Analysis of Ohmic Loss in Oversized Smooth Walled Circular Waveguide using FEM

Analysis of Ohmic Loss in Oversized Smooth Walled Circular Waveguide using FEM

Riddhi Gadhavi1, Abhay Patel2, Ravi Butani3, S. K. Hadia4

1, 4 CSPIT, CHARUSAT, Changa, Gujarat.

2, 3Marwadi Education Foundation Group of Institutions, Rajkot, Gujarat.

AbstractIn this paper we discuss the attenuation occur due to ohmic losses in oversized smooth walled circular waveguide. Ohmic losses depend on the radius of the waveguide and material used for the wall of the waveguide. It also depends on the mode propagating in the waveguide. We calculate the

ohmic loss for W-band frequency that ranges from 70-110 GHz and have verified the results using COMSOL v2.a software.

1. TM Mode

   We know that the wave made up of Transverse Electric (TE) and Transverse Magnetic (TM) components. First we see the TM modes. In these modes Z component of magnetic field must be zero (Hz = 0).[2] Therefore

   Keywordsoversized waveguide; smooth walled waveguide; ohmic loss; attenuation constant

   Ez E0 Jm

   (k r) sin(m) e jkz z

   (1)

   r

   cos(m)

   1. INTRODUCTION

      Delivery of electromagnetic waves in dielectric and conducting media is difficult because of radiation at high frequencies. Circular waveguides are one type of

      Where, E0 is arbitrary amplitude of the mode.

      Rest of the field equations can be derived using Maxwell equations and dispersion relation for cylindrical waveguide.

      (2)

      2 2 m r

      transmission line in which air is used as dielectric because it has low loss than other insulation material. Circular waveguides offer implementation advantage over rectangular waveguide as its installation is much

      Er

      j kz kr E0 J (k r) sin(m) e k k cos(m)

      • jkz z

      z

      simpler.The circular waveguide supports Transverse Electric (TE) & Transverse Magnetic (TM) modes. The cut off frequency of circular waveguide depends on the waveguide dimensions and shape. The electromagnetic

      E j kz E0 m J

      z

      k 2 k 2 r m

      (k r) cos(m) e

      r

      sin(m)

      jkz z

      (3)

      wave at frequency greater than the cut-off frequency can propagate in the waveguide. The TE0n modes of circular waveguide have very low attenuation in the case of oversized waveguide. More than one mode propagates in the oversized waveguide so it is called overmoded. The

      H j E0 m J

      z

      r k 2 k 2 r m

      cos(m) jk z

      (kr r) e z

      sin(m )

      (4)

      reason it is used is that the resistive losses are reduced as the waveguide becomes oversized. [1][4]

   2. MODES IN SMOOTH WALL CIRCULAR WAVEGUIDE

      We consider the parameters of smooth wall circular waveguide for mode calculations as shown in figure 1.

      H j kr E0 J (k r) sin(m) e jkz z

      z

      (5)

      2 2 m r

      k k cos(m)

      Where,

      k X mn r a

      (6)

      And Xmn is the nth root of the mth Bessel function of the first kind, so that Jm(Xmn)=0.

      Fig. 1 smooth walled cylindrical waveguide with radius a[2]

      kz

      2 k 2

      r

      (7)

   3. OHMIC LOSS

      The loss occurs in waveguide known as ohmic loss as a result of finite conductivity of waveguide wall. Ohmic losses arise due to small field penetration into the conductor walls of the waveguide.The attenuation coefficient for the TEmn modes inside circular waveguide are given by, [3]

      TE R

      2 m2

      f

      (c )mn s ( c )

      • Np / m

      Fig. 2 TM01 & TM11 mode pattern respectively

      As a result of mode analysis with radius of 36 mm we

      a 1 fc 2

      ( )

      f

      f

      'mn2 m2

      (13)

      get the mode patterns of TM mode as shown in figure 2. And for the TM modes c is given by,

2. TE Mode

We can perform the same for the TE modes. In these modes Z component of electric field must be zero (Ez = 0).[2] Therefore

TM

)

(

c mn

a

Rs Np / m

1 ( fc )2

f

H J

(k r) sin(m) e jkz z

(14)

