The disclosed embodiments address these challenges by (1) an algorithm-based array synthesis approach, to generate a sparse array with non-uniform element distribution which fundamentally enables low side lobe beamforming capability over desired broadband/multiband frequency range across large scanning angles; and (2) design of a multi-band antenna with a stable pattern and beamwidth across wide frequency range.

Various embodiments provide different topologies and optimization methods of planar array element distribution, along with antenna element design to achieve ultra-broadband phased array system. Based on the disclosed methods, an antenna in package (AiP) antenna array hardware will be implemented along with fully integrated circuit front end to demonstrate wide angle beam steering capability across ultra-broadband/multi-band frequency range with reduced side lobe level performance. Compared to current narrow-band phased array system, this system disclosed herein significantly boosts the capacity and enables new frequency agile functionalities in application of wireless communication and sensing.

Various embodiments provide topologies, and methods for the design of such topologies, implementing an ultrabroadband/multiband phased array antenna. The topologies overcome the bandwidth limitations of the conventional uniform phased arrays. The general topology works both for mm-wave and RF frequencies and can be implemented either on integrated technology or PCB technology which can be a potential candidate for future broadband and frequency agile high speed mobile 5G/6G communication and sensing platform.

Various embodiments provide systems and methods using an algorithm-based array synthesis approach of designing and manufacturing a sparse array with non-uniform element distribution which fundamentally enables low side lobe beamforming capability over desired broadband/multiband frequency range across large scanning angles; and design of a multi-band antenna with a stable pattern and beamwidth across wide frequency range.

In particular, a 2D non-uniform sparse antenna array configured to operate at a minimum frequency according to an embodiment comprises a plurality of planar sections having disposed thereat a respective beamformer RF integrated circuit (IC) and a respective plurality of broadband dual port antenna array elements wherein a constrained location perturbation &n introduced to each antenna array element is subjected to 2D iterative optimization to correspondingly update the antenna array element locations until a desired broadband side lobe level (SLL) reduction of the antenna array has been achieved.

That is, instead of current narrow band phased array architectures, the disclosed approach provides spectrally agile array EM interfaces with multi-band operating frequency range over an octave (illustratively >3:1) bandwidth. This aims toward a demonstration of a spectrally agile phased array system over shared, licensed, and/or unlicensed bands. The disclosed approach provides dynamically programmable, frequency agile operation with high spectral efficiency, while simultaneously targeting 5G, V band, E band/new unlicensed 5G and W band as the proof of concept. Combination of the proposed architectures with the current existing MIMO approaches, such multi-band phased array system can potentially form the backbone of the next generation of wireless networks utilizing multiple available spaced spectra.

Various embodiments provide topologies, and methods for the design of such topologies, implementing a universal array topology (nonuniform, sparse spaced) capable of operating across multiple frequencies over more than an octave range of frequencies, overcoming simultaneously trade-offs between grating lobe issues, directivity and inter-element coupling.

FIG. 2 is a high-level block diagram graphically illustrating a universal array design method configured to generate a universal array topology (nonuniform, sparse spaced) according to various design criteria. Specifically, FIG. 2 illustrates the use of various optimized 2D array distribution to achieve grating lobe removal (acceptable side lobe levels) across ultra-broadband frequency range with wide range beam steering. As can be seen in the spectral diagrams of FIG. 2, unwanted grating lobes (i.e., SLL above 0 dB) above octave bandwidth are not present in the various examples.

Generally speaking, the various embodiments overcoming ULA bandwidth limitation by introducing a non-uniform geometry of antenna array element distribution and guaranteeing sparsity of the antenna array such that minimal distance between two elements larger than 0.51 at lowest frequency of interest.

Referring to FIG. 2, one of illustratively four candidate array types is selected 210 for use as a 2D non-uniform sparse array; namely, a raised power series (RPS) array 210A, an aperiodic tiling array 210B, a first non-transitional symmetrical array (circular or oval array in a multiple ring configuration) 210C, and a second non-transitional symmetrical array (circular or oval array in a rotational symmetry or “pizza” slice configuration) 210D. Other non-uniform antenna array element distribution geometries may also be used within the context of the various embodiments.

The spacing/location of the antennas forming the selected candidate array type is then optimized 220 in accordance with a respective optimization technique (as will be described in more detail below) to provide thereby an optimized array exhibiting a desired ultra-broadband performance.

In various embodiments, the RPS array 210A is optimized using a 2D iterative convex optimization; the aperiodic tiling inspired array is optimized using a constraint genetic algorithm (GA); the first non-transitional symmetrical array is optimized using RPS radius distribution; and the second non-transitional symmetrical array is optimized using slice-by-slice constraint GA optimization.

The 2D topology for the four types of arrays depicted in FIG. 2 are significantly different from a conventional 2D ULA. FIG. 3A graphically illustrates, for several ultra-broadband 2D array topologies, exemplary initial conditions, optimization method, and resulting optimized array. The performance of these four arrays in terms of worst-case side lobe level across 3:1 bandwidth across-60-to-60-degree beam steering angle is summarized in FIG. 3B. Briefly, all four designs exhibit good sparsity (minimal distance between two element is larger than λ0/2) which minimizes the coupling issue between elements compared to conventional ULA.

1.3.1 Problem Formulation and Definition

Consider an N-element (each element is a point source) randomly spaced 1D array with n_thelement location of x_n(n=1,2 . . . . N). The total aperture size of the array is (x_n−x₁). Define minimal spacing between two elements as d_min.

Each point source has a complex excitation (weight) W_n

W
n

=

A
n

⁢

e

j
⁢
β
⁢
n

(
1
)

Where A_nis the amplitude control and β_nis the phase control. The array far field radiation pattern |AF| at arbitrary elevation angle θ at frequency of interest f is:

❘
"[LeftBracketingBar]"

AF
⁢

(

θ
,
f

)

❘
"[RightBracketingBar]"

=

❘
"[LeftBracketingBar]"

∑

n
=
1

N

⁢

A

n

⁢

e

j
⁡
(

k
⁡
(
f
)

⁢

x
n

⁢

cos
⁡
(
θ
)

+

β
n

)

❘
"[RightBracketingBar]"

(
2
)

Where k(f)=2πf/C is the free space wave number, C is the light speed.

1.3.2 Condition of Maximum Flux at Intend Direction, Side Lobe and Optimization Goal.

From (2), for all beam coherently added (maximum radiated power) at certain angle θ₀, choose β_nsuch that the argument of the exponential function is zero, so β_ncan be chosen as:

β
n

=

-
k

⁢

(
f
)

⁢

x
n

⁢

cos
⁢

(

θ
0

)

(
3
)

β_nis determined if x_nis known, or one can say β_nand x_nare dependent. Substitute (3) into (2), the array far field radiation pattern |AF| with peak power at certain steering angle of θ₀at frequency of interest f can be written as:

❘
"[LeftBracketingBar]"

AF
⁢

(

θ
,
f
,

θ
0

)

❘
"[RightBracketingBar]"

=

❘
"[LeftBracketingBar]"

∑

n
=
1

N

⁢

A
n

⁢

e

j
⁡
(

k
⁡
(
f
)

⁢

x
n

(

cos
⁡
(
θ
)

-

cos
⁡
(

θ
0

)

)

)

❘
"[RightBracketingBar]"

(
4
)

At θ=θ₀, array factor and its flux achieve maximum value:

❘
"[LeftBracketingBar]"

AF
⁡
(

θ
,
f
,

θ
0

)

❘
"[RightBracketingBar]"

max
2

=

❘
"[LeftBracketingBar]"

∑

n
=
1

N

A
n

❘
"[RightBracketingBar]"

2

=

N
2

,

when
⁢

A
n

=
1

(
5
)

The second-highest peak in (5) after θ=θ₀maximum is called peak side lobe level SLL(in dB) which is defined as:

SLL
⁡
(

f
,

θ
0

)

=

10
⁢

log
10

(

secondhighestpeakof
⁢

❘
"[LeftBracketingBar]"

AF
⁡
(

θ
,
f
,

θ
0

)

❘
"[RightBracketingBar]"

2

max
⁢

❘
"[LeftBracketingBar]"

AF
⁡
(

θ
,
f
,

θ
0

)

❘
"[RightBracketingBar]"

2

)

(
6
)

Example 1: For a uniformly spaced linear antenna array with Nyquist sampled space such that x_n+1−x_n=λ/2, where λ=C/f is the wavelength of operation, and A_n=1, SLL(f,θ0) is independent of θ₀and roughly −13 dB.

Example 2: For the same array when operated at 2f such that x_n+1−x_n=λ, where λ=C/2f is the wavelength of operation, and A_n=1, SLL(2f,θ₀) is independent of θ₀and 0 dB. (i.e., numerical value of 1) demonstrating grating lobe formation.

Synthesis goal: Synthesis of non-uniform array with N elements with dmin≥0.5λ0 (λ₀=C/f₀), determine element positions of x_n, and excitations A_ne^jβⁿfor maximization of flux at the intended direction at θ=θ₀, where θ₀can assume discrete values distributed between 0<θ₀<π(e.g. θ₀=0+MΔθ, where M∈ [Image Omitted] ⁺, Δθ≈π/20), such that SLL(f, θ₀)<∈₁and SLL(2f,θ₀)<∈₂and SLL(Mf, θ₀)<∈_M, where M is the ratio between the highest frequency and lowest frequency across the broadband range, and ∥AF(θ, f, θ₀)|_max²−N²|<δ. The last relation eliminates a trivial solution such that A₁=1 and A_n=0 for n>1. To guarantee broadband performance for the frequency agile phased array application, several choices may be made including the following: M=3, ∈₁, ∈₂, ∈₃=−13 dB and δ=0.1N².

1.3.3 Extension to 2D Array

For an N-element 2D planer array structure in X Y plane, with location of each element to be (x_n, y_n), the optimization problem formulation is similar as 1D problem except the far field radiation pattern is a function of both elevation angle (θ) and azimuth angle (ϕ). For the broadside array pattern:

❘
"[LeftBracketingBar]"

AF
⁡
(

θ
,
ϕ
,
f

)

❘
"[RightBracketingBar]"

=

|

∑

n
=
1

N

A
n

⁢

e

jk
⁡
(
f
)

[

(

x
n

⁢

sin
(
θ
)

⁢

cos
(
ϕ
)

+

y
n

⁢

sin
(
θ
)

⁢

sin
(
ϕ
)

)

]

❘
"[RightBracketingBar]"

(
7
)

Similarly, if one wants to have all beam coherently added (maximum radiated power) at a certain angle (θ₀, ϕ₀), then AF becomes:

❘
"[LeftBracketingBar]"

AF
⁡
(

θ
,
ϕ
,
f
,

θ
0

,

ϕ
0

)

❘
"[RightBracketingBar]"

=

❘
"[LeftBracketingBar]"

∑

n
=
1

N

A
n

⁢

e

jk
⁡
(
f
)

[

x
n

(

U
-

U
0

)

+

y
n

(

V
-

V
0

)

]

❘
"[RightBracketingBar]"

(
8
)

where U=sin (θ) cos (ϕ),U₀=sin (θ₀) cos (ϕ₀),V=sin (θ) sin (ϕ), V₀=sin (θ₀) sin (ϕ₀).

The synthesis goal is similar to that of a 1D case. For the examples and result presented in the following sections, assume the amplitude excitations for all elements are uniform, so only phase excitations are adjusted for beam steering.

1.4 Non-Uniform Array Geometries

From a general optimization point of view, a “brute-force” optimization starting from a random initial condition may lead to undesired result. The importance of initial conditions in optimization problems cannot be underestimated because: (1) The initial conditions can affect whether an optimization algorithm converges to a solution, and how quickly it does so; (2) The initial conditions partially determines whether an optimization algorithm converges to a local or global optimum. In some cases, starting from different initial conditions can lead to different local optima, or prevent the algorithm from finding the global optimum; and (3) The choice of initial conditions can also impact the efficiency of the optimization process. Choosing initial conditions that are closer to the optimal solution can reduce the number of iterations or computational resources needed to converge to a solution. Therefore, this section presents various nature and mathematics inspired array topologies as good initial conditions, base on which an efficient optimization of broadband array geometry can be developed.

1.4.1 Raised Power Series Array

Consider a 2N+1 element symmetrical 1D array x_n, where

x
n

=

{

d
×

n
r

,

if
⁢

n

=
0

,
1
,
N

-
d

×

❘
"[LeftBracketingBar]"

n

❘
"[RightBracketingBar]"

r

,

if
⁢

n

=

-
N

,

-
N

+

1
⁢

…

-
1

(
9
)

- Where d is reference spacing and r is an introduced power series parameter to adjust the element spacing as n changes.

When r=1, x_nconverges to an ULA. When r≠1, x_nbecomes a raised power series (RPS) array. In particular, when r>1, the array becomes sparser at the array end while the array becomes sparser at the array center when r<1 (FIG. 4). This exponentially tapered array format provides new broadband properties, as shown in FIG. 5 wherein 2D maps exhibit the calculated SLL at broadside radiation, as a function of frequency (f₀to 10f₀), different r values, and different number of elements, for all the calculated cases; the d_minis 0.5λ at f₀. The following can be concluded: 1) when r=1, as expected, the SLL jumps to 0 dB at 2f₀frequency, which is independent of number of elements. 2) For both 0.5<r<1 and r>1 case, the SLL gets significantly improved at higher frequency, demonstrating broadband performance. r<0.5 case showing worse SLL at low frequency should be precluded in the design. 3) As number of elements increases, the overall SLL improves. The bottom part exhibits the 101-element array pattern with a choice of r=0.8 with promising worst-case SLL of −10 dB at 2f₀.

This concept is extended to a 2D array by applying the RPS distribution on both X and Y direction as shown in FIG. 6. At 3f₀, a 9×9 array has the worst-case SLL of −2.8 dB at θ of 60° beam steering angle, even though better than 2D ULA, the limited improvement is due to the small number of RPS element in both X and Y. Since RPS prototype is able to improve SLL performance only at a cost of increasing the number of elements significantly (FIG. 5), given the desired total number of elements for real application 2D array (˜100-200), the 2D RPS prototype is not able to meet the target. Therefore, a further optimization is required, which will be shown in the following session.

1.4.2 Aperiodic Tiling Array

As illustrated in FIG. 7, aperiodic tilings are collections of polygons, devoid of any translational symmetries, capable of covering a plane without gaps and overlaps. This lack of regular periodicity makes aperiodic tilings useful in the design of broadband antenna arrays, if each geometry vertex is replaced by an antenna element. Aperiodic tiling arrays have been inspired by natural patterns found in various biological systems, such as quasi crystals. They exhibit a complex and seemingly random arrangement of elements that is highly efficient at achieving specific functions. Penrose and Danzer patterns, which are based on a set of mathematical rules and basic building polygons include kites, darts and various triangles, are two examples of aperiodic tilings that are investigated.

A Danzer prototype array example with N=158 and d_min=0.5λ(f₀) shows the worst-case SLL across beam steering angles of −5.5 dB at 3f₀, which still needs to be improved by optimization to fulfill the frequency agile array application requirement.

1.4.3 Non-Transitional Symmetrical Array-Circular Array with Uniform Radial Distribution

Motivated by the broadband aperiodic tiling array, which entails only rotational symmetry rather than transitional symmetry, an array with perfect rotational symmetry such as a multi-turn circular may be used. FIG. 8 graphically illustrates a multi-turn circular or oval array having a multiple ring configuration, and its bandwidth improvement gained by applying RPS distribution along radius direction. As shown in FIG. 8, an N=223, 9 turn circular array is generated with a uniform distribution along radius direction, which shows worst case SLL of −8.8 dB at 3f₀. Inspired by the RPS distribution, the bandwidth of the array can be improved by applying RPS distribution along radius direction, an N=222 array improves the worst-case SLL to be −11.3 dB at 3f₀.

