60-GHz Unbalanced-Fed Bandpass-Filtering On-Chip Yagi Antenna in GIPD Technology

60-GHz Unbalanced-Fed Bandpass-Filtering

On-Chip Yagi Antenna In GIPD Technology

Hsiang-Chieh Wang

, Yung-Hsiang Chuang, Wen-Yi Ruan,

Chine-Chang Chou and Huey-Ru Chuang

Institute of Computer and Communication Engineering

Department of Electrical Engineering

National Cheng Kung University

Tainan, Taiwan, ROC

Outline



Introduction and Motivation



60-GHz Unbalanced-Fed Bandpass-Filtering On-Chip Yagi

Antenna In GIPD Technology (tMt GIPD Process)



λ

/4 Coupled Line Resonator



60-GHz GIPD Bandpass-Filtering Yagi Antenna Design



Microwave Probe-Station On-Wafer Measurement



Simulation and Measurement Results



Conclusion



Reference

Introduction & Motivation



In 2001, the FCC has allocated

57-64 GHz

for

unlicensed applications

 Wireless personal area network (WPAN)

 60 GHz Standards

 IEEE 802.15.3c, ECMA/387, Wireless HD,

WiGig MAC and PHY, IEEE 802.11.ad

 The attenuation of the electromagnetic wave is about 10-15 dB/km near the 60-GHz band

 Due to the oxygen effect

 The attenuation is too high for long-range communication

 57-64 GHz band is suitable for

short-range wireless communication

 Wide bandwidth, high data-rate transmission (2 Gb/s), privacy

Spectral

availability

Channel BW

Tx power

Effective

Max. possible

data rate

to get to 1 Gbps

Bit/Hz Req’d

60 GHz

7000 MHz

2000 MHz

8000 mW

_{(39 dBm)}

25000 Mbps

0.4 bps/Hz

802.11n

670 MHz

40 MHz

_{(22 dBm)}

160 mW

1100 Mbps

25 bps/Hz

Introduction & Motivation

 Pursue the

integration

of

on-chip antenna

and

passive components

in mm-wave RF front-end circuits



Multifunction mm-wave components:

 combine

antenna

and

band-pass filter

into

one device



low loss

&

compact size



60-GHz Unbalanced-Fed Bandpass-Filtering

On-Chip Yagi Antenna In GIPD Technology

(tMt GIPD Process)

Glass-substrate Integrated Passive Device (GIPD) Process

 tMt GIPD process:



Three-metal-layer

structure in thin film technology

 Realize integrated

passive components

(resistors, capacitors, and inductors)

 It is capable of integrating with other process (

TSMC 0.18-μm CMOS

) by

flip chip

technology



Low-loss glass substrate

:

 Suitable for

microwave

and

mm-wave

passive circuit design

 Good

radiation efficiency

for

on-chip antennas

Glass-substrate Integrated Passive Device (GIPD) Process

 To achieve a better performance of radiation

 The on-chip antenna is printed on the M3 layer

 Advantages in GIPD on-chip antenna design:



Improve lossy silicon substrate in CMOS process

:

Silicon substrate (TSMC 90-nm CMOS) loss tangent:

0.1

Glass substrate (GIPD) loss tangent:

0.003



High radiation efficiency → high antenna gain

Power-Gain = [Radiation-Efficiency] × [Directivity]

On-chip

balun-filter

On-chip

balanced

antenna

Mixer

RF Receiver

LNA

On-chip balun On-chipRF BPF

U/B

_{filtering-antenna}

Single-ended

This Work

Glass substrate

M1

M3

Dielectric

M2

Dielectric

Bandpass-Filtering Yagi Antenna Structure

 Consists of:

λ/4 coupled line resonator,

monopole antenna & directors

@ M3

Mark Unit (μm) Mark Unit (μm)

L

G

920

W

G

650

L

RAD

730

W

RAD

50

L

D1

1000

W

D1

50

L

D2

800

W

D2

50

L

C

740

W

C

10

S

1

250

S

2

550

C

G

10

W

FEED

10

L

GCPW

180

W

PAD

70

L

1

140

W

GCPW

120

L

2

120

L

3

105

60-GHz GIPD Bandpass-Filtering Yagi

Antenna Design

λ/4 Coupled Line Resonator [2]



Designed λ/4 coupled line resonator

 Geometry:

 Input admittance of

λ/4 coupled line resonator

:





_

_



_{ }



_



_



_

2 2

_

0 0 2 0 0 0 0

cos

2

sin

o e o e o e in

Z

Z

Z

Z

Z

Z

j

Y

*Z

0e

, Z

0o

: even- & odd-mode characteristic impedance, θ=πf /2f

r

 Analysis by transmission line input impedance:

 Consisted of

λ/4 open-stub & λ/4 short-stub transmission line



open-stub  series LC circuit; short-stub  parallel LC circuit

 Coupling gap → J-inverter

Transform

parallel LC circuit to series LC circuit

, or vice versa.

 Contributed

two transmission zeros: f

a

& f

b

, (f

a

< f

r

< f

b

).

'

b

C

' b

L

L

a

a

C

f

r

I in

Y

λ/4 Coupled Line Resonator

 At Δf around the resonant frequency f

r

,

(

dY

in

/

df

)

_f

_r





f



Y

in

II

:

When f =Δf ,

(

dY

in

/df

)

_fr





f



Y

inII

:









1

1

2

0

0

0

0

2

L

C

Z

Z

Z

Z

o

e

o

e









 Two conditions:

At resonated frequency, f = f

r

(θ=π/2):





 





cos

0

2

sin

2

2

0

0

2

0

0

0

0

_

















o

e

o

e

o

e

in

j

_Z

_Z

Z

Z

_Z

_Z

Y

At transmission zeros,

Y

in

→∞;

1 ₀ 0 ₀0 1 ₀ 0 ₀0

]

2

[

sin

and

]

2

[

sin

o e o e o e o e

Z

Z

Z

Z

Z

Z

Z

Z













 

:

]

2

[

sin

2

0 0 0 0 1 o e o e r a

f

_Z

Z

_Z

Z

f









;

f

b

 2

f

r



f

a



Chosen Z

0e

, Z

0o

which satisfied above conditions.

a

L

a

C

f

r

I in

Y

II in

Y

r

f

λ/4 Monopole Antenna and Filtering Antenna



λ/4 monopole



series RLC circuit

 λ/4 resonator & λ/4 monopole antenna



Second-order bandpass filter



L

r



L

2

,

C

r



C

2

,

R

r



R

0

,

C

1

'



C

1



C

g



Second-order Chebyshev response

 f

0

= 60 GHz, Δf = 11.7 %, Z

0

= 50 Ω



0.5-dB equal ripple



Z

0e

= 50 Ω, Z

0o

= 31.6 Ω

'

1

C

1

L

2

C

2

L

0

R

1

C

1

L

C

_g

r

C

r

L

r

R

g

C

r

C

r

L

r

R

Simulation Results:

Filtering Yagi

(1/3)



Add directors on bandpass filtering antenna



VSWR

< 2 @ 58 - 64 GHz



Max. power-gain @ 60 GHz =

2.6 dBi



Radiation efficiency @ 60 GHz

=

47 %



Bandpass response

can be observed



Transmission zeros

@ 52 GHz & 74 GHz

57 58 59 60 61 62 63 64

Frequency (GHz)

1 2 3 4 5

VS

W

R

Filtering Yagi 30 35 40 45 50 55 60 65 70 75 80 85 90

Frequency (GHz)

-20 -15 -10 -5 0 5

M

ax

. p

ow

er

-g

ai

n

(d

Bi

)

Filtering Yagi

Simulation Results:

Filtering Yagi

(2/3)

0 45 90 135 180 225 270 315 0 0 -5 -5 -10 -10 -15 -15 -20

X

Y

60 GHz

0 45 90 135 180 225 270 315 0 0 -5 -5 -10 -10 -15 -15 -20

Z

Y

60 GHz

0 45 90 135 180 225 270 315 0 0 -5 -5 -10 -10 -15 -15 -20

Z

X

60 GHz

XY-plane

YZ-plane

XZ-plane

60-GHz Filtering Yagi

Power-gain

_{Max. Min. Avg. Max. Min. Avg. Max. Min. Avg.}

E

co-pol.

(dBi)

-2.9

-32.2 -10.5

2.6

-15.6 -5.4

-3.0

-30.3 -11.0

E

cross-pol.

(dBi)

-9.0 -18.8 -12.2 -25.5 -42.3 -31.0 -9.1 -18.8 -12.2

Simulation Results:

Filtering Yagi

(3/3)

 Current distribution

Z

Y

X

52 GHz

Z

Y

X

60 GHz

Z

Y

X

74 GHz

Chip Layout &Micrograph

 Chip size:

1.62 × 1.34 mm

2

=

2.17 mm

2

Microwave Probe-Station On-Wafer Measurement

On-wafer Measurement:

VSWR

 On-wafer measurement setup:

 Agilent 67-GHz PNA series network analyzer, mm-wave test set controller, mm-wave

downconverter (OML)

 Cascade Probe station

 Cascade 110GHz G-S-G probes with pitch of 100

μm

On-wafer Measurement:

Antenna Power-Gain

(1/3)

 The power-gain was measured with the technique presented in [9] and [10]



Two identical

on-chip antennas: a

transmitting antenna

& a

receiving antenna

+

[9] R. N. Simons and R. Q. Lee, "On-wafer characterization of millimeter-wave antennas for wireless applications," IEEE

Trans. Microw. Theory Tech., vol. 47, no. 1, pp. 92-96, Jan. 1999.

[10] H.-R. Chuang, L.-K. Yeh, P.-C. Kuo, K.-H. Tsai, and H.-L. Yue, "A 60-GHz millimeter-wave CMOS integrated

on-chip antenna and bandpass filter," IEEE Trans. Electron Device, vol. 58, no. 7, pp. 1837-1845, Jul. 2011.

Friis Power Transmission Formula

:

PL(dB)

dB

G

dB

G

dBm

P

dBm

P

_r

_t

_t

_r









(

)

(

)

(

)

)

(

G

t

& G

r

:

power-gain

of transmitting &

receiving antenna

P

t

& P

r

: transmitted & received power

On-wafer Measurement:

Antenna Power-Gain

(2/3)

 Frii’s power transmission formula (free-space):

)

(

)

(

)

(

)

(

)

(

dBm

P

dBm

G

dB

G

dB

PL

dB

P

_r



_t



_t



_r



G

t

& G

r

:

power-gain

of the transmitting/receiving antenna

P

t

& P

r

: transmitted and received power

PL:

(free-space)

path loss,

PL

(

dB

)



10

log

 

₄

_



_R

2



20

log(

R

km

f

GHz

)



92

.

4

 Assume the two antennas are identical 

G

t

= G

r

= G

 Separated distance R should be satisfied with the

far-field condition

[8]

0 0 2

,

2

_

_





D

if

D

R

far

_,

R

_far



3



₀

,

if



₀



D

 (P

r

/ P

t

) (dB) =

direct transmission coefficient, |S

21

|

2

(dB) from the vector network analyzer



S

21

(

dB

)



(

P

r

P

t

)(

dB

)



2

G

(

dB

)



PL

(

dB

)

On-wafer Measurement:

Antenna Power-Gain

(3/3)

 Metallic ground-plane consideration[11]:

Path loss with

perfect planar ground plane



modified PL formula



















































































_

_







2

4

2

2

2

2

2

1

2

2

2

0

2

0

1

0

4

1

4

log

10

4

log

10

)

(

R

h

R

jk

r

jk

r

jk

PEC

e

h

R

R

R

r

e

r

e

dB

PL









_

_











2





2



2



2 2 1

,

4

*

r

R

d

R

r

R

d

h

a

h

b

R

h



G

(

dB

)



₂

1

[

S

21

(

dB

)



PL

PEC

(

dB

)]

Measurement Results:

VSWR



Yagi: VSWR < 2 @ 54 – 64 GHz (meas.)

45 50 55 60 65 70 75

Frequency (GHz)

1 2 3 4 5

VS

W

R

Simulation Measurement

Measurement Results:

Antenna Power-Gain

 Measured from two identical antennas

(R = 15 mm)

 Power-gains are basically in reasonable compliance

@ >60GHz

 Two transmission zeros:

42GHz

&

72GHz

30

35

40 45

50

55 60

65

70

75 80

85

90

Frequency (GHz)

-20

-15

-10

-5

0

5

Po

w

er

-g

ai

n

(d

Bi

)

Simulation

Measurement

Filtering Yagi

Simu.

Meas.

Power-gain

@ 60 GHz (dBi)

2.6

2.4

Filtering Yagi

Metallic plate (perfect ground plane)

R = 15 mm

Y

Z

X

Absorber On-chip antenna Acrylic_board Y Z X R = 15 mm

Discussion

 Maximum

separated distance R

are limited in

15 mm

(probe station’s limitation)



R

may not

satisfied with

far field condition

while f < 60 GHz

(D = 4.7 mm)

0

0

2

,

2

_







D

if

D

R

_far

_,

_R

_far

_

₃



₀

_,

_if



₀

_

_D

_[7]



2-port transmission simulation

with

R = 15 mm



good agreement @ low band

20

30

40

50

60

70

80

90

100

Frequency (GHz)

-25

-20

-15

-10

-5

0

5

Po

w

er

-g

ai

n

(d

Bi

)

Measurement

Simu. power-gain (single antenna)

Simu. power-gain from S21 (R = 15 mm)

Performance Comparison

Type

Tech. Freq.

_{(GHz) VSWR}

Antenna

radiation

efficiency

(simu.)

Size(mm

2

)

Power-gain (dBi)

[14]

AP-S 2011

Antenna

(Patch)

Si-IPD 60

< 2

N/A

N/A

(simu.)

5

Antenna

_(simu.)

4.1

[15]

APMC 2011

Antenna

(Yagi)

+

Balun-Filter

GIPD

77

< 3

_{(Yagi+filter) 2.2×4.7 Antenna +}

33 %

Balun-Filter

_(meas.)

