Modeling and Analysis of Open-End Microstrip line Discontinuity on Multilayer Semiconductor Substrate for Microwave Integrated Circuits

Abstract

In this paper, the modelling and analysis of open-end microstrip line discontinuity on multilayer semiconductor substrate is presented. The equivalent lumped circuit model is used to compute the frequency dependent reflection coefficient from the open-end microstrip line discontinuity. The lumped circuit elements, capacitance, inductance and resistance, are computed using closed-form expressions in term of the width of microstrip line discontinuity and thickness of the dielectric substrate. To compute the characteristic impedance of microstrip line on multilayer dielectric substrate, static Spectral Domain Analysis (SDA) method and Single Layer Reduction (SLR) techniques are used.

Introduction

I. INTRODUCTION

Microstrip line are extensively used in the design of microwave components such as couplers, filters, interconnects and matching components in hybrid and monolithic integrated circuits. Different types of discontinuities such as open-end, gap and step discontinuity are essential part in the design of planar microwave components. In the complex circuits, the microstrip line and discontinuities are integral part in designing process. Various types of transmission line discontinuities, open-end, short-end, step and bend have been analyzed using equivalent circuits model at low frequency. Full wave methods have been used for frequency dependent analysis. Full wave methods are difficult to implement and time consuming. For fast microwave circuit design the equivalent circuit model of discontinuities are widely used [1-7]. Most of the circuit model are frequency independent. The frequency dependent parameters of microwave components can be further improved by incorporating the frequency in the lumped circuit model. The circuit model for open-end discontinuity has been modified and results are compared with full-wave spectral domain analysis [5].

In the hybrid and semiconductor based integrated circuits, the microwave circuits are designed on multilayer substrates. Therefore, it is essential to analyze and characterize the microstrip line discontinuities on multilayer substrate. This paper presents analysis of open-end microstrip line discontinuity on multilayer dielectric substrate. For this, the static spectral domain analysis method along with single layer reduction technique are used to obtain the characteristic parameter i.e., characteristic impedance and effective relative permittivity of the microstrip line. The equivalent circuit model has been used to compute the frequency dependent magnitude and phase of the reflection coefficient of open-end microstrip line discontinuity. The static spectral domain analysis method for multilayer microstrip line is discussed in section-II. The circuit model for open-end discontinuity and computed numerical results are discussed in section-III and Section-IV respectively.

II. ANALYSIS OF MULTILAYER MICROSTRIP LINE

For the computation of characteristic impedance of multilayer microstrip line several full wave methods, spectral domain Approach (SDA) and Mode Matching Method are discussed [8]. At low frequency, quasi static methods, conformal mapping, variational method are used for computation of characteristic impedance and effective relative permittivity. In this paper, Galerkin’s techniques based static spectral domain analysis method is used for calculating the capacitance of multilayer microstrip line. The characteristic impedance of multilayer microstrip line is computed from the line capacitance. The Green’s function in Fourier domain for multilayer microstrip line structure is obtained using transverse transmission line (TTL) technique [8-11].

The cross section of a shielded multilayer microstrip line is shown in Fig.1. The structural parameters of microstