MODELING OF JUNCTION CIRCULATOR USING ANN
1
Ch.Harini, 2Dr.K Sri Rama Krishna, 3G.V.Subrahmanyam
1
PG Student, Department of ECE, VR Siddhartha Engineering College, Vijayawada,
[email protected]
2
Professor and Head, Department of ECE, VR Siddhartha Engineering College, Vijayawada
3
Research Scholar, Department of ECE, Acharya Nagarjuna University, Guntur
applied at the port 1, at port 2 two signals will arrive and at
ABSTRACT
port 3 signals will be cancelled. According to the applied
The most frequently utilized microwave ferrite devices
in most microwave systems is the circulator because it
finds wide range of applications in the transmission ,
reception and manipulating of electromagnetic signals
like controlling of power flow and isolate various
magnetic field, maximum signal flow will be from port1to
port2 and minimum signal flow will be from port 1to port
3. The signal in the circulator may be clockwise or counter
clockwise by depending on the polarization of the magnetic
biasing field.
components in high frequency applications. A precise
model is necessary for the analysis and design of ferrite
junction circulator that can be obtained from EM
simulations,
computational
but
it
cost.
is
expensive
Therefore,
for
Artificial
its
high
Neural
Networks (ANNs) become very useful especially when
several model evaluations are required for design and
optimization. In recent times ANNs have been solving
wide variety of RF and Microwave CAD problems.
Modelling of circulator is presented in this paper using
ANN forward and reveres models.
Index
terms-
Artificial
neural
networks
(ANN),
circulator, forward and reverse models, computer aided
design (CAD), Splitting Constant (k/µ).
1.
INTRODUCTION
Figure 1: The schematic diagram shows a basic Yjunction circulator and flow of energy
Circulators are essential elements in high-power microwave
Artificial Neural networks are efficient alternatives to
systems and antenna networks in which energy can be
conventional methods such as numerical modelling
directed and isolated [1]. Circulator is a versatile
methods, which is computationally expensive or analytical
microwave device, has low electric loss and can handle
methods and could be difficult to obtain for new devices or
huge powers and can operate over no more than octave
empirical models, whose range and accuracy are limited
bandwidth. RF circulator is a ferromagnetic passive device
[1]. Neural networks have also been used for wide variety
with three ports, passing the signal from one port to another
of RF and Microwave computer aided design (CAD)
port in circular motion. Circulator is alternative to the
problems.
expensive duplexers and mesh networks. When signal is
Analysis of junction circulator using microstrip line will be
testing sufficiently. For microwave applications data can be
implemented by Artificial Neural Network (ANN) model to
generated either by simulation of MATLAB or by
determine the magnitude and phase variations (S-
measurement.
Parameters) for various frequencies. Analysis ANN
Multi Layered Perceptron neural network is the
forward model is used for the analysis, where the inputs are
geometrical parameters and the outputs are electrical
parameters. RF and microwave components are designed
by considering inverse model, where the inputs are
electrical parameters and the outputs are geometrical
parameters. The performance of the model is determined in
terms of average and maximum estimated errors using
different neural network training algorithms.
following equations:
Q=
layers they are input layer, hidden layer and output layer.
MLP
best
suits problems
like
arbitrary nonlinear
continuous approximation problems.
III.
ANN MODEL FOR THE ANALYSIS
OF
FERRITE JUNCTION CIRCULATOR (FORWARD
MODEL)
For a circulator to get circulation perfectly it should satisfy
P=
architecture used for the ANN model. It consists of three
ANN model analysis is done by forward model
where inputs are physical or geometrical parameters and
outputs are electrical parameters. Ferrite anisotropic
M.(M2 −3.N2)
(1)
M2 +N2
splitting (𝑘 ⁄𝜇) is the physical parameters and junction
wave impedance ratio
N.(3.M2 −N2 )
(2)
M2 +N2
The two equations are derived from the electromagnetic
(𝑍𝑒𝑓𝑓 ⁄𝑍𝑑 ) is the electrical
parameters. Neural Network architecture interconnects all
the neurons
(EM) field solution for perfect circulation given [2].
and weights are updated to reduce the error. MLP is trained
Parameters P, M, and N are defined as:
using many different learning algorithms.
ψ B0
P= .
2 A0
M=
ψ.B0
2.A0
+ ∑∞
n=1
sin(n2 .ψ) An .Bn
+ ∑∞
n=1
sin( n2 .ψ) An. Bn
n2 .ψ
n2 .ψ
.
.
(3)
Dn
DN
2nπ
. cos(
3
)
(4)
n k
N = ∑∞
n=1
2
sin(n2 .ψ) (s.R. μ ).Bn
n2 .ψ
.