0.5

[16]

AP-S 2013

(Vivalid)

Antenna

GIPD

60

<2

N/A

3×3

4

This work

Filtering

_antenna

GIPD

60

< 2

_{(Yagi + filter) 1.62×1.34 Yagi: 2.4}

47 %

(meas.)

[14] C. Calvez, C. P., J. Coupez, F. Gallee, R. P., F. Gianesello, D. Golria, D. Belot, and H. E., "Miniaturized hybrid antenna combining Si

and IPD technologies for 60 GHz WLAN applications," in Antenna and Propag. Soc. Int. Symp., Jul. 2011, pp. 1357-1359.

[15] Y.-H. Chuang, H.-L. Yue, C.-Y. Hsu, and H.-R. Chuang, "A 77-GHz integrated on-chip Yagi antenna with unbalanced-to-balanced

bandpass filter using IPD technology," in Asia-Pacific Microw. Conf., Dec. 2011, pp. 449-452.

[16] A Bisognin, C. Luxey, G. Jacquemod, R. Pilard, F. Gianesello, D. Gloria, D. Titz, C. Laporte, H. Ezzeddine, F. Ferrero and P. Brachat,

“End-fire radiating antenna on IPD technology for 60 GHz communications,” in Antennas and Propag. Soc. Int. Symp., July 2013,

pp.1830,1831.

Conclusion



60-GHz GIPD unbalanced-fed bandpass-filtering Yagi antenna

 Fabricated with tMt GIPD technology

 HFSS FEM-based 3-D full-wave EM solver is used for simulation



Measured performance of the designed bandpass-filtering antenna

 Meas. VSWR <2@ 54-64 GHz

 Maximum radiation power-gain is about 2.4 dBi @ 60 GHz

 Antenna gain versus frequency has bandpass response

 Transmission zeros @ 42-GHz & 72-GHz



The presented bandpass-filtering Yagi antenna realizes integrating

Reference

[1]

J. A. Howarth, A. P. Lauterbach, M. L. J. Boers, L. M. Davis, A. Parker, J. Harrison, J. Rathmell, M.

Batty, W. Cowley, C. Burnet, L. Hall, D. Abbot, and N. Weste, "60 GHz radios: enabling next

generation wireless applications," in Proc. TENCON 2005 region 10, Nov. 2005, pp. 1-6

[2] C.-T. Chuang and S.-J. Chung, "New printed filtering antenna with selectivity enhancement," in Proc.

39th Eur. Microw. Conf., Sep. 2009, pp. 747-750.

[3] Z. Ma and Y. Kobayashi, "Design and realization of bandpass filters using composite resonators to obtain

transmission zeros," in Proc. 35th Eur. Microw. Conf., Oct. 2005, pp. 1255-1258.

[4] D. M. Pozar, Microwave Engineering, 3nd ed. New York: Wiley, 2005

[5]Jia-Sheng Hong, M. J. Lancaster, Microstrip Filters for RF/Microwave Applications, 1st ed. John Wiley

and Sons Inc, 2001.

[6] C.-T. Chuang and S.-J. Chung, “A compact printed filtering antenna using a ground-intruded coupled

line resonator,” IEEE Trans. Antennas and Propag., vol. 59, no. 10, pp. 3630-3637, 2011.

[7] C. A. Balanis, Antenna Theory: Analysis and Design, 3rd ed. New York: Wiley, 2005.

[8] Y. Huang and K. Boyle, Antenna From Theroy to Practice, 1st ed. John Wiley and Sons Ltd, 2008.

[9] P.-J. Guo, and H.-R. Chuang, “A 60-GHz Millimeter-wave CMOS RFIC-on-chip Meander-line Planar

Inverted-F Antenna for WPAN Applications,” IEEE Antennas and Propag. Society, pp. 1-4, July 2008.

[10] K.-H Tsai, L.-K. Yeh, P.-C. Kuo, and H.-R. Chuang, “Design of 60-GHz CPW-Fed CMOS On-Chip

Integrated Antenna-Filter,” European Conference on Antennas and Propagation, pp. 1-3, Apr.2010.

[11] S. Saunders and A. Aragón-Zavala, Antennas and propagation for wireless communication systems, 2nd

ed. John Wiley and Sons Ltd, 2007.

[12] R. N. Simons and R. Q. Lee, "On-wafer characterization of millimeter-wave antennas for wireless

applications," IEEE Trans. Microw. Theory Tech., vol. 47, no. 1, pp. 92-96, Jan. 1999.

[13] H.-R. Chuang, Lung-Kai Yeh , Pei-Chun Kuo, Kai-Hsiang Tsai, H.-L.Yue "60-GHz Millimeter-Wave

CMOS Integrated On-Chip Antenna and Bandpass Filter" IEEE Transactions on Electron Devices, vol.

