elec_2016_nguyen_huy

Development of High-Performance Radiometer Cali-
bration Switch for Millimetre Waves
Huy Nguyen
School of Electrical Engineering
Thesis submitted for examination for the degree of Master of
Science in Technology.
Espoo 16.09.2016
Thesis supervisor:
Prof. Antti Räisänen
Thesis advisor:
D.Sc. (Tech) Janne Lahtinen

i
AA LT O U NI VE R SIT Y
S C H O O L O F E LE CT RI C AL E N GIN EE R IN G
AB ST R ACT O F T HE
M AS T E R ’S T HE SI S
Author: Huy Nguyen
Title: Development of high-performance radiometer calibration switch for millimetre
waves
Date: 16.09.2016 Language: English Number of pages: 8+69
Department: Department of Radio Science and Engineering
Supervisor: Prof. Antti Räisänen
Advisor: D.Sc. (Tech) Janne Lahtinen
In microwave remote sensing radiometers, calibration switches are needed in the ap-
plication of internal calibration references. Very low insertion loss is beneficial in view
of low receiver noise and good radiometric resolution (ΔT). Low insertion loss can be
achieved with ferrite junction switches. In developing millimetre wave ferrite junction
switches, however, the small dimensions of the ferrite become a challenge.
Targeting towards W band (89 GHz), two frequency-scaled switches at Ka band
(36.5 GHz) have been developed and manufactured in the current work. One of the
switches applies higher order mode operation, resulting in larger ferrite dimensions. A
reference switch to apply dominant mode operation has been developed as well.
Through the development of two Ka band ferrite switches, the feasibility of both dom-
inant mode and higher order mode operation switches has been confirmed, and
relatively good compliance between electromagnetic simulations and measurement re-
sults is observed. The switches have average insertion losses of 0.85 dB and 0.3 dB
over 1.0 GHz and 4.7 GHz, respectively.
Keywords: ferrite switch, radiometer, calibration, higher order modes.

ii
Preface
This thesis has been written to fulfil the graduation requirements of the Master’s pro-
gramme in Radio Science and Engineering at Aalto University. The thesis is the outcome
of more than two years of pursuing the study at Aalto University and more than one year
of employment at Harp Technologies Ltd. I am happy to be engaged in the project of
millimetre-wave switch development by Dr. Sc. Janne Lahtinen, the managing director
of Harp Technologies and my thesis’s advisor. Working in the project teaches me greatly
in many aspects, from technical knowledge to practical skills.
I am indebted to many people for their helps, supports and advices in different ways
to make this thesis complete.
First of all, I would like to thank Dr. Sc. Janne Lahtinen for offering me the challenge,
for his excellent guidance through the work and for numerous supports and valuable ad-
vices. I also benefitted from many discussions with him. Special thank goes to Mr. Teemu
Ruokokoski, senior design engineer at Harp Technologies, for all practical tips and assis-
tance during manufacturing and testing of the switches.
I would like to thank Prof. Antti Räisänen for accepting to supervise my thesis and for
his helpful advices, especially regarding simulation of the switches. He also sacrificed
part of his time to help review my writing and give comments.
To all other colleagues at Harp Technologies, I wish to thank you for your supports as
well. To teaching staffs, thank you for wonderful programme and courses. And to my
friends in RAD department, thank you for fruitful debates about electromagnetic/antenna
problems.
Finally, my family in Vietnam deserve particular thanks for their great supports and
keeping me motivated, and thanks are also due Hanny, my girlfriend, for her patience and
encouragement.
Espoo, 16.09.2016
Huy Nguyen

iii
Contents
Abstract .........................................................................................................................i
Preface..........................................................................................................................ii
Contents.......................................................................................................................iii
Symbols........................................................................................................................v
Abbreviations ............................................................................................................viii
1 Introduction............................................................................................................1
2 Overview of radiometric measurement..................................................................3
2.1 Radiometry......................................................................................................3
2.2 Radiometer......................................................................................................4
2.3 Calibration of radiometer................................................................................5
2.4 Critical parameters of calibration switch........................................................7
2.4.1 Insertion loss............................................................................................7
2.4.2 Isolation...................................................................................................9
2.4.3 Return loss.............................................................................................10
2.4.4 Switching time.......................................................................................10
2.4.5 Bandwidth .............................................................................................11
2.4.6 Repeatability, self-heating and stability ................................................11
3 Background study of switching technologies ......................................................12
3.1 mHEMT FET switch technology..................................................................12
3.2 MEMS switch technology ............................................................................15
3.3 Ferrite switch technology..............................................................................19
3.4 Switch technologies trade-offs......................................................................21
4 Theory of ferrite junction circulators ...................................................................24
4.1 Basics of microwave ferrite..........................................................................24
4.2 Junction ferrite circulator..............................................................................27
4.2.1 Analytic field equation approach...........................................................28
4.2.2 Eigenvalues approach............................................................................30
4.3 Higher order modes ferrite junction..............................................................34
4.3.1 Observation of higher order resonance modes in ferrite junction .........34
4.3.2 Application of higher order modes in circulator and switch .................35
5 Design of Ka band ferrite switches......................................................................37
5.1 Design methodology.....................................................................................37
5.2 Ferrite material..............................................................................................38
5.2.1 Saturation magnetization.......................................................................38
5.2.2 Curie temperature..................................................................................38
5.2.3 Resonance line width.............................................................................39
5.2.4 Spin-wave line width.............................................................................39
5.2.5 Materials selection.................................................................................39
5.3 Electrical design of SPDT switch variant #1................................................40
5.4 Electrical design of SPDT switch variant #2................................................41
5.5 Magnetic circuit design.................................................................................43
5.6 Mechanical design ........................................................................................44
5.6.1 Switch variant #1...................................................................................44
5.6.2 Switch variant #2...................................................................................45
5.7 Manufactured switches .................................................................................46
6 Switch functionality measurements and results ...................................................47
6.1 Laboratory setup ...........................................................................................47
6.2 Measurement results .....................................................................................48
6.2.1 Switch variant #1: measurement vs. simulation....................................49

iv
6.2.2 Switch variant #2: measurement vs. simulation....................................57
7 Summary ..............................................................................................................63
References ..................................................................................................................65

v
Symbols
𝐴1,2 Cross section area of magnetic core [m2
]
𝐴 𝑔 Cross section area of the airgap [m2
]
𝑎 Width of a rectangular waveguide [m]
𝑎 Slope constant of the radiometer transfer function
𝒂 𝒙,𝒚,𝒛 Unit vectors on x-, y-, z-axes
𝐵 Bandwidth [Hz]
𝐵𝑓 Spectral brightness [W/(m2
∙Hz∙sr)]
𝑏 Height of a rectangular waveguide [m]
𝑏 Constant of the radiometer transfer function
𝑒 Emissivity
𝑓0 Operating frequency [Hz]
𝑔 𝑒𝑓𝑓 Effective Lande´ factor
𝐻 𝑏𝑖𝑎𝑠 Biasing magnetic field strength [A/m]
𝑯 𝟎 External static magnetic field vector [A/m]
Δ𝐻 Resonance line width [A/m]
Δ𝐻 𝑘 Spin-wave line width [A/m]
ℎ 𝑥,𝑦,𝑧 x-, y-, z-components of the time-varying magnetic field vector [A/m]
𝒉 Time-varying magnetic field vector [A/m]
𝐼 Electric current [A]
𝐼 𝑜𝑢𝑡 Radiometer output indicator [V, Hz]
𝑱 Electron angular momentum vector [kg∙m2
/s]
𝐾 Radiometric constant depending on radiometer types
𝑘 𝐵 Boltzmann’s constant (1.38×10-23
J/K)
𝐿 Ferrite cylinder length [m]
𝐿1 Turnstile cavity length [m]
𝐿𝑖𝑠𝑜 Switch isolation
𝐿 𝑠𝑤𝑖𝑡𝑐ℎ Switch loss
𝑙1,2 Lengths of the magnetic core parts [m]
𝑙 𝑔 Length of airgap [m]
𝑴 𝟎 Static magnetization vector [A/m]
𝑴 𝑺 Saturation magnetization vector [A/m]
𝜇0 𝑀𝑠 Saturation magnetization level in SI [T]
4𝜋𝑀𝑠 Saturation magnetization level in Gaussian units [G]
𝑚 𝑥,𝑦,𝑧 x-, y-, z-components of magnetization vector [A/m]
𝒎 Time-varying magnetization vector [A/m]
𝒎 𝒅 Electron magnetic dipole moment vector [A∙m2
]
𝑁 Number of winding turns in the solenoid
𝑃2 Output power at port 2 [W]
𝑃3 Output power at port 3 [W]
𝑃 𝑖𝑛 Input power at port 1 [W]
𝑄 𝐿 Loaded quality factor
𝑅 Ferrite cylinder radius [m]
𝑅1 Turnstile cavity radius [m]
𝑅𝑡𝑟 Radial transformer radius [m]
𝑠 Radial transformer height [m]
𝑆 𝑚𝑛 Elements of scattering parameter matrix
[𝑆] Scattering parameter matrix

vi
𝑇𝐴 Antenna output temperature [K]
𝑇𝐵 Brightness temperature [K]
𝑇𝑐 Curie temperature of ferrite [o
C]
𝑇𝑝ℎ𝑦𝑠 Physical temperature [K]
𝑇𝑅𝐴𝐷 Backward noise temperature from the receiver [K]
𝑇𝑅𝐸𝐶 Equivalent noise temperature of the receiver [K]
𝑇𝑅𝐸𝐹 Reference source noise temperature [K]
𝑇𝑆𝐼 Noise temperature at the switch input [K]
𝑇𝑆𝑂 Noise temperature at the switch output [K]
𝑇𝑠𝑦𝑠 Equivalent system noise temperature without the calibration switch [K]
𝑇′ 𝑠𝑦𝑠 Equivalent system noise temperature including the calibration switch [K]
𝑻 Torque vector [Nm]
Δ𝑇 Radiometric resolution or radiometer sensitivity [K]
Δ𝑇𝑅𝐴𝐷 Fluctuation of the backward noise temperature from the receiver [K]
𝑉𝑜 Voltage at the three-port junction [V]
𝑍0 Reference characteristic impedance [Ω]
𝑍01,02,03 Characteristic impedances at each arm of the three-port junction [Ω]
𝑍1,2,3 Impedances looking into each port of the three-port junction [Ω]
𝑍′1,2,3 Impedances looking from the three-port junction [Ω]
𝑍𝑆𝑊2.𝑆𝑊3 Impedances of the switches at port 2 and 3 [Ω]
𝑥± Constant numbers determined from magnetized ferrite resonator equation
[𝑥]𝑖 Eigenvectors or eigenexicitations of symmetrical 3-port junction, i = 1,2,3
𝛼 Damping factor of gyromagnetic resonance
𝛽 Transmission coefficient in circulator S-parameter
𝛾 Gyromagnetic ratio [A∙s/kg]
𝜀0 Vacuum permittivity ( 8.854 A∙s/(V∙m))
𝜀𝑓 Ferrite dielectric constant
𝛿∗
Fractional frequency deviation
tan 𝛿 Dielectric loss tangent
κ Element in the Polder tensor
κ∗
Off-diagonal component of effective susceptibility
𝜆 Wavelength [m]
𝜇 Element in the Polder tensor
𝜇0 Vacuum permeability (= 4π×10-7
V∙s/(A∙m))
𝜇 𝑒 Scalar effective relative permeability of demagnetized ferrite
𝜇 𝑚 Relative permeability of magnetic cores
𝜇 𝑟 Scalar relative permeability
𝜇± Scalar relative permeabilities of magnetized ferrite for two rotating modes
μ 𝑟̿̿̿ Relative permeability tensor or the Polder tensor
𝜌 Reflection coefficient
𝜎 Transmission coefficient in circulator S-parameter
𝜏 Integration time of radiometer detector [s]
𝜙𝑖 Eigenvalues of symmetrical 3-port junction, i=1,2,3
𝜒 Scalar susceptibility
𝜒 𝑚𝑛 Elements of susceptibility tensor
χ̿ Susceptibility tensor
ω Angular frequency [rad/s]
ω0 Gyromagnetic resonance frequency or the Larmor frequency [rad/s]
ωm Angular frequency corresponding to saturation magnetization level [rad/s]
ωr Resonance frequency of demagnetized ferrite resonator [rad/s]

vii
ω± Splitting resonance frequencies of magnetized ferrite resonator [rad/s]

viii
Abbreviations
ACL Active cold load
ACSS Active calibration sub-system
AMR Advanced microwave radiometer
CAD Computer aided design
CALLOAD Calibration loads for radiometers
CPW Coplanar waveguide
ERS European remote sensing satellite
ESA European Space Agency
FET Field effect transistor
HE Hybrid mode, larger contribution of magnetic field (H) to the axial field
HIRAD Hurricane imaging radiometer
IAF Institut für Angewandte Festkörperphysik (Institute of Applied Physics)
JMR Jason microwave radiometer
KTH Kungliga Tekniska Högskolan (Royal Institute of Technology)
LNA Low-noise amplifier
MEMS Micro-electro-mechanical system
MetOp-SG Meteorological operational satellites – Second generation
mHEMT Metamorphic high-electron-mobility transistor
MMIC Monolithic microwave integrated circuit
RF Radio frequency
SI International System of Units
SMMR Scanning multichannel microwave radiometer
SMOS Soil moisture and ocean salinity
SP3T Single-pole triple-throw
SPDT Single-pole double-throw
SPST Single-pole single-throw
SSM/I Special Sensor Microwave Imager
SSMIS Special Sensor Microwave Imager Sounder
TE Transverse electric
TM Transverse magnetic
TMR Topex/Poseidon microwave radiometer
VNA Vector network analyser
VSWR Voltage standing wave ratio
VTT Teknologian Tutkimuskeskus Oy

1
1 Introduction
Radiometer is a passive remote sensing instrument that is used to measure brightness
temperature emitted by observed scenes or objects. In most passive remote sensing appli-
cations, the good absolute accuracy of the data is seminal. This leads to high calibration
requirements. Traditionally, spaceborne microwave remote sensing radiometers have
used external calibration references, such as blackbody loads and cold sky reflectors.
However, implementation of external calibration is not always practical [1], [2], and
sometimes internal calibration references would offer several benefits and could comple-
ment or even substitute the external references (see, e.g., [3], [4], [5]). In addition to the
internal references themselves, one critical element in the calibration sub-system is a ra-
dio frequency (RF) switch that connects the receiver to the reference noise source(s). With
the exception of noise diodes (which can use a directional coupler), all internal reference
targets need a switch to be connected to the receiver chain. In practice, it is often neces-
sary to connect two different calibration references into the receiver chain, requiring a
single-pole triple-throw (SP3T) switch.
The non-idealities of a calibration switch, such as loss and imbalance and the changes
thereof, can have a significant (degrading) influence in the quality of the calibration and
the measurement data [6], [7], [8]. Considering the requirements for spaceborne micro-
wave radiometry, the availability of high-performance switches suitable for space borne
passive microwave radiometry is very limited, especially at millimetre wave frequencies.
For instance, commercial p-i-n diode single-pole double-throw (SPDT) switches have
typically an insertion loss of around 3 dB at W band. High insertion loss would signifi-
cantly increase the noise figure of the receiver, bias the output of (cold) calibration
reference, and degrade the radiometric resolution (ΔT) of the radiometer.
In an ongoing activity commissioned by the European Space Agency (ESA) and exe-
cuted by Harp Technologies Ltd (Espoo, Finland), low-loss ferrite calibration switches
will be developed for W band (approximately 90 GHz). The calibration switch could be
integrated with the Active Cold Load (ACL) and a matched termination to realize a com-
pact internal calibration method for spaceborne radiometers. Ferrite switches are chosen
due to their very low insertion loss and their heritage in space missions (see, e.g., [6]) and
in many radar missions as well (see, e.g., [9]). In practice, the elementary switches will
be latching switchable ferrite circulators – SP3T calibration switches are obtained by
combining two of the elementary switches. The project will culminate in spring 2017 with
complete development, manufacturing and testing of two W band SP3T calibration switch
variants. As the first half phase of the project, frequency scaled switches have been de-
veloped for Ka band (36.5 GHz) to study design principles and support the W band switch
detailed design. This thesis presents the operational principles, designs, manufacturing
and testing of two elementary SPDT Ka band switch variants. One switch design is based
on conventional ferrite junction at dominant mode (the lowest mode) operation. This is a
common ferrite switch design. As the dimensions of the ferrite become tiny at millimetre
wavelengths, increasing the manufacturing challenge at W band, the other switch applies
an innovative higher order modes ferrite operation, which allows larger ferrite dimensions
to be used than in conventional designs.
The whole thesis tasks can be summarized as follows:

2
1. Literature survey on different switching technologies for W band (around 90
GHz) radiometer calibration.
2. Electrical designs and electromagnetic simulations for two scaled model
switches at Ka band (36.5 GHz).
3. Mechanical design of the switch housing and magnetic circuit design.
4. Manufacturing, assembling and testing of two Ka band switches to verify their
performance.
The thesis is organized in the following way. First of all, the basic overview of radio-
metric measurement, with related topics including radiometry, radiometer and radiometer
calibration, are discussed in the three first sections of Chapter 2. Calibration switch crite-
rions in the W band application point of view follow in the end of Chapter 2. Literature
study on some switching technologies for W band radiometer calibration is presented in
Chapter 3. Subjects are described in such details that can clarify the reason for choosing
ferrite switch technology for W band calibration switch development. After that, Chapter
4 is devoted to present ferrite circulator theory, including theory of microwave ferrite.
The chapter also provides theoretical explanation and simulation of higher order modes
excitation in ferrite junction for circulation/switching operation. Higher order modes op-
eration increases ferrite piece sizes; hence, enables application of ferrite circulator/switch
in higher frequencies. The next two chapters, Chapter 5 and Chapter 6, comprise of the
detailed designs, testing and discussions on results of two manufactured Ka band switch
variants. Finally, the thesis work is concluded by the summary given in Chapter 7.

3
2 Overview of radiometric measurement
Radiometer and radar are among the two major instruments used in remote sensing ap-
plications. However, unlike radar, which transmits RF waves to objects and detects
reflected or back-scattered signals from objects, the radiometer does not have a transmit-
ter to send RF waves. It consists of only a receiver to measure incoherent radiant
electromagnetic power from objects. Thus, radiometers can be described as “highly sen-
sitive receivers designed to measure thermal electromagnetic emission by material
media” [10].
This chapter gives a short introduction to radiometry and the use of radiometer as an
instrument in radiometry. Then the need of calibration for radiometer is explained and
followed by the discussion on calibration switch parameters.
2.1 Radiometry
All materials at a physical temperature above absolute zero radiate electromagnetic en-
ergy, which is called thermal emission. Reversely, materials also absorb electromagnetic
radiation incident upon them. According to thermodynamic principles, absorption of en-
ergy corresponds to a rise in the internal kinetic energy and consequently in thermometric
temperature of materials. At thermodynamic equilibrium state, radiation absorption and
emission happen at the same rate, and the physical temperature of materials stays con-
stant. A blackbody is defined as an idealized body, which absorbs all incident radiations
at all frequencies and reflects none. The resulting fact is that blackbody is also a perfect
radiator. The spectral brightness (or power), which a blackbody radiates, is expressed by
Planck‘s radiation law. In the microwave frequency region, the Rayleigh-Jeans law pro-
vides a mathematically simple and yet very applicable approximation of Planck’s law
[10]:
𝐵𝑓 =
2𝑘 𝐵 𝑇𝑝ℎ𝑦𝑠
𝜆2
, (1)
where 𝐵𝑓 is spectral brightness of a blackbody, 𝑘 𝐵 is Boltzmann’s constant, 𝑇𝑝ℎ𝑦𝑠 is phys-
ical temperature, and 𝜆 is wavelength. In practice, real materials emit less than a
blackbody does at the same physical temperature and do not absorb all radiation incident
upon them. Emissivity is a measure of a ratio between the brightness of a real material to
the brightness of a blackbody at the same temperature. The observed brightness of a real
material is usually expressed by the equivalent brightness temperature 𝑇𝐵. The brightness
temperature is different from the physical temperature for real materials and is related to
the physical temperature through emissivity [10]:
𝑒(𝜃, 𝜙) =
𝑇𝐵(𝜃, 𝜙)
𝑇𝑝ℎ𝑦𝑠
. (2)
It can be seen that 0 ≤ 𝑒(𝜃, 𝜙) ≤ 1; hence, 𝑇𝐵 of a real material is smaller than or equal
to its physical temperature 𝑇𝑝ℎ𝑦𝑠.
Radiometry is a field of science and engineering of measuring electromagnetic radia-
tion to derive information about electromagnetic emission characteristics of scenes or

4
objects under observation. In radiometric remote sensing, the radiometer, comprising the
receiving antenna and receiver, is used to observe brightness temperature of a scene. Out-
put power of the receiving antenna, measured by the receiver and often expressed by the
antenna temperature 𝑇𝐴, consists of both radiation from the observed scene collected by
antenna and self-emitted radiation from antenna. Therefore, the objective of radiometric
measurement is to relate the antenna temperature to the brightness temperature of the
observed scene or object, or to extract the observed brightness temperature from the an-
tenna temperature.
2.2 Radiometer
The most common radiometers types are total power, Dicke, and noise-injection radiom-
eter. This section, however, will not give details about those radiometer receiver types;
but instead, will examine a system-level perspective of radiometer operation.
Figure 1. Simplified block diagram of a radiometer.
As mentioned, a radiometer is built from a microwave receiver and a receiving antenna
to measure power (see Figure 1). The antenna collects electromagnetic radiation power
from observed targets. The receiver filters antenna output to a certain bandwidth around
a centre frequency, amplifies it and then delivers it to a power detector (power meter or
square-law detector). As a result, the antenna temperature 𝑇𝐴 is translated linearly into
output indicator of the receiver as [10]:
𝐼 𝑜𝑢𝑡 = 𝑎(𝑇𝐴 + 𝑏), (3)
where 𝑎 and 𝑏 are constants to be determined, 𝑇𝐴 is the antenna temperature and 𝐼 𝑜𝑢𝑡 is
the receiver output indicator. In some radiometer configurations, b is given by the refer-
ence load temperature 𝑇𝑅𝐸𝐹 (e.g., Dicke radiometer type), or the receiver temperature
𝑇𝑅𝐸𝐶 (e.g., total power and noise adding types). To estimate the antenna radiometric tem-
perature 𝑇𝐴, which represents the radiation power delivered by antenna, the knowledge
on receiver transfer function has to be known, namely to determine 𝑎 and 𝑏. On the other
hand, it is not enough if the antenna temperature could only be measured but it must also
be related to the brightness temperature 𝑇𝐵 of the observed scene. Therefore, the receiving
antenna properties also need to be characterized to make that interpretation from 𝑇𝐴 to 𝑇𝐵.
Such knowledge of 𝑎, 𝑏 and receiving antenna properties is rarely available, which leads
to the necessity for calibration. The processes of determining receiver transfer function
and receiving antenna properties are referred as receiver calibration and antenna calibra-
tion respectively.

5
Assuming that the constants of receiver transfer function do not change, the absolute
accuracy of the acquired data (correspondence between the real and the measured values
[11]) is dominated by the accuracy of the calibration references. In practise, impedance
mismatches within the receiver and between the antenna/calibration loads and the re-
ceiver input cause reflection. The first mismatch gives changes to the value of 𝑎 and 𝑏
due to temperature variation and fluctuation of reflection coefficients’ phase and magni-
tude. The latter mismatch biases the outputs of calibration references, which will be
shown in the next section. All in all, they compromise the measurement accuracy of 𝑇𝐴.
Besides that, not only the absolute accuracy is of interest but also the precision of the
measurement. In radiometric measurement, the precision at which 𝑇𝐴 can be measured by
a radiometer is referred as radiometric resolution or radiometer sensitivity Δ𝑇, which
presents minimum detectable change at the input determined by the standard deviation of
the output [11]. The radiometric resolution is a parameter of a radiometer that is affected
by the receiver’s architecture and characteristics of components. Thus, derivation of the
radiometric resolution formula depends on each type of receiver designs. Δ𝑇 is often con-
sidered to be the figure of merit to qualify a radiometer performance. Generally,
radiometric resolution can be described as [10], [12]:
Δ𝑇 = 𝐾
𝑇𝑠𝑦𝑠
√𝐵 ∙ 𝜏
= 𝐾
𝑇𝐴 + 𝑇𝑅𝐸𝐶
√𝐵 ∙ 𝜏
, (4)
where 𝐾 is a constant depending on the radiometer type, 𝑇𝑠𝑦𝑠 is the equivalent noise tem-
perature of the radiometer system, 𝑇𝐴 is the antenna temperature, 𝑇𝑅𝐸𝐶 is the equivalent
noise temperature of the receiver, 𝐵 is the bandwidth, and 𝜏 is the integration time. It is
worth noting that the receiver gain fluctuation also gives rise to Δ𝑇 but is not considered
in (4). More experiments and discussion on the stability or radiometric resolution of dif-
ferent radiometer systems due to the receiver gain fluctuation can be found further in [13].
2.3 Calibration of radiometer
Calibration is a fundamental procedure in microwave radiometry, which relates the ob-
served brightness temperature to an absolute scale. As discussed above, radiometer
calibration consists of receiver calibration, relating the receiver output indicator to the
antenna temperature at the receiver input, and antenna calibration, relating the antenna
temperature to the informative radiation characteristics of observed scene. Regarding re-
ceiver calibration, microwave radiometers are typically calibrated frequently by a
so-called two-point method. This means that signals from two calibration sources of dif-
ferent and known brightness temperature are observed. This way, the transfer function of
the radiometer can be determined from raw counts to antenna temperature, and linear
interpolation or extrapolation can be used to retrieve the brightness temperature from the
raw counts. Calibration is performed not only at the initial phase, but due to some drifts
and instability of various components, it is also necessary to repeat the calibration proce-
dure after some intervals to keep the calibration drifts acceptably low within a calibration
cycle.

6
The calibration source can be a matched load kept at a fixed physical temperature, a
material with well-known emissivity and temperature (an absorber), cosmic space, a cold
sky reflector or a solid-state circuit. Typically, external calibration is established by point-
ing the receiving antenna (feeds) to the calibration references. Thus, the entire system is
calibrated (with the exception of antenna reflector). This method has been most frequently
used in spaceborne microwave remote sensing radiometers and provides a convenient and
accurate end-to-end calibration solution. External calibration sources can also be ob-
served via an auxiliary antenna horn, which is connected to the receiver chain through a
switch. However, some errors could be generated since the receiving antenna feeds are
not included in the calibration chain, and the waveguides from the switch to the auxiliary
antenna horn are prone to temperature fluctuation.
Alternatively, calibration references can be arranged internally in radiometer system
and are connected to the receiver through an RF switch placed as close as possible to the
receiving antenna. External hot and cold load targets can be replaced with an internal 50Ω
termination and a noise diode. Recently, thanks to advances in transistor technology, the
invention of semiconductor active cold loads (ACLs) as cold references has brought a
viable concept for internal calibration [14]. ACL is an active transistor-based device,
which can generate stable lower intensity noise power than a matched load at the same
physical temperature. In the context of earth remote sensing, ACLs have potential up to
approximately 100 GHz, and activities on development and demonstration of ACLs have
been conducted, such as [6], [15], [16]. The internal calibration references could be inte-
grated with a calibration switch to realize a complete low-weight calibration subsystem
for radiometer. So far, there have already been a few examples of the use of internal
calibration targets (matched loads and noise diodes) in space borne microwave remote
sensing radiometers. Sample instruments include the nadir pointing (non-scanning)
Topex/Poseidon Microwave Radiometer (TMR) [7], the conically scanning Scanning
Multichannel Microwave Radiometer (SMMR) on-board Seasat [17], (non-scanning) Eu-
ropean Remote Sensing Satellite (ERS) Microwave Radiometer, Jason Microwave
Radiometer (JMR) on-board Jason-1 satellite, Advanced Microwave Radiometer (AMR)
on board Jason-2 [18], and Soil Moisture and Ocean Salinity (SMOS) [2], [19]. In addi-
tion, other examples of the application of ACLs to calibrate (non-space) remote sensing
radiometers include U.S. Hurricane Imaging Radiometer (HIRAD), an interferometric C-
band radiometer [20], ELBARA II ground based radiometer [21], and Helsinki University
of Technology experimental L-band radiometer [22].
Both external and internal calibration references have their own advantages and dis-
advantages. As advantages of the internal ones can be mentioned the elimination of
complex mechanical supports to carry out the calibration, the reduction of unwanted
torque and momentum compensation due to reduction of moving parts, and the benefits
in terms of size, mass, power and cost. Reducing in mechanical complexity makes the
system less vulnerable to mechanical stress and wear. Calibration quality could poten-
tially be improved, because internal calibration can typically be performed faster than
external calibration and more frequently to reduce rapid gain fluctuations. Furthermore,
internal calibration references can be better shielded from solar radiation that may cause
temperature gradients in external targets [23], [24]. However, a calibration switch is
needed when using internal calibration targets (excepting noise diodes, which can be used

7
with directional couplers). The use of a switch as an additional component in the receiver
chain (see Figure 2) has some effects, such as increase in front-end losses and receiver
noise temperature, generation of changes on antenna and calibration output signals. These
would eventually degrade the calibration quality and the radiometer performance. There-
fore, a switch for radiometer calibration needs to achieve certain requirements to
minimize its effects and ensure the calibration performance.
Figure 2. Block diagram of a radiometer with internal calibration references (a
matched load and an ACL) and a SP3T calibration switch (built from two SPDT
switches).
2.4 Critical parameters of calibration switch
The critical performance parameters of a calibration switch depend on application and
exact instrument configuration. In general, the most critical parameters are insertion loss,
return loss, isolation, switching speed, repeatability, low excess noise, low self-heating,
and stability. Below, the most important parameters are shortly discussed in the scenario
of a W band radiometer application.
2.4.1 Insertion loss
The calibration switch would be in front of the radiometer’s receiver chain. Therefore,
low insertion loss would be most important in order not to degrade the radiometric reso-
lution. This is because the radiometric resolution of the data is one of the most important
parameters for the user community, even often seen as the most important figure of merit.
The importance of low insertion loss is amplified at higher frequencies, where the receiver
noise temperature dominates the system temperature (due to higher receiver noise tem-
perature with respect to scene brightness temperature). As seen in (4), the rise in the
system temperature directly increases the radiometric resolution. According to the noise
characteristic of a cascaded system (see [25]), the equivalent noise temperature of the
radiometer system referred to the antenna output, including the calibration switch, can be
expressed as:

8
𝑇𝑠𝑦𝑠
′
= 𝑇𝐴 + (𝐿 𝑆𝑤𝑖𝑡𝑐ℎ − 1)𝑇𝑝ℎ𝑦𝑠 + 𝐿 𝑆𝑤𝑖𝑡𝑐ℎ 𝑇𝑅𝐸𝐶, (5)
where 𝐿 𝑆𝑤𝑖𝑡𝑐ℎ is the insertion loss (in linear scale) of the calibration switch, 𝑇𝑝ℎ𝑦𝑠 is the
physical temperature of the switch and the radiometer frontend. Without the switch or the
switch is lossless (𝐿 𝑆𝑤𝑖𝑡𝑐ℎ = 1), the system temperature in (5) reduces to [25]:
𝑇𝑠𝑦𝑠 = 𝑇𝐴 + 𝑇𝑅𝐸𝐶. (6)
Using (4), the degradation in radiometric resolution due to the switch’s loss can be com-
puted as:
𝐷𝑒𝑔𝑟𝑎𝑑𝑎𝑡𝑖𝑜𝑛 𝑜𝑓 Δ𝑇 =
𝑇𝑠𝑦𝑠
′
− 𝑇𝑠𝑦𝑠
𝑇𝑠𝑦𝑠
=
(𝐿 𝑆𝑤𝑖𝑡𝑐ℎ − 1)(𝑇𝑝ℎ𝑦𝑠 + 𝑇𝑅𝐸𝐶)
𝑇𝐴 + 𝑇𝑅𝐸𝐶
. (7)
The other parameters (𝐾, 𝐵 and 𝜏) are eliminated. Assuming that the receiver noise tem-
perature 𝑇𝑅𝐸𝐶 (without the switch) and antenna output temperature are 450 K and 200 K,
respectively, which approximately correspond the situation at W-band, the increase of the
radiometric resolution has been illustrated as a function of switch losses in Table 1 below.
Table 1. The (degradation) of system noise temperature and radiometric resolution with
increasing switch loss. (Assuming that physical temperature 𝑇𝑝ℎ𝑦𝑠 is 300 K.)
LSwitch [dB] TSYS [K] degradation of ΔT [%]
0.0 650 0%
0.5 741 14%
0.8 800 23%
1.0 842 30%
1.2 887 36%
1.5 937 44%
2.0 1085 67%
2.5 1228 89%
It can be seen that considering the tight requirements for the radiometric resolution of
future remote sensing missions (such as the second generation of Meteorological Opera-
tional satellites MetOp-SG [23]), the insertion loss higher than 1.5 dB, specifically for the
current W band switch development project, is hardly acceptable, since the radiometric
resolution would be increased (degraded) by over 44%. Insertion losses below 1 dB
should be taken as goal for a calibration switch.
Besides that, the loss of calibration switch also affects the antenna or calibration load
output to the receiver. Considering a switch with source noise temperature 𝑇𝑆𝐼 at one of
its input port and the output temperature 𝑇𝑆𝑂, the relationship between those temperatures
is:

9
𝑇𝑆𝑂 =
𝑇𝑆𝐼
𝐿 𝑆𝑤𝑖𝑡𝑐ℎ
+ (1 −
1
𝐿 𝑠𝑤𝑖𝑡𝑐ℎ
) 𝑇𝑝ℎ𝑦𝑠. (8)
In the case that the antenna connection is turned on, 𝑇𝑆𝐼 = 𝑇𝐴. If the antenna temperature
and the physical temperature are still 200 K and 300 K, an insertion loss of 0.5 dB results
in around 211 K at the switch output (or at the receiver input). Similarly, a bias is also
generated to calibration signals when the receiver is connected to reference sources. How-
ever, this affection can be corrected if the physical temperature is monitored and the
switch’s loss can be determined at the same time with sufficient accuracy.
2.4.2 Isolation
In order to calibrate the radiometer reliably, the level of the reference noise has to be
known accurately during calibration. Therefore, the flow of “wrong” noise signal should
be cancelled during calibration. In practise, however, there is always some cross-talk be-
tween the ports of the switch, i.e., the isolation is limited. When the calibration switch is
connected to a reference load during calibration, 𝑇𝑆𝐼 = 𝑇𝑅𝐸𝐹, the noise temperature at its
output to the receiver is expressed by1
:
𝑇𝑆𝑂 = 𝑇𝑆𝐼 +
𝑇𝐴
𝐿𝑖𝑠𝑜
= 𝑇𝑅𝐸𝐹 +
𝑇𝐴
𝐿𝑖𝑠𝑜
, (9)
where 𝐿𝑖𝑠𝑜 is the isolation level of the calibration switch. Assuming an unknown antenna
temperature of 100 K during calibration, an acceptable (unknown) cross-talk of 0.1 K
from antenna port to receiver port (switch output) requires an isolation of 30 dB. How-
ever, it can be argued that this requirement can be relaxed for the isolation between
calibration ports (connecting to calibration references) during calibration, and between
the calibration ports and receiver port during antenna measurement, since the noise level
of the calibration references is accurately known as well as the switch isolation (e.g. by
on-ground characterization). For the isolation in those cases, 20 dB or even 15 dB should
be sufficient. In practise, this means that if an SP3T calibration switch is constructed by
combining two SPDT switches in series between antenna and receiver ports, an isolation
of 15-20 dB could be sufficient for one individual SPDT switch. It is also noted the re-
quirement would be relaxed significantly if the measured target does have low brightness
temperature and low variation (such as oceans). Therefore, lower level of isolation would
be acceptable for specific mission scenarios, such as ocean measuring missions, or if the
antenna temperature can be estimated more accurately, e.g., via interpolation. Assuming
that an unknown antenna temperature of 10 K during calibration and an acceptable (un-
known) cross-talk of 0.1 K from antenna port to receiver port during calibration, the
isolation requirement is reduced to 20 dB from the antenna port to the receiver port. A
20dB isolation between calibration ports and the receiver port also means 1% of 𝑇𝑅𝐸𝐹 is
coupled into antenna signal during observation through the antenna.
1
Assuming that the switch insertion loss is 0 dB.

10
2.4.3 Return loss
The radiometer front-end produces noise in both backward and forward directions (to-
wards its input and towards its output). In order to suppress the potential backward
flowing noise from biasing the reference noise (when reflected back from the switch to
the receiver), the reflection coefficient of the switch to the receiver should be sufficiently
small. The power level of the backwards flowing noise depends on the radiometer design.
It could be possible that the reflected noise is not critical since it stays constant and can
be calibrated out if an end-to-end calibration can be applied from time-to-time. However,
this assumption only holds accurately if the amplitude and phase of the backwards flow-
ing noise remain constant, as well as physical dimensions, since the backwards and
forwards flowing noise of a low noise amplifier (LNA) are correlated. Since these param-
eters do not remain fully stable (e.g., due to temperature fluctuation) and no external
calibration means can be taken as granted, the backwards flowing LNA noise will cause
some fluctuation in the bias. This is true especially at higher frequencies with short wave-
lengths; the physical signal paths become more susceptible to length variations with
temperature changes.
Considering a mismatch at the interface between switch output and the input of re-
ceiver, we get:
𝑇𝑆𝑂 = 𝑇𝑅𝐴𝐷 ∙ 𝜌 + 𝑇𝑆𝐼(1 − 𝜌), (10)
where 𝜌 is the reflection coefficient caused by mismatch between the switch and the re-
ceiver, and 𝑇𝑅𝐴𝐷 is the backward noise temperature from the receiver to the switch.
Assuming a backward noise temperature from the receiver of 400 K in average, and as-
suming that the fluctuation Δ𝑇𝑅𝐴𝐷 of the backward flowing noise would be 5% of the
average value, the requirement for return loss becomes 23 dB, regardless of 𝑇𝑆𝐼, to have
tolerable uncertainty of 0.1 K at the switch output to the receiver. The requirement for the
calibration and antenna ports is the same, and the justification is analogous. If the tem-
perature fluctuations of the switches are reduced by thermal stabilization of the
radiometer front-end, the above requirement could be relaxed to approximate 20 dB level.
2.4.4 Switching time
The required switching speed in typical remote sensing radiometer application is not very
fast, since there is sufficient unused time (i.e., time not used for measurement) in the
revolution cycle of conically scanning radiometers, for example. In such an application,
1ms switching speed should be sufficient. The associated trade-off when shortening the
switching speed are related to the switch technology. In ferrite switch technology, for
example, shortening the switching speed may restrict ferrite material selection and/or
complexity of the switching electronics and electromagnetic circuits. However, switching
speeds in microsecond range have been reported for existing ferrite switches [26], [27],
[28].

11
2.4.5 Bandwidth
The bandwidth of the switch should cover the bandwidth of the radiometer. Considering
W-band, for example, the remote sensing radiometers use typically 89 GHz or 92 GHz
with a typical bandwidth of 4 GHz. This corresponds 4.5% and it should be sufficient for
most applications of remote sensing radiometry. For some instruments and applications,
even 3.4% (3 GHz) could be sufficient, especially if the instrument has super heterodyne
architecture, where double side-band operation can be applied.
2.4.6 Repeatability, self-heating and stability
The repeatability of a switch refers to the stability of the key performance parameters at
different switch occasions. Irrespectively of the switch technology, this parameter shall
be very high, in order to allow accurate pre-characterisation of the remaining non-ideali-
ties (and their removal in data processing). Any deviations should cause 0.1 K calibration
uncertainties at maximum.
The self-heating refers to the increase of the physical temperature of a switch due to
its operation (switching). This self-heating may influence the radiometric measurement if
it affects the insertion loss balance between the antenna and reference branches. The im-
pacts of this changed imbalance shall remain very small (<0.1 K) or it shall be
characterised as a function of switch temperature (and the temperature of the switch
should be monitored). Otherwise, however, potential insertion loss change of a switch is
not critical, as long as the loss change remains reasonably low (<0.1 dB) so that it does
not increase receiver’s noise temperature significantly. The changes of switches’ own
noise (due to loss changes) have negligible impact on the receiver noise temperature, as
long as the noise temperature change of the switch remains reasonable (<10 K) (assuming
a low-loss switch).
The stability of a switch refers to the stability of the key performance parameters with
time. Similar to the repeatability, this parameter shall be very high, irrespectively of the
switch technology, in order to allow accurate pre-characterisation of non-idealities (and
their removal in data processing). Any deviations should cause 0.1 K calibration uncer-
tainties at maximum.

12
3 Background study of switching technologies
As discussed in the previous chapter, a switch is needed for the use of internal references
in radiometer calibration, and high performance characteristics of the calibration switch
are required to reduce the switch’s effects on radiometric measurement and to ensure
calibration quality. There are several potential, fundamentally different potential switch
technologies to be considered for airborne and spaceborne radiometer use at W band. In
this chapter, potentially suitable switch technologies and their characteristics are pre-
sented and discussed. Three different technologies have been selected for the literature
survey: 1)-Metamorphic High Electron Mobility (mHEMT) Field Effect Transistor
(FET), 2)-MEMS technology, and 3)-Y-junction ferrite switch. As frequency, 36.5 GHz
(Ka-band) has been selected with further development potentially up to W-band, it is
worth mentioning that electromechanical waveguide switches (or rotary switches) would
be superior in terms of insertion loss, isolation and high power handling. For instance,
waveguide switches at W-band (75 – 110 GHz) can be found from some manufacturers,
like Aerowave Inc. or Flann Microwave Ltd., with very low insertion loss of 0.5 - 0.8 dB,
and high isolation of 50 - 60 dB as well as 26dB return loss at minimum. However, rotary
switches have not been included in the study since their operational lifetime (number of
switch operations) is not sufficient for space applications. Typically, for remote sensing
application the switch is required to operate roughly 10 years in space without failures
(i.e., the number of required switching operations is in the order of 100 million). Addi-
tionally, switching function is done by a mechanical motor, and hence is slow and requires
high switching power. Motorised switches nowadays can achieve over 80ms switching
time, but that is still deemed too slow for the calibration switch application in a radiome-
ter.
3.1 mHEMT FET switch technology
The analysis of mHEMT FET-switch technology is based on the switch developed by the
Fraunhofer Institute of Applied Physics (IAF) (Germany) in the “Calibration Loads for
Radiometers (CALLOAD)” activity of ESA [16]. The switch was designed as a compo-
nent in the Active Calibration Sub-System (ACSS) with the ACL integrated in the sub-
system. There are three designed versions of the switch operating at three different fre-
quencies (31.4 GHz, 52 GHz and 89 GHz); however, only two higher-frequency versions
were actually manufactured as MMICs.
Figure 3 shows the schematic of the SP3T switch, 89GHz version used in CALLOAD
project, but general circuit of multiple-throw FET switch can also be seen from there. The
design utilized a mHEMT transistor as a shunt switch reflecting back signals in the OFF
state. Two transistors were integrated in each arm to achieve the desired isolation level.
Short-circuited shunt stub and lines between two transistors on each arm were used to
tune to the desired operating frequency. The input branch was used as the radiometer port.
One output branch was connected to a match load (50 Ω) as an internal calibration refer-
ence, and the other two output branches were connected to antenna and the ACL. The
switch was controlled in three states (given in Table 2) by applying suitable combination
of bias voltages to transistors in three arms.

13
The 89 GHz SP3T switch design was simulated and manufactured using the 100 nm
mHEMT process by Fraunhofer IAF. The on-wafer test results and simulation results of
the switch are presented in [16] and are not repeated here. Fairly good agreement between
the simulated and measured values can be observed. The summary of on-wafer measured
values at 89 GHz are presented in Table 3, showing the best insertion loss of 2.8 dB at
the ACL arm.
Figure 3. Schematic for the SP3T switch at 89 GHz [16].
Table 2. Controlling states of the switch.
State Description
1. Antenna The switch connects radiometer to antenna
2. ACL The switch connects radiometer to the ACL
3. Matched Load The switch connects radiometer to the matched load
Table 3. Summary of switch (on-wafer) performance at 89 GHz. Simulated values are
shown in parenthesis [16].
State S21 [dB] S31 [dB] S11 [dB] S22 [dB] S33 [dB]
1. Antenna
-2.9
(-3.8)
-39.5
(-36.7)
-14.9
(-22.4)
-13.0
(-21.3)
-2.4
(-3.9)
2. ACL
-42.6
(-36.7)
-2.8
(-3.8)
-14.5
(-22.4)
-2.1
(-3.9)
-12.5
(-21.3)
3. Matched Load
-41.3
(-36.5)
-43.7
(-36.5)
-14.9
(-21.9)
-2.4
(-3.9)
-2.1
(-3.9)
Port 1
Port 2
Port 3
Port 4

14
Other SPDT mHEMT switches manufactured by Fraunhofer IAF have been presented
in [29]. The switch designs have been done for 94GHz operation in both single shunt-
FET and double shunt-FET configuration. The measurement showed that the single
shunt-FET design had insertion loss of 1.8 dB at 94 GHz, 1.9 dB at 120 GHz, and better
than 20 dB isolation between 77 and 120 GHz. On the other hand, the double shunt-FET
configuration achieved 2.2 dB insertion loss and better than 29 dB isolation on average.
Those results are presented in Figure 4. Performance comparison of mHEMT SPDT
switches in different topologies has been studied in [30]. It revealed that the double-shunt
and asymmetrical topologies are more suitable than the series-series topology for opera-
tion in higher-end of millimetre-wave frequencies. The insertion loss of around 2 dB was
measured for the double-shunt topologies and isolation of better than 18 dB was achieved
in the same design.
Regarding the return loss, both switches in [29] were reported to have better than 8 dB
return loss from 77 to 120 GHz. Besides that, the experimental results in [30] showed
different return loss values on different branches in the same switch topology. In the
asymmetrical switch, for example, return loss of the common port exceeded 10 dB in the
whole bandwidth. The series branch had the return loss of 10 dB from 60 to 80 GHz and
15 dB from 80 to 90 GHz at smallest, while the value in shunt branch was better than 20
dB from 60 to 80 GHz and in excess of 15 dB from 80 to 90 GHz.
Note that in [29] and [30], the switches were realized using 50nm and 100nm mHEMT
technologies, and all results mentioned above were measured on wafer-level, not from
packaged modules.
Figure 4. ON-wafer measured and simulated insertion loss and isolation of SPDT
mHEMT switches [29].

15
From the analysis above, the achievable on-wafer performance of the mHEMT switch
(regarding both 50nm and 100nm mHEMT technologies) can be summarized as below:
 Frequency: W-band
 Bandwidth: wide band
 Insertion loss: 1.5 - 3 dB
 Return loss: 8 – 20 dB
 Isolation: 20 – 40 dB
 Switching time: Information not available
 Self-heating: Information not available
3.2 MEMS switch technology
Radio frequency microelectromechanical systems (RF MEMS) technology has seen enor-
mous growth in recent decades. RF MEMS technology is attractive due to its excellent
performance (high linearity, low loss, very small size, and fast response [31], [32]).
Therefore, RF MEMS in general is also a technology of interest in developing the switch
in mm-waves. Here, the study describes a novel RF MEMS switch technology, which is
fundamentally different from conventional RF MEMS technologies (e.g., the shunt ca-
pacitive MEMS switch). This technology is referred as “MEMS-reconfigurable surface”
waveguide switch and has been developed in Royal Institute of Technology (KTH),
Stockholm, Sweden by the group led by Prof. J. Oberhammer, see for example [33].
The basic working concept of the switch can be summarized as following (see Figure
5). In blocking state, the fixed and movable cantilevers are aligned and create a grid of
vertical columns that short-circuits the electric field of the predominant TE10 mode in
rectangular waveguide. In ON state, the cantilevers are not in contact, which allows wave
to propagate freely through the switch. The number of cantilever columns determines the
isolation in OFF state, while in the ON state the ratio between the number of horizontal
bars (the number of cantilever contact points) to the number of cantilevers columns is the
figure of merit affecting the insertion loss.
Figure 5. Schematic showing working concept of the switch in ON state and OFF state
[33].

16
A prototype of the E-band MEMS Single-Pole Single-Through (SPST) switch in WR-
12 waveguide has been reported in [33]. Figure 6 shows RF measurement results based
on different switch configurations of vertical column number (Vxx) and horizontal bar
number (Hxx). An isolation of better than 30 dB and insertion loss between 0.4 – 1.1 dB
were measured and reported for all designs across the frequency range of 60 – 70 GHz.
A return loss of 25 dB was achieved in the best design (V30H21), while other configura-
tions were able to keep better than 15 dB return loss in the whole frequency band. With
noticeable major contribution of the insertion loss of 0.3 dB from the measurement setup
itself (in comparison with the reference V0H0), it can be seen that the performance of the
switch prototype is promising. In addition, switching speed was mentioned to be faster
than 100μs, and a device-level yield analysis showed a fabrication yield of 95% for suf-
ficiently close-to-best performance [33]. Initial test indicated that the MEMS switch
element exhibited no degradation in performance or in actuation voltage after continuous
actuation in contact mode during 14 hours, e.g. 4.3 million cycles with a saw tooth signal
of 80 Hz.
Although [33] reports the measurement results only up to 70 GHz (due to limitation in
measurement setup as information from the author), the simulation of the switch was ac-
tually expected to work for the whole V-band (60-90 GHz). Overall, the RF performance
of the SPST MEMS switch element only, i.e., losses from the flanges and measurement
setup have been deducted from the retrieved values, is summarized below:
 Frequency: V-band (extendable to W-band)
 Bandwidth: wide band
 Insertion loss: 0.1 – 0.8 dB
 Return loss: 15 – 25 dB
 Isolation: 30 – 45 dB
 Switching time: faster than 100 μs
The reported MEMS switch element here is a SPST switch, but the desired switch for
radiometer calibration is a SPDT or SP3T. One simple solution to realize a SPDT or even
SP3T functionality is to integrate the SPST MEMS switch element with a passive multi-
port waveguide component, such as a waveguide junction.
For instance, let us consider a simple three-port lossless waveguide junction, which
can be modelled as a junction of three transmission lines, as shown in Figure 7. For con-
venience, following assumptions were made in the next analysis:
 The SPST switch element acts as a perfect shunt switch, i.e., perfect short circuit
in OFF state;
 Reactive effect at the junction is neglected.

17
Figure 6. S-parameter measurement of the SPST MEMS switch integrated into WR-12
waveguide [33].
Figure 7. Transmission line model of a three-port lossless junction.

18
The SPDT switch is constructed by a three-port junction. Port 1 of the junction is used
as a common port, and port 2 and 3 are selectable ports. Two SPST switch elements are
placed quarter-wavelength (at operating frequency) away from the junction at port 2 and
3. 𝑍𝑆𝑊2 and 𝑍𝑆𝑊3 represent the impedance of two SPST switches. Considering the case
that the switch at port 2 is in OFF state and port 3 is ON, which means 𝑍𝑆𝑊2 = 0 and 𝑍𝑆𝑊3
is neglected. Due to the property of the quarter-wave transformer, the impedance 𝑍2′
looking to port 2 is:
𝑍2
′
=
𝑍02
2
𝑍𝑆𝑊2
= ∞. (11)
So port 2 is seen as open circuit at the junction. Similarly, the impedance 𝑍1′ and 𝑍3′
looking to port 1 and port 3 respectively are:
𝑍1
′
=
𝑍01
2
𝑍0
, (12)
𝑍3
′
=
𝑍03
2
𝑍0
. (13)
If the voltage at the junction is 𝑉0 as shown in Figure 7, the input power delivered from
port 1 is:
𝑃𝑖𝑛 =
1
2
𝑉0
2
𝑍1′
, (14)
while the output power to port 2 and port 3 are following respectively:
𝑃2 =
1
2
𝑉0
2
𝑍2′
= 0, (15)
𝑃3 =
1
2
𝑉0
2
𝑍3′
. (16)
It can be seen that no power outputs at port 2 since 𝑍2
′
= ∞. Considering the input im-
pedances at three ports, the followings are obtained:
𝑍1 =
𝑍01
2
𝑍𝑗𝑢𝑛𝑐1
= 𝑍01
2
(
1
𝑍2′
+
1
𝑍3′
) =
𝑍01
2
𝑍3′
=
𝑍01
2
𝑍03
2 𝑍0, (17)
𝑍3 =
𝑍03
2
𝑍𝑗𝑢𝑛𝑐3
= 𝑍03
2
(
1
𝑍1′
+
1
𝑍2′
) =
𝑍03
2
𝑍1′
=
𝑍03
2
𝑍01
2 𝑍0, (18)
𝑍2 = 0 (since 𝑍𝑆𝑊2 = 0). (19)

19
If the characteristic impedances 𝑍01 and 𝑍03 are identical, then 𝑍1
′
= 𝑍3′. From (17)
and (18), port 1 and port 3 are matched, and (14) and (16) indicate that all power coming
into port 1 emerges at port 3 as expected from a lossless device. Therefore, the S-param-
eter matrix of the lossless SPDT switch can be derived in case port 2 in OFF state as:
[𝑆] = [
0 0 1
0 −1 0
1 0 0
]. (20)
The operational principle is similar in the other case when switching port 3 off and
port 2 on. Analogous analysis suggests that it is also possible to realize a SP3T switch.
The above analysis has been done at circuit level (with some ideal assumptions). In prac-
tice, however, the excitation of localized evanescent modes at waveguide junction would
lead to stored energy, which is equivalent to a lumped susceptance at the junction. Alt-
hough the effect of lumped susceptance can be compensated in practice, there are still
impacts on matching level and other parameters of a resulting SPDT or SP3T switch.
Simulation would be needed to confirm the switch element operation in a real waveguide
junction and predict how much the degradation in performance is.
3.3 Ferrite switch technology
Microwave ferrite has been well known for long time and found its application in a large
number of microwave devices, especially in nonreciprocal components such as circula-
tors. The switching technology discussed here bases on a Y-junction waveguide ferrite
circulator. Adjusting the direction of a biasing magnetic field, the circulation state can be
changed or switched, i.e., from 1=>2=>3 to 3=>2=>1 (where 1, 2, and 3 represent differ-
ent ports). Hence, the Y-junction ferrite switches are actually Y-junction ferrite
circulators with ability to reverse the direction of the magnetic field.
Y-junction ferrite circulators have been already manufactured commercially up to W
band frequencies. Examples of W band circulators can be found from some providers,
such as Ferrite Domen (Russia) or Millitech (USA). In general, the RF performance of
those passive circulators fulfils the requirement of high-performance calibration switch
set for the current activity (below 1 dB insertion loss, around 20 dB isolation, and about
20 dB return loss). However, to obtain a switching function, an additional magnetic circuit
is needed to modulate the direct biasing magnetic field.
As the circulation state directly depends on direction of the applied magnetic field, the
common method to control the bias magnetic field is to use an electromagnet. This
method has a shortcoming that constant power is needed to keep a certain switching state.
Moreover, the switching power is rather large and switching time is bounded to minimum
of 10 μs because of the demagnetizing field and shielding effect caused by eddy currents
on waveguide. Those drawbacks can be overcome by using the latching geometry, a fer-
rite shape that can be biased by a wire loop through the ferrite body (Figure 8). Thanks to
close magnetic return path for magnetized ferrite part and the entire structure embedded
inside the junction housing, the demagnetizing fields of ferrite piece and the eddy currents
on junction housing are minimized. Therefore, no energy is required to hold a switching

20
state, the magnetic energy required to change between two states of the hysteresis loop is
small, and the switching time can be reduced less than 0.5 μs. [34]
Figure 8. One example of a ferrite shape with conductive wire loop inside, presented
in [35]. Ferrite parts outside the wire loop form three magnetic return paths for the
magnetized ferrite part inside the wire loop; hence, magnetization state of the ferrite
piece is remained after removing current in the wire loop.
In the electromagnetic coil method, the switching time is dependent on the shielding
effect of the waveguide, and in the latching geometry the switching response is deter-
mined by the time taking to reverse the remanence magnetization of ferrite piece.
Ferrite circulator switches have been successfully applied in spaceborne radiometers.
Examples include nadir pointing (non-scanning) Topex/Poseidon Microwave Radiometer
(TMR) [7] and conically scanning Scanning Multichannel Microwave Radiometer
(SMMR) on-board Seasat [17]. On the other hand, many literature publications report
about junction ferrite switch designs in different frequencies. Y-junction ferrite switches
can provide very low attenuation (as ferrite circulator) at limited bandwidth. For example,
COM DEV International (UK) provides waveguide junction ferrite switches in Ka-band
with approximate 0.5-0.6dB insertion loss. Although ferrite circulators are available in
W-band as mentioned above, there are very few ferrite switches made in that band or
higher than that. In this survey, only example of W band ferrite switch has been identified
in EMS technologies’ White Paper on Beam Forming Network [36]. EMS Technologies,
Inc. (Atlanta, GA, USA) provides space qualified switches with 0.1...0.4 dB in 7...94 GHz
range as reported in [36]. Note that these values include the package and interface mis-
matches. In millimetre wave frequencies the limiting factor is the ferrite material itself.
The material properties (e.g., saturation magnetization) dictate the usable highest fre-
quency, since the ferrites at current technologies are not designed and optimised for
millimetre or sub-millimetre wave frequencies use [37].
Specifications at waveguide module level of the ferrite latching circulator switch in
[36] is taken here as reference in W band for Y-junction ferrite switches:
 Frequency: 94 GHz
 Bandwidth: about 4.7 GHz (5%)
 Insertion loss: 0.4 dB max
 Return loss: 18 dB min

21
 Isolation: 18 dB min
 Switching time: 1 μs max
 Switching energy: 10 μJ
Figure 9. A 20-GHz switch from EMS Technologies (USA), with a ferrite in the junction
and biasing latching going inside the ferrite [36].
3.4 Switch technologies trade-offs
The technology trade-off here considers the RF performance and possible engineering
issues of each technology and the maturity of them.
First, mHEMT switch has the advantage that both the switch and the ACL can be
manufactured on the same MMIC chip; thus reducing the losses when connecting the
switch to the ACL and matched load. mHEMT switch can be designed in different fre-
quency bands with wide-band operation, and as a FET-based component it consumes only
a little amount of energy for switching function [16]. Yet, matching levels are not the
same but can vary from port to port in mHEMT switches as discussed in Section 3.1.
Finally, the switch (or switch + calibration load combination) needs to be integrated into
a waveguide package to provide waveguide interface (for antenna horn, for example),
which produces additional insertion loss of 1 - 1.5 dB. The mHEMT technology is quite
mature, and it has been demonstrated, e.g., in CALLOAD project. However, it is not yet
used in ground-based or spaceborne switches.
The MEMS switch technology based on the SPST switch from KTH is also a very
promising technology in view of the RF performance. The switch element chip itself is
not inherently a waveguide structure and hence special flanges need to be designed to
integrate the switch elements into a waveguide junction. The efficiency of integration into
a waveguide block determines how much the RF performance decreases. Furthermore, as
mentioned in Section 3.2 fringing fields and higher order modes at a junction would have
some effects and need further simulation or measurement to evaluate the actual perfor-
mance. Based on further discussions with the leader of the research group (Prof.

22
Oberhammer), the results presented in [33] for E-band should be also applicable at W-
band [38]. The KTH MEMS switch is fundamentally different technology than other con-
ventional MEMS switches, such as the shunt capacitive MEMS switch; hence, failure
mechanisms and reliability limitations are different as well. Its reliability is still a concern
here, since the available data is limited. For instance, the KTH MEMS switch features all
metal design; thus, the dielectric charging is not a problem in this MEMS. On the other
hand, another issue arising is that the cantilevers stick together if the switch remains in
the OFF state for a long time. One problem of MEMS switch element from KTH (which
is also common to all MEMS switch technologies) is its sensitivity to dust and other par-
ticles. However, due to its nature KTH MEMS switch technology is probably not suitable
for zero-level packaging like more traditional MEMS devices. Therefore, some kind of
low-loss microwave windows and hermetic packaging would be needed for testing and
use outside high-class clean room. The MEMS technology from KTH is relatively novel
and thus, it is still highly experimental technology at the moment. In fact, the SPDT or
SP3T switch using this MEMS technology has still to be demonstrated in practice. Thus,
the KTH MEMS technology is the least mature technology in comparison with the others.
Latching ferrite switches have a long heritage in terrestrial and space applications.
Their performance and manufacturing techniques have been proven for many real appli-
cations and products and by many research groups and manufacturers. This applies
especially for lower frequencies. Ferrite switches exhibit low losses and high isolation.
With latching method, short switching times in the order of microseconds and low switch-
ing power can be accomplished. Ferrite switches can be realised in a waveguide for
different frequencies. In other words, it is inherently a waveguide component and no tran-
sition to planar structures is required. This is optimal in terms of losses. Although only
few examples can be found in literatures for W-band and no commercial products exist
by European vendors, waveguide junction ferrite switches can be realised up to W-band
frequencies with high performance [36]. For such high frequencies, the challenge is to
manufacture a small ferrite insert at tight tolerances. Due to the small dimensions, it is
also extremely challenging to install a wire loop through the ferrite body (as in the latch-
ing geometry).Therefore, external magnetization would be much more attractive
approach. Another issue is that the ferrite switch is inherently of SPDT type. To realize a
higher-level switch than SPDT, two or more switches need to be combined together, and
depending on configuration, either insertion loss or isolation can be optimized (but not
both at the same time). An additional advantage of a ferrite switch is its robustness against
dust and other particles. Thus, prototyping and evaluating could be done in conventional
laboratory conditions and conventional ISO 5 clean room (i.e., class 100,000) would be
sufficient for the manufacturing, assembly, integration, test, and storage of space flight
hardware. In addition, no special packaging or careful protection would be needed.as in
case of MEMS switches.
Based on existing literatures available and the discussion presented in this chapter,
realistic and achievable performance parameters for an 89GHz SP3T switch have been
estimated for the three switch technologies under study. These estimations were made at
waveguide module-level. They are summarized in Table 4 for comparison.
Low insertion loss is the main driver of the high-performance radiometer calibration
switch as discussed. The effects of the insertion loss of a calibration switch on the system

23
noise temperature and radiometric resolution have already been evaluated in Section 2.4.
When integrated into a waveguide package, mHEMT is not suitable due to high insertion
loss. On the other hand, the MEMS switch technology and the latching ferrite switch
show a compliance with the insertion loss requirement.
Table 4. Estimated (realistic) performance parameters of the three switch technologies
under study; waveguide module at 89 GHz.
Parameter mHEMT KTH MEMS2
Ferrite3
Elementary
Switch type
SPDT or SP3T SPDT SPDT
Bandwidth Wide band Wide band about 5% (4.7 GHz)
Insertion loss 2.5 – 4.5 dB 0.4 – 1.1 dB 0.6 dB
Return loss 8 – 20 dB 15 – 25 dB 18 dB min
Isolation 20 – 40 dB 30 – 45 dB 15 – 20 dB min
Switching time Fast < 100 μs < 100 μs
Maturity of
technology
Relatively ma-
ture
The least mature The most mature
As already discussed above, the three different technologies present different stages of
maturity. The mHEMT technology itself is relatively mature, and for example, the Fraun-
hofer IAP has manufactured low noise amplifiers for more than 10 years using its own
process. MEMS processes, on the other hand, are more experimental. There are still on-
going activities to assess the reliability of RF MEMS in general and the KTH MEMS in
particular. The KTH MEMS technology is very new, only few initial estimations can be
done for its reliability. The ferrite switch technology, on the other hand, has decades of
heritage both on-ground and in space and the technology is routinely applied in space at
lower frequencies.
2
Estimated values based on measurement results in [33]. However, simulations and measurements in a
waveguide structure would be required to give estimation that is more accurate.
3
Given values estimate the achievable performance for ferrite switch.

24
4 Theory of ferrite junction circulators
This chapter presents a background theory of ferrite junction circulators. At first, funda-
mentals of soft ferrite at microwave frequencies are discussed, which helps to understand
the gyromagnetic behaviour of ferrites under static biasing magnetic field and being ex-
posed to electromagnetic waves. Next, Y-junction ferrite circulator is described in two
approaches. The first approach uses field equations to explain circulation operation of
ferrite circulators. The latter one applies the eigenvalues analysis, which is then utilized
as the design method for two Ka band switches.4
4.1 Basics of microwave ferrite
At microwave frequencies, ferrimagnetic compounds (ferrites) have a special character-
istic that under the external static magnetic field 𝑯0 the permeability of a ferrite is not a
single scalar number but instead a tensor, which can be represented as a matrix. The per-
meability tensor is obtained from the linearized equation of motion.
Considering that an electron having a magnetic dipole moment 𝒎 𝒅 is exposed to an
external static magnetic field 𝑯0, the electron experiences a torque that is given by
[39], [40]:
𝑻 = 𝒎 𝒅 × 𝜇0 𝑯 𝟎. (21)
In addition, the electron has its own spin motion, which is represented by the spin mo-
mentum or the angular momentum 𝑱 of the electron. For electrons, the magnetic moment
𝒎 𝒅 and the corresponding angular momentum 𝑱 are parallel vectors, but, in opposite di-
rections. Thus, the relationship between 𝒎 𝒅 and 𝑱 can be expressed by:
𝒎 𝒅 = −𝛾𝑱, (22)
where 𝛾 is a constant called the gyromagnetic ratio. The time rate of change or time de-
rivative of the angular momentum is equal to the exerting torque, which means:
𝑻 = −
1
𝛾
𝑑𝒎 𝒅
𝑑𝑡
. (23)
Combing (21) and (23) results in:
−
1
𝛾
𝑑𝒎 𝒅
𝑑𝑡
= 𝒎 𝒅 × 𝜇0 𝑯 𝟎 , (24)
4
At this point, it is necessary to notice that nearly all research studies on ferrite express their results in
Gaussian units, where magnetic field is given in Oersted [Oe] and magnetization is given in Gauss [G]. For
that reason, ferrite literature and manufacturing documents/datasheets also use Gaussian or cgs units. In
this thesis, the International System of Units (SI) is used and the corresponding units of Oe and G are A/m
and T. All equations related to ferrite theory and circulation calculations are, therefore, written in forms
under the SI system.

25
which is known as the equation of motion for a magnetic dipole. In a macroscopic view,
if there are 𝑁 free magnetic dipoles per unit volume of ferrite material, equation (24)
becomes:
−
1
𝛾
𝑑𝑴 𝟎
𝑑𝑡
= 𝑴 𝟎 × 𝜇0 𝑯 𝟎 , (25)
where 𝑴 𝟎 is the total magnetization per unit volume. The larger an external static field
is, the more magnetic dipoles are coupled. When all free magnetic dipoles in material are
coupled, a larger external static field does not couple more magnetic dipoles, and the
magnetization saturates, 𝑴 𝟎 = 𝑴 𝒔. In practice, saturation magnetization level is often
expressed as 4𝜋𝑀𝑠 Gauss in Gaussian units or 𝜇0 𝑀𝑠 Tesla in SI.
Now, let us consider a situation where an infinite ferrite medium is exposed to an ex-
ternal static magnetic field along z-axis. Besides the static field, the total magnetic field
applied on the ferrite medium also consists of a time-varying magnetic field in xy-plane
(ℎ 𝑧 = 0). Hence, the equation of motion is written as:
−
1
𝛾
𝑑(𝑴 𝒔 + 𝒎)
𝑑𝑡
= (𝑴 𝑺 + 𝒎) × 𝜇0(𝑯 𝟎 + 𝒉) , (26)
where 𝒉 is the time-varying magnetic field, and 𝒎 is the time-varying part of the mag-
netization which is induced by 𝒉. If the time-varying parts are much smaller than the
static ones, equation (26) could be approximated as:
𝑑𝒎
𝑑𝑡
= −𝛾𝜇0(𝑴 𝟎 × 𝒉) + (𝒎 × 𝑯 𝟎) . (27)
Assuming that the time dependence of 𝒉 and 𝒎 is in form of 𝑒 𝑗𝜔𝑡
, we get:
𝑗𝜔𝒎 = −𝛾𝜇0(𝑴 𝟎 × 𝒉) + (𝒎 × 𝑯 𝟎) , (28)
Furthermore, the time-varying vectors 𝒎 and 𝒉 can be decomposed as:
𝒎 = 𝑚 𝑥 𝒂 𝒙 + 𝑚 𝑦 𝒂 𝒚 + 𝑚 𝑧 𝒂 𝒛 ,
𝒉 = ℎ 𝑥 𝒂 𝒙 + ℎ 𝑦 𝒂 𝒚.
(29)
Substituting (29) into (28) and solving for the components of the magnetization vectors,
we get:
𝑚 𝑥 =
𝜔0 𝜔 𝑚ℎ 𝑥 + 𝑗𝜔𝜔 𝑚ℎ 𝑦
𝜔0
2
− 𝜔2
,
𝑚 𝑦 =
𝜔0 𝜔 𝑚ℎ 𝑦 + 𝑗𝜔𝜔 𝑚ℎ 𝑥
𝜔0
2
− 𝜔2
,
𝑚 𝑧 = 0,
(30)
where