Dn
. sin(
2nπ
3
) (5)
II. ANN MODELLING TECHNIQUES
ANN represents promising modelling techniques,
especially for data sets having nonlinear relationships that
are frequently encountered in engineering [3-10]. The
important factors of ANN model is architecture and the
Figure 2: Neural network for calculating junction wave
algorithms to be used [10]. There are several architectures
impedance ratio of circulator (Forward model)
and algorithms in ANN model. According to the problem
the selection of architectures and algorithm is used. ANN is
similar to a black box and the accuracy depends on the data
to be used while training. For the best accuracy the data to
be randomized and distribute data for training and for
Simple accurate ANN forward model is proposed for
calculating the junction wave impedance ratio 𝑍𝑒𝑓𝑓 ⁄𝑍𝑑 of
ferrite junction circulator as shown in Figure 2. The data
used in the model is obtained from the simulation results
and contain samples nearly 5400. For training 3500
samples are used from the simulated data.
Neural network use learning rate of 0.1 to 120
epochs. In the forward model training and testing is
performed and training error is reduced to the minimum
Table 1: training and testing results of ferrite junction
circulator in forward model
value so that the target output and actual output is similar.
After several trails it is observed that three layered MLP is
the accurate model and suitable configuration is 2:8:1 for
(a) Training Results
the analysis of ferrite junction circulator
The neural network forward model is trained with
Learning algorithm
Training error
ABP
0.00583684
AUTO PILOT
0.002471552
(CG), Adaptive Back Propagation
BP
0.007034414
(MLP), Quasi Network (QN), Huber Quasi Network
CG
0.00583486
HQN
0.00247155
QN
0.00247155
QN(MLP)
0.002471787
junction circulator and simulated model is performed for
SM
0.00247156
validation. The neural model trained by Quasi Network
ST
0.274387
nine learning algorithms namely Back propagation
algorithm (BP), Sparse Training (ST), Conjugate Gradient
(ABP), Quasi Network
(HQN), Auto Pilot (MLP3) and Simplex Method (SM) [34]. Training and testing results of many algorithms are
listed in Table 1. Quasi Network (MLP) and Quasi
Network are the two learning algorithms in which train
error is less. Comparison of analysis model of ferrite
(MLP) for forward model and is compared with simulated
results and is presented graphically in Figure 3.
(b) Testing Results
Learning
algorithm
Testing
Average
Error
Worst
Case Error
Correlation
Coefficient
ABP
0.5810733
3.855173
0.99897424
AUTO
PILOT
BP
0.24243173
3.4189374
0.99971044
0.6928214
4.0629745
0.99968994
CG
0.58910733
3.855173
0.9970491
HQN
0.24243173
3.4189374
0.99979679
QN
0.24243173
3.4189374
0.9999675
QN(MLP)
0.24243173
3.4184374
0.99996796
SM
0.24243173
3.4189374
0.99974674
ST
0.6928214
4.0629745
0.99974674
Figure 3: Comparison of Ferrite anisotropic
splitting (𝒌⁄𝝁) and junction wave impedance ratio
(𝒁𝒆𝒇𝒇 ⁄𝒁𝒅 ) obtained using simulated results with
forward model of circulator
IV. ANN MODEL FOR THE DESIGN OF FERRITE
model is suitable only for the monotonic functions. Now
JUNCTION
the aim is develop the ANN model for the Non-monotonic
CIRCULATOR
(DIRECT
INVERSE
MODEL)
responses.
For the design of ferrite junction circulator, direct
inverse model is used where the inputs are electrical
parameters and output is physical/geometrical parameters
just reverse to the forward model. The two methods used
are optimization method and direct inverse method.
Optimization method is the method in which EM simulated
model or forward model is evaluated repeatedly for the
optimal solutions. Neural inverse model is compared with
simulated results and presented graphically in Figure 4.