58, no. 7, pp. 1837-1845, July 2011.

[14] C. Calvez, C. P., J. Coupez, F. Gallee, R. P., F. Gianesello, D. Golria, D. Belot, and H. E., "Miniaturized

hybrid antenna combining Si and IPD technologies for 60 GHz WLAN applications," in Proc. IEEE Ant.

Propag. Soc. Int. Symp., Jul. 2011, pp. 1357-1359.

[15] Y.-H. Chuang, H.-L. Yue, C.-Y. Hsu, and H.-R. Chuang, "A 77-GHz integrated on-chip Yagi antenna

with unbalanced-to-balanced bandpass filter using IPD technology," in Asia-Pacific Microw. Conf., Dec.

2011, pp. 449-452.

[16] A Bisognin, C. Luxey, G. Jacquemod, R. Pilard, F. Gianesello, D. Gloria, D. Titz, C. Laporte, H. Ezz., F.

Ferrero and P. Brachat, “End-fire radiating antenna on IPD technology for 60 GHz communications,” in

Antennas and Propag. Soc. Int. Symp., July 2013, pp.1830,1831.

λ/4 Coupled Line Resonator(1/2)



Coupled line impedance[4]:

























































csc

)

(

2

csc

)

(

2

cot

)

(

2

cot

)

(

2

0

0

32

23

41

14

0

0

42

24

31

13

0

0

43

34

21

12

0

0

44

33

22

11

o

e

o

e

o

e

o

e

Z

Z

j

Z

Z

Z

Z

Z

Z

j

Z

Z

Z

Z

Z

Z

j

Z

Z

Z

Z

Z

Z

j

Z

Z

Z

Z

 Port-2 & port-4 open

(I

2

=I

4

=0)

, port-3 short

(V

3

=0)

:

₃

₃₁

₁

₃₃

₃

3

13

1

11

1

I

Z

I

Z

V

I

Z

I

Z

V









λ/4 Coupled Line Resonator(2/2)

Port-3 short (V

3

=0):

1 0 0 0 0 0 0 0 0 1 33 31 3 3 33 1 31 3 33 1 31 3

cos

)

(

(

)

cot

)

)(

2

/

(

(

/

2

)(

)

csc

0

I

Z

Z

Z

Z

Z

Z

j

Z

Z

j

I

Z

Z

I

I

Z

I

Z

I

Z

I

Z

V

o e o e o e o e









































Port-1 voltage:

]

cos

)

(

(

)

[

csc

)

(

2

cot

)

(

2

]

cos

)

(

(

)

[

csc

)

(

2

cot

)

(

2

csc

)

(

2

cot

)

(

2

1 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 1 0 0 3 0 0 1 0 0 3 13 1 11 1

I

Z

Z

Z

Z

Z

Z

j

I

Z

Z

j

I

Z

Z

Z

Z

Z

Z

j

I

Z

Z

j

I

Z

Z

j

I

Z

Z

j

I

Z

I

Z

V

o e o e o e o e o e o e o e o e o e o e











































































Coupled line input impedance:





















2

sin

)

(

)

cos

(

2

sin

)

(

(

)

0

0

2

2

0

0

0

0

2

0

0

1

1

o

e

o

e

o

e

o

e

in

V

_I

j

_Z

Z

_Z

Z

j

Z

_Z

Z

_Z

Z



[

₍

(

₎

₍

)

sin

2

₎

2

_cos

2

]

0

0

2

0

0

0

0

1



















o

e

o

e

o

e

-in

in

Z

j

_Z

_Z

Z

Z

_Z

_Z

Y

L

Z

in

Z

0

Z

0

z

l



z

λ/4 Coupled Line Resonator: Transmission Line(1/3)



Transmission Line

tan(

)

)

tan(

)

(

0

0

0

_Z

Z

_jZ

jZ

_l

l

Z

l

Z

L

L

in



_



_





Input impedance at l away from load

(lossless):

Open stub (Z

L

=∞):

Z

in

(

l

)





jZ

0

cot(



l

)

Short stub (Z

L

=0):

Z

in

(

l

)



jZ

0

tan(



l

)



Equivalent circuits ofλ/4 transmission line

(l=λ/4)

Open stub: Z

in

=0; like series LC in resonate freq.

Short stub: Z

in

=∞; like shunt LC in resonate freq.

L

C

 j , Z0 Z_L



-

-

3₄

-

₂

-

₄   in Z Zin0 Zin Zin0

C

L



-

-

3₄

-

₂

-

₄   in Z  j , Z0 Z_L0 0 Zin Zin0 Zin

λ/4 Coupled Line Resonator: Transmission Line(2/3)



Admittance J inverter

Coupling gap can be considered as J inverter[5]

J-inverter:

The ABCD matrix of ideal admittance inverters may generally be expressed as

















_











0

1

0

jJ

jJ

D

C

B

A



the input admittance :

L

in

_Y

J

Y



2



Transform parallel-connected elements to series-connected elements and vice versa.

C

C'

J

±90

o

Yin

= jωC/(1-ω

2

_LC)

L'

L

L

j

C

L

J

Y

in



₍

₁

_

_

2

_

_

₎

_/

_

_

2

LC

C

j

Y

C

L

L

j

J

L

j

C

L

J

Y

J

Y

in L j C L Y L in L 2 2 2 2 2 / ) 1 ( 2

1

:

Series

1

/

)

1

(

2



















































     

λ/4 Coupled Line Resonator: Transmission Line(3/3)

 /4 coupled-line resonator

equivalent circuits



Admittance of equivalent circuit type II

:

]

)

)

2

/(

1

1

(

2

1

)

)

2

/(

1

1

(

2

1

[

]

2

1

2

1

2

1

2

1

[

2

2

b

b

b

a

a

a

b

b

a

a

I

in

C

L

f

fL

C

L

f

fL

j

fC

fL

fC

fL

j

Y





































Since

a

a

C

L

f





2

1

a

,

b

b

C

L

f





2

1

b

=>

1

/

L

a

C

a



(

2



f

a

)

2

,

1

/

L

b

C

b



(

2



f

b

)

2

]

)

/

1

(

2

1

)

/

1

(

2

1

[

]

)

)

2

/(

)

2

(

1

(

2

1

)

)

2

/(

)

2

(

1

(

2

1

[

]

]

)

2

)(

)

2

/(

1

(

1

[

2

1

]

)

2

)(

)

2

/(

1

(

1

[

2

1

[

]

)

)

2

/(

1

1

(

2

1

)

)

2

/(

1

1

(

2

1

[

2 2 2 2 2 2 2 2 2 b 2 2 a 2 2 2

f

f

fL

f

f

fL

j

f

f

fL

f

f

fL

j

f

f

fL

f

f

fL

j

C

L

f

fL

C

L

f

fL

j

Y

b b a a b b a a b a b b b a a a I in













































































Geometry

Equivalent Circuit

Type II

Equivalent Circuit

Type I

λ/4

Y

in

Z

0e

, Z

0o

J

a

C

_b'

L

a

C

a

' b

L

{

L

a

}

a

C

f

r

L

b

C

b

X

a

(f

a

)

(f

_b

)

X

b

I in

Y

λ/4 Coupled Line Resonator: Coupling gap(1/2)[5]

 Coupling gap can be considered as a capacitance C

m

1

2

2

2

1

1

V

C

j

CV

j

I

V

C

j

CV

j

I

m

m

















Using π model

m

C

j

Y

Y

C

j

Y

Y















21

12

22

11

It equals to

L

C

1

V





L

C

V

2 m

C





C

m

m

C

2

₂

_C

_m

m

C

J 



L

C

1

V





L

C

V

2 m

C

λ/4 Coupled Line Resonator: Coupling gap(2/2)

Using ABCD matrix:











































3 1 3 2 1 2 1 3 3 2

1

1

1

Y

Y

Y

Y

Y

Y

Y

Y

Y

Y

D

C

B

A

Y

1

=-jωC

m

; Y

2

=-jωC

m

; Y

3

=jωC

m







































































































0

1

0

)

1

(

1

2

1

)

1

(

1

1

1

1

3

1

3

2

1

2

1

3

3

2

m

m

m

m

m

C

j

j

C

C

j

C

j

j

C

Y

Y

Y

Y

Y

Y

Y

Y

Y

Y

D

C

B

A

 Let J=ωC

m





















































0

1

0

0

1

0

jJ

jJ

C

j

j

C

D

C

B

A

m

m

; ABCD matrix J inverter (Pozar):



















0

1

0

jJ

jJ

λ/4 Coupled Line Resonator



Two transmission zero (

f =f

a

or

f =f

b

)Y

in

→∞(assume

θ=πf /2f

r

):



(

Z

0

e



Z

0

o

)

2



(

Z

0

e



Z

0

o

)

2

cos

2





0

o e o e o e o e o e o e o e o e

Z

Z

Z

Z

Z

Z

Z

Z

Z

Z

Z

Z

Z

Z

Z

Z

0 0 0 0 1 0 0 0 0 1 0 0 0 0 2 2 0 0 2 0 0

2

sin

or

2

sin

2

sin

cos

)

(

)

(































 







₂



f

_f

a

_r

and

₂



f

_f

b

_r

,

f

r



f

a



₂

f

b

, θ=π/2 (f=f

_r

):

r

a

o

e

o

e

f

f

Z

Z

Z

Z

2

2

sin

0

0

0

0

1

_







=>

f

a

f

r

_Z

_e

Z

e

_Z

Z

_o

o

0

0

0

0

1

2

sin

2









;

f

b

 2

f

r



f

a



At resonated freq(

f=f

r

)

0

]

/2)

(

cos

)

(

)

(

(

)

sin

[

]

cos

)

(

)

(

(

)

sin

2

[

₂

₂

0

0

2

0

0

0

0

2

2

0

0

2

0

0

0

0



































o

e

o

e

o

e

o

e

o

e

o

e

in

Z

Z

Z

Z

Z

Z

j

Z

Z

Z

Z

Z

Z

j

Y

λ/4 Coupled Line Resonator: Susceptance Slope

 The susceptance slope parameter

b

, for resonators having a

zero susceptance

at center

frequency ω

0

 

0

2

0





_

_

_





d

dB

b

_=>





























0 0 0 2 0

b

C

b

b

L

p p

B(ω): the susceptance of the distributed resonator

p p p p p p p p p p p p p p

C

L

C

L

C

L

C

L

C

C

L

C

L

C

B

2 0 2 0 2 0 2 0 0 2

1

1

0

1

1

1

1

1

₀





































 





























 

0 0 0 1 2 0 0 2 0 0 0

/

2

1

2

1

2

1

2

2

2 0 0 0 0



























 



















































































          

b

C

C

L

C

L

C

L

C

L

C

L

C

d

d

d

dB

b

p p p p p p C L p p p p p p p p

λ/4 Coupled Line Resonator: Resonated Circuit(1/3)

 The admittance slope parameter of

λ/4 coupled line resonator



Geometry







₂



_f

f

_r

;

[

₍

(

₎

₍

)

sin

2

₎

2

_cos

2

]

0 0 2 0 0 0 0

















o e o e o e in

j

_Z

_Z

Z

Z

_Z

_Z

Y

 Let

A



(

Z

0e



Z

0o

)

,

B



(

Z

0

e



Z

0

o

)

}

])

2

/

(

cos

2[

cos(

/

)

(cos

(

/

2

])

[)

/

(

2

{

/

]}

)

2

/

(

cos

/

)

sin(

[

{

2

2

2

2

2

2

2

2

2

2

r

r

r

r

r

r

in

f

f

B

A

f

f

B

f

f

A

f

B

j

df

f

f

B

A

B

f

f

j

d

df

dY































When f=f

r

: cos(πf /f

r

)=-1, cos(πf /2f

r

)=0

2 0 0 0 0 2 ) ( ) ( 2 2 2 2 2 2 2 2

)

(

(

)

}

)

/

(

{

}

)

/

(

{

}

])

2

/

(

cos

2[

cos(

/

)

[(cos

(

/

2

])

[)

/

(

2

{

0 0 0 0 o e r o e r in Z Z BA Z Z r r r r r in

Z

Z

f

Z

Z

j

A

f

B

j

df

dY

A

f

B

j

f

f

B

A

f

f

B

f

f

A

f

B

j

df

dY

o e o e













































     

λ/4 Coupled Line Resonator: Resonated Circuit(2/3)

 Input admittance at Δf around the resonated frequency f

r

(f = f

r

+



f).

When f=f

r

,

₀

₀

2

0

0

)

(

(

_e

_o

)

r

o

e

in

Z

Z

f

Z

Z

j

df

dY









At Δf,

dY

in

df

f





f



j

_f



_r

_Z

Z

_e

e

_



_Z

Z

_o

o

2



f

0

0

0

0

)

(

(

)

)

/

(

_r

Coupled line input admittance, θ=πf /2f

r

:

]

cos

)

(

)

(

(

)

sin

2

[

₂

₂

0

0

2

0

0

0

0

1



















o

e

o

e

o

e

-in

in

Z

j

_Z

_Z

Z

Z

_Z

_Z

Y

1. At resonated freq. θ=π/2, Y

in

=0

2. f < f

r

, θ < π/2: Y

in

> 0  inductance

3. f > f

r

, θ > π/2: Y

in

< 0  capacitance

λ/4 Coupled Line Resonator: Resonated Circuit(3/3)



Since

parallel LC

input impedance (







0







):

Z

in



j

2

C





1

, [4]



Y

_Z

j

C

j

C

f

in

II

in



1



2

1







4



1



1 1 2 0 0 0 0 1 1 1 2 0 0 0 0 2 / 1 1 2 0 0 0 0

2

)

(

(

)

4

2

)

(

(

)

4

)

(

)

(

)

/

(

1 1 r

L

C

Z

Z

Z

Z

C

C

L

Z

Z

Z

Z

C

j

Z

Z

f

Z

Z

j

Y

f

df

dY

o e o e o e o e C L f o e r o e II in f in r















































 



Equivalent circuit type II









f 2

/

f

r

;

2

(

1

/

)

]

1

)

/

1

(

2

1

[

₂

₂

₂

₂

f

f

fL

f

f

fL

j

Y

b

b

a

a

I

in





_

_



_

_

]

)

/

1

(

2

(

1

/

)

)

/

1

(

2

(

1

/

)

[

/

]}

)

/

(

2

1

)

/

(

2

1

[

{

2 2 2 2 2 2 2 2 2 2 2 2 2 2

f

f

f

L

f

f

f

f

f

L

f

f

j

df

f

f

f

L

f

f

f

L

j

d

df

dY

b b b a a a b b a a I in































II

in

Y

r

f

L

1

C

1

Equivalent Circuit

Type III

a

L

a

C

f

r

I

in

Y

λ/4 Coupled Line Resonator:(1/2) [3]

a

L

a

C

a

X

 



_a

b

L

b

C

_{ }

X

b

b



0



r

L



₀

C

_r

)

(

)

(

2

2

2

2

1

1

b

b

a

a

b

a

c

X

X

_L

_L

B

















































1

1

0

₂

2











_r

r

r

r

C

_L

C

B

b

a









₀



_,



_a



1

L

_a

C

_a

_,



_b



1

L

_b

C

_b

_,



₀



1

L

_r

C

_r



At ω

0

, B

c

(ω

0

) = B

r

(ω

0

) = 0

'

'

'

'

2

b

a

b

a

r

_L

L

_L

L

L







_,

r

r

L

C

₂

0

1





_,

₍

₎

₍

2

2

₎

0

2

2

0

b

a

b

a

L

L























_a

a

a

a

L

L

₂

0

2

2

0

'

)

(

1

)

(

1















_,





_b

b

b

b

L

L

₂

0

2

2

0

'

)

(

1

)

(

1















45

50

55

60

65

70

75

Frequency (GHz)

-80

-70

-60

-50

-40

-30

-20

-10

0

S 2

1

(d

B

)

Composite resonator

Equivalent LC resonator

λ/4 Resonator (2/2)

Δf = 0.117, g

1

= 1.4029, g

2

= 0.7071

 L

1

= 0.221 pH, C

1

’ = 31.8 pF

 L

2

= 16.3 pH, C

2

= 0.44 pF

)

(

)

(

₀

2

_b

2

₀

2

_a

2

b

a

L

L



















_{, f}

_a

_{= 52 GHz, f}

_b

_{= 72 GHz, f}

₀

_{= 60 GHz}

 L

a

= L

b

× 1.77

 L

a

’ = 0.0354 × L

a

= 0.0625 × L

b

 L

b

’ = 0.0793 × L

b

L

r

= L

1

= 0.221

= 0.0099 × L

b

2

/ 0.1419 × L

b

 L

b

= 3.16 pH, C

b

= 1.55 pF

 L

a

= 5.56 pH, C

a

= 1.68 pH

Metallic Plate Effect

 On wafer measurement



Path loss is not still in free space

Formula of path loss with reflection of perfect

ground plane PL

PEC

[8]:



































2

₁



0



2

4

log

10

)

(

jk

R

r

R

d

r

d

d

PEC

dB

_R

R

_R

e

PL

_



 Transmitter and receiver antennas place on the

height h and separated with distance R:



R

d



R

2





h

b



h

a



2



R



R

r



R

2





h

b



h

a



2



R

2



4h

2























































2

4

2

2

2

_{2 2} 0

4

1

4

log

10

)

(

jk

R

h

R

PEC

e

h

R

R

R

dB

PL

Metallic Plate Effect

20 30 40 50 60 70 80 90 100

Frequency (GHz)

0 5 10 15 20 25 30 35 40

Pa

th

lo

ss

(d

B)

Free space Ground effect Distance between two antenna, r = 10 mm

Height ha = hb = 20 mm

20 30 40 50 60 70 80 90 100

Frequency (GHz)

0 5 10 15 20 25 30 35 40

Pa

th

lo

ss

(d

B)

Free space Ground effect Distance between two antenna, r = 10 mm

Height ha = hb = 1000 mm 0 100 200 300 400 500 600 700 800 900 1000

Height (mm)

20 25 30 35 40 45

Pa

th

lo

ss

(d

B)

Free space Ground effect Distance between two antennas, r = 10 mm

Frequency @ 60 GHz 0 10 20 30 40 50 60 70 80 90 100

Height (mm)

20 25 30 35 40 45

Pa

th

lo

ss

(d

B)

Free space Ground effect Distance between two antennas, r = 10 mm