Antennas and Propagation
Chapter 5b: Mutual Coupling in
Antenna Arrays
Definition
IEEE Standard Definitions and Terms for Antennas
Defines mutual coupling as follows:
2.244 mutual coupling effect (A) (on the radiation pattern of an array antenna). For array antennas, the
change in antenna pattern from the case when a particular feeding structure is attached to the array and
mutual impedances among elements are ignored in deducing the excitation to the case when the same feeding
structure is attached to the array and mutual impedances among elements are included in deducing the
excitation.
(B) (on input impedance of an array element). For array antennas, the change in input impedance of an
array element from the case when all other elements are present but open-circuited to the case when all other
elements are present and excited.
(A) ⇒ Radiation patterns are modified by nearby antennas.
(B) ⇒ Input characteristics (like impedance) modified
In this lecture we will study this effect in detail.
Antennas and Propagation
Slide 2
Chapter 5b
Mutual Coupling Effect
From Standpoint of Radiation Integrals
What does placing an antenna nearby do?
Change the boundary condition of the problem
Will affect both radiation and terminal properties
Two scenarios
Different function of
antennas
But, can be analyzed
using same
equations
Antennas and Propagation
(a) Transmit Mode
Slide 3
(b) Receive Mode
Chapter 5b
Transmit Mode
Intuitive Explanation of Modified Radiation
Drive element m
Radiated field intercepted by n
Causes radiation from n
Total radiation is combination of m and n
Effective radiation when we drive m
is thus changed
Input Characteristics
Power radiated by n is intercepted
again by m
Changes current flowing on m
Input impedance at m is modified
Antennas and Propagation
Slide 4
Chapter 5b
Transmit Mode Analysis
Example 2-antenna system
Load/drive port 1
Goal: Find impedance/pattern
looking into port 2
Analysis
Clearly, the input characteristics at port 2 change due
to what we connect at port 1!
Antennas and Propagation
Slide 5
Chapter 5b
Transmit Mode Analysis (2)
Radiation Pattern
Pattern of kth antenna,
other antennas “open circuit”
Important note:
This is called an “embedded pattern”
In contrast to “isolated pattern” of
single element
Let
Also, effective pattern of element 2 has
changed due to load on antenna 1!
Antennas and Propagation
Slide 6
Chapter 5b
Receive Mode
Intuitive Explanation
Plane wave impinges on element m
Current flows on m
Power reradiated (scattered!)
Some reradiated power received by n
This causes radiation by element n
Some power received by m
Current on m is modified
Important Point
Effective receive aperture of element m
depends on loading of element n
(and vice versa!)
Antennas and Propagation
Slide 7
Chapter 5b
Mutual Coupling Effect
Severity Controlled by
Radiation patterns of the two antennas
or distribution of near-fields
Spacing of the antenna
Orientation of antennas
Loading
Ways to avoid coupling
Place elements far apart
Careful design of antennas
Antennas and Propagation
Slide 8
Chapter 5b
Infinite Array
Purpose
Simplifies analysis
Can understand effect more intuitively
Also useful to analyze performance of
large arrays
Assume
Regular array of elements (uniform spacing)
Identical elements
Uniform phase shift driving / uniform plane-wave excitation
Leads to
Just constant phase shift in signals from one element to next
Antennas and Propagation
Slide 9
Chapter 5b
Infinite Array: Transmit Mode
Analysis
Voltage on mnth element (element at mth row, nth column)
Mutual impedance from pqth to mnth element.
“Driving impedance” of mnth element
For uniform plane-wave excitaiton
linear phase shift across array of voc
because array is infinite, have linear phase shift of currents also!
Antennas and Propagation
Slide 10
Chapter 5b
Infinite Array: Transmit Mode (2)
Implications
Driving impedances of all the elements are identical
Makes analysis much simpler
Complete system can be understood by driving 1 antenna
Antennas and Propagation
Slide 11
Chapter 5b
Infinite Array: Receive Mode
Infinite resistive sheet model
Reflection of sheet
Receive power is scan angle dependent.
Antennas and Propagation
Slide 12
Chapter 5b
Compensating Mutual Coupling
Practical Uses of Mutual Coupling?