1.4.4 Non-Transitional Symmetrical Array-Circular Array with Uniform Sectional Distribution

To overcome the finite RPS resolution along radius direction for potential better performance, an array with uniform radial sections or “pizza slices” may be used. FIG. 9 graphically illustrates a circular or oval array having a multiple section or slice configuration, and its bandwidth improvement gained by providing a uniform initial antenna distribution which, after optimization, is transformed into aa random optimized distribution rather than a uniform distribution. As shown in FIG. 9, each of a plurality (illustratively 6-15) of array slices are provided within which a uniform array of antenna is distributed. Forcing the rotational symmetry here by repeatedly copying a single array slice rotationally to cover the whole 2pi space, a “pizza” array is created. The apex angle of each slice is 2π/Nfold, where Nfold is the number of rotationally repeated fold and is a design parameter.

As an example, the prototype with N=195, Nfold=13 and d_min=0.5λ(f₀) enables worst-case SLL of −13.7 dB at 3f₀, even without any introduced optimization techniques. Table1 presents a systematic study of calculated worst-case SLL across whole 2D steering angles and f₀-3f₀frequency range, versus different design choice of Nfold and total number of element N. Interestingly, an odd number choice of Nfold overall allows a better SLL performance especially for N=13 and N=15. The SLL improves as the number of elements in each slice increases, as shown below with respect to Table 1, which tabulates worst case SLL across θ∈(−60,60°), ϕ∈)(0,360°) and f∈(f0,3f0) versus different geometry parameters.

TABLE 1

NFold
N
Worst case SLL (dB)

9
261
−10

10
260
−10.1

11
264
−12.6

12
288
−5.6

13
260/195/169/117/70
−13.2/−13.7/−12.8/11.8/−10.5

14
266
−11.1

15
270/210/180/120/90
−13.7/−13/−12.8/−11.8/−11.3

16
272
−11.2

17
272
−12.8

1.5 Optimization of Broadband Non-Uniform Sparse Array Geometry

Section 1.4 introduces multiple array topologies with considerably bandwidth improvement over conventional ULA, but they still suffer from limited SLL performance unless a large number of element (>200) is adopted, which is not affordable for the low-cost frequency agile mmWave link. Therefore, multiple effective array optimization methods will be discussed in this section, building upon the optimization goals discussed above.

1.5.1 Simplification of the Optimization Problem

The original synthesis flow in 3.2 is a multi-dimension optimization problem: it assumes discrete values for different beam steering direction θ₀between 0<θ₀<π(e.g., θ₀=0+MΔθ, where M∈ [Image Omitted] ⁺, Δθ≈π/20). For each steering angle (which means determined phase excitations), a separate optimization to minimize SLL at highest frequency needs to be performed. Obviously, such optimization is time-consuming and with high computational cost due to large number of steering angles.

To reduce the optimization problem dimension approaching fast optimization, reformulate the beam pattern equation for a desired beam direction θ₀.

AF
⁡
(

θ
,
f
,

θ
0

)

=

∑

n
=
1

N

A
n

⁢

e

j
⁡
(

2
⁢
π
⁢
f

C

⁢

x
n

(

sin
(
θ
)

-

sin
(

θ
0

)

)

)

=

AF
⁡
(

f
,
U

)

(
10
)

- where U=sin (θ)−sin (θ₀), and θ₀, is the angle referring to the normal direction of the array. If the beam steering range is θ₀∈−θ_max, θ_max), then

U
∈

-
1

-

❘
"[LeftBracketingBar]"

sin
(

θ
max

❘
"[RightBracketingBar]"

,

1
+

❘
"[LeftBracketingBar]"

sin
⁡
(

θ
max

)

❘
"[RightBracketingBar]"

)

=

R
×

Range
(

sin
⁡
(
θ
)

)

(
11
)

- where Range represents the range of a function.

Here, R=1+|sin (θ_max)|. Looking at the beam pattern of the same array x_nat broadside but with a different frequency F=f×R

AF
broadside

(

θ
,

R
×
f

,

θ
0

)

=

∑

n
=
1

N

A
n

⁢

e

j
(

2
⁢
π
⁢
f
×
R

C

⁢

x
n

(

sin
(
θ
)

)

(
12
)

From (11), one can see that:

Range
(

AF
⁡
(

θ
,
f
,

θ
0

)

)

=

Range
(

AF
broadside

(

θ
,

R
×
f

,

θ
0

)

)

(
13
)

This means the initial problem of evaluating multiple steering angles may be converted to a less complex problem of evaluating a single broadside pattern, but at an equivalent higher frequency F=f×R. R is proportional to the maximum steering angles of the design, for example, 0% of 60° leads to a multiplication of frequency by 1.86.

1.5.2 Converted Convex Optimization

Given an initial distribution of array elements, the location of each element can be optimized for broadband SLL reduction. That is, for a 2D beam scanning in space (e.g., range of elevation angle (θ) of 30°-90° and range of azimuth angle (ϕ) from 0° to 180°), the SLL is reduced with the main beam pointing to most or substantially all angles within this space, and at most or substantially all frequencies across a frequency range of interest. This problem is highly nonlinear and non-convex. Well known algorithm such as Evolution algorithm, Particle swarm algorithm, and gradient based methods can be applied to such problem, but due to the relatively large number of element needed for the array, the number of optimization variable is typically too large (100 elements means 200 X, Y coordinate variables for the optimization) for these algorithms, along with a non-linear cost function, makes the conventional optimization methods slow and cost-ineffective.

This section introduces a method of converting the original problem to an approximate convex problem that can then be efficiently solved by leveraging the advanced convex optimization algorithm and optimizers.

Instead of optimizing the absolute location coordinate of each element x_n, first introduce a location perturbation δ_nto each element, then the perturbed array pattern at equivalent frequency F (section 1.5.1), with A_n=1 is expressed as:

AF
perturb

(

θ
,
F
,

θ
0

)

=

∑

n
=
1

N

e

j
(

2
⁢
π
⁢
F

C

⁢

(

x
n

+

δ
n

)

⁢

(

sin
(
θ
)

)

(
14
)

Then the optimization variables are now δ_n. Since δ_nis a small perturbation compared to absolute location, to provide thereby a Taylor expansion:

e

j
(

2
⁢
π
⁢
F

C

⁢

δ
n

(

sin
(
θ
)

)

≈

1
+

j
(

2
⁢
π
⁢
F

C

⁢

δ
n

(

sin
⁡
(
θ
)

)

(
15
)

Substitute (15) to (14), the array pattern becomes:

AF
perturb

(

θ
,
F
,

θ
0

)

≈

AF
⁡
(

θ
,
F
,

θ
0

)

+

j
⁢

2
⁢
π
⁢
F

C

⁢

sin
⁡
(
θ
)

⁢

∑

n
=
1

N

δ
n

×

e

j
⁡
(

2
⁢
π
⁢
F

C

⁢

x
n

⁢

sin
(
θ
)

)

(
16
)

To guarantee the equation's accuracy, the perturbation should be small enough, such as for example:

❘
"[LeftBracketingBar]"

2
⁢
π
⁢
F

C

×

δ
n

❘
"[RightBracketingBar]"

≪
1

(
17
)

From (16), it is clearly that the optimization variable δ_nchanges from an argument variable to the coefficient variable, making fast convex optimization possible. FIG. 10 graphically illustrates an algorithm flow applying multiple iterations of such iteration for a converged solution, while accounting for minimal distance (sparsity) and accuracy constraints.

FIG. 11 graphically illustrates a 2D Converted Convex Optimization for a 2D RPS array. Specifically, it can be seen in FIG. 11 that a 9×9 2D RPS array (discussed above with respect to section 1.4.1) optimized with converted convex optimization exhibits and a significant worst-case SLL improvement of 8.2 dB, validating the effectiveness of the methods discussed herein.

1.5.3 Constraint Genetic Algorithm with Reduced Variables

Compared with brute-force optimizing numerous variables in the full phased array, a reduction of number of optimization variables leads to better optimization efficiency.

Example 1: Danzer aperiodic tiling array consists of 3 different basic building block triangles, as shown in FIG. 12, which graphically illustrates high efficiency optimization of a Danzer array with GA algorithm using the reduced number of variables. Optimization variables may be defined by adding antenna elements (2 elements in this example) within each basic triangle of the initial Danzer pattern. For each added point, two variables A and B can be used to uniquely define the position of the newly added point, given the vertex coordinate (V1, V1 and V3) of each triangle. Therefore, only 12 variables are needed for the added 6 points within 3 different triangles. Applying GA to optimize only 12 variables to efficiently synthesize a large number of elements Danzer array (N=164) while considering the constraints of 0<A<1 and 0<B<1 (guarantee that the added points are within each triangle). The array demonstrates the worst-case SLL of −11.5 dB and =−10.5 dB at f₀and 3f₀, respectively, exhibiting considerable improvement over −5.5 dB initial case with similar number of element (see, e.g., FIG. 7 and related).

Example 2: The “Pizza” array is a candidate to apply to reduce the number of variables for GA. This is because the full array pattern can be easily calculated based on the element location of a single slices, attributed to the rotational symmetry nature of the array. As shown in FIG. 13, GA is applied to randomize and optimize only the 15 elements within each array slice under the constraint of d_minand angular range Δϕ<2π/Nfold. A decent array SLL of −16.3 dB (improved by 2.6 dB) the worst-case SLL over f₀-3f₀is a manifest of the noise-like shuffled side lobe distribution, due to the essence property of non-uniformity and sparsity.

1.6 Summary of Optimized Broadband Array Performance

Table 2 summarizes the performance and optimization methodology of the various broadband arrays. It is noteworthy that the “broadband” does not only mean decent performance at the harmonics of the lowest frequency (f₀), but a continuous frequency range between lowest to highest frequency.

TABLE 2

Before
After

optimization
optimization

Min
worst case
worst case

distance
SLL (3:1
SLL (3:1

Starting
Optimization
Number of
between 2
bandwidth,
bandwidth,

Topology
geometry
method
elements
elements
θ = −60-60°)
θ = −60-60°)

Conventional

E.g., 256
0.5λ(f0)

0
dB

ULA

BroadBand
2D RPS
Converted
81
0.5λ(f0)
−2.8
dB
−11.1
dB

array A
array
convex

optimization

BroadBand
Danzer
GA with
164
0.5λ(f0)
−5.5
dB
−11
dB

array B
Aperiodic
reduced

tiling
variables

BroadBand
Multiturn
RPS distribution
183
0.5λ(f0)
−8.9
dB
−11.2
dB

array C
circular
in radial

array
direction

BroadBand
“Pizza”
GA with
90(fold 15)/
0.5λ(f0)
−10 dB/−13.7 dB
−13.7 dB/−16.3 dB

array D
array
reduced
195 (fold 13)

variables

BroadBand
Golden
Regular GA
90
0.5λ(f0)
10.7
dB
−11.5
dB

array E
spiral

array

1.6.2 Implementable Array Structure and Optimized Array Performance for Different N

For frequency agile antenna array hardware implementation, considering array performance, both 2D optimized array and “pizza” array (among others as described herein) are good candidates. However, from the perspective of system implementation difficulty, the “pizza” array may be considered more straightforward for either antenna in package or package-less RFIC-array package. This is because the rotationally repeatable fashion of “pizza” array allows a 1 to 1 mapping between a multichannel RFIC and a single array slice with a repeatable antenna feeding network, making the fabrication and assembly process much easier than the “random” distributed RPS elements, where the irregular feeding network design across the whole array is of great challenge.

Therefore, the “pizza” array was selected for experimental implementation with Nfold=15 (which is close to 2^N, making global RF dividing simpler). 4 different arrays with N=30, 60, 120, and 240 are optimized separately. Considering the physical size of a real broadband antenna, which will be discussed below, d_minmay be selected as 0.75λ(f₀) to avoid the overlap between two adjacent antennas. The calculated array performance as a function of number of array element are summarized in FIG. 14, which graphically illustrates optimized array performance for different N.

1.6.3 Optimized Array Performance for Different d_min

Generally speaking, a 3:1 frequency ratio has been used for real applications as discussed herein. It is noted that the performance for extremely wideband operation is also of interest for potential applications using narrow pulses as a carrier. As an example, optimized SLL performance for an N=104, Nfold=13 “pizza” array versus different d_min, where each d_minfrom 1.5λ to 10λ of the array is optimized separately, results in a d_minof 3λ manifesting a bandwidth ratio (f_max/f_min) of 6:1. The array is still able to maintain SLL below −11 dB even with d_minof 10λ or an extremely large bandwidth ratio of 20:1.

Based on the techniques of broadband circuits and sparse array synthesis presented in the previous chapters, this chapter sheds light on the system design of a frequency agile 120-element Tx phased array covering 3:1 bandwidth.

Ultra-Broadband Transmit Array with 8×1 Beamforming IC

2.1 120-Element Frequency Agile Transmit Phased Array
2.1.1 System Architecture

FIGS. 15A and 15B depict, respectively, a top view of a system architecture according to an embodiment, and a cross-section view of a portion of the system architecture. Referring to FIG. 15A, the depicted system architecture 1500 comprises a 120-element Tx Phased array formed as a “pizza” array with 15 folds (i.e., sections or “pizza” slices) 1510-1 through 1510-15 where each array slice “X” comprises (illustratively) eight antenna array elements formed as broadband dual port elements 1530-X-1 through 1530-X-8 and is paired with a respective 8-channel beamformer RFIC 1520-X using (illustratively) flip-chip packaging. Eight RF outputs (ch 1 through ch8) from one RFIC are routed to the eight respective antenna elements through coplanar waveguide (CPW) implemented in a high frequency package.

For each broadband radiating element 1520, its bandwidth should be evaluated in the perspective of both input matching and beamwidth of the radiation pattern. Especially for the broadband phased array, maintaining wide beamwidth (or close to isotropic pattern) is desired across the frequency range to mitigate the main-lobe reduction (or equivalent, side lobe side augmentation) due to beam steering.

The conventional ultra-broadband antenna topology such as spiral antenna can provide a large impedance matching bandwidth, but its beamwidth decreases remarkably as frequency increases due to the fixed aperture, narrowing down the beamwidth bandwidth.

Vivaldi antenna slightly moderates the above trade-offs by allowing antenna aperture to expand towards the third dimension, such antennas are typical with very high vertical profiles which restrict the capability of planar integration.

ME dipole antenna simultaneously uses an electric dipole and a magneto dipole to widen the beamwidth for both E and H plane, however, the reported bandwidth is still limited considering a reasonable antenna size.

Therefore, these single-port element topologies are deemed by the inventors to be not practically suitable for a 24-100 GHz planar array application. Rather, the inventors propose to use a dual-port antenna element wherein the entire operating frequency range is divided into a low band (LB) spectral region of approximately 32-55 GHz (˜53% fractional bandwidth) and a high band (HB) spectral region of approximately 55-100 GHz (˜58% fractional bandwidth). By using a 1-bit switching aperture according to operating frequency, the antenna beamwidth overall decreases slowly versus frequency and a wide beamwidth is maintained. In various embodiments, the HB part and LB part of the antenna may utilize a spiral antenna or bowtie antenna architecture. With this wideband structure, each antenna sub-block can cover roughly 60% fractional bandwidth without increasing size or profile, and while satisfying bandwidth needs.

Referring to FIG. 15B, the depicted cross-section view of a portion of the exemplary system architecture 1500 comprises with multi-layer high frequency high precision HDI PCB for antenna implementation, RF routing and RFIC IOs. A heat sink attaching to the backside of the RFIC chip using a thermal interface is needed for stable thermal dynamics.

The antenna array architecture discussed herein with respect to FIGS. 15A and 15B is full-wave EM simulated, and the radiation pattern with beam-steering performances at 37, 75 and 100 GHz are demonstrated in FIGS. 16A, 16B, and 16C respectively. The low side lobe across frequency and across steering angles validates the broadband nature of the disclosed antenna architecture.

2.1.2 IC-Antenna RF Interface

FIG. 17A illustrates details of antenna mounting and signal routing on a surface of the system architecture of FIG. 15A; namely, nonuniform physical routing from RFIC output to antenna element input on an IC-Antenna interface suitable for use in the system architecture of FIGS. 15A-15B, and FIG. 17B graphically illustrates wideband performance of the antenna mounting and signal routing of FIG. 17A. Specifically, FIG. 17A shows the RF routing between a RFIC 1520 and several non-uniformly distributed antenna elements 1530 (using 4 channels routing as an example). Due to the dual-port antenna topology, the HB-LB switch is implemented on chip with a “ground-signal-ground-signal-ground” (GSGSG) output pad allocation. For either LB or HB RF output, the RF copper pillar flip-chip bump along with two ground bumps form a CPW type transition which connects to the PCB CPW line, guaranteeing the broadband transition between RFIC and PCB. As shown in FIG. 17B, the routing to each non-uniformly located antenna is carefully addressed to keep the same electrical length, leading to very small phase difference between each channel. A less than-15 dB input reflection coefficient is achieved across 30-100 GHz for all CPW transmission lines.

2.1.3 8×1 Beamformer RFIC Architecture

FIG. 18 schematically depicts an eight-channel beamforming transmitter chip suitable for use in a RFIC in the various embodiments. The RF beamforming architecture consists of 1) 8-channel beamformers with independent phase and amplitude control; 2) A_nultra-wideband 1 to 8 RF power dividing network and 3) IQ direct up-convert transmitter for frequency conversion from baseband IQ signal pluses to RF frequency.

Each beamformer channel includes a band-select single-pole double throw (SPDT) switch connecting to the dual-port antenna, an ultra-wideband RF chain including PA, variable gain amplifier (VGA), high accuracy phase shifter (PS) and active balun for single-ended to differential conversion. The beamformer input is fed by an 8:1 ultra-wideband single-ended power dividing network with isolation enhancement between each output ports. The input of the power dividing network directly connects to the IQ up convert transmitter output, where a band select switch alternates between LB (30-55 GHZ) and HB (55-100 GHz) upconverter output ports. LB or HB IQ mixers are fed with quadrature LO generated by on-chip broadband quadrature hybrid, preceding with the LO chain. The LO chain starts from a frequency doubler with external LO signal fed between 15-50 GHz, followed by an on-chip filter for doubler harmonic filtering and a LO amplifier to enhance the LO swing. Each mixer's IF input is generated from an IF signal chain where an external IQ baseband data pulse (single-ended) firstly passes through an active balun, then fed to a differential IF VGA. 4 transmission gate switches are used to route the I and Q data input to either LB or HB upconverter IF input. The RF outputs of the two mixers are power combined using transformer based compact Marchand balun for a single-ended output. For debugging purpose, another SPDT switch is added between the IQ upconverter output and divider input such that the RF blocks (divider+beamformers) can be separated tested with an external input RF signal. The chip has a 128-bit serial peripheral interface (SPI) digital control block with a pad for external serial control bit input.

FIG. 19 schematically depicts a transmit chain of the beamforming transmitter chip of FIG. 18 suitable for analyzing gain and linearity thereof. FIG. 19 5 shows the simulated gain and OP1 dB of each Tx chain block for link analysis at widely separated frequencies, demonstrating 59.2 dBm, 64.4 dBm and 62.6 dBm Tx linear OP1 dB EIRP with N=120 element array, at 37, 64 and 94 GHz respectively. It is noted that simulated saturation output power and efficiency of a single beamformer as function of frequency demonstrates a bandwidth of 36-96 GHz over which the efficiency is >10%.

2.2 Broadband Beamformer Circuits Design
2.2.1 General Broadband Design Methodology: Interface Co-Design

Conventional multi-stage RF design are typically block based: for narrowband operation, each stage or blocks are designed for a 50Ω load and source impedance and then the different blocks can be easily cascaded. However, the 50Ω impedance assumption is not accurate for an ultra-wide band multi-stage design because it is intrinsically impossible to design matching networks for a broadband 50Ω, which means at any interface between two stages, the impedance looking back and look forward is not a 50Ω across a wide frequency range (unless using resistive matching). Therefore, a co-design method is essentially necessary for broadband cascaded blocks where one should assume the impedances at any interface are a function of frequency and the goal is to design impedance at stage interface a conjugate match at broadband frequency range, the interface impedance can be complex number and not necessarily to be 50 ohm. By doing this, a single broadband matching network can be inserted between two stages with complex frequency dependent input/output impedances, rather than using two matching networks where one is to match the previous output stage to 50Ω while the other to match the next input stage to 50Ω. A potential simpler interface matching network can lead to a lower power loss across wide frequency range while reduce the matching network area/footprint.

2.2.2 Ultra-Wideband Switch and PA Co-Design

The broadband co-design method is applied for designing the PA and Band-select switch interface. As shown in FIG. 20 (upper portion), the traditional design method focuses on a broadband design of PA, switch, and antenna, assuming a 50Ω source/load impedance. The loss (with mismatch) of a broadband output matching network for the PA loadpull impedance target is shown. Similarly, the switch transducer power loss across frequency is also plotted. By directly cascading the three stages, the total transducer power loss from PA collector to antenna port is 3 to 7.8 dB from 32-100 GHz (red loss plot from bottom half the figure). This loss accounts for the mismatch loss between 1) switch and antenna interface 2) matching network output and switch input interface and 3) matching network input and PA collector interface.

On the contrary, a co-design method shown in the bottom portion of FIG. 20 aims to add a simple matching network between PA collector and switch input such that it can directly match the complex antenna input impedance to the PA load pull impedance across 30-100 GHz. In this case, only an extremely simple network of a shunt inductance and a series cap is added after the PA collector, where the original complex broadband PA matching network is removed. As a result, the total transducer power loss from PA collector to antenna port significantly improves to 2 to 4.3 dB from 32-100 GHz, an overall larger than 2 dB loss reduction than the conventional method.

The detailed schematic of the SPDT band select switch and its large signal performance are exhibited in FIG. 21. The architecture is based on shunt switch topology where the transmission line T1/T1′ transforms the low impedance of a turn on switch to a higher impedance at the common input node, thus alternating the input signal to the other branch with the switch turned off. Due to the different load impedances for each branch (one connects to LB antenna port and one with HB port), the SPDT switch has asymmetrical parameters where T1≠T1′ and T2≠T2′, which provides more design freedom for optimality comparing to an ultra-wideband design with same load and forcing the symmetry between two paths. To guarantee enough linearity for the switch, it is proposed to use a stacked switch topology to alleviate the stress of each transistor and push the voltage that turns on and off transistor to a higher value. In addition, a reverse saturated HBT connection can reduce the parasitic capacitance between RF node to ground for lower loss. Due to the higher potential barrier between emitter-base junction than between collector-base junction, connecting the emitter to the RF node leads to a higher threshold voltage swing that turns on the emitter-base junction, leading to superior linearity. Motivated by this, the emitter of the top transistor in the stack is connected to the RF node, forming an E-B-C-B-E switch topology. The simulated gain versus output power curves demonstrates >20 dBm OP1 dB and >15 dB isolation across 30-100 GHz. The isolation is defined as the ratio of power delivered to the desired port to the power delivered to the other port. The high OP1 dB of the switch enables the high linearity of the whole Tx chain.