(8)

z m r

cos(m)

Where a, f, fc, mn, , n, and m are the radius of waveguide, propagating frequency, cut-off frequency, nth

Using Maxwell equations solution for other transvers electric (TE) field is given by,

zero of the derivative of the Bessel function, impedance of the material, no of circumferential variations, no of radial variations respectively and surface resistance given by

H j kz kr J (k r) sin(m) e jkz z

r k 2 k 2 m

r cos(m)

z

(9)

Rs 2

(15)

H j kz

m cos(m)

(10)

J (k r)

e jkz z

Where = electrical conductivity of material.

z

k 2 k 2 r m

r sin(m)

The ohmic loss in circular waveguide depends on the mode propagate in it and radius of the waveguide.

E j m J

cos(m)

(k r)

e jkz z

0.03

0.028

0.026

0.024

0.022

z

(11)

r k 2 k 2 r m r sin(m)

c (dB/m)

jk sin(m)

E r J (k r) e jkz z

80mm

72mm

z

k 2 k 2 m

r cos(m)

(12)

0.02

70

80

90

100 110

Frequency (GHz)

Fig. 3 TE11& TE01 mode pattern respectively

As shown in figure 3 we can observe that the field intensity is low in theTE01 mode at the boundary compare to the TE11 mode. Sothe ohmic attenuation of the TE01 is low for the oversized waveguide.

Fig. 4 Comparison of ohmic attenuation of TE11 mode

We calculate the ohmic attenuation of the TE11 mode into entire W-band for the diameter 72mm and 80 mm for the same conducting material aluminum. And we observe that for higher diameter ohmic loss is low.

0.029

0.027

0.025

0.023

0.021

0.019

0.017

0.015

70.00

Ohmic loss (db/m)

By observing the above values, we can say that the ohmic attenuation of the TE01 mode is much lesser than The TE11.

CONCLUSION

TE11(al)-T

TE11(cu)-T

110.00

100.00

90.00

Frequency (GHz)

80.00

We have seen that the ohmic attenuation of the waveguide mainly depends on the radius and conductivity of material used by waveguide wall. Ohmic loss can be decreases by increasing the diameter of the waveguide andusing highly conductive material. By observing the characteristics of TE11 and TE01 mode in smooth wall circular waveguide we can conclude that the TE01 is the lowest attenuated mode in oversized smooth walled circular waveguide.

TE11(al)-S TE11(cu)-S

Fig. 5. Comparison between analytical and simulationvalues of ohmic attenuation for TE11 mode using aluminum and copper as wall material.

As shown in Fig. 5 we calculate the ohmic loss for the TE11 mode using two different material copper and aluminum for the 72 mm diameter of the waveguide. Continuous and dotted lines represent the theoretical and simulated values respectively. Result shows that there is a good agreement between theoretical and simulation values.

0.00025

0.00020

REFERENCES

1. Achmad Munir, Muhammad Fathi, Yakan Musthofa, Rectangular to circular waveguide converter for microwave devices characterzation, international journal on electrical engineering and informatics , 2011, pp 350- 359

2. Kowalski, Elizabeth Joan, Miter bend loss and HOM content measurements in overmoded millimeter-wave transmission lines,

   Massachusetts Institute of Technology, 2010

3. Constantine A. Balanis, Advanced Engineering Electromagnetics, wiley, new york, 1989, circular waveguides pp 643- 653

4. Shafii, J.; Vernon, R.J., "Investigation of mode coupling due to ohmic wall losses in overmoded uniform and varying-radius circular waveguides by the method of cross sections," Microwave Theory and Techniques, IEEE Transactions on , vol.50, no.5, pp.1361,1369, May 2002

c (dB/m)

0.00015

0.00010

0.00005

0.00000

70.00 80.00 90.00 100.00 110.00

frequency (GHz)

Fig. 6 Ohmic attenuation of TE01 mode

Up till now we have studied the impact of radius or the material used for wall for the TE11 mode. We observe the same for the TE01 mode as shown in the figure 6.

TABLE 1. Attenuation constants of TE11& TE01 mode