms of two coupled synchronized elements oscillating:
(a) V and V3, and (b) V and V4 in Fig. 2-8(b). . . . . . . . . . . . . 34
2-10 Model of injection locking that is resulted from injected current gener-
ated by differential-mode voltages between two partially coupled res-
onators. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
2-11 Simulation of AO and AA/Ao as the result of coupling two 250-GHz
self-feeding oscillators using network in the model: (a) fix o = 22.50
and Aw = 1.5 GHz, change Zo; (b) fix Zo = 60Q and Aw = 1.5 GHz, change p; (c) fix Zo = 60Q and p = 22.50, change w. . . . . . . . . 40
2-12 Theoretical E-field distributions in branched resonator at different har-
monics: (a) fo, (b) 2fo, (c) 3 fo, and (d) 4fo. The darker the arrow
color, the higher the field intensity. . . . . . . . . . . . . . . . . . . . 42
2-13 HFSS simulation of magnitude and phase of E-field vector in dielectrics
at different harmonics: (a) fo, (b) 2fo, (c) 3fo, and (d) 4fo. Input power
at all frequencies are normalized to be the same. . . . . . . . . . . . . 45
2-14 HFSS simulation of antenna gain of a single element at (a) fo, (b) 2fo, (c) 3fo, and (d) 4 fo. Note that only at 4fo is peak antenna gain positive. 46
2-15 Structure of DC-floating AC short implemented with two MIM capac-
itors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 6
2-16 Structure of the upper-left boundary of the entire array along including
notch filters. The structure is repeated for each row, except that DC
pads are connected to different biases depending on routing. . . . . . 47
2-17 Structure of the upper-left boundary of the entire array along with
impedance analysis of filter networks. . . . . . . . . . . . . . . . . . . 48
2-18 Die photo of the chip and zoomed-in image of a single element. ..... 49
2-19 Setup of measuring fo frequency using even-harmonic mixer. . . . . . 50
2-20 Measurement results of leaked fo radiation: (a) IF spectrum, and (b)
frequency and relative power at different VB bias . . . . . . . . . . . . 51
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2-21 Setup of measuring radiated 1 THz power using zero-bias diode. . . 52
2-22 Measured radiation pattern of 1-THz signal: (a) E-plane, (b) H-plane. 53
2-23 Setup of measuring total radiated RF power using Thomas-Keating
(TK) photo-acoustic powermeter. . . . . . . . . . . . . . . . . . . . . 55
2-24 Measured total radiated RF power when chip is power-on, then power-
off, then power-on again. . . . . . . . . . . . . . . . . . . . . . . . . . 55
3-1 Active terahertz imaging systems with different types of receivers: (a)
single-pixel receiver, (b) multi-pixel incoherent receiver, and (c) multi-
pixel coherent receiver. . . . . . . . . . . . . . . . . . . . . . . . . . . 58
3-2 Block diagram of the architecture of the proposed heterodyne coherent
receiver array. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
3-5 E-Field distribution of fo wave in slotlines. . . . . . . . . . . . . . . . 70
3-6 E-Field distribution of 2fo wave in slotlines. . . . . . . . . . . . . . . 71
3-7 Block diagram of the architecture of the proposed heterodyne coherent
receiver array. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
3-8 Block diagram of the architecture of the proposed heterodyne coherent
receiver array. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
List of Tables
2.1 Table I. Comparison of Mid-THz Coherent Radiators in Silicon . . . . 54
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1.1 Motivation
Terahertz spectrum is the least explored spectrum for on-chip electronics since at
such high frequency almost all silicon-based on-chip devices are unable to operate
efficiently. However, due to the potential advantages of terahertz waves in applications
like spectroscopy and imaging (both will be introduced with more details in later
chapters) thanks to small wavelength, researchers have been working on improving
the power generation efficiency of transmitter and sensitivity of receiver.
However, many of the researchers focus on optimizing standalone oscillator and
mixer design, without systematically exploring the architecture of coherent array.
Note that, for transmitter, coherency in the array makes total radiated power from
coupled oscillators be proportional to the number of array elements N2 , instead of
N in the incoherent case. For receiver, coherency makes local oscillation signal for
mixer inside each element to be equi-amplitude and in-phase, so that signal-to-noise
ratio is proportional to N 1, instead of not being a function of N in the incoherent
case, where both signal and noise are combined incoherently.
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1.2 Contribution
Multiple coherent radiating arrays in the sub-THz band have been reported, however,
these arrays are (i) not 2D-scalable and (ii) not designed for operation across a wider
band up to mid-THz. The chip to appear in the thesis, a 1-THz radiating source
in 130nm SiGe technology, is based on an array architecture that fully addresses
the challenges. It features true two-dimensional scalability, strong coupling among
adjacent units, high radiation efficiency, owing to compact yet multi-functional elec-
tromagnetic structure in each unit aimed for scalability. It achieves 13-dBm EIRP
and 80-piW total radiated power-the highest among all Si-based coherent radiators
operating near mid-THz band.
For the receiver, there has yet been no work on THz coherent heterodyne receiver
array reported . In this thesis, we are also going to present our 240 GHz 16-element
coherent heterodyne receiver array. The array also has 2D scalability and strong
coupling scheme of oscillation of adjacent elements. Inside each unit there are two self-
oscillating mixers generating local oscillation (LO) signal , receiving RF signal, and
down-converting them to baseband (IF) signal which are sent out for further digital
processing. Thanks to coherency among LO signals of all elements, both amplitude
and phase information of the received RF signal are preserved in the baseband, so
with amplitude-scaling and phase-shifting at baseband, receiver is able to achieve
beam-steering.
The 240 GHz imager chip to appear in the thesis will tackle the scalability problem
using techniques applied in 1 THz source design, i.e. building scalable units (serve
as pixels) that possess complete functions yet are able to synchronize with oscillation
in adjacent units. No local oscillation network will be needed since each pixel has
self-sustaining oscillation; plus, due to the deterministic phase relationships between
adjacent units resulting from synchronization, digital beam-steering is achievable, which makes the system be the first electronically-scannable terahertz imager.
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1.3 Thesis Organization
In Chapter 2, more background on mid-THz wave generation and our design, simula-
tion and measurement of the 1-THz radiating array will be presented. In Chapter 3,
more background on mid-THz wave generation and our design and simulation of the
240-GHz heterodyne imaging array will be presented.
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42-Element 1-THz Radiating Array
Mid-THz waves (with frequency around 1 THz) possess properties that are critical
to chip-based sensing applications, such as: (i) high-resolution THz imaging [1], (ii) vibrational spectroscopy of large bio-molecules (e.g. DNA) [2], and (iii) sub-Am-
precision vibrometry based on Doppler effect [3]. However, since the frequency lies
well beyond the fmax of all silicon-based transistors, generating high-power radiation
in this band is very challenging, which is clearly reflected in previous publications. In
[4] and [5], using active multipliers based on SiGe heterojunction bipolar transistors
(HBTs), waves at 0.82 THz and 1 TH are generated respectively, with an effective
isotropic radiated power (EIRP) of -37 dBm and -17 dBm respectively. In [6] and [7], using frequency multipliers based on MOS varactors, waves at 0.73 THz and 1.33 THz
are generated with an EIRP of -22 dBm and -13 dBm, and a total radiated power
(Prad) of -21 dBm and -23 dBm, respectively. In [8], using active multipliers and
non-linear feedback loop, 0.92-THz radiation was generated with an EIRP of -1OdBm
and a Prad of -17dBm.
To further increase the radiated power, a multi-antenna/element source with free-
space power combining is preferred. The rule that should be noted when forming an
antenna array is that: to minimize grating lobes in the radiation pattern, spacing
between antennas should be half-wavelength (A/2) in both axes of the array [17].
Therefore, in a given chip area, when the operation frequency is higher, a larger
number of radiators can be implemented which are able to radiate narrower beam [17].
This is summarized in Fig. 2-2. Specifically, at 1 THz, in theory the radiator density
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5 U ISSCC 2015 U / * Coupled Array 0 Non Coupled Array
E o ISSCC 2013 JSSC 2014
E JSSC 2015 (incoherent Sum)
-5- U ISSCC 2012
-15-
-30-,.....,.......,.......,.......,....... 0.2 0.4 0.6 0.8 1.0 1.2 1.4
Frequency (THz) Figure 2-1: Comparison of output power and architecture of sub- and mid-THz radiators from some representative works [10] [11] [9] [14] [13] [6] [5] [8] [7].
can reach ~100/mm2. The resultant high power compensates the high-frequency path
loss while the narrow beam enhances the spatial resolution in imaging and material-
probing applications.
However, large-scale radiator arrays in mid-THz range were not reported previ-
ously (illustrated in Fig. 2-1). The sources in [7] and [8] have two antennas fed by a
single input and a power-splitter; such solution, although offering higher EIRP, does
not increase the total radiated power. In [5], four antennas are placed at the chip
center and fed by four multiplier chains at the chip periphery. All of these config-
urations are not scalable due to their centralized nature: for a large-size array, the
complexity and loss of the signal-distribution network increase significantly. The re-
quired input power level of the multiplier array at low-THz frequency is also too high
to be accessible on chip.
In comparison, coupled coherent harmonic oscillator array is more effective and
has been extensively used in sub-THz radiators [9][10][14]. Due to its self-sustaining
nature and synchronization mechanism using inter-unit mutual coupling (hence a
decentralized scheme), it is expected to have larger potentials in scalability. There
are, however, a few challenges that hindered the implementation of large-scale coupled
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4)
Optical Yagi-Uda Antenna Array
-108 0
-106 0
102
aI
Figure 2-2: Estimation of number of coherent radiators integrated on a 10mm2 area and the corre- sponding beam width across the spectrum from RF to visible light. Works shown are [15] [9] [10] [16].
radiator array previously:
Size of Radiator Unit
For a 1-THz wave in the inter-metal-layer dielectrics of standard chip processes, there
is merely 100 x 100pm 2 (A10 ., /2~100 ym) area for a radiating unit. Meanwhile, each
unit should contain several non-trivial components, such as:
" Harmonic oscillator running at a fraction of the output frequency (fo=N-fot,
N=2, 3, ... ), which requires a large fundamental resonator with a size of
N-Af0,u/4. Since the fmax of mainstream silicon transistors is below 0.5 THz
[26], N is 4 or greater in practice.
* Resonant antenna, which is typically Af,,/2 in length (e.g. dipole and slot
antennas). Other antennas such as patch antenna occupy even larger area,
leaving very little space for other components [14].
" Filters to prevent radiation of undesired low-order harmonics and to recycle
their power for further up-conversion to N-fo. Prior works based on multi-
phase interference at the central power-combining node (Fig. 2-3(a)), however,
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270"@ fo, 180*@ 2fo, 90*@ 3fo, 0*@ 4fo
0. @ fo 180- @ fof,2,3,4 0* @ 2fo 0* @ 2fo 0' @ 3 fo :180* @ 3fo
@4 @ 4fo Resonator (fo), Filter (fo, 2fo, 3fO),
Antenna (4fW)
A/8 @ fo 900@ fo, 1800@ 2fo, 270'@ 3fo, 0*@ 4fo A/2 @ 4fo
(a) (b)
Figure 2-3: (a) Conventional 4th-harmonic oscillator and (b) the compact 4th-harmonic oscillator presented in this paper using a multi-functional electromagnetic structure.
requires N sub-oscillators (hence large area) and leads to long (Af0 . in Fig. 2- 3(a)) and lossy path for the output signal.
* Four frequency/phase couplers to synchronize with neighboring units in all four directions. Previous schemes in THz circuits are based on linear coupling [11] and ring coupling [10], which are unable to scale to large 2D array.
Phase Mismatch in 2D Coupling
The coupling among oscillators is based on injection locking. PVT (process-voltage- temperature) variation of these oscillators leads to different natural oscillation fre- quencies and hence proportionally non-zero phase difference between them at steady state. Quantitatively, for a simplified two-oscillator system with free-running oscilla- tion frequency of wo and wo+Aw, the phase shift AO between the oscillators after a mutual injection locking is governed by Adler's equation at steady state (d9/dt = 0) [18]:
AO = arcsin Q . L-. AC (2.1) (WO linj
where Q is the quality factor of the resonators, I,,, and hir, are the AC currents in the resonator from the oscillator itself and the injection of another oscillator. If Q=10, wo=250 GHz, and IoEc/linj=3, even a small frequency mismatch Lw of 1 GHz
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causes a large AO of 70, which corresponds to a phase mismatch A04f" of 28' for the
4th-harmonic output.
Since the PVT variations in a large array usually follow gradient pattern [20],
gradient of above phase shift could potentially be distributed across the array, which
causes severe tilting of the combined output beam. A stronger coupling scheme, by
which a large lij/Iosc can be generated, is therefore very desirable.
In this chapter, we present a new architecture applicable for large-size coupled
array in mid-THz band - an architecture that is enabled by a highly-compact, multi-
functional radiator structure that addresses all the aforementioned challenges (Fig. 2-
3(b)). A 1-THz 2D radiating array consisting of 6 x 7 coherent units and 91 antennas
is prototyped using IHP 130-nm SiGe HBT process [25]. The measured total radiated
power and EIRP of the chip are 80 pW and 13 dBm (20 mW), respectively.
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2.1 Overview of the Array Architecture
In this section, we present the structure of the array, which is based on a square
slotline mesh architecture. In Fig. 2-4, a 3 x 3-element array (expandable in both
directions) is shown. Each mesh element consists of two radiating units, and each
unit consists of a square ring of slotlines in the top metal layer of the chip. At the
horizontal center of the mesh element, the two radiating units share two slotlines,
which are driven by a 250-GHz oscillator. As is described in details in Section 2.2
and 2.3, once the oscillation starts, the slotlines guide the generated waves to the
upper and lower units, and simultaneously performs the following functions:
" Optimization for the fundamental oscillation at 250 GHz (fo) and harmonic
generation at 4fo
" Coupling and Synchronization for the oscillation among neighboring mesh ele-
ments
* Cancellation of the undesired radiation at fo, 2 fo and 3 fo
* Backside radiation at 4fo (1 THz) through all horizontal slots of the mesh
For strong inter-element coupling, the array elements abut each other (Section 2.3);
in particular, the two horizontal slots of adjacent elements in a column even merge
and form a single slot. As a result, although there are 3 horizontal slot radiators
shown in the mesh element in Fig. 2-4a, there are in fact 2 radiators per element on
average, inside the actual implemented array structure (shown in Fig. 2-4b).
Lastly, it is also important to note that each radiator unit has a size of about
A/2x A/2 at 1 THz (Fig. 2-4a). Therefore, the pitch of the horizontal radiating slots
(acting as dipole slot antennas, see Section 2.3) is the optimal value of Af'.,/2 in both
the horizontal and vertical directions, which meet one of the stringent requirements
of large-scale active arrays outlined previously.
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(b)
Figure 2-4: A 3x3-element array: (a) basic conceptual diagram, and (b) physical implementation, including the DC bias connections.
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2.2 Design of 1-THz Oscillator
In this section, part of our circuit-electromagnetic co-design approach for the radi-
ating mesh element is shown, with the major focus on the principles of fundamental
oscillation at 250 GHz (fo). Although an individual element effectively radiates the
1-THz signal regardless of being in an array or not, most of the operations at 2fo
to 4fo benefit from the interactions of adjacent elements inside an array configura-
tion. Therefore, those details are presented later in Section 2.3, where inter-element
coupling and array formation are also introduced.
The electromagnetic structure of a single mesh element is shown in Fig. 2-5a).
To understand its operations, we need to point out that, our circuit widely adopts
highly-distributed slot structures, where the enclosed electromotive force is non-zero
due to the time-varying magnetic flux, the concept of "ground" can only be defined
locally for each individual distributed structure (e.g. transmission line). In fact, even
if two "local grounds" are physically associated with one piece of metal, they should
not be treated as electrically connected. For that reason, some slot are illustrated as
two-conductor transmission lines (i.e. explicit "ground"), unlike those in conventional
millimeter-wave circuits.
Based on such principle, the equivalent circuit schematic of the oscillator is shown
in Fig. 2-5b, which consists of a pair of branched resonators and a differential oscillator
core.
2.2.1 250-GHz Oscillator Core
The oscillator core is located at the lower radiating unit of each element (Fig. 2-5a). It
can be regarded as two identical oscillators coupled together, with each one composed
of (i) a HBT transistor and a short vertical slotline (TL1) connecting to the emitter,
and (ii) a microstrip line (TL2) connecting TL1 with the transistor base.
First, for differential-mode oscillation, we note that due to symmetry, all electrical-
field vectors in the oscillator structure is perpendicular to a central orthogonal plane
(shown in Fig. 2-5b). This plane is therefore a virtual perfect conductor plane (PEC).
Accordingly, the oscillator can then be analyzed through its half-circuit equivalent,
shown in Fig. 2-6. The PEC and one conductor plane of TL1 form a new slot line
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PEC
A/16
zo
(b)
Figure 2-5: Structure of a single element. Left inset shows the 1-THz oscillator, and the right inset shows the branched resonator. For clarity, the signal trace of microstrip, which in the actual layout is implemented using stacked metal 2-4 (as is illustrated in the upper half figure) is drawn in the left inset to be above the ground plane, which in the actual layout is implemented using top-metal 1.
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Vd
+ E-FlI*d nM ft (Q. *- Ground Curront (f) *--S1gtl Current (h)l
Branched Resonator
a' A I
b ZA/2 ZG ZR ZATL2
Figure 2-6: Transformation of the half-circuit equivalent of Fig. 2-5b to a standard self-feeding oscillator topology (in which ZG=oo).
TLl' that connects Node a and Note b. Since the field distribution of this TL1' is exactly the same as half of that in TL1 (shown in Fig. 2-5a), the relationships of their impedances and electrical lengths are: ZTL1=0. 5 ZTL1 and S0TL1'=STL1, respectively. The triangle opening in the metal plane, essentially a tapered slot resonator, provides a broadband open-circuit termination [21]; and half of this large impedance ZA is presented to the half circuit in Fig. 2-6. The role of this triangle opening is to enclose the slot TL1, while not affecting the wave propagation inside it.
As is shown in Fig. 2-6, a feedback path at fo is created from the collector to the base through TL1' and TL2. In practice, (PTL1 is very short, and ZTL1/ 2 equals to
ZTL2. This is then a self-feeding oscillator originally presented in [10], where the feed- back loop greatly destabilizes the transistor, and enables strong oscillation. Previous works [22] [23] have shown that to maximize the oscillation power of transistor, the complex voltage gain A of the transistor should have a phase of:
LA = z - (Y21 + Y*2), (2.2)
where yij is the element of the transistor Y-parameter matrix. Such condition com- pensates the THz signal delay inside transistor that is caused by the finite transit time and a base-to-collector feedforward current through C,, [10]. To meet the re-
'Although a PEC does not have resistance, these two nodes still cannot be treated as directly connected due to the reason presented in the beginning of this section.
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quirement in (2.2), the total length (PTL1+TL2 of the self-feeding transmission line
should follow [10]:
Y'TL1 + 'PTL2 =arcsin .2R A) (2.3) (ZTL2 - Re (yi, + A - Y12))
It is noteworthy that a complete self-feeding topology also contains a reactive
termination at the base (ZG in Fig. 2-6), which does not exist in our oscillator.
Fortunately, ZG can normally be avoided by choosing the proper (ZTL and 'PTL)
combination. After iterations between linear theory and large-signal simulation, we
use JAj=2.2, ZTL2= 4 0 Q, and OTL2= 3 4 '.
Next, by symmetry, in-phase oscillation may also exist. Fortunately, this undesired
mode is effectively suppressed; because as is shown in Fig. 2-5a, the wave associated
with this excitation mode inside TL1 is not supported. That means there is no
feedback path for such an oscillation [11].
Lastly, given that the collector voltages of the two HBTs at fo are out-of-phase,
the harmonic signal at 2fo and the output signal at 4fo, generated at the collectors,
are in-phase and thus blocked by the slotline TL2 for the same reason. So they do
not travel back to the lossy base of transistors through the oscillation feedback loop.
In other words, generation efficiency of even harmonics is improved.
2.2.2 Branched Resonator
A pair of branched resonators shown in Fig. 2-5a) are used for regulating the oscilla-
tion frequency at 250 GHz. Each resonator is essentially the shunt of two quarter-wave
slot transmission lines with an impedance of ZO and short terminations at their far
ends. We note that when the two branches of the resonator are combined at the
central T-junction, the signal current does not change, but the voltage is doubled;
as a result, the impedance of the combined section of the resonator is 2ZO, in order
to avoid internal wave reflections. In Section 2.3, we will show how this special res-
onator geometry assists the inter-coupling and radiation interference among multiple
elements.
In our design, the slot width of the branched section of the resonator is 4 Pm,
which gives a ZO of 61 Q. Fig. 2-7a shows the simulated impedance when two differ-
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ential excitations are applied to the collector-source ports of HBTs (and without the
presence of TL2), which is approximately:
Zsim ~ (ZR,left + ZR,right) //ZA= 2ZR//ZA, (24)
where ZR and ZA are defined in Fig. 2-6. Such approximation is based on the fact
the vertical slot TL2 between ZR and ZA is very short. For the 250-GHz resonance,
the simulated quality factor is ~17.
2.2.3 Simulation Results
Using the design parameters presented in this section, the DC power consumption of
the oscillator is 25.2 mW from a 1.8-V supply. Meanwhile, the power injected into
the branched resonator at 4fo from the transistors is 3.4 puW. In the next section, we
will show how this 1-THz signal is radiated into the free space.
30
(b)
Figure 2-7: HFSS simulation of resonance tank impedance looking into two collector-slotline inter- faces. In (a) excitations are out-of-phase, and in (b) excitations are in-phase.
31
2.3 Formation of the Large-Scale Radiating Mesh
In this section, we discuss the multi-fold functions of the branched resonators when
forming a large-scale array.
. IAntenna Fh S
I/ [1X1] [1 x2]
CPW Coupling Slotline Coupling
Figure 2-8: Array forming from a single element. Field distribution of fo is shown in 1 x 1, 1 x 2, and 2 x I case to show coupling between horizontal and vertical elements. Field distribution of 4fo is shown in 2 x 2 case to demonstrate coherent radiation as the result of coupling.
2.3.1 Inter-Element ]Frequency/ Phase Synchronization
The details of the evolution from a single element (Fig. 2-5) to a radiating mesh are
shown in Fig. 2-8. Next, we discuss how the inter-element coupling is achieved for fre-
quency/phase synchronization, which happens via the slotlines on all four boundaries
of each element 2.
Horizontal coupling
For two horizontally adjacent elements, their branched resonator slots share the same
outer metal plane. Such a metal plane eventually becomes a narrow metal strip;
meanwhile, a metal bridge is used to enforce the equal-potential condition for the rest
two metal planes of the two slots. This way, the two vertical sections of the branched 2When the phase/frequency of signals at fo from different elements are synchronized, the
phase/frequency at other harmonics are synchronized as well. Therefore, the following discussion focuses on synchronizations at fo.
32
resonators form a standard co-planar waveguide (CPW), in which the electrical fields
of the two slots are oriented to opposite directions (i.e. out-of-phase mode). The
undesired in-phase coupling mode is suppressed. Note that theoretically only standing
waves exist, and that at steady state the collector voltages (see Fig. 2-8) of two
oscillators satisfy the following relationship:
V = -V2 = -V = V4 (2.5)
We also note that the CPW interface (for horizontal coupling) has the same voltage
as the slot of a single element, but twice of the current. Hence, its characteristic
impedance is designed to be half of ZO in Fig. 2-5. Such a adjustment then keep the
operations introduced in Section 2.2 unchanged.
Vertical coupling
For two vertically adjacent elements, their horizontal slots on the top/bottom bound-
aries are directly merged into a single slot (Fig. 2-8). As explained in Fig. 2-5b,
only quasi-TE mode is supported in the merged slot so that the two elements are
only allowed to be coupled in the mode, where the electrical fields associated with
the original horizontal slots of these two elements are oriented to the same direction.
This means the two oscillators are in-phase, and the following relationship holds:
V = -V2 = V = -V4 (2.6)
This is in contrast with the horizontal coupling scheme introduced previously. In
Section 2.3.3, we show that this choice leads to a multi-harmonic interference that
selectively facilitates the radiation at 4fo.
Although by symmetry, the out-of-phase coupling mode of the oscillators also
exists, we note that it is suppressed in reality; because in this mode, the merged slot,
which is unable to support the associated central-symmetric TM wave, presents open-
circuit termination. In this case, each branched resonator becomes a 67.5'open stub
and presents a ~26-fF capacitance to the collector of each oscillator. The oscillation
is therefore unable to start. Lastly, we also note that the merged slot has the same
33
current as the slot of a single element, but twice of the voltage. So the characteristic
impedance of the merged slot is designed to be 2ZO.
As a result of the above coupling schemes, in our simulations for an element in-
side the mesh, the left/right boundaries are regarded as perfect magnetic conductors
(PMC), whereas the top/bottom boundaries are regarded as perfect electrical con-
ductors (PEC). Using ANSYS HFSS, the simulated waveforms as the result of 2D
coupling are shown in Fig. 2-9, which match our previous analysis.
01
0
0
0)
1 2 3 4 5 6 7 8 Time (ps)
--.- 180*0-.
V, (Vertical)
........ ------- V4 (Vertical)
Times (ps, 5 6 7 8
Figure 2-9: Simulated waveforms of two coupled synchronized elements oscillating: (a) V and V3 , and (b) V and V4 in Fig. 2-8(b).
Up to this point, all analyses and simulations are based on the assumption that no
mismatch between oscillators exists. Next, a general model of transmission-line-based
coupling, which assists quantitative analysis of the result of oscillator mismatch, is
given.
34
I
('t bl It03 202IIW V-AVIjtq StAl pg.. I I
S AVl Phasor Visulizatlon of Avand Resultant Ani Av A1 1(exaggerated and not drawn to scale) For re ance
(44) (b)o (dc
Figure 2-10: Model of injection locking that is resulted from injected current generated by differential-mode voltages between two partially coupled resonators.
2.3.2 Quantitative analysis of transmission-line-based cou-
pling
The essence of coupling in our circuit is injection locking, though the injection process
is not explicit, since between oscillators from adjacent elements there is a non-trivial
network consisting of two branched resonators. An essential characteristic shared
by both horizontal and vertical coupling is that the injected current is generated
by voltage difference between collector voltages of two oscillators. To this end, we
propose a model to analysis the strength of injection locking and it is applicable to
both coupling cases, as shown in Fig. 2-10. Here, free-running oscillation in each
oscillator is modeled as a parallel RLC tank being sustained by negative resistance
attributed to transistors. Two oscillators are coupled by a transmission line network
consisting of two 90 'transmission lines shorted at phase W away from the oscillators.
This model characterizes horizontal coupling. Starting from W = 22.50, there
is CPW mode, corresponding to Zeven In the design, 2 Zeven is made close to ZO,
so that common-mode signals experience small reflection. Meanwhile, differential
signals being in two slotlines corresponds to coupled-slotline mode with Zodd. Since
ZOdd < Zeven, they are largely reflected back as meet with short circuit; and when
they meet with an air bridge, they are fully reflected back. In addition, this model
is also suitable for vertical coupling, if slightly modified, as will be shown later. We
firstly analyze this model before applying it to horizontal/vertical coupling.
35
Suppose that the resonance frequency of the tanks of oscillator 1 and oscillator 2
are w, and w2 (Jwi - w 21 < w1) respectively, quality factors are Q ~ Q2 = Q, tank
resistance are Rtank,1 ~ Rtank,2 = Rtank, and that negative resistances provided by
transistors in both oscillators are -Rtank,1 -Rtank,2 = -Rtank. Let voltage across
two tanks be v1 (t) and v2 (t) respectively, expressed as
vi(t) = (Ao + A A) - exp (j(wot + 0o + A6)) ,
v 2 (t) = (Ao - A A) -exp (j(wot + O0 - AO)) ,
(2.7)
(2.8)
where amplitude mismatch AA/AO and phase mismatch AO are assumed to be small.
Without the loss of generality, let 0 = 0. Also, we define common-mode voltage vo
as
V 1 + V2=O 2 =eJwot (A cos AO + jAA sin AO) ~ AO cos AO - e (2.9)
and differential-mode voltage voltage Av as
Av - -eiV - 2 ( AAcos AO+jAosin AO) 2
(zA 2 / = Aosin AO 1+ A 2 ) exp jwot + j arctan
I+(AOtan AO
This network resembles the Wheatstone bridge:
* for vo in each oscillator, connection at p is "invisible" and thus it sees a
90'transmission line.
* for iAy in each oscillator, connection at p is "visible" and it sees a so-length
short-circuit stub, since Av and -Av form a virtual ground at yo.
Therefore, we model each oscillator as an injection-locked system with
iosc,j = (vo t Av)/Rtank w vo/Rtank
iinj,i = ~FAv/(jZo tan so)
(i = 1, 2) (2.11)
36
(2.10)
where s and iiaj,i are defined the same as the model in [18]. Also, here we assume
the loss of the branched resonator is low (see Fig. 2-7(a)). Fig. 2-10 shows the current
decomposition details of oscillator 1. (For oscillator 2, the only difference is that
current is injected in the reverse direction.)
Before proceeding further, we need to obtain the relationship between AO and
AA. This can be done using energy conservation. The power injected into oscillator
1 is
1 - v * _ Im(voAv*) A 2cos AO sin AB Pinj,l = -Re (vo + Av) - ~ . (2.13)
2 (JZ0 tan o 2ZO tan y p 2ZO tan p
It is positive, meaning that oscillator 1 receives power from oscillator 2 via two con-
nected stubs. Pij,, 1 can be calculated in another way. From (2.9)(2.10)(2.13) we see
that the perpendicular-to-vo component of Av, Av_Lv. jAo sin AO - eiwot, generates
the current that is in-phase with vo and thus brings power in; meanwhile, the parallel-
to-vo component of Av, Avlv = AA cos AO - eiwot, reflects the result of adding extra
power APosc,1 on Rtank:
S|Vo + Avi 0 | 2 - ||vo| 2 AOAA cos (1 2 Rtank Rtank
Fig. 2-10 gives qualitative phasor visualization. Note that
APosc,1 = Pinji . (2.15)
2Zotan AA AA( sin A = -R A = k(W)-- - ~ tanA, (2.16)
which can be substituted into (2.10) and get
Av = A0 sinAO "1 + k(W) 2 . exp (jwot + j arctan(k()-1 ))
~ Aok(p) sin AO - exp (jwot + jk(p) 1). (2.17)
Note that k(W) >> 1, i.e. Rtank > Zo tan W, is used in the above approximation. (As
37
a side note, k(o) > 1 also indicates that far more injected current is used to tune
frequency than to inject power.) Under low-level injection, Av < vo, and thus we
can apply the Adler's equation in the case of modulated sinusoid injection [27], i.e.
dOOSC Wi liinj I - dt - - - 2Q z - sin( 0sc - 6Oij), (2.18)
where wi is the resonance frequency of the tank of oscillator 1 or 2. Using (2.9)(2.11)(2.12)(2.17),
we have I iinj,i/iosc,il ~ k(p) 2 - tan AO, Osc = f = (AA/Ao) - tan AO ~ 0, Oinj,1 =
k(W)-'+7r/2 ~/2, 6 inj,2 = k(')-1 -r/2 -7r/2. So we have the following equations
for oscillator 1 and 2:
0 = w 1 - wO - k(p)2 tan AO sin(0 + 7r/2), (2.19) 2Q
0 = W 2 - wo - W 2 k(yi )2 tan AO sin(0 - 7r/2). (2.20) 2Q
Adding them, we get
WO = +W2 k()2 tanAO ~ ; (2.21)C0 2 2Q rI 2 ,(.1
the approximation holds when
AW Aw-L, AA> -. k() 2 tan AO <-> < 1 (2.22) Q ZO tan o AO
((2.16) is applied), which is easy to satisfy. Also, subtracting (2.19)(2.20) and using
O + W 2 ~ 2wo, we have
W1 - w2 = W-O. k(p)2 tan AO, (2.23)
by which we have the phase difference between vi and v 2
(_____2 Z02 tan2 s'2A6 = 2 arctan O - Q- CO - 2 .k (2.24) No Stank
We see that, two Zo-y' stubs serve as "amplifier" for the injection current, and the
result is, the small ratio between ZO tan p and Rtank is able to reduce the phase
difference quadratically. Also note that, the phase difference only manifest itself on
two stubs, decreasing from the device to p following the cosine curve; beyond p, on
38
the remaining 900 - p section, since only the standing waves of vo exists, there is no
phase difference between waves in two transmission lines.
To verify the model, as shown in Fig. 2-11, we let two 250-GHz self-feeding oscilla-
tors from our circuit to couple using network in the model, and compare simulated re-
sults of AO and AA/Ao under different conditions and compare them with theoretical
calculation. Self-feeding oscillator is essentially Colpitts oscillators at single frequency
point, and thus can be characterized by parallel RLC with voltage-divided output.
Rtank = 120Q and ratio between output voltage and tank voltage is 0.34. Results
show that model well characterize the coupling; some overestimation in Fig. 2-11(b)
is due to k(p) > 1 not being well satisfied when p is big. Note that Fig. 2-11(c) can
be used for predicting the phase and amplitude mismatch in horizontal coupling.
Now we show how the model is applied to vertical coupling. Considering at steady
state, two oscillators oscillate 180'-out-of-phase, we let vi(t)' = vi(t), v2 (t)' = -V2(t),
and hence differential-mode voltage Av' = vo and common-mode voltage v' = Avo
(hence /Av'J > lv'). Now, the coupling network has such properties:
" for Av' in each oscillator, there is no discontinuity at p and thus it sees a
90'transmission line.
* for v' in each oscillator, there is open circuit at o and the rest of the trans-
mission liene is "invisible", and thus it sees a yp-length open-circuit stub.
Therefore, Oi' = iosc,i, and notably
i,= /(-jZ cot) (i = 1, 2). (2.25)
Following similar derivations, we are able to get
(__-___ Z2 cot2y 2AO' = 2 arctan - Q. 2 J. (2.26)
WO Rtank
So the larger the p the better (making vertical coupling like the dual of horizontal
coupling). This may not be intuitive, but we can examine the worst case O = 0.
It means although there exists v6 (which shows oscillation imbalance), but slotline
network is unable to provide any reflected current to achieve current injection, hence
no injection locking, and at the same time power attributed to v' still circulates
39
1
0.5
Dw(GHz) (c)
Figure 2-11: Simulation of AO and AA/Ao as the result of coupling two 250-GHz self-feeding oscilla- tors using network in the model: (a) fix <p = 22.50 and Aw = 1.5 GHz, change Zo; (b) fix Zo = 60Q and Aw = 1.5 GHz, change p; (c) fix Zo 60Q and <p = 22.50, change Aw.
40
AO (s uatioIn)
-0.00 .0
-- 9D (theory) A 0S U D9 (simulation) - DI4 A (theory) A EWA, (simulation) -0
0
Zo (Ohm) (a)
A EWA, (simulation)
inside each oscillator. Note that tan 22.50 = cot 67.50, (2.24), (2.26) generate the
same result, so Fig. 2-11(c) can also be used for predicting the phase and amplitude
mismatch in vertical coupling.
2.3.3 Selective 4fo radiation using branched resonator
The property of selective radiation can be traced back to folded slot antenna, which
was proposed in [28]. Input wave may excite either radiative or non-radiative mode
depending on phase relationship of standing waves in different sections of the slotlines.
This property has been further exploited in [11] to radiate 2fo for a super-harmonic
oscillator. Nevertheless, there has not been a selective antenna for 4fo radiation.
Interestingly, our branched resonator pair, due to its shape and dimensions, has
such function. It also has a radiative mode and a non-radiative mode, and radiative
mode is only excited at 4fo. Details on radiation are explained using field distribution
of standing waves at fo to 4 fo, as is shown in Fig. 2-12. For all vertical slotlines, it
is clear from the figure that next to each vertical slotline there is another slotline
from the horizontally adjacent element. As discussed before, they form co-planar
waveguide, and thus they do not radiate. Therefore, now only radiation property of
horizontal slotlines are of interest. Note that the length of AiBiCiDi(i = 1, 2, 3, 4) is
equal to .A, 1A, A, A at fo, 2fo, 3fo, 4 fo, and their respective standing wave patterns
should be paid attention to.
At fo (Fig. 2-12(a)), collector voltages of transistors from each half of the oscillator
pair are 180'-out-of-phase, so waves injected into left and right branched resonators
are 180'-out-of-phase; we denote it as odd mode of the branched resonator pair. In
odd mode, the following slotline pairs - (A 1B1 , A 2 B2 ), (DiC1, D2 C2), (D 3C3 , D 4 C4 )
- satisfy such property: the standing wave in the former slotline is a flipped (180-
out-of-phase) replica of standing wave in the latter one. Therefore, far-field radiation
in all horizontal slotlines are canceled.
At 2fo (Fig. 2-12(b)), collector voltages of transistors from each half of the os-
cillator pair are in-phase, so waves injected into left and right branched resonators
are in-phase; we denote it as even mode of the resonator pair. In even mode, the
following slotline pairs - (A1B1, A 2B2), (D1 C1 , D2 C2 ), (D3C3 , D4 C4 ) - satisfy such
property: the standing wave in the former slotline is an in-phase replica (vs. flipped
41
(d)
Figure 2-12: Theoretical E-field distributions in branched resonator at different harmonics: (a) fo, (b) 2fo, (c) 3fo, and (d) 4fo. The darker the arrow color, the higher the field intensity.
42
in odd mode) of standing wave in the latter one. So these horizontal slotline pairs
cannot cancel radiation by themselves alone. However, because of "folding", for the
following slotline pairs, standing wave in the former slotline is a flipped replica of
that in the latter one: (A1B1, D1 C 1), (A1B 1,D3C3 ), (A 2B2 ,D2 C2 ), (A 2 B2 , D4 C4 ).
Therefore, in the far field, radiation of (A1B1 , A 2B2) pair is canceled by half of the
(DiC1 , D 2C 2 ) pair and half of the (D 3C3 , D4 0 4 ) pair. By half we mean that, each
DiCi(i = 1, 2,3,4) slotline on the boundary is shared by two elements, so on average
each element effectively has half. The final result is far-field radiation in all horizontal
slotlines are canceled.
At 3fo (Fig. 2-12(c)), similar to fo case, odd mode is excited and far-field radiation
in all horizontal slotlines are canceled.
At 4fo (Fig. 2-12(d)), similar to 2 fo case, even mode is excited. As is discussed
before, in even mode, slotline pairs, (A 1B1 , A 2B2), (DiC1 , D2C), (D3 C3 , D4 C4 ), are
radiative in their own right. However, the difference between 4 fo and 2fo case is
that, for the following slotline pairs, because of the phase flip at each midpoint of
BiCi(i = 1, 2, 3, 4), wave in the former slotline is an in-phase replica of that in the
latter one: (A 1 B1 , D1 C1 ), (A 1B1 , D3C3), (A 2B2 , D2 C2 ), (A 2 B 2 , D4 C4 ). Therefore,
in the far field, radiation of (A 1B1 , A2 B 2) pair interferes constructively with radiation
from by half of the (D1 C 1, D 2C 2 ) pair and half of the (D3C 3, D4 C4 ) pair. In other
words, in each element there are on average two 4fo antennas (also two radiating
units).
Since our ultimate goal is to build coherent 1-THz array, it is necessary to check
whether in-phase wave replicas exist in all horizontal slotlines from multiple elements.
This is done by drawing field distribution of 4 fo waves in a 2 x 2 sub-array, which is
sufficient for generalizing to any array scale. Note that inter-element phase relation-
ships introduced in the last subsection is applied here. Results are shown in Fig. ??.
Clearly, all horizontal slotline pairs radiate in-phase.
Fig. 2-13 shows the simulated E-field distributions in inter-metal dielectrics at
different harmonics, which agree with theoretical counterparts in Fig. 2-12. In the
EM simulation structure and actual layout, on the upper metal plate of the element
there is a "dummy" triangular opening in the same shape as its lower counterpart;
its function is to make field distribution more symmetric. Fig. 2-14 shows simulated
43
3D plot of antenna gain of each element at different harmonics, from which we see
that only at 4 fo is the element radiative. In addition, simulated radiation efficiency
at 4fo is 63%.
2.3.4 Routing of DC bias
Each oscillator pair, and thus the entire array, requires the following DC signals:
Vcc for transistor collector bias, VB connected with RB for transistor base current
bias, and GND. Since base current IB is only 0.3 mA per element, metal 1, 6 pm
below top-metal 1, is used to feed VB. In contrast, collector current 1C is 14 mA per
element, top-metal layers, with much larger maximum allowed current density, are
used to feed Vcc and GND. Inside each element, slotline pair (A 1B1, A 2B2) divides
top-metal 1 into two DC-isolated metal plates: the upper one is connected to Vcc
and transistor collectors; the lower one is connected to GND and transistor emitters.
At the left/right boundary of the element, there is an air bridge connecting the metal
plate in the current element to the equi-potential metal plate in the horizontally
adjacent element. Fig. ?? shows the element structure annotated with DC voltages,
and Fig. ?? gives a clearer view of how Vcc and GND connected between elements.
Another issue is that, on the boundary of two vertically adjacent elements, there is
a short circuit for the branched resonator (Fig. ??). If short circuit is implemented by
connecting two metal plates, Vcc is shorted to GND. To address the problem, we use
two 300 fF MIM capacitors to form DC-floating AC short, as is shown in Fig. 2-15.
2.3.5 Boundary of the entire array
At the array boundary, there is no horizontally and/or vertically adjacent elements.
What should be taken care of are: (i) undesired radiative loss of fo, and (ii) undesired
leakage of fo and 4 fo out of the array boundary.
For the radiation of fo, according to Fig. 2-12(a), we see that even for a standalone
element, there is theoretically no radiation at fo. In the vertical direction, adjacent
element is replaced with a metal "wall" stacked from Metal 1 to Top-Metal 2, but
still, standing waves in AiBi(i = 1, 2, 3, 4) are able to cancel with those in CiDi(i =
1, 2, 3, 4). In the vertical direction, adjacent element is replaced with a Top-Metal
44
(d)
Figure 2-13: HFSS simulation of magnitude and phase of E-field vector in dielectrics at different harmonics: (a) fo, (b) 2fo, (c) 3fo, and (d) 4fo. Input power at all frequencies are normalized to be the same.
45
d(Gainfotal)
-65.0
(c)
Figure 2-14: HFSS simulation of antenna gain of a single element 4fo. Note that only at 4fo is peak antenna gain positive.
Boundary
Top-Metal 1 Vlas Metal 5
Metal 1
Figure 2-15: Structure of DC-floating AC short implemented with two MIM capacitors.
46
di(GainTotal)
-12.8
-14.e
-18.0
-12.9
(b)
(d)
1 plate, despite the absence of co-planar waveguide, standing wave in B1C1 cancels
with that in B3C3 , and standing wave in B2C2 cancels with that in B4C4.
For the potential leakage of fo and 4 fo, we should see that potential paths are air
bridges. To this end, a notch filter connected to each boundary air bridge is designed.
Fig. 2-16 shows structure of filters and other neighboring components at the upper-left
boundary of the entire array. All filters are identical and they present high impedance
near fo and 4 fo. Each is implemented by three sections of microstrip lines: AB, DB
and CB, whose lengths are lA4 f0 , 4fo, and A4f0 respectively. Termination A is
short circuit, whereas termination D is open circuit. It can be inferred from smith
chart (Fig. 2-17(a)) of this network that at both fo and 4fo impedance looking into
C are high; simulation results of the impedance are shown in Fig. 2-17(b).
MIM Cap B
GND AD
B C
Figure 2-16: Structure of the upper-left boundary of the entire array along including notch filters. The structure is repeated for each row, except that DC pads are connected to different biases depending on routing.
47
Frequency (GHz)
Figure 2-17: Structure of the upper-left boundary of filter networks.
------ Imaginary Impedance
Frequency (GHz)
48
2.4 Prototype and Experimental Results
The chip is fabricated in IHP 130-nm SiGe BiCMOS process featuring a HBT fm
of 450 GHz. There are in total 6x7 elements and 91 slot antennas 3 on the 1xlmm 2_
area chip. The micrograph of the chip and a single element are shown in Fig. 2-18.
As mentioned previously, a hemispheric, high-resistivity silicon lens is attached on
the chip back for the radiation coupling to the free space. The total DC power
consumption when chip reaches maximum output power is PDC VCC 'C + VB 'IB
1.8V x 0.6A + 1.15V x 12mA = 1.1 W.
1 mm
2.4.1 Measurement of the Oscillation/Output Frequencies
Previously, the spectrum in the mid-THz range was measured using Fourier transform
infrared spectrometer (FTIR) [7]. Alternatively, the radiation can also be down-
converted by an even harmonic mixer (EHM); however, at this frequency band, there
is no commercial available EHM.
Due to the inaccessibility of these instruments for us, we use an indirect approach:
the down-conversion of the leaked radiation at the fundamental frequency to get fo,
with which 4 fo can then be inferred. The leaked radiation at fo radiation is mainly 3 The radiators on the top and bottom of the array do not share antennas. The total number of
antennas is therefore 6 x7x2x+7=91.
49
(Tektronix RSA3303A)
E I Signal Generator - 0--0 (Keysight E8257D)
Figure 2-19: Setup of measuring fo frequency using even-harmonic mixer.
due to device mismatch across the array. Fig. 2-19 shows the measurement setup. The
radiation leakage at fo is received by a WR-3.4 diagonal horn antenna placed closely
to the lens and is then fed into a 16th-harmonic WR-3.4 mixer from Virginia Diode
Inc. (VDI). Meanwhile, a 10-dBm LO signal at around 15.8 GHz is applied. The
output IF spectrum from the EHM, amplified by an amplifier chain and measured by
a spectrum analyzer, is shown in Fig. 2-20a. Only one peak is obtained, indicating
that the fundamental oscillations of all elements are synchronized. The frequency of
fo can be calculated as:
fo = 1 6 fLo + fIF, (2.27)
where the factor of 16 is verified by slightly increasing fLo and measuring the resultant
change of fIF (jAfIF=16 fLo|). The sign of " " is the opposite of that of |Afrol.
According to (2.27), the fundamental oscillation frequencies at various HBT base
bias voltages VB are shown in Fig. 2-20b. When increasing VB from 1.05 to 1.2 V, fo
decreases from 254 GHz to 252.8 GHz (due to larger C, of each HBT). The actual
tuning range may be larger than this, but it is not characterized due to the small
SNR in Fig. 2-20a.
The output radiation at 4 fo should then change from 1011.2 GHz to 1516 GHz.
Lastly, Fig. 2-20a also shows the measured IF power (normalized) at various VB, which
we use to evaluate the the oscillation activity. It peaks at VB=1.15V, corresponding
50
-91.46 dBmn
253.0 -I
(a)
1.10
Figure 2-20: Measurement results of leaked fo relative power at different VB bias.
VB (V)
1.15
-0
--10
51
N
0
Function DC Power Lock-in Amplifier SR865A Generator Supply (Integration Time=100ms)
Triggr
WR-1.0 WR-1.0 Antenna ZBD
Figure 2-21: Setup of measuring radiated 1 THz power using zero-bias diode.
to fo of 253.2 GHz (4fo=1.013 THz).
2.4.2 Characterizations of the 1-THz Radiation
The total radiated power of the 1-THz signal is measured using a VDI WR-1.0 di-
agonal antenna (directivity=25 dBi) cascaded with a WR-1.0 zero-bias diode detec-
tor (ZBD). The detector has a calibrated responsivity of 1.1 kV/W and a NEP of
57 pW/v/Itz at 1 THz. The testing setup is shown in Fig. 2-21. The chip and the
diagonal antenna are separated with a far-field distance of 3 cm. First, the radiation
is electronically modulated by connecting the VB of the chip with a 18-Hz 50%-duty-
cycle square wave with 1.15-V peak-to-peak voltage. This is to facilitate the lock-in
amplifier for narrow-band noise suppression, and to ensure that the slow-varying heat
radiation is not included. From the reading of the lock-in amplifier, the power re-
ceived by the ZBD is calculated to be 4 pW, which is associated with a transmitter
EIRP of 13.1 dBm. Here, we note that the lock-in amplifier basically measures the
root-mean-square (RMS) voltage of the fundamental sinusoidal component of the de-
tector output signal; therefore, an additional multiplication factor of 7r/v/2 (or 2.22x)
is used when calculating the peak-to-peak voltage of the output square wave [29].
Next, the chip is rotated with different azimuthal (0) and polar (p) angles. Fig. 2-
22 shows the measured and simulated 1-THz radiation patterns in the E-plane and
H-plane, respectively. According to these data, the calculated peak directivity of the
chip output beam is 24.0 dBi. This, along with the aforementioned 13.1 dBm of
measured EIRP, gives a total radiated power of -10.9 dBm (80 piW) according to the
52
Theta (Degree)
-
90 Phi (Degree)
(b)
Figure 2-22: Measured radiation pattern of 1-THz signal: (a) E-plane, (b) H-plane.
53
------- Simulated -- Measured
This Work [4] [5] [8] [7] [6]
Circuit Type Oscillator Active Multiplier Passive Multiplier
fout (THz) 1.01 0.99 0.82 0.92 1.33 0.73
P0 ut (dBm) -10.9 -37 -29 -17.3 -22.7 -21.3
EIRP (dBm) 13.1 N/A -17 -10 -13 -22.2
PRF,in (dBm) N/A 8 14 8 18 13.8
PDC (W) 1.1 4 3.7 5.7m 0 0 Number of An- 91 4 4 2 2 1 tennas
Method of Syn- 2D Oscillator Input RF Power Splitting Output RF Power Splitting N/A chronizing Coupling ____________________________
Area (mm2 ) 1.0 3.28 3.22 0.37 0.36 0.26
Technology 130-nm SiGe 250-nm SiGe 250-nm SiGe 130-nm SiGe 65MOS CM OS
Friis equation.
It is noteworthy that the supported frequency band of the WR-1.0 waveguide used
in our setup ranges from 750 to 1100 GHz. As a result, any leakage at 253 GHz and
506 GHz is completely excluded in our power measurement results. Although the
3rd-harmonic leakage at 759 GHz cannot be filtered by the waveguide, we believe its
impact is negligible because the differential field distribution at 3fo should suppress
the leakage by 10-(-28)=38 dB (Fig. 2-12), compared to the radiation at 4fo. This is
also verified by the good consistency between the simulated and measured radiation
patterns in Fig. 2-22.
Lastly, the total radiated power is also measured using a photo-acoustic TK ab-
solute power meter, which has a large input window to capture radiation in most
directions (Fig. 2-23). Similar to the setup in Fig. 2-21, the power meter also uses
a lock-in function to minimize the impact of the thermal radiation. The measured
results are shown in Fig. 2-24. During the presented time period, the SiGe chip is
firstly turned on (i.e. VB is connected to a 30-Hz 50%-duty-cycle 1.15-Vpp square
wave), then off (i.e. VB grounded), and finally on again. The measured radiated
power is ~100 pW (-10 dBm). The 0.9-dB difference between that and the radiated
power measured by the ZBD is believed to be caused by the leaked radiation at fo,
as well as limited instrumental accuracy.
54
Heater
TK Powermeter
Figure 2-23: Setup of measuring total radiated RF power using Thomas-Keating (TK) photo-acoustic powermeter.
LIN,
0_pW
Figure 2-24: on again.
Measured total radiated RF power when chip is power-on, then power-off, then power-
55
56
Imager
Terahertz imaging has gained attention due to the small wavelength of terahertz wave
compared with mm wave, and non-ionizing nature compared with X-rays. Building
terahertz imaging system on chip offers much flexibility in terms of front-end archi-
tecture and baseband data processing. In this chapter, we focus on the receiver part
of the whole imaging system.
Estimation of Received Power of Different Terahertz Imaging Setups
First of all, we introduce the setups of different types of terahertz imaging systems. A
typical such system consists of (i) radiation source, (ii) beam collimation setups (e.g.
multiple-lens systems), (iii) objected being imaged, and (iv) receiver. For passive
terahertz imaging system, which relies on the black-body radiation in the terahertz
band, no explicit source or collimation systems is needed; however, due to the low
power density in the frequency domain, it requires long integration time at the receiver
side to improve the signal-to-noise ratio. In comparison, active imaging system has
a dedicated source radiating high-power narrow-band terahertz wave, which leads to
much shorter integration time at the receiver and hence higher imaging rate.
Fig. 3-1 shows two typical active terahertz imaging systems along with the system
we propose. Now we analyze the operation of each system.
System in Fig. 3-1(a) has one lens system used to collimate the divergent beam
57
Source Multi-Pixel Incoherent Receiver
Transmittance: ao
Source Lens System 1 Lens System 2 Multi-Pixel Incoherent Receiver
Path Loss 1: a1 Path Loss 2: a 2
Transmittance: ao (b)
Antenna Pattern
Path Loss 1: a1 Path Loss 2: C2
Transmittance: ao
Figure 3-1: Active terahertz imaging systems with different types of receivers: (a) single-pixel receiver, (b) multi-pixel incoherent receiver, and (c) multi-pixel coherent receiver.
58
from the source. The imaged object is also mounted on a stepper which aligns the
imaged region with the center of the collimated beam which has highest power density.
The receiver has multiple incoherent pixels (i.e. the response from the received RF
signal does not contain phase relation ship and thus cannot be combined) generating
independent outputs. Receiver is also aligned with the imaged region and each on-
chip pixel is aligned with a small area in the region. Assume in the small imaged
region the power distribution is uniform, we have
PRX(Xi, yi) = PTx - Ad1 d ) Dx - ao(Xi, yi)Cia2 - GRX, (3-1) (47r(di + d2))
where (xi, yi) is the imaged location on the object corresponding to the ith pixel of
the receiver, d, the distance from the source to the convex lens, and d2 the distance
from the imaged object to the receiver, DTx the peak directivity of the antenna of
the source, GTx the peak gain of the antenna of the receiver. Previous works within
this category include [31][33][36]
System in Fig. 3-1(b) has two lens systems focusing the radiated wave from the
source to a small area on the imaged object and refocusing the transmitted wave onto
antennas on the receiver. This is why this kind of receiver chip is named as "focal-
plane array". Note that the imaged object is mounted on a mechanical stepper which
enables different locations on the object can be imaged. The power received by
each antenna when radiation is focused at point (x, y), which is proportional to the
intensity of the image pixel (x,y), is approximately
PRx(x, y) = PTX - ozo(x, y) - aia2 r/Rx/N, (3.2)
where PTx is the total radiated power from the source, ao(x, y) the ratio of the
transmitted power and the incident power (i.e. transmittance) at location (x,y) of
the imaged object, a, the total path loss from source to the imaged object, a2 the
total path loss from the imaged object to the receiver, /Rx the radiation efficiency of
the receiver, N number of antennas on chip. Note that N is primarily determined
by the size of beam waist. Unlike the receiver in Fig. 3-1(a) where array is used
to achieve parallelism hence increase scan speed, the array here is mainly used to
59
improve signal-to-noise ratio since theoretically the signal outputs from all pixels are
the same. Previous works within this category include [30] [32] [34] [35] [37]
System in Fig. 3-1(c) has one lens system used to collimate the divergent beam
from the source. The imaged object is no longer on a stepper but fixed to a position
where the power density of the beam is highest. Note that here the size of the object
should be small so that it is power density of the incident wave on the entire object
is approximately uniform. The receiver is a multi-pixel coherent receiver, which is
the very type of receiver introduced in this thesis. Its antenna pattern serves as a
reconfigurable spatial filter, so unwieldy slow-speed mechanical stepper is not needed,
and more flexibility is shifted to the receiver side. Suppose the angle between the x-
axis (shown in the inset) and the projection of boresight on the xy-plane is #, the
angle between the z-axis (shown in the inset) and the boresight 9, distance between
imaged location and receiver r, then r, # and 9 can be represented using d2 and (x, y)
coordinates on the image:
(r, q, 0) = x 2 + y2 + d,arccos , arcos 2 . (3.3) V1x2 +y2 VX_2 + y2 + d2
Now we have the expression for PRx corresponding to (x, y) on the imaged object:
PRX(X, y) = PTx - (D A )DTX - ao(x, Y)ala2 - GRX- (3.4) 47r(di + r)
There has been yet no terahertz imager falling into this category yet.
Comparison between Homodyne and Heterodyne Receiver
The fundamental difference between homodyne receiver (e.g. [30] [31] [32] [33] [35] [36])
and heterodyne receiver (e.g. [34][37]) is that, in homodyne receiver, RF signal is
down-converted by iteself, so that phase information is lost, while in heterodyne
receiver, RF signal is down-converted by LO signal with deterministic phase shift, so
that phase information is preserved. To see this, suppose VRF = VRF cOS(WRFt + 95RF)
, and suppose the square term coefficient of a square-law homodyne receiver is k,
'For imaging, single-tone signal suffices since we only care about signal's attenuation passing through the object, unlike communication where a substantial amount of baseband information is modulated onto the RF carrier hence a certain bandwidth is needed.
60
then
1 1 VIF = HLPF (jW) kvF = HLPF* 2V RF (1 + cos(2WRFt 2oRF)) = 2 F - (3
In contrast, for a heterodyne receiver, suppose VRF = VRF cOS(wRF + PRF) and VLO =
VLO COS(WLOt + SOLO), WIF = WRF - WLO, conversion gain of the mixer k, then
VIF =HLPF (jw) kVRFVLO = HLPF - kVRFVLO[coS(WIFt + (PRF - SLO)2 1
+ cos((WRF + WLO)t + PLO + WRF)l kVRFVLO cOS(WIFt + SRF - SLO), (3.6) 2
from which we are able to infer the relative amplitude and phase of the incident RF
signal. As a side note, comparing the above two equations, we see that as long as
VLO > VRF, heterodyne receiver generates stronger IF signal. There has yet been no
scalable heterodyne receiver array reported.
Operation of Beam-Steerable Coherent Heterodyne Receiver Array
By coherent we mean that SLO of mixers inside all elements are the same. For
pixel (i, j), suppose the voltage amplitude of incident RF signal is VRF,ij, phase wRF,ij,
the voltage amplitude of detected IF signal VIF,ij, phase wIF,ij 2, then
VIF,ij = kVRF,ij, (3.7)
where k and AW1 are certain constants.
Before discussing how to realize digital beam-forming in a 2D rectangular planar
array, we discuss how RF beam-forming is performed in a ID linear array. Suppose
that the wavenumber vector is k (note Jkl = 27/A), the coordinate of ith array
elements placed on the x-axis is xi (hence the vector from origin to the element
Xi = xi - X), and that the spacing between elements xi - xi_1 = dx. Therefore, for
element at xi, the phase delay is k -xi, therefore at time t, incident E field at ith
element is (here we assume the power of the planar wave impinging on each element
2Both voltage amplitude and phase can be measured using a lock-in amplifier.
61
Ei(t) = EO -ejWRFt . -(39)
Note that normally the voltage at the antenna feeder VRF is proportional to E(t), so
we have
PRF,i = LE(t) + AP02, (3.11)
where k' and A 2 are certain constants. Therefore, if we perform "delay-and-sum"
operation on all VRF,i (suppose there are M elements in total), we get the output
M
Vsum = VRF,i - ejkxi M - VRF ejwRFiA2 (312)
Clearly, by changing the delay, we enhance the received signal from a different direc-
tion (i.e. different k). In fact, A02 is an arbitrary number since we do not care about
the phase of E(t), so we set ZA 2=0. After amplitude detection, we get the output,
which is proportional to the intensity of the pixel (x, y)
Vout = M - VRF- (3.13)
After discussing the basic ID RF beam-forming, we discuss the more complicated 2D
digital beam-forming. Suppose that the coordinates of the array element at row i
column j is (xi, yj) (xi + y in the vector form), and xi - xi_1 = dx, yj - yj_ = dy.
For planar wave with wavenumber vector k, at time t, we have the incident E field
and RF voltage at the antenna feeder VRF of the element at row n column m:
Enm(t) = Eo ejWRFt . e(kXn+k-ym) (3.14)
VRF,nm(t) = VRF ' ejWRFt . ej(kXn+kYm+AW2). (3.15)
Similar to the 1D case, VRF oc EO and A02 is a constant. Note that digital beam-
forming means beam-forming is performed after RF signal is down-converted to base-
62
band. Using (3.7)(3.8), we have
VIF,nm = kVRF e e j x .e k 'm+Ac1+A ) (3.16)
Then, by doing delay-and-sum (suppose the size of the array is N x M), we have
N,M
Vsum = S VIF,nm ' eij(k-xn+k-ym) - NM. kVRF ( ejWIF . (1W2 3.17) n=1,m=1
That is to say, element (n, m) requires phase-shift of k -n + k -ym, where
k mn d sin x Cos n -X (3.18) A V/rX2 + y 2-+2A d~ sin~cos~5=+ d2 2
2mir yk ym = dysin6coso m. 2 7. (3.19) A2 + y2 + d
Here we suppose dx = dy = A/2. Again, without loss of generality, set A 02 = 0. For
Aoi, we can set it to 0 by tuning the phase of the LO signal. Finally, by extracting
the amplitude of Vsum, we have the output signal that is proportional to the intensity
of the pixel (x, y)
Vout = NMk- VRF- (3.20)
Now we analyze the noise performance of the array (we do not consider the input-
referred noise and quantization noise of the ADC). At antenna, the power of received
signal is PRF,s = VRF/Rant, and we assume the noise power received by antenna is
PRF,n = V/Rant. Thus we have the signal-to-noise ratio (SNR) at a single antenna:
SNRant RF (3.21) n
Let the noise factor of the mixer inside each element be Fmix, then after down-
conversion and delay-and-sum processing, SNR at output is
(NMk VRF) 2 /Rout = NM (3.22) SNROUt = F=N.(v)/ 0 1 SNRant~ F 3.2
F -NM - (kine)2/Rout F
Note that signals are coherently added while noise are incoherently added. We see
63
that, as long as NM > F, the coherent array architecture is able to improve SNR.
64
3.1 Array Architecture
Fig. 3-2 shows the diagram of the array architecture used in our receiver. The array consists of 16 elements, each with dimensions of A"F/2 x A"F/2. Inside each unit there are two self-oscillating mixers, each connected to its own antenna. By self-oscillating mixer we mean that the LO signal of the mixer is provided the mixer itself. This is implemented by connecting the oscillator to the receiving antenna directly, so that RF signal is directly injected into the oscillator. It will be introduced later that, using design techniques that, the antenna does not radiate signals generated from the oscillator but only intercepts the incoming RF signals. By exploiting the non- linearity of transistors in the oscillator, received RF signal is mixed with LO generated by oscillator. The resultant IF signal is sent out of the element.
ARF/ 2
External Reference
Figure 3-2: Block diagram of the architecture of the proposed heterodyne coherent receiver array.
Now we introduce how to achieve coherency among all mixers. As we discussed in the last section, the key to coherency is to ensure that the phase of LO signals in all mixers are synchronized, or specifically, all oscillators are coupled. In this array, like the 1-THz radiating array introduced in the last Chapter, we use slotlines and co- planar waveguides to achieve coupling. On top of mutual coupling among elements, to
65
-
synchronize fLo with fRF so that IF signal can be detected using a lock-in amplifier,
we integrate a PLL on the chip, making the oscillation phase-locked with an external
frequency reference. Elements on the array boundary inject a small amount of fLO/ 2
signal into the divider chain of the PLL module for phase comparison, and PLL
module sends back control signal to the varactor of every oscillator in the array.
66
3.2 Design of Array Element
Fig. 3-3 shows the structure of a single element. As is introduced before, it consists
of two identical receiver units. Fig. 3-4 shows the equivalent circuit of one such unit.
3.2.1 Design of Standalone 120-GHz Oscillator
The central piece of each receiver is the self-oscillating mixer. Its essence is an oscil-
lator pair with a slotline in the center for coupling two self-feeding oscillators. The
fundamental oscillation frequency (fo) is 120 GHz, and second harmonic (2 fo) is
240 GHz, which is used as the LO signal of the mixer (i.e. fLo = 2fo). A 135 0(at
fo) short-circuit slotline stub is connected to the top of the central slotline, while a
450 (at fo) short-circuit slotline stub is connected to the bottom of the central slotline.
Clearly, two stubs in parallel present open circuit at fo. Since the central slotline is
short, we can approximately regard two slotlines together serve as a resonator at fo.
For the determination of length and impedance of the feedback transmission line, we follow the steps introduced in the previous chapter, and Zo = 55Q, p = 70'
is used. The gate of two transistors are DC-connected to the DC bias VG,N. The
routing is: gate -+ transmission line -+ virtual ground node D -+ antenna feed -+
bias line. The drain of two transistors from two oscillators are DC-connected to a
current source. The routing is: drain -+ transmission line -+ virtual ground node C
-+ low-level metal between under the central slot -+ drain of PMOS. Therefore, node
C is a high-impedance node, so that IF signal is not shorted but can be read out.
From simulation, in total 10 mW fo flows inside the oscillator pair, with DC power
consumption of 40mW.
3.2.2 Inter-element Phase Synchronization
Two receiver units inside the same element are coupled by co-planar waveguides
(CPW), consisting of slotlines extended from the top of the oscillator pairs and air
bridges. Between elements, coupling is achieved in this way: for left and right bound-
aries, adjacent slotlines from two elements are coupled using CPW; for top and bottom
boundaries, adjacent slotlines are coupled by merging them. The resultant E-field dis-
tribution of fo inside the entire element is shown in Fig. 3-5. As can be observed,
67
for all slotlines that are part of a CPW, they do not radiate. For the remaining
horizontal slotlines, we see that the radiation from each horizontal slotline on the left
side of the element is canceled by its counterpart on the right side of the element.
For central slotlines between oscillator pairs, radiation is canceled by slotlines from
the horizontally adjacent element. Therefore, theoretically, there is no radiation of fo
that would dissipate the generated fo power.
CPW Coupling
Slotline Coupling
3.2.3
Second harmonic is used as the LO signal of the mixer: the frequency of RF signal is
tuned to be 2fo + fIF, where fIF is in the range of several MHz to ensure low flicker
noise at baseband and the detectability of lock-in amplifier. 2fo signals generated
from two oscillators in a pair are in-phase. As is discussed in the last chapter, slotline
blocks the propagation of two in-phase signals on its two metal plates. As a result,
2fo signals are not able to be injected into the slotline network connnected to the top
of the central slotline; they are only allowed to propagate into the antennas connected
to the bottom of the central slotline. The E-field distribution is given in Fig. 3-6. As
68
D
Figure 3-4: Equivalent circuit of a receiver unit.
can be seen, in the same element, E-field in two antennas in the same element are
180 0-out-of-phase, so theoretically there is no radiation of 2fo either.
3.2.4 Analysis of Mixing Function of the Oscillator
Two antennas in the same element are nevertheless able to receive the incoming RF
radiation, because the phase relationship of E-filed of RF signals in these two antennas
are no longer determined by oscillators, but RF signal itself. Signal collected by
antennas are injected into the gate of the oscillators through antenna feeders and
transmission lines. Therefore, at gate, LO and RF are able to mix, generating IF
signal at drain. To ensure impedance matching between gate and antenna, part of
the feedback transmission line is used as matching network (while another part is
between drain and the central slotline). Simulated radiation efficiency is 50 %. On
the other hand, for slotlines on the top and bottom boundaries, although they are also
in the form of slotline antenna, they are not able to collect energy from RF signal.
This is because wave in the antennas are unable to be injected into oscillators because
69
E
Figure 3-5: E-Field distribution of fo wave in slotlines.
Now we analyze the phase of IF signals. Inside each element, in two antennas,
the generated LO signals, i.e. 2fo signals, are out-of-phase. Therefore, according to
(3.6), on top of the phase shift of incident RF signals the generated IF signals will
have an extra 18 0'phase shift, which should be compensated in baseband processing.
For the phase relationships between different elements, it can be inferred from Fig. 3-
5 that E-field distributions of fo are the same in all elements. And also the same
are the distributions of 2 fo waves which are generated from fo waves. Therefore, no
additional phase compensation is needed when processing IF signals from different
elements. The simulated conversion loss is 20 dB with 50 Ohm resistance load. The
simulated noise figure is 21 dB, under the condition of fIF = 100 MHz, which is
greater than the corner frequency of output noise.
70
I
- I
I Figure 3-6: E-Field distribution of 2fo wave in slotlines.
71
-? I
I
3.3 Design of PLL
In this section we introduce the function of PLL with regard to the entire array and
the design details of the PLL.
Fig. 3-8 shows the block diagram of the PLL. A distinct feature of this loop is that
it controls the oscillation of an array of 2d-coupled VCOs. The control signal is sent
into the array through a network of wires underneath the signal trace of all CPWs, as shown in Fig. 3-3. A small portion of the generated fo is coupled out of the array
using the structure shown in Fig. 3-8. The output wave is injected into an NMOS
switch of a divided-by-4 injection-locked frequency divider. Simulated injection power
is 200 pW. NMOS switch is biased at 0.9V, and DC signal is sent in through a short-
circuit stub. The simulated locking range under this condition is 118 - 122.7 GHz
when central oscillation frequency of the divider is tuned to 120 GHz.
VCTRL Network
fref = 75 MHz o
P hase Charge -V LPF V ) Detector PumpH fo in eton
DFF -.%60 4- TSPC +2 +- CML +4 +- ILFD +
Figure 3-7: Block diagram of the architecture of the proposed heterodyne coherent receiver array.
72
I- -
VD D
VOUT,P VOUT,N
Figure 3-8: Block diagram of the architecture of the proposed heterodyne coherent receiver array.
73
74
Conclusion
This thesis presents a 1-THz source and a 240-GHz imaging receiver chip. Both are
based on 2D coupled-array architecture, which is used to generate coherent oscillation
across the entire array.
Large-scale coherence brings benefits to both circuits. In 1-THz source, coherent
1-THz radiation is constructively combined so that total radiated power is greatly
improved compared to the state-of-the=art. In 240-GHz receiver, received RF signals
in every pixel is down-converted with the same phase-locked LO signal so that IF
signals retain the phase information of the received RF signal and beam-forming can
be performed at baseband.
Compactness and multi-functionality of array elements are the keys to building
such coherent, scalable, and functional arrays. In both circuits, there are slotline
networks with small footprint to perform coupling and selective radiation. Also,
notably, in the imaging receiver circuit, traditionally separated mixer and oscillator
are merged into a single circuit. There will be more applications of such compact
terahertz circuits as the research of high-performance large-scale terahertz circuits
going further.
75
76
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