FIG. 22 graphically illustrates SPDT switch waveform at large signal excitation. Specifically, FIG. 22 shows the voltage waveform across the stacked switch under large signal output power (20 dBm) at 70 GHz. For the off branch, the key voltage to observe is the VBE of the top and bottom device where it can be seen that the swing (0.5 V) is well below the transistor VBE turn on voltage, demonstrating the linear behavior. As a comparison, when the output power reach P1 dB (21.8 dBm), the VBE swing of the top transistor increases which means the slight turn on of the top switch, reducing the transmission gain. The VCB of both top and bottom devices are far below the VB_cbobreakdown voltage at 20 dBm output power, guaranteeing the robustness of the switch at high power condition. For the on branch, VBC voltage swing is within the safe region for both transistors while the close to zero swing of VCE verifies the turn on operation of the switch.

The last stage of PA is based on a common-base stack topology while the first three stage are with single common-base transistor, coupled with transmission line based broadband matching networks. The PA delivers 16.4/17.8/16.3 OP1 dB and 21.2/25/19.7 dB gain at 37/64/94 GHz respectively.

2.2.3 Ultra-Wideband Phase Shifter with Quadrature Phase Bandwidth Extension Network

Achieving gain independent high accuracy phase control across broadband (>3:1 bandwidth) poses strong challenges on phase shifters design. Recent progress in broadband mm Wave phase shifters above 24 GHz utilizes RF switches to demonstrate “reconfigurable multi-band” on either passive or active phase shifter core, suffering from limited phase control range and high RF switch loss. All “RF switch-less” broadband vector IQ modulator phase shifter using Quadrature All pass Filter (QAF) broadband quadrature phase generation has been explored, but the network is very sensitive to the load (e.g., transistor gate capacitance) which significantly degrades the bandwidth. Inductive loading and de-Q techniques mitigate the issue, but the intrinsic loss due to resistance components in QAF is typically high (>10 dB loss). Moreover, the code-dependent input impedance of the active stage exacerbates the loading effect of QAF

To enable a broadband IQ vector modulator across 30-88 GHZ, use a 90° hybrid and Marchand balun-based network for wideband single-ended to differential quadrature phase generation with accurate phase/amplitude response. For the IQ VGAs and analog adder, a differential Common-base (CB) buffer stage allows ideal broadband and code independent impedance loading to the quadrature phase generation network. 5-bit accuracy with maximum phase error smaller than half LSB is demonstrated across 98.3% bandwidth up to W band.

For broadband quadrature phase generation, a compact transformer-based classic quadrature hybrid (FIG. 23A) can enable a 0.1° phase imbalance fractional bandwidth of 23% while a broadband quadrature hybrid in (FIG. 23A) enhances the phase imbalance bandwidth to 90.5%. However, the amplitude imbalance bandwidth for both hybrids still limits the bandwidth of a quadrature phase generation network. FIG. 23B graphically illustrates the amplitude response of the “through” and “couple” paths of the classic and broadband 90° hybrid circuitries of FIG. 23A;

Specifically, FIG. 23B shows the amplitude versus frequency response of the ‘through’ and ‘couple’ path of both hybrids where a better amplitude imbalance can be seen for broadband hybrid, but a 0.5 dB amplitude imbalance bandwidth around 40% still cannot fulfill the need of ultra-wideband phase shifter application. A key observation is that the ‘through’ and ‘couple’ port has an inverse amplitude response away from the center frequency. To generate two differential quadrature phase signals feeding differential I/Q VGAs, a balun is used to feed its balanced output to two 90° hybrids (either classic or broadband) (FIG. 24A). In this work, the two differential outputs of this network are fed to a bandwidth extender, shown in FIG. 24B. The bandwidth extender generates each output by combining two signals generated by ‘through’ and ‘couple’ path respectively. As an example, the 0o output can be generated by combining 1) the coupled output of a 0o input signal and 2) the ‘through’ output of a 90° input signal. Utilizing the property of the inverse amplitude response between ‘through’ and ‘couple’ paths, the gain compensation across frequency results in a more broadband amplitude response. FIG. 24C compares the electromagnetically (EM) simulated phase and gain imbalance across frequency among the three networks, exhibiting a significant gain imbalance improvement using the bandwidth extender network(<0.5 dB across 30-100 GHz). The bandwidth extender consists of four compact transformer-based classic quadrature hybrids; therefore, the whole network is relatively simple to build based on a single unit block. The EM simulated insertion loss of the whole quadrature generation network(without Marchand balun) is 2.4-3.1 dB across 30-100 GHz.

The conventional Gilbert cell VGAs has a three-stack architecture which limits the headroom or power. More importantly, the gain control is done by varying the transistor bias current which causes parasitic capacitance variation, therefore the change of input impedance. Variations in the input impedance affect the quadrature generator network, resulting in additional gain and phase error. To reduce this effect, various embodiments implement a CB buffer embedded with phase quadrant control as the interface between quadrature generation and active VGA core.

FIG. 25A schematically depicts an ultra-wideband phase shifter with a differential quadrature phase generation network according to an embodiment. FIG. 25B graphically illustrates broadband matching and code insensitive input impedance of a CB buffer of the network of FIG. 25A. FIG. 25C graphically illustrates insertion loss across 30-100 GHz of the EM simulated ultra-wideband differential quadrature phase generation network of FIG. 25A. FIG. 25D depicts an integrated circuit micrograph image of the phase shifter of FIG. 25A.

As shown in FIG. 25A, the four outputs from the quadrature generation network are fed to the emitter of the CB transistor for broadband matching. At the same time, the differential I/Q buffers allow the polarity change of the I/Q signals by controlling the base voltage of the CB transistors. Each output from the quadrature network always sees one on-transistor and off-transistor across different polarity control, therefore offering a broadband code-independent input impedance Zin (FIG. 25B). The output of the buffer is followed by I/Q differential VGAs and analog adder with 3-bit bias current control. Along with 2-bit polarity control in the first buffer stage, the phase shifter can work across all four quadrants with 5-bit control.

FIG. 26 schematically and graphically depicts inductive peaking to enhance high frequency gain close to G_max. Specifically, FIG. 26 describes the inductive peaking technique at the output of the IQ VGAs, for bandwidth broadening across 30-100 GHz. First extract the fully differential G_max(top curve) of the phase shifter and a proper series high impedance Transmission line (130 μm Length) is added to enhance high frequency (>70 GHz) gain by 4 dB and to be close to G_max. The simulated differential gain of the phase shifter is about −6 to 4 dB across 30-88 GHz and the gain slope can be compensated by another high pass amplifier in the design of the full beamformer chain.

The phase shifter operates fully differential in the beamformer chain, but on-chip single-ended to differential conversion needs to be designed for evaluation performance. A Transformer-based broadband Marchand balun is contemplated as described herein. The layout is based on the lumped modeling shown in FIG. 27A where coupling factor K determines the balun impedance transformation ratio. The compact layout, insertion loss and balancing metrics are summarized in FIGS. 27B-27D. Lower than 0.5 dB gain imbalance and lower than 2° phase imbalance over 30-100 GHz are exhibited.

The prototype is implemented in 90 nm SiGe, and an image of the implemented IC is depicted in FIG. 25D. It consumes 24 mW power under 2V supply. The phase/amplitude response is measured using Anritsu M4647B VNA with a frequency extender up to 110 GHz. Even though the ultra-wideband quadrature generation network allows a frequency-independent code setting, a post-silicon frequency-dependent code optimization which can correct the potential quadrature phase mismatch due to process variation, allows a further performance improvement.

FIG. 28A graphically illustrates measured amplitude/phase at 34, 54, 64 and 84 GHz for the ultra-wideband phase shifter schematically depicted in FIG. 25A, FIG. 28B graphically illustrates measured gain variation and rms gain error vs. frequency for the ultra-wideband phase shifter schematically depicted in FIG. 25A, and FIG. 28C graphically illustrates measured max phase error and rms phase error vs. frequency for the ultra-wideband phase shifter schematically depicted in FIG. 25A. Specifically, FIG. 28A shows the measured amplitude/phase polar plot at 34, 54, 64 and 84 GHz. Across 30-88 GHZ, the gain variation across 32 codes is about 0.7-1.8 dB while the rms gain error is 0.19-0.48 dB (FIG. 28B). The very low rms phase error (FIG. 28C) of 1.34-3.1° and a maximum phase error of 2.63-5.4° are achieved across the 98.3% bandwidth. Maximum phase error lowering than half LSB) (5.625° demonstrates the 5-bit accuracy of this work.