Figure 5: Neural model for calculating ferrite
anisotropic splitting (inverse model)
V. PROPOSED ANN INVERSE MODEL FOR THE
DESIGN OF CIRCULATOR (INDIRECT INVERSE
MODEL)
Original forward input-output relationship is not
monotonic, the non-uniqueness become inherent problem
Figure 4: comparison of Ferrite anisotropic splitting
in inverse model. To solve the problem, we start by
(𝒌⁄𝝁) and junction wave impedance ratio (𝒁𝒆𝒇𝒇 ⁄𝒁𝒅 )
addressing multivalued solutions in training data [11].
obtained using simulated results with direct inverse
model of circulator
Inverse model produces two output values for single input
value it mean it arise a contradiction. To match two
Neural Network inverse model is faster than Optimization
different out values simultaneously, neural network can’t
model but it produced non uniqueness in input and output
be trained. Training error can’t be reduced so the model is
relationship. It mean for one input value it produces two
not accurate. To overcome the problem proposed inverse
output values so there produce a non uniqueness. It is also
model is developed.
called as multi valued solutions. So there is difficulty in
training inverse model accurately and it is very challenging
than training the forward model. Inverse model simulation
of ferrite junction circulator output graph shows non-
The methodology of propose inverse model summarized in
the following steps:
Step 1
monotonic nature. From the graph it is observed that it is
difficult to train the non-monotonic functions and inverse
Define input and output of model. Obtain the data from EM
simulator or by measurement. Swap both input and output
Table 2: training and testing results for ferrite
to get inverse model. Divide data for training and testing
anisotropic splitting of ferrite junction circulator direct
and perform training and testing operations. If model
inverse model
accuracy is satisfied then stop. Obtained result is the
Inverse model output.
(c) Training Results
Step 2
Learning algorithm
Training error
ABP
0.222696
AUTO PILOT
0.19127993
BP
0.2251623
CG
0.223833
HQN
0.19128
QN
0.217751
QN(MLP)
0.2177519
SM
0.217353
ST
0.227012
Total data is divided into sections. Between step 2 and 5 if
there are more consecutive iterations go to step 6.
Step 3
Segmented data is trained and tested
Update
neural
network
weight
parameters
Compute
derivation
of training
error w.r.t
weights
Elevate
training
error
Perform
feed
forward
for all
samples
in training
set
(d) Testing Results
Learning
Algorithm
Testing
Average
Error
Worst
Case
Error
Correlation
Coefficient
ABP
22.21608
72.93674
0.91694254
AUTO
PILOT
19.701601
96.26017
0.91787285
BP
22.426493
64.45932
0.9141668
CG
22.359877
72.598495
0.9181931
HQN
19.701601
96.26017
0.9047372
QN
21.87189
82.60372
0.9194394
QN(MLP)
21.87189
82.60372
0.9194394
SM
21.815876
83.95987
0.90376586
ST
22.498896
69.74231
0.91579363
Assign
initial
values for
all weight
parameter
s using a
gradient
based
algorithm
Perform
forward
computatio
n for all
samples
Eleva
te
valid
ation
Select a
neural
network
structure
STAR
T
Desir
ed
accur
acy
achie
ved
Sto
p
trai
ning
Evaluate
test error
as an
independe
nt quality
measure
for ANN
model
reliability
Perform
feed
forward
computatio
n for all
samples in
test set
Figure 6: Flow chart showing neural network training
and neural model testing of proposed inverse Model
Step 4
Figure 6 shows the flow chart showing neural network
training and neural model testing. Figure 7 shows proposed
If trained and tested data is accurate in step 3 stop. Inverse
model is also called as synthesis method. To obtain
geometrical results from electrical parameters is difficult in
analytical method. Neural network model became the
logical choice because it is trained by inverse data. So the
inputs are electrical parameters and outputs are geometrical
parameters. This method is called as direct inverse model.
inverse model closely following simulated results. The
results of direct inverse model and proposed inverse mode
are compared graphically and are presented in Figure 7.
Receiver and its device capability, it can choose the
refinement bits further required to meet the device’s
requirements.
2. CONCLUSION
If direct inverse model is executed, it gives output
immediately unlike optimization method. So it is faster
Accurate and simple neural models are presented to
compute junction wave impedance ratio and ferrite
method and it is similar to forward method the only
difference is swapping the inputs and outputs. Figure 5.
Gives the neural network for calculating junction wave
impedance ratio and ferrite anisotropic splitting. Table 2 is
anisotropic splitting of ferrite junction circulator using
forward model, direct inverse model, proposed inverse
model and proposed inverse model is showing better results
than direct inverse model.
training and testing results for all learning algorithms. If
accuracy is acquired then proceed to next step.
Step 5
From models training data check for multivalued solutions.
If it is not found, go for the further segmentation in step 2
Step 6
Train the neural network forward model
Step 7
Ad-joint neural network of the forward model, divide the
training according to derivation criteria.
Step 8
All sub model are trained. Now will get two forward submodels and two reverse sub-model
Step 9
Figure 7: comparison of inverse model and proposed
model
Combine all sub-models in step 8. If inverse model
accuracy is achieved then stop. Otherwise go to step 7 for
the other segmentation of data according to the derivative
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