26
𝜔0 = 𝛾𝜇0 𝐻0 ,
𝜔 𝑚 = 𝛾𝜇0 𝑀𝑠.
(31)
(32)
𝜔0 is referred as the Larmor frequency.
A susceptibility tensor is defined to relate the time-varying parts of the magnetization
and the magnetic field to each other:
𝒎 = χ̿ ∙ 𝐡 , (33)
where
χ̿ = [
𝜒 𝑥𝑥 𝜒 𝑥𝑦 0
𝜒 𝑦𝑥 𝜒 𝑦𝑦 0
0 0 0
], (34)
Comparing (30), (33) and (34), one can derive the expression for each component of χ̿ as:
𝜒 𝑥𝑥 = 𝜒 𝑦𝑦 =
𝜔0 𝜔 𝑚
𝜔0
2
− 𝜔2
,
𝜒 𝑥𝑦 = −𝜒 𝑦𝑥 =
𝑗𝜔𝜔 𝑚
𝜔0
2
− 𝜔2
.
(35)
(36)
When dealing with ferrite applications involving the analysis of electromagnetic prob-
lems with Maxwell’s equations, it is more convenient to use the permeability to relate the
magnetic field and the magnetic flux density. The relative permeability of a medium is
defined as:
𝜇 𝑟 = 1 + 𝜒. (37)
So the relative permeability tensor can be obtained from (34), which is often referred as
the Polder tensor:
μ 𝑟̿̿̿ = [
𝜇 𝑗𝜅 0
−𝑗𝜅 𝜇 0
0 0 1
], (38)
𝜇 = 1 + 𝜒 𝑥𝑥 ,
𝜅 = −𝑗𝜒 𝑥𝑦 .
(39)
(40)
Up to this point, the analysis does not consider any losses in ferrite. Losses cause
damping in precession motion of magnetic dipoles in ferrite. The damping effect can be
accounted by replacing 𝜔0 with 𝜔0 + 𝑗𝛼𝜔:
𝜔0 ⇠ 𝜔0 + 𝑗𝛼𝜔 (41)
The factor 𝛼 in the expression above is called the damping factor of ferrite material. It is
calculated by:

27
𝛼 =
𝜇0 𝛾Δ𝐻
2𝜔
(42)
where Δ𝐻 is the resonance line width of ferrite material, which is usually measured and
provided by ferrite manufacturers. Using (41) we can re-write the Polder tensor’s com-
ponents including the damping effect:
𝜇 = 1 + 𝜒 𝑥𝑥 = 1 +
(𝜔0 + 𝑗𝛼𝜔)𝜔 𝑚
(𝜔0 + 𝑗𝛼𝜔)2 − 𝜔2
,
𝜅 = −𝑗𝜒 𝑥𝑦 =
𝑗𝜔𝜔 𝑚
(𝜔0 + 𝑗𝛼𝜔)2 − 𝜔2
.
(43)
(44)
4.2 Junction ferrite circulator
Y-junction circulator is a nonreciprocal three-port device. Circulator’s non-reciprocity
depends on the characteristics of ferrites.
Ferrite junction circulator operates based on the resonant modes of ferrite in the junc-
tion. When an input port is excited, the power flows equally to the other two ports if there
is no static biasing magnetic field. When a bias magnetic field is present, the electromag-
netic field pattern of the ferrite resonator is rotated (see Figure 10) since the permeability
of the ferrite becomes a tensor. The bias field strength is selected so that the resonance
pattern rotates and the null of E-field appears at one port. Thus, isolation at that port is
achieved and power only flows to another output port [40], [41], [42].
Figure 10. The field plot in CST simulation of magnetized ferrite junction in the domi-
nant mode. Rotation of the resonance pattern creates circulating operation.
From theoretical point of view, it is possible to match a nonreciprocal lossless three-
port device at all ports. Its scattering matrix will look like:
[𝑆] = [
0 0 1
1 0 0
0 1 0
]. (45)

28
The scattering matrix above indicates that the power flowing direction is 1-2-3 with per-
fect isolation, zero insertion loss and perfect matching at all ports. This is known as the
performance of an ideal circulator. Now let examine a not-perfectly-matched but lossless
three-port circulator, the scattering matrix of such circulator can be expressed by:
[𝑆] = [
ρ 𝛽 𝜎
σ ρ 𝛽
𝛽 𝜎 ρ
], (46)
where ρ is a reflection coefficient and 𝜎, 𝛽 are transmission coefficients. If the circulation
direction is 1-2-3 for example, insertion loss is proportional to 𝜎 and isolation is propor-
tional to 𝛽. When the matching is ρ ≪ 1, the following dependence holds [39], [40]:
|𝜎| ≈ 1 − |ρ|2
,
|𝛽| ≈ |ρ|.
(47)
(48)
So the scattering matrix in (46) can be rewritten as:
[𝑆] = [
ρ ρ 1 − ρ2
1 − ρ2
ρ ρ
ρ 1 − ρ2
ρ
]. (49)
The result indicates one important property of a circulator: both the insertion loss |𝜎|−2
and the isolation |𝛽|−2
are functions of input matching level, and both deteriorate as the
ports become mismatched. Moreover, the deviation from an ideal circulator performance
is enlarged further by losses in ferrites, which is always the case in reality.
4.2.1 Analytic field equation approach
As mentioned, the phenomenological description of the circulator is based on the rotation
of resonant modes of a ferrite insert in the junction under the application of a biasing
magnetic field. In the absence of a biasing field, two counter rotating modes are degener-
ate and the resonance modes due to them are at the same frequency.
To retrieve the initial estimation for the resonance frequency and ferrite radius, we can
use the formulas for stripline junction circulators. The resonant modes can be found by
solving Maxwell’s equations with proper boundary conditions at the junction. The first
resonance mode of a demagnetized ferrite disk is determined as [39], [43]:
𝜔 𝑟 =
1.841
𝑅√ 𝜀0 𝜀𝑓 𝜇0 𝜇 𝑒
. (50)
Here, only the first root of the first Bessel function is considered, which results in the
value of 1.841 in the nominator.
When the ferrite piece is magnetized, the resonance splits into two different modes,
referred as two counter-rotating modes (denoted by “+” and “-” signs). Their resonance
frequencies are slightly different and are expressed by:
𝜔± =
𝑥±
𝑅√ 𝜀0 𝜀𝑓 𝜇0 𝜇±
, (51)

29
where 𝑅 is the ferrite radius, 𝜀𝑓 is the ferrite dielectric constant, 𝜇± is the corresponding
scalar permeability of the ferrite for each rotating mode, 𝜇 𝑒 is the scalar effective perme-
ability of the ferrite, and 𝑥± is the constant numbers determined from analysis equations.
For small splitting, two frequencies 𝜔+and 𝜔− are considered to be symmetrical about
the original resonance frequency 𝜔 𝑟.The superposition of these two modes results in a
rotation of the resonant pattern in the ferrite resonator (Figure 10). The amount of fre-
quency splitting of two counter-rotating modes affects the amount of rotation of the
resonance pattern and is essential to achieve the circulation of power flow in the junction
correctly and optimally.
It is observed that 𝜔+ and 𝜔− bracket the centre frequency, 𝜔 𝑟. If an operating fre-
quency of the junction is given, the ferrite radius can be chosen so that suitable frequency
splitting for circulation is occurred. For designing purpose, the original resonance 𝜔 𝑟 can
be used to determine the ferrite insert radius at the first glance:
𝑅 =
1.841
2𝜋𝑓0√ 𝜀0 𝜀𝑓 𝜇0 𝜇 𝑒
. (52)
The ferrite radius and the biasing magnetic field can be adjusted to tune the junction for
correct operation.
In case of waveguide junction, although the ferrite does not fill entirely the cavity and
the junction boundaries are poorly defined, the above analysis is still valid to roughly
estimate the ferrite radius [43], [44]. Besides that, the work of Butterweck [45] gave es-
timation for the relationship of 𝜔0 and 𝜔±, when a ferrite insert is a thin full-height ferrite
post:
𝛿∗
=
𝜔+ − 𝜔0
𝜔0
= −
𝜔− − 𝜔0
𝜔0
≈ 1.54 (
𝑅
𝑅1
)
2
𝜅∗
, (53)
where 𝛿∗
is the fractional frequency deviation, 𝑅 is the ferrite radius, 𝑅1 is the cavity
radius, and 𝜅∗
is the off-diagonal component of effective susceptibility:
𝜅∗
=
4𝜅
(1 + 𝜇)2 − 𝜅2
. (54)
The required frequency deviation of the two counter-rotating modes is also described by
another expression in [43]:
𝛿∗
=
tan 300
2𝑄 𝐿
. (55)
Term tan 300
appears in the nominator since each rotating mode has a 30-degree admit-
tance phase at centre frequency 𝜔 𝑟.The loaded quality factor of the junction is related to
the operating bandwidth and the highest permissible VSWR over that bandwidth. Apply-
ing (52) – (55), analytic estimation of parameters for a waveguide junction circulator can
be computed.
All the formulas above are only approximations and cannot directly result in a working
design of waveguide junction circulator. However, they provide a good starting point to
determine ferrite size and junction parameters. In addition, some design principles can be
understood. For example, the biasing field strength can be used to refine the operating

30
frequency, the saturation magnetization should be as high as possible to maximize oper-
ating bandwidth, and the ferrite dimension becomes larger if a ferrite with low dielectric
constant is available.
4.2.2 Eigenvalues approach
Exact solutions of the operation modes can be obtained through analytic equations. How-
ever, it requires heavy and complex computation, which is often done by simplification
and approximation of those equations. There is an alternative method to avoid mathematic
complication and to determine the modes of operation of the ferrite junction. This method
is based on eigenvalues of 3-port junction as studied in [46] and [47].
From the scattering matrix theory, it is known that the non-reciprocal and symmetrical
junction is described by a matrix of S-parameters as following:
[𝑆] = [
𝑆11 𝑆12 𝑆13
𝑆13 𝑆11 𝑆12
𝑆12 𝑆13 𝑆11
], (56)
where
𝑆11 = 𝑆22 = 𝑆33,
𝑆12 = 𝑆23 = 𝑆31,
𝑆13 = 𝑆21 = 𝑆32.
(57)
Moreover, the [S] matrix of a symmetrical 3-port junction can also be characterized by
three eigensolutions:
[𝑆][𝑥]𝑖 = 𝜙𝑖[𝑥]𝑖, (58)
where [𝑥]𝑖 are the eigenvectors, 𝜙𝑖 are the eigenvalues, and the index 𝑖 takes values from
1 to 3. In physical interpretation, the eigenvectors represent three ways to excite the junc-
tion simultaneously at three ports, and eigenvalues are simply the reflection coefficients
for the respective excitations (Figure 11). Three eigenvectors or eigenexicitations can be
expressed as:
[𝑥]1 =
1
3
[
1
1
1
], (59)
[𝑥]2 =
1
3
[
1
1𝑒+
𝑗2𝜋
3
1𝑒−
𝑗2𝜋
3
], (60)
[𝑥]3 =
1
3
[
1
1𝑒−
𝑗2𝜋
3
1𝑒+
𝑗2𝜋
3
]. (61)

31
Figure 11. Three excitation ways and a phase displacement between eigenvalues results
in circulation. (a) 𝜙2 is phase retarded and 𝜙3is phase advanced for clockwise circula-
tion. (b) 𝜙2 is phase advanced and 𝜙3is phase retarded for anti-clockwise circulation
[47].
The excitation [𝑥]1, which has the same phase at each port, is called the in-phase ex-
citation, while [𝑥]2 and [𝑥]3, which have phase displacement by
2𝜋
3
from port to port, are
referred to as rotating excitations. It can be seen that superposition of the three excitations
results in exciting one port only. Correspondingly, different combinations of eigenvalues
can also describe the junction scattering parameters:
𝑆11 =
1
3
(𝜙1 + 𝜙2 + 𝜙3), (62)
𝑆12 =
1
3
(𝜙1 + 𝜙2 𝑒−
𝑗2𝜋
3 + 𝜙3 𝑒+
𝑗2𝜋
3 ), (63)
𝑆13 =
1
3
(𝜙1 + 𝜙2 𝑒+
𝑗2𝜋
3 + 𝜙3 𝑒−
𝑗2𝜋
3 ). (64)
According to (62), (63), and (64), when the eigenvalues are mutually displaced
by 2𝜋/3, two sets of S-parameters can be obtained {𝑆11 = 0; 𝑆12 = 1; 𝑆13 = 0} or
{𝑆11 = 0; 𝑆12 = 0; 𝑆13 = 0}. This corresponds to two circulation states of the junction
(Figure 11). For broad bandwidth operation, that 2𝜋/3 displacement must be maintained
over a large frequency range. This implies that the rate of change of phase of the three
eigenvalues with frequency must be identical.
Applying this eigenvalues analysis, the circulator operation can be understood rela-
tively easily. The typical structure of the nonreciprocal junction consists of a quarter-
wavelength long cylindrical ferrite piece short-circuited at one end and dielectric-loaded
at the other end. Two rotating excitations couple two modes that propagate along the
ferrite cylinder. They are reflected off the short-circuited end into the junction and radiate
back out into the three ports. The in-phase excitation cannot couple into the cylindrical

32
ferrite piece due to 2𝜋/3 separation in space (fields from three feeding arms cancel each
other at the junction), and is simply reflected back into the three ports from the junction
centre. When the ferrite is not biased, propagating constants of two rotating modes in the
circular waveguide are identical. Hence, the eigenvalues 𝜙2 and 𝜙3 are in phase, and the
junction is reciprocal, i.e. 𝑆12 = 𝑆21. Magnetizing the ferrite makes its permeability be-
come a tensor. The propagation constant of one rotating mode is increased, while the
propagation constant of the other is decreased. This is because the two rotating modes
have two circular polarizations in opposite senses and experience different permeability.
Consequently, the phases 𝜙2 and 𝜙3 are separated since one mode is travelling and re-
flected faster than the other. By adjusting ferrite radius, ferrite length, biasing field
strength and the coupling level of the resonator, the relative phase shift between eigen-
values can be tuned to be 2𝜋/3 and the junction is made to circulate. In fact, phase
displacement close to 2𝜋/3 is enough achieve good performance of a circulator in prac-
tice.
The diagrams in Figure 12 to Figure 14 are contour plots obtained by plotting equations
(62), (63), and (64) in dB. They display the levels of return loss and transmission losses
with respect to the phase displacement of 𝜙2 and 𝜙3 to 𝜙1. According to those, the rela-
tive phase shift in range of 1200
± 170
is good enough to result in isolation and return
loss better than 20 dB, and insertion loss5
below 0.5 dB. In designing process, those dia-
grams are useful tools to keep track the relative phase shift of the eigenvalues while tuning
the circulator performance.
Figure 12. The return loss in dB at port 1 as a function of the phase angles between the
eigenvalues.
5
Note that the insertion loss indicated in the diagram is for an ideal circulator and does not account for
losses of ferrite material and resistive losses.

33
Figure 13. The transmission loss coefficient in dB from port 1 to port 2 as a function of
phase angles between eigenvalues.
Figure 14. The transmission loss coefficient in dB from port 1 to 3 as a function of the
phase angles between eigenvalues.

34
4.3 Higher order modes ferrite junction
The operation of conventional ferrite junction circulators presented in Section 4.2 are
primarily based on the dominant mode operation, meaning the lowest mode HE11. How-
ever, a circulator could be realized by a higher-order modes ferrite junction. The use of
higher order modes has been investigated in ferrite circulators as reported in, e.g., [48]. It
benefits the manufacturing and assembly process by having larger ferrite piece, which
can operate at the same operating frequency as the smaller ferrite at the dominant mode.
This section presents the higher order modes junction as the alternative approach for junc-
tion circulators at high frequencies.
4.3.1 Observation of higher order resonance modes in ferrite junction
Typically, the TE10 mode in the rectangular waveguide excites the HE11 mode in the fer-
rite. The field pattern of HE11 mode in circular dielectric cavity looks similar to the pattern
of TM11 mode in circular cavity with a magnetic boundary condition as explained and
illustrated in [41]. However, the ferrite-loaded cavity can be considered as a dielectric
resonator and can support various resonating modes other than HE11 [47], [49]. It has
been observed in the design process that the feeding TE10 mode in rectangular waveguide
also excites other higher modes in the ferrite body, which resonate at higher frequencies
than HE11. Thus, if the ferrite size is dimensioned correctly to have one or some higher
order modes excited around a desired frequency, larger ferrite piece is obtained in com-
parison to the ferrite piece operating with the dominant mode at the same frequency.
Electromagnetic simulation models of circulators at W band were built in CST to
check the higher order modes operation. It was observed that the higher order modes was
excited in the ferrite cylinder when its diameter was increased. Figure 15 and Figure 16
illustrate the standing wave pattern in the junction of two W band circulator models. The
plots show electric field lines and intensity at two cutting planes. The ferrite-loaded cavity
resonated in the dominant HE11 mode in the first model, while higher order modes were
excited in the latter model. It is worth mentioning that both models operate at the same
frequency, and the latter one (with higher order modes) has a larger ferrite cylinder.
Besides the observation in electromagnetic simulation, the numerical analysis in [50]
also identified the higher order circulation modes in ferrite cylinder. The demagnetized
ferrite cylinder was treated as a dielectric resonator. The characteristic equation for the
modes in a cylindrical dielectric resonator was solved numerically with roots of different
order n of the Bessel functions of different order m to determine possible hybrid HEmn
modes in the structure. The calculation results of several higher order modes up to HE31
were compared with experiment data to check the existence of those modes in the ferrite
cylinder.
These confirm that higher order modes are supported in the ferrite-loaded waveguide
junction.

35
Figure 15. Electric field of the dominant mode at junction of the W band circulator
model. The intensity plot (left) shows field strength at the junction’s top view. The field
vector plot (right) presents the cross section along the dashed line on the left picture.
Figure 16. Electric field lines at junction of the other W band circulator model having
higher order modes excited. The intensity plot (left) shows field strength at the junc-
tion’s top view. The field vector plot (right) presents the cross section along the dashed
line on the left picture.
4.3.2 Application of higher order modes in circulator and switch
Since the circulation operation is dependent on relative phases between eigenvalues (re-
gardless of mode excitation), a circulator could be realized with higher order modes in
the junction as long as their eigenvalues are in correct relative phases. In other perspec-
tive, waveguide junction in a circulator behaves like a transmission cavity between
waveguide ports as explained before. Due to the presence of gyromagnetic materials in
the junction (such as magnetized ferrites), a standing wave pattern of the cavity rotates,
all ports can be matched and circulation occurs. This is also true when higher order modes
are excited in the junction. As seen in Figure 16, the standing wave pattern of the higher
order modes was rotating 30° to result in circulating operation. The use of higher order
circulation modes drew attention and has been explored before [48], [50]. The studies in
[50] indicated the novelties of the higher order modes in cylindrical ferrite inserts for the

36
use of mm-wave waveguide circulators. It eliminates the principal disadvantages of wave-
guide circulators, such as low reproducibility and narrow bandwidth. The experimental
works in [50] and some circulator prototypes in [48] have further proved the feasibility
to have circulation operation with higher-order modes in ferrite junction.
However, no open access reference is known for the application of higher order mode
junction to a switch. In ferrite junction circulators, permanent magnets are used to gener-
ate the required magnetic field to bias the ferrite. In a ferrite junction switch, a switchable
magnetic field is needed. Provided the magnetic circuit can provide enough magnetic
field strength for biasing and has a function to alternate the field direction, a switch can
be made out of the higher order mode circulator.
The higher order mode ferrite switch finds its applications especially in mm-wave-
lengths region, where uncertainty in tiny ferrite dimensions creates challenges in
repeatability and makes manufacturing yield low. Using equation (52) leads to Table 5,
which shows how the ferrite diameter in the dominant circulation mode shrinks down
with respect to frequency. This gives the motivation to apply higher order mode ferrite
junction in ferrite switch designs at higher frequency bands, since greater dimensions
offer better reproducibility. It also enables the application of internal latching magnetic
design for ferrite switches at higher frequencies, which offers advantages in switching
time and switching power as discussed further in Section 5.5. Furthermore, the use of
multiple adjacent higher modes can solve the issue of narrow bandwidth at high frequen-
cies.
Table 5. Approximation of ferrite diameter for the dominant circulation mode. (In the
calculation, typical value of 13 is used for the ferrite dielectric constant.)
Frequency [GHZ] Ferrite diameter [mm]
15 3.2
36.5 1.3
60 0.8
90 0.55

37
5 Design of Ka band ferrite switches
This chapter is focused mainly on presenting the designs of two Ka band switch variants.
It starts by a brief mention on the design methodology. Short discussion about important
parameters of ferrite material is also provided for more understanding.
5.1 Design methodology
As presented in Section 4.2.2, the analysis of a ferrite junction circulator can be done
more conveniently by the scattering matrix theory of a 3-port network. Hence, the eigen-
values method is employed to design two Ka band switches with the help of CST
Microwave Studio 3D electromagnetic simulator software package.
The turnstile junction is modelled according to the principal structure shown in Figure
17. To start with, the ferrite resonator is made fully outside the junction, i.e., 𝐿1 = 𝐿, and
the transformer height (𝑠) is set to zero. Different values of ferrite radius (𝑅) and ferrite
length (𝐿) are swept in the simulation, and the corresponding relative phase shifts between
three eigenvalues (known as ‘‘active S-parameters’’ in CST) are then calculated for each
pair of R and L.
Figure 17. Schematic diagram of a turnstile resonator [52]; clarifying texts added by
the author of this thesis.
Pair values of R and L, which create suitable phase displacements, are determined. The
suitable amount of phase displacements is chosen with respect to the required return loss
based on the contour plot in Figure 12. Then the transformer is implemented for those
designs. Proper tuning of transformer height (𝑠) and transformer radius (𝑅𝑡𝑟) has an effect
to linearize the eigenvalues’ phase response in vicinity of the operating frequency, and
thus broadens the operating bandwidth. However, the transformer also interferes with the
phase response and affects the original phase displacement. Correct phase displacement
is recovered by adjusting the amount of insertion of the resonator into waveguide junction
(𝐿1), since it affects the coupling of TE10 mode into the resonator. A standard WR-28
waveguide is also used in this design, so 𝑎 = 7.11 mm and 𝑏 = 3.56 mm.

elec_2016_nguyen_huy

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