2.2.4 Multi-Stage VGA with Tailored Peaking Frequency Response

FIG. 29A schematically depicts a 4-stage differential cascode broadband VGA implemented with tail current control to allow 10 dB gain control range. FIG. 29B schematically depicts a T type network for peaking frequency response including a graphical illustration of this response. R-C feedback is added between the output and input for stability enhancement. To reduce the control-depended input/output impedance change, only middle stages (stage 2 and 3) are implemented with the 3-bit control. The first three stages are identical and interface with broadband 50Ω input impedance (Zin in FIG. 29B) under 50 12 differential load. To compensate for the dropping gain of the phase shifter at the higher end of the spectrum, the output network of each VGA stage is designed to have a peaking frequency response to allow a flat gain response of the chain. As shown in (FIG. 29B), the impedance (Z_L) looking into the transmission line based broadband T network demonstrates a higher value as frequency increases in both its magnitude and real part. FIG. 29C shows the simulated differential S₂₁gain with gain peak of 30 dB at 85 GHz. The inventors created a VGA test structure (with an additional balun for broadband measurements). The measured S₂₁plot shows acceptable correlation with simulation and is limited to narrower bandwidth due to the additional balun on both input and output that are not present in the Tx chain.

2.2.5 Active Balun

A balun is needed to convert the RF signal from power divider single-ended output (broadband 50Ω) to a differential signal feeding full differential phase shifter (100Ω differential input impedance). For conventional passive Marchand baluns, a large impedance transformation ratio such as 2 to 1 limits its bandwidth and introduce more passive loss at band edge. Therefore, this work adopts an active balun implementation for broadband and low loss.

FIGS. 30A-30B schematically depict a RF active balun design and end to end layout of the active balun, respectfully. It is based on differential pair topology with one side AC ground. Due to the imperfection of the common mode rejection ratio of the differential pair at mmWave frequencies (e.g., the current source parasitic capacitance to ground), an asymmetrical inductive load is chosen here (L1≠L2) which can compensate the gain and phase mismatch between the two signal paths.

Attributed to the mismatch compensation techniques, the balun achieves a decent amplitude imbalance and phase imbalance of 0.1-0.4 dB and 0-4° across 30-100 GHz (FIG. 30C), with all three-port terminated as 50Ω (A 2:1 impedance transformation ratio). The input return loss is below −10 dB across 30-100 GHz (FIG. 30D) by implementing a dual-band input matching network. FIG. 30E shows the gain (the total output from differential output divided by input power) versus total output power at 34/64/94 GHz exhibiting gain of 0.2/0/−1 dB and OP1 dB of −10/−8/−7 dBm, respectively. Due to the high gain of the beamformer chain after the active balun, the active balun has enough output linearity range to drive the following stages. The active balun consumes 7 mA from a 2.5V supply.

2.2.6 Ultra-wideband Divider with Improved Isolation

FIG. 31A schematically depicts a 1 to 8 ultra-wideband power dividing network with a 1 to 2 divider core implementation. The network is based on 50Ω 1 to 2 power divider cores with coplanar waveguide (CPW) broadband routing transmission lines. The ultra-wide bandwidth of the 1 to 2 divider core is enabled by a coupled line network following a traditional Wilkinson type divider. The odd and even mode resonances create a dual peak broadband loading response for the first dividing stage. For multichannel phased array, the isolation between each channel input is of great importance because a poor isolation leads to an interaction of phase tuning between channels, degrading the phase setting accuracy. A_nisolation enhancement technique by cascading another branch with a second isolation resistor significantly improves the isolation across band (FIG. 31B) while introduce only up to 0.2 dB insertion loss. As shown in FIG. 31C, the transducer gain from input to any of the output is from −12.1-13.5 dB, demonstrating an insertion loss of 4.5 dB at 100 GHz. The isolation between two adjacent ports originating from a same divider core (Pout_cn3 and Pout_cn1) is below-20 dB across 40-100 GHz (−20 to −15 dB across 30-40 GHz) while the isolation between two adjacent ports originating from a different divider core (Pout_cn3 and Pout_cn5) is below-30 dB across 37-100 GHz (−30 to −20 dB across 30-37 GHz).

2.2.7 Measurement Results

A fabricated beamformer transmitter was implemented in a 90 nm SiGe. As a key enabler, this 36-91 GHz ultra-broadband Tx beamformer maintains 1) maximum phase error below 0.5 LSB, r.m.s. phase error of 1.24-2.8°, r.m.s. gain error of 0.24-0.35 dB across the frequency range, 2) broadband PA with a deep-learning enabled matching network, and 3) broadband VGA with tailored frequency response across 87% bandwidth. The system operates with a 2V supply. The phase shifter and VGA consumes maximum power of 30 mW and 52 mW across code settings, respectively. The beamformer phase/amplitude response is measured using a 125 GHz Anritsu M4647B VNA. While the ultra-wideband quadrature generation network was designed to allow frequency-independent code setting for phase control, a frequency-dependent code optimization algorithm was employed that can correct the potential quadrature phase mismatch due to process variation and allowing a further performance improvement in terms of phase error and gain variation across frequency. With a one-time measurement across 30-100 GHz with a 10 GHz step, the process automates optimized code synthesis within the slotted 10 GHz bandwidths. In a measured linear phase response and amplitude plot across phase control code over 36-91 GHz, gain variation across phase control codes is about 1.1-1.6 dB while the r.m.s. gain error is 0.24-0.35 dB. The extremely low r.m.s. phase error of 1.24-2.8° and a maximum phase error of 2.4-5.6° are achieved across the 87% bandwidth. Maximum phase error smaller than half LSB) (5.625° demonstrates the effectiveness of the 5-bit phase control accuracy. The phase control code optimization can also be applied to compensate chip to chip variation. Due to process variation, by applying the same code to chip 2 as chip 1, the gain/phase error at the band edge of chip 2 degrades, but the accuracy can be recovered by applying new optimized code for chip 2. Measured S₂₁of the Tx chain across the VGA 3-bit control settings is excellent. The phase control code applied is the one optimized for 60 GHz. The results demonstrate 30-35 dB gain across 36-90 GHz, broadband input return loss, and 10 dB of gain control as expected.

Measured large-signal performance (P_outVS. P_in) across 32 phase control codes exhibited a peak Psat of 15 dBm and OP_1dBof 13.5 dBm. At this OP_1dB, the total DC power consumption is 206 mW with a total Tx efficiency of 10.9%. The measured maximum OP_1dBis from 9 to 13.5 dBm across 36-90 GHz.

A custom setup for multi-Gb/s modulation measurements was created. A broadband mixer modulates the carrier frequency with high-speed data from the arbitrary waveform generator, and the output signal from the chip is down-converted by an external mixer and digitized by an 80-GS/s oscilloscope and analyzed by Keysight VSA software. The beamformer is measured with a 1.8 GHz bandwidth 64QAM signal (PAPR=9.65 dB). Without pre-distortion, the Tx chip demonstrates the EVM/ACLR of −25.6 dB/−31.9 dBc with average output power of 4 dBm at 10.8 Gbps at 60 GHz. The linear power corresponding to an EVM of −25 dBm are measured to be 4.1 dBm and 4.3 dBm for 10.8 Gbps and 9 Gbps data rates. Compared with the state-of-the-art mm Wave Tx phased array and broadband phase shifters (as noted in Table 3 below), the various embodiments demonstrate high gain, high data rate transmission and the best phase/amplitude errors over one of the widest bandwidths.

TABLE 3

BroadBand phase

mmWave beamformer channel
shifters

This
Alhamed
Chen
Roy
Shahramian
Lee
Anjos
Pepe

work
JSSC 22′
TMTT 21′
RFIC 19′
TMTT 18′
JSSC 19′
TMTT 20′
JSSC 17'

Technology
90 nm
90 nm
28 nm
28 nm
180 nm
130 nm
250 nm
28 nm

SiGe
SiGe
CMOS
CMOS
SiGe
SiGe
BiCMOS
SOI

0.5 LSB Error
36-91
—
—
—
—

14-50
—

BW (GHz) *
(87%)

(112.5%)

S21 BW
36-90
16-50
34-43
35-41
75-100
94GHz
14-50
78-93

(GHz) **
(5 dB, 86%)
(5 dB, 97%)
(5 dB, 23%)
(5 dB, 16%)
(5 dB, 29%)

(112.5%)
(16.3%)

Phase range
360°
360°
360°
360°
360°
360°
180°
360°

Phase
5
5
4
5
4
8
2
4

resolution

(bit)

Gain control
10
16.2
20
10.2
—
10
—
—

(dB)

Beamformer
30-35
29.3-34.3
27.3-32.3
43-38
14-19
38.5
−7.2 @
0.83 @

gain (dB)

32 GHz
89 GHz

Max phase
2.76-5.5
—
—
—
0.5-5
0.77
5.8-22.5
—

error (°)

(82-105)

RMS gain
0.24-0.35
<1.7
0.65-0.8
—
0.57
0.36
<0.94
1.68-2

error (dB)

(37-40 G)

(90 G)

RMS phase
1.24-2.8
<5.6
0.75-4.75
—
0.27
0.26
<9.7
9.4-11.9

error (°)

(37-40 G)

(90 G)

OP1 dB
11-13.5
13.5-14.7
10.8
10.2-12.3
4.5-8.5 Psat
3-4
—
−5.2@

(dBm)
(36-80 G)
(20-50 G)
(38 G)
(37-40 G)
(75-98)
(91-97)

89 GHz

P_DC(mW)
214 @
250 @
187.5
339 @
500 (Tx + Rx)
154
0
21.6

P1 dB
P1 dB

P1 dB

@60 GHz

Modulation
1 Gbps
2.4 Gbps
0.6 Gbps
0.6 Gbps
5MS/s

—
—

64QAM
64QAM
64QAM
64QAM
256QAM

EVM (dB)/
−25 dB
−22 dB
−32 dB
−32 dB
3%

—
—

Pavg (dBm)
EVM
EVM @
@−2 dBm
@−2 dBm
0 dBm

@
6.8 dBm
@37 GHz
@37 GHz
90 GHz

4.8 dBm
@

@
44 GHz

54 GHz

Chip area
3 (with
0.85(w/o
2.2 (with
—
0.5 (w/o
1.7 (with
0.48 (w/o
0.12 (w/o

(mm²)
pad)
pad)
pad)

pad)
pad)
pads)
pads)

2.3 Broadband IQ Direct Up-Converter Design
2.3.1 IQ Mixer

FIG. 32 depicts an exemplary IQ direct up-convert transmitter architecture according to an embodiment. The architecture consists of two upconverters which cover LB (30-55 GHz) and HB (55-100 GHz), respectively. A band select switch (similar design principle as shown in section 2.2) is used to alternate between the LB and HB upconverter RF outputs. The 2 bands reconfigurable structure is necessitated: The LO generation chain requires a frequency multiplier to lower the frequency of the external LO input and thus the loss of PCB LO routing. If using a full broadband (approximately 24-100 GHZ, 30-100 GHz, etc.) LO generation chain, the unwanted harmonics from the frequency multiplier will lie in band due to the more than octave bandwidth of the system. For instance, a frequency doubler that generates a 40 GHz LO signal will simultaneously produce an unwanted 80 GHz 4th harmonic, while a frequency quadrupler generating 80 GHz would yield an undesired 2nd harmonic, which necessitates the filtering of these undesirable harmonics before they enter the mixer to avoid the mixing spurs. The challenge here is that the change of carrier frequency requires the use of a frequency reconfigurable filter, a multi-bit switchable filter that proves exceedingly difficult to implement at mm Wave frequency, particularly in the LO chain, where a large voltage swing leads to nonlinearity issues. Consequently, a two-band separation architecture was implemented that features a fixed filter in each of the chains, where both chains (with a frequency doubler) cover a carrier frequency range that is less than 2:1. As a result, an inband band-pass filter enables the complete removal of unwanted harmonics.

FIG. 33 depicts an IQ mixer schematic and Marchand balun combining network. As shown in FIG. 33, each mixer follows a Gilbert cell based double balanced topology with a bias tail current. Because the IF inputs are resistive biased with the previous stage (IF VGA), the tail current is needed to reduce the sensitivity of the input transistor's transconductance to the common mode voltage changes. The output current combining with a broadband Marchand balun for single-ended output is illustrated. The balanced mixer topology aims to improve the LO leakage due to the ideal balanced coupling path from LO+ and LO− to the RF port. The mixer layout at high frequency has critical impact on the LO leakage performance.

FIG. 34A-34B depict an active mixer IQ core design with balanced and unbalanced layouts, respectively. FIG. 34C graphically illustrates a comparison of IRR and LO rejection for the active IQ mixer core design with balanced and unbalanced layouts as respectively depicted in FIGS. 34A-34B. Referring to FIG. 34B, a balanced layout enables a roughly equal physical path between differential LO port to output node, compared to the unbalanced LO-RF allocation in FIG. 34A, it improves the LO rejection significantly (>15 dB) at 60-90 GHz frequency while maintaining the same image rejection ratio (a parameter defined to evaluate the IQ mismatch of the transmitter) as seen in FIG. 34C.

2.3.2 IF Active Balun and IF VGA

FIG. 35A schematically depicts a baseband balun and IF VGA. FIGS. 35B, 35C, and 35D graphically illustrate frequency response of the IF chain for different gain state, phase and amplitude imbalance frequency response, and performance versus input swing, respectively of the baseband balun and IF VGA of FIG. 35A.

Specifically, FIG. 35A is a schematic of the IF chain where a differential VGA precedes a baseband active balun. The baseband balun substantially reduces the complexity of differential 1 to 15 baseband routing on PCB. It follows the similar principle as the RF active balun where a neutralization cap is added to compensate the influence of the finite impedance looking into the current source on the balancing performance. A cascode current source is used to further boost the low frequency resistance for higher common mode rejection ratio. The diode connected load is used to bias the VGA stage for smaller process variation compared to resistors. The VGA adopts switchable source degeneration resistor for different 4-bit gain control. This mitigates the gain code dependent phase change of the VGA. The IF chain demonstrates a 4 GHz 3 dB bandwidth with 6 dB gain control range from 7-13 dB (FIG. 35B). From DC to 4 GHZ, the phase mismatch is below 0.50 while amplitude imbalance is below 0.1 dB (FIG. 35C). At 2 GHz IF frequency, FIG. 35D shows the voltage swing for each output as a function of input swing. The input 1 dB compression swing is about 250 mV which is high enough for real application and both phase and amplitude balancing performance is still maintained under large swing.

2.3.3 LO Chain

FIG. 36A schematically depicts a frequency doubler and LO buffer, and FIG. 36B graphically illustrates simulated output LO power and 4th harmonic across frequency. In the schematic of the LO chain shown in FIG. 36A it can be seen that an input balun feeds the differential input of a stacked push-push doubler where the bottom stage is biased at deep class AB mode for better second harmonic generation. The common mode second harmonic signal then passes through the top common base like transistor for a stacked higher gain. The doubler is followed by a cascode LO buffer for further boost of LO chain gain and LO swing. The output of the LO buffer is connected to the harmonic filter, followed by a quadrature hybrid, whose design is detailed in section 2.2.3, to deliver the LO signal for I and Q mixers. The simulated output 2nd harmonic and undesirable 4th harmonic power is plotted from 15-46 GHz fundamental input frequency range (