~ I ~ ~ ~ ~ T I Q N AND COUPLING ANALYSIS OF SHORT ELECT LOSSY, COUPLED MIGROSTRTP LINES

R. 0. Veliz and J. R. Souza Center for Telecommunications Studies - CETUC

Pontifical Catholic University of Rio de Janeiro - PUCRio Rua Marques de S%o Vicente, 225 - 22453-900 Rio de Janeiro - RJ, Brazil

Abstract

The propagation characteristics of short electric pulses on lossy, coupled microstrip lines is thoroughly investigated using fullwave methods. It is shown that mode coupling is the main cause of pulse distortion. and that it can be controlled by appropriate choice of the substrate coniposition. The results obtained indicate the feasibility of VLSI circuit with high conductor density, keeping the crosstalk and distortion due to mode coupling under control.

1. INTRODUCTION

In VLSI circuits. short electric pulses are not only affected by the intrinsic frequency dispersion of the transmission lines, but also by the small interline spacings. which introduce undesired coupling to adjacent lines. The net results of these effects are the distortion of the signal pulse and crosstalk. The adequate design of such circuits then requires a rigorous study of the propagation characteristics (mode coupling, dispersion, attenuation) of the transmission lines along which the pulses are transmitted.

This paper presents a thorough investigation of the propagation characteristics of short electric pulses on lossy, coupled microstrip lines, considering single- and double-layered substrates. Due to the high frequency contents of short pulses, it is necessary to use fullwave techniques for this analysis. The well known Spectral Domain Approach (SDA) was, due to its ease of fomiulation and accuracy. chosen for the calculation of the phase and attenuation constants of the microstrip lines An algorithm based on the Fast Fourier Transform (FFT) is used to simulate the pulse propagation along the transmission lines. The present analysis goes beyond the ones found in the literature, e. g. [l], [2], as losses due to imperfect ground planes and substrates are fully taken into account. The possibility of controlling mode coupling through adequate choice of the substrate coniposition is also investigated.

For signals propagating on a pair of coupled lines, ?he distortion mechanism can be conveniently analyzed with the odd- and even-mode formalism [3], where each mode is described by a distinct propagation constant:.

Even-mode: yze(o) = rxzs(m) +jfi,,(o) ; Odd-mode: yZo(m) = a,,(o) +.ipzo(o) (1)

Considering that an input signal V(t,z=O) is applied to only one of the coupled lines (say, line l), after a propagating distance D the signals on the two lines, V,(t,z=D) and V,(t,z=D), can be expressed as:

V, (t,z=D)=$’ { 3[V(t ,z=O) J .ex- [ -yaY(m)D] .cosh(A.y, D) } (2)

where 3 represents the Fourier Transform, and

0-7803-2674-1/95/$4.00 8 1995 IEEE. a42 SBMOllEE IvlTT-S IMOC’DS Proceedings

The equations (2) and (3) above can be used to calculate the transient response of the coupled lines. The Fourier transforms are calculated with the FFT algorithm, while the odd- and even-mode propagation constants are rigorously calculated via the Spectral Domain Approach 131461.

3. RESULTS

3.1 Coupled microstrip lilies with single substrate

Initially, the Spectral Domain Approach (SDA) was used to calculate the propagation constant of the coupled microstrip lines over a suf'ficiently wide frequency range, considering lossy, single-layered substrate, and lossy ground plane. The latter is easily incorporated in the SDA formulation simply by representing it as an extra substrate layer [6]. The results obtained for the odd- and even-mode propagation constants are shown in Figure 1, for different values of the substrate conductivity The dispersive nature of the c:oupled microstrip lines is clearly seen in this figure. It is observed that the phase and attenuation constants of the even-mode are 1,arger than those of

Lossy coupled microstrips

3.4

3.2 0 Y

Qa

3.0

2.8

un = 0.000 S/m 01 uh = 0.025 S/m - uh = 0.075 S/m - Uh = 0.125 s/

T

I " i t

Lossy coupled microstrips w=OSmm h=0.635mm ~,=12.2 1 s=l .Omm t=0.012mm u,=4.1 E ~ s / ~ P

c C 2 40.0 C 0 0

-60.0 E \ m V v

0.0 bW,, ,-, , , ,

! 20.0 i

1 0 - j 1 l b 10' Frequency (GHz:I

(4 (b) Figure 1 : Variation of the even- and odd-mode normalized phase (a) and attenuation (b) constants with frequency for a

pair of coupled microstrip lines, considering different values for the substrate conductivity.

the odd-mode at the lower frequencies. At very high frequencies, the two modes become degenerate, and are equivalent to the mode propagating in a single strip of 5ame dimensions. These results indicate that mode coupling is fundamentally i% low frequency phenomenon, as the electrical distance between the strips increases with frequency, thus reducing the amount of coupling.

Next. a Gaussian pulse of 30ps (FWHM) was launched along line 1. The resulting pulse after propagation along the line, for a distance of 4Cl.Onim, and the pulse coupled to line 2 are shown in Figures 2-a and 2-b, respectively. Different values were considered for the substrate conductivity, as indicated in these figures, which a150 show two other pulses for comparison: one propagated along a dispersion and loss free transmission line, which presents no distortion; another one propagated along a single microstrip line of the same width as the coupled lines. Figure 2-a shows that the pulse along line 1 was strongly distorted: its amplitude was severely reduced, while its width increased considerably. Cornparing this pulse with that propagated in a single microstrip line 171, it is observed that the former suffers greater distortion, indicating the importance of mode coupling. Figure 2-b shows the signal coupled to line 2, whose magnitude reflects the strong coupling between the two lines. It is also seen in Figures 2 that the substrate conductivity affects mostly the amplitude of the pulses, with little distortion. This means that the difference in the mode attimuation constants does not contribute much to the coupling, and hence to pulse distortion. These results agree with those of reference [2].

The effect of the separation between the conductor of the coupled mcrostrip lines was also investigated. For this purpose, four different values of the strip spacing were considered, representing the cases of stroiig, moderate and very little coupling: S = 0.5, 1.0, 2.0 and 4.0nini. A low conductivity substrate was chosen for Ithis investigation (rrh=0.025S/m) The attenuation and phase constants calculated for the odd- and even-modes are shown in Figures 3-a and 3-b, respectively. 'The results confirm that, as the strip spacing increases, the odd- and even-mode

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attenuation and phase constants tend to those of a single microstrip line of the same width, as the coupling between the lines reduces.

Lossy coupled microstrips w=0.5mm h=0.635mm E =12.2 s=l.Omm t=0.012mm u,L4 1E7S/m

Lossy coupled microstrips ' ' O 4 w=0.5mm h=0.635mm e,=12.2 4 s = l Omm t=0.012mm ut=4.1E7S/m

4 -0.0 ...... Undistorted i

......... isolcted line ' ,' uh = 0.000 s / m '..,,: 1 uh = 0.025 S/m - uh = 0.075 S/m

m u , = 0.125 S/m i - 0 5 ; , > I , I I I I I , I l I I I t # I I I Z I I I / I I I I , I I / / I , I I / / I I \ 8 r r W - r

300 350 400 450 500 550 300 350 400 450 500 550 -05'

Time (DS) Time (ps)

(a> @) Figure 2: Pulse distortion along coupled microstrip lines, for different value of the substrate conductivity: (a) Line

1, (b) Line 2 . (FWHM = 30ps, z = 40").

3.6

3.4

3.2

0

Q2 3.0

2.8

2.6

.............. * ........... ............ ............ , . . . . . . . . . . . . ~ .' ,.' ,x&x+:.:<<.:.!.!x: _.-- .a ...... 1::- ........P........... ..* 3 ................................

27.0

--. E \ g 22.0 d

12.0

Lossy coupled microstrips w=0.5mm ah=0.025S/m h=0.635mm c,=12.2 t=0.012mm al=4.1E7S/m

- s = 0.5 mm (even mode me++a s = 1.0 mm - s = 2.0 mm

10 -I I O 10 -' I 10 10' Frequency (GHz)

2.4 ~

Frcsuencv fGHzl

(4 (b) Figure 3 : Variation of the odd- and even-mode normalized phase constant (a) and attenuation constant (b) with

frequency, for different values of the separation between the pair of coupled microstrip lines.

Next, the effect of the strip separation on a Gaussian pulse of 30 ps (FWHM) was investigated, and the results are shown in Figure 4. The pulse was launched in line 1, and Figure 4-a shows the pulse shape after a propagating distance of 40.0". For the smaller separation (S = 0 5mm), the effects of a strong mode coupling are clear: the pulse is considerably distorted, and its amplitude is reduced to less than half of the original value. The deformation experienced by the pulse is such that it is almost divided in two. The pulse coupled to line 2 is shown in Figure 4-b; its magnitude and shape confkn the strong coupling. This pulse is similar in amplitude and shape to that in line 1, except for an inversion of the peaks. These results illustrate the odd- and even-mode formulation for coupled lines [3]: for strong mode coupling, the temporal response of the lines show a separation of the even and odd pulses, i. e.. an in-phase pair of pulses appear in line 1, while in line 2 the two pulses have phase difference of 180". Figure 4-a also indicates that, as the separation between the conductors increases, the pulse in line 1 is less affected by mode coupling: its amplitudes increases, and its shape tends to that of a pulse propagating along a single inicrostrip line. On the other hand, the amplitude of the pulse in line 2 decreases, indicating a reduction in the amount of coupling as the conducting strips are moved apart.

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Lossy coupled microstrips w = O , 5 m rn h = 0 . 6 3 5 m m E,-12.2 t=O.OlZrnm ol=4.1E7S/m

rrh=O. 025S/m LLossy coupled micirostrips w=0.5mm oh=0.025S/m h=0.635mm c,=12.2 t=0.012mm 1 E7S/m

M s = 0.5 rnm ",,v - s = 1.0 mm <, drQdrcdrs = 2 0 mm '.' - s = 4.0 mm

0.5

-0.0

- s = 0.5 mm - s = 1.0 mm - s = 2.0 m - s = 4.0 m

- - isoloted line

-051"""";;To""4Jo~"""4do"~"~'5Jo'n 530 Time ( p s )

Illrllrlnl"n 330 380 430 480 530

Time (ps)

(a) CO> Figure 4: Pulse distortion along lossy, coupled microstrip lines, for different values of the sepalration between

the conduc:ting strips: (a) Line 1, (b) Line 2 (FWHM = 30ps, z = 40m1n).

3.2. Coupled microstrip lines with composite substrate

One technique that allows a considerable reduction of mode coupling, and hence the crosstalk in coupled lines is known as substrate compeinsation [SI. This technique consists simply in a composite substrate, with an extra layer, with a lower dielectric constant, between the original substrate and the ground plane. In ordler to maintain the dimensions of the structurle, the total thickness of composite substrate is made equal to that of the original layer.

e extra layer considereid here has a dielectric constant ~,=2.2 and conductivity o=O.OSOS/m. Three different thickness combinations of the composite substrate layers were considered: hl/h2=0.318/0.3 18, 0.159/0.476, 0 102/0.533, which will, from now on, be refened to as C1, C2, C3, respectively. Again, the structure was characterized in temis of the odd- and even-mode normalized phase constant and attenuation constant. The results obtained for the phase constant, considering two values of conductor separation (S), are shown in Figure 5 .

It is seen in Figure 5 that ithe various combinations of the composite substrate control the difference between the odd- and even-mode phase constants For a conductor separation S=l.Omm (Figure 5-4, this difference is minimum for the second combination (C2), while for S=O.Smm (Figure 5-b), the minimum difference is obtained for the third conibination (C3). There exists one at least one combination that equalizes the odd- and even-mode phase velocities. In Figure 5, with combinations C2 and C3 smaller pulse distortion is expected, as illustrated in Figure 6 and 7 for a Gaussian pulse of 30ps (FWHM)

Figure 6 confirms what was said above: the greater (or smaller) equalization of the odd- and even-mode phase velocities, produced by the combinations of the composite substrate, results in weaker (or stronger) coupling between the lines or, in other words, little (or much) pulse distortion. For comparison, Figure 6 also shows (in dashed line) the pulses corresponding to the case of a single substrate layer. It is seen that the composite substrate leads to more favourable results, for any of the layer combinatiosn, than the latter. With combination C2, which provided the smaller difference between the odd- and even-mode phase velocities, the pulse in line 1 (line 2) has larger (smaller) amplitude. This results follow from the significant reduction in the mode coupling due to substrate compensation.

Thc results shown in Figure 7 are similar to those in Figure 6. In this case, the substrate combination C3 now affords the better conditions for pulse propagation with minimum distortion due to mode coupling.

It is worth mentioning that the pulses obtained after equalization of the odd- and even-mode phase velocities present less distortion than pulses propagated along a single microstrip line of siinilar dimensions as one of the coupled lines. This means ithat substrate compensation can not only control mode coupling, but also improve the dispersive characteristics of the transmission line.

3.5

3.0

2.5 B a

2.0

Lossy coupled microstrips w=0.5mm s = l .Omm h=0.635mm c -12.2 t=0,012mm u'14 I E ~ S / ~ E,,=z.z uh,=o.d.GoS/m ea= l 2.2 ~,~==0.025S/m

Sm* hl=hZ=h/2=0.318mm waea hl=0.159mm h2=0.476mm - hl=O.lOZmm h2=0.533mm

1.5 10 10

Frequency (GHz)

2.3

3.0

0

a 2.5

T

1: 2.0

Lossy coupled microstrips w=0.5mm s=OSmm h=0.635mm r,=l2.2

crl=2.2 uh,=0.050S/m c,=12.2 u,=0.025S/m

- hl=h2=h/2=0.318mm hl=0.159mm h2=0.476mm

1.5 10 10 '

frequency (GHZ)

(4 (b) Figure 5: Variation of the normalized phase constant with frequency for the odd- and even-modes of a pair of

coupled microstrip lines, considering a composite substrate (S=l .Omm and S=O.Smm).