Reconfigurable antennas: modify pattern, matching
RFID / spatial modulation: send information by switching a load
Coupling normally detrimental
Modifies radiation patterns of elements
Complicates analysis of array
Can correlate signals
Compensation methods
1. Matching-based methods
2. Digital compensation
Antennas and Propagation
Slide 13
Chapter 5b
Matching-Based Methods
Method allows “perfect” decoupling
Decoupling network:
Input reflection matrix is the Hermitian of the antenna reflection
Matrix extension of 1-port conjugate match
Design so Γ is 0 for reference impedance (Z0=ZL)
Input characteristics / patterns of ports are independent
Problem: Designing D.N. for large N!
Antennas and Propagation
Slide 14
Chapter 5b
Digital Compensation
Given: we know ZA and ZL
Measure v on array elements
Can use linear equations to get voc
For “minimum scattering” elements, voc of element
very close to v on an isolated element (i.e. other
antennas not present)
Problems with Digital Compensation
Requires detailed array calibration (ZA, ZL, embedded patterns)
Signals corrupted before noise and quantization (info. loss)
Antennas and Propagation
Slide 15
Chapter 5b
Supergain / Superdirectivity
Phenomenon
Allows high gain for small antennas
Mathematics shows it is possible
Not practical: why?
High Q
High matching sensitivity
Low efficiency (ohmic losses)
Antennas and Propagation
Slide 16
Chapter 5b
Supergain Analysis
Consider
ULA along x-axis
Uniform linear array
Radiation in azimuth (xy) plan (θ = π/2)
Dipoles
Assume embedded patterns are
approximately same as isolated patterns
(minimum scattering assumption)
Radiation pattern of array
Antennas and Propagation
Slide 17
Chapter 5b
Supergain Analysis (2)
Radiation intensity of uniform
radiator with same input power:
Radiation intensity in direction φ is
Antennas and Propagation
Slide 18
Chapter 5b
Supergain Analysis (3)
Goal: directivity in direction φ0 as
large as possible
Simplify by remove A from
constraint.
Problem:
or
Now, we have a new problem:
What is the solution?
Antennas and Propagation
Slide 19
Chapter 5b
From Linear Algebra
Optimization Problem
Solution
x = eigenvector corresponding to the largest eigenvalue of A
refer to this as the “dominant” eigenvector
For our Problem:
a′ = dominant eigenvector of G′(φ0)
Antennas and Propagation
Slide 20
Chapter 5b
Supergain Analysis (4)
Analyze N=2 elements: Simple
Reveals main effect
For φ0=0 and N=2, eigenvectors are close to
(a) Odd mode
(b) Even mode
For φ0=0, odd mode dominates
Let
Note: α is an arbitrary scale factor
Antennas and Propagation
Slide 21
Chapter 5b
Supergain Analysis (5)
For odd excitation radiated field is
Directivity becomes
Radiated power is
Consider limit as kΔ→0
Radiation intensity of isotropic radiator
or U0 = Prad/(2π) = aHAa
D0 = 2
Antennas and Propagation
Slide 22
Chapter 5b
Result of Supergain Analysis
Two Elements
Odd-mode excitation
Vanishing separation
Directivity D0=2
For single antenna D0=1
Meaning
Can put two dipoles as close together as we like
Get twice directivity of single dipole
If we pack in N, get factor of N
Can make a tiny antenna as directive as we like
Contradiction?
Antennas and Propagation
Slide 23
Chapter 5b
Result of Supergain Analysis (2)
Consider Antenna Weights
J1 = +∞
J2 = -∞
Currents are infinite but opposite
Now, as separation diminishes
Not practical
High ohmic losses
High sensitivity
Meaning
For finite radiated power,
Antenna weights become infinite!
Antennas and Propagation
For most analyses
Set constraints to avoid supergain
solutions
Slide 24
Chapter 5b
Summary
Mutual Coupling in Antenna Arrays
Antenna elements affect each other
Network characteristics
Radiation patterns
Compensation
Possible through decoupling network
or digital (SP) calibration
Supergain effect
Coupled dipoles can have higher gain than uncoupled
Mostly mathematical. Should be avoided in real designs.
Antennas and Propagation
Slide 25
Chapter 5b