Forum for Electromagnetic Research Methods and Application Technologies (FERMAT)

A Microwave Transmission Line Courseware

Based on Multiple 1-D FDTD Method on

Mobile Devices

By

Zaifeng Yang and Eng Leong Tan

Speaker: Zaifeng Yang

School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore.

Abstract: This paper presents a multiple 1-D finite-difference time-domain (FDTD) method to analyze

transmission line with stubs on mobile devices for educational courseware. The update equations of the

proposed method are given for the main transmission line and open/short-circuited stubs. The proposed

method is efficient and requires low memory compared with 2-D or 3-D FDTD method. It realizes an

efficient real-time simulation of microwave transmission line circuit on mobile devices without lagging.

The proposed multiple 1-D FDTD method is programmed and demonstrated on the mobile device as a

courseware.

Keywords: Multiple 1-D FDTD, education courseware, transmission line, mobile device.

References:

[1] D. M. Pozar, Microwave Engineering, 4th ed., Wiley, 2011.

[2] A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain

Method, 3rd Ed., Boston, MA, USA: Artech House, 2005.

[3] G. Cakir, M. Cakir and L. Sevgi, “A novel virtual FDTD-based microstrip circuit design and analysis

tool [Education Column],” IEEE Antennas Propag. Mag., vol. 48, no. 6, pp.161-173, Dec. 2006.

[4] Z. Yang and E. L. Tan, “A mircostrip circuit tool kit app with FDTD analysis including lumped

elements,” IEEE Microw. Mag., vol.16, no.1, pp.74-80, Jan. 2015.

Zaifeng Yang received the B.Eng. (Electrical) degree and M.Eng. degree from

Shanghai University, China. He is currently a Ph.D. student in Nanyang

Technological University, Singapore. His research interests include computational

electromagnetics, RF/microwave circuit and antenna design.

Eng Leong Tan received the B.Eng. (Electrical) degree with first class honors from

the University of Malaya, Malaysia, and the Ph.D. degree in Electrical Engineering

from Nanyang Technological University, Singapore. From 1991 to 1992, he was a

Research Assistant at the University of Malaya. From 1999 to 2002, he was a

Member of Technical Staff at the Institute for Infocomm Research, Singapore. Since

2002, he has been with the School of Electrical & Electronic Engineering, Nanyang

Technological University, where he is currently an Associate Professor. His

research interests include computational electromagnetics and acoustics,

RF/microwave circuit and antenna design.

*This use of this work is restricted solely for academic purposes. The author of this work owns the

copyright and no reproduction in any form is permitted without written permission by the author.*

Outline

I. IntroductionII. Implementation of Multiple 1-D FDTD MethodIII. Implementation on Mobile devicesIV. Conclusion

2

Outline

I. IntroductionII. Implementation of Multiple 1-D FDTD MethodIII. Implementation on Mobile devicesIV. Conclusion

3

I. Courseware in Class

4

Courseware with demonstration on bulky computers in class

Handy mobile devices with courseware apps in class

5

Commercial full‐wave Simulators  Complicated  modeling and setting up

I. Commercial Full-wave Simulators

6

Results with S‐parameters Current distribution

I. Commercial Full-wave Simulators

Lack of real‐time simulationHow EM waves propagate?

Outline

I. IntroductionII. Implementation of Multiple 1-D FDTD MethodIII. Implementation on Mobile devicesIV. Conclusion

7

II. Implementation of Multiple 1-D FDTD Method

8

Circuit diagram with main transmission line, open stub(OS), short stub (SS).

Interface between the main transmission line and 

the stub

9

Update Equations of the main transmission line

, ,1 1 1

1

y OS SSxx p x q

y x

HE J Jt z

H Et z

1 12 2

1 1 , ,2 2

1 11 2 21 1 12 2

| | ( | | ) ( | | )

| | ( | | )

n n n n OS n SS nx k x k y y x p k x q kk k

n nn ny y x k x kk k

t tE E H H J Jz

tH H E Ez

II. Update Equations of Multiple 1-D FDTD Method

10

Update Equations of the Stubs

, ,

, ,

, ,

, ,

1

1

1

1

OS OSx p z p

OS OSz p x p

SS SSx q z q

SS SSz q x q

E Ht y

H Et y

E Ht y

H Et y

1 12 2

, , , 1 , 12 2

1 11 2 2

, 1 , 1 , 1 ,2 2

1 12 2

, , , 1 , 12 2

1, 1 ,

2

| | ( | | )

| | ( | | )

| | ( | | )

| |

n nOS OS OS n OS nx p j x p j z p z pj j

n nOS n OS n OS OSz p z p x p j x p jj j

n nSS SS SS n SS nx q j x q j z q z qj j

SS n SSz q z qj

tE E H Hy

tH H E Ey

tE E H Hy

H H

1 12 2

1 , 1 ,2

( | | )n nn SS SS

x q j x q jj

t E Ey

II. Update Equations of Multiple 1-D FDTD Method

11

The program flowchart of the multiple 1‐D FDTD method

II. Implementation of Multiple 1-D FDTD Method

Outline

I. IntroductionII. Implementation of Multiple 1-D FDTD MethodIII. Implementation on Mobile devicesIV. Conclusion

12

III. Implementation on Mobile Devices

13

Some Examples of Real-time Microstrip Circuits Simulations

on iPad / iPhone

Outline

I. IntroductionII. Implementation of Multiple 1-D FDTD MethodIII. Implementation on Mobile devicesIV. Conclusion

14

IV. Conclusion

• This paper has presented a multiple 1-D FDTD method to analyzetransmission line with stubs on mobile devices for educationalcourseware.

• The update equations of the proposed method have been given forthe main transmission line and open/short-circuited stubs.

• The proposed method is efficient and requires low memorycompared with 2-D or 3-D FDTD method.

• It realizes an efficient real-time simulation of microwavetransmission line circuit on mobile devices without lagging.

• The proposed multiple 1-D FDTD method has been programmedand demonstrated on the mobile device as a courseware.

15

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