Lossy coupled microstrips w=0.5mm c,,=2.2 re=12.2 s=l.Omm t=O.OlZmm ut=4.iE7S/m

- h l =h2=h/2=0.318mm %we& h l =0.159mm h2=0.476mm - hl=0.102mm h2=0.533mm . . . . . . - single substrate (~,=12.2)

T '.O i z -0.0

LOSSY coupled microstrips w=OSmm cII=2.2 ea=12.2 s=l .Omm t=0.012mm ul=4.1 E7S/m

- h l =h2=h/2=0.318mm hl=0.159mm h2=0.476mm - h t =0.102mm h2=0.533mm

. . . -. - - single substrate (c,=12.2)

' . < I I I , I I , , I

I , * I , I , * , I , ,

-0.5 , , I , , , , , , , , , , , , , , , , , , , , , , , ? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 250 350 450 550 250 350 450 550

Time (ps) Time (ps)

(4 (b) Figure 6: Pulse distortion in lossy, coupled microstrip lines for different substrate combinations: (a) Line 1, (b) Line 2

(FWHM = 30ps, z = 40").

4. CONCLUSIONS

Based on the Spectral Domain Approach, a rigorous investigation of short electric pulse propagation along coupled microstrip lines was carried out considering the material losses. It was observed that mode coupling, originated by thc different odd- and even-mode phase velocities, was the main cause of pulse distortion. For the small loss structures considered here, the different mode attenuation constants do not contribute much to pulse distortion. It was shown that substrate compensation is an effective way reducing mode coupling and, in consequence, pulse distortion, even for very small spacing between the conducting strips.

This work was supported by TELEBRAS - Telecomunicaqdes Brasileiras S.A. under the contract PUC-TELEBRAS 5 1 ~ 9 3 .

846

t,o ~ Lossy coupled niicrostrips w=OSmm c,,=2.2 cn=12.2

i s=0.5mm : = 0 ~ 1 2 m m ut=4.tE7S/mw s w

" - h l =hZ=:h/2=O.J18mm O-esea h l =O.l!59mm h2=0.476mm - h 1 =O. 102mm h2=0.533mm . . . -. . single substrate (c,=12.2)

Lossy coupled microatrips w=O.Smm ~ , ~ = 2 . 2 cn=12.2

1 -- hl =h2=h/2=0.31 Bmm maw hl=O.l59mm h2=0.476mm - hl=O.lOZmm h2=0.533mm .__ single substrate ( ~ , = 1 2 . 2 )

(a) (b) Figure 7: Pulse distortion in lossy, coupled microstrip lines for different substrate combinations: (a) Line 1, (b) Line 2

(FWHM = 30ps, z = 40").

5. REFERENCES

1. Y. Qian and E. Yamaishita: "Characterization of Picosecond Pulse Crosstalk Between Coupled Microstrip Lines with Arbitrary Conductor Width", IEEE Tran. Microwave Theory Techn., Vol. MTT-41, pp 101 1-1016, Qm.-JuB 1993.

2. J. P. Gilb and C A. Balanis: "Transient Analysis of Distortion and Coupling in Lossy Coupled Microstrips", IEEE Trans. Microwave Theory Techn., pp 1894-1899, Dec. 1990.

3. R. 0. Veliz: "Spectral Domain Approach of Short Electric Pulse Propagation in Printed Transmission Lines", MSc. Di.wertation, Pontifical Catholic University of Rio de Janeiro, Rio de Janeiro - RJ, Brazil, Feb. 1994 (in Portuguese).

4. T Uwano and T. Itoh, "Spectral Domain Approach", in: "Numerical Techniques for Microwave and Millimeter-Wave Passive Structures", T. Itoh (ed.), John Wiley & Sons, New York, 1989.

5. J. R Souza: "Spectral Domain Analysis of Printed Transmission Lines in Multilayered Substrate and Superstrate Configuration", Proc. 8th Annual Rev. Progress in Appl. Comp. Electromagn., pp 290-295, Monterey, CA, U.S.A., 1992.

6- J .R. Souza and R. 0. Veliz: "Application of the Spectral Domain Approach to the Analysis of Planar Transmission Lines wilh Thick Ground Plane", Proc. X Electrical Engineering Congress, Valdivia, Chile, Nov. 1993.

7. R. 0. Veliz and J. R. Souza: "Ultra-Short Electric Pulse Propagation in Printed Transmission Lines", Proc. VI Brazilian Microwave and Optoelectronics Symposium, pp 115 -120, Belem-PA, Brazil, 1994 (in Portuguese).

8. 5. P. Gilb and C. A. Balanis: "Asymmetric, Multi-Conductor Low-Coupling Structures for High-speed, High-Density Digital Initerconnects", IEEE Trans. Microwave Theory Techn., Vol. MTT-39, pp 2100-2 106, Dec. 1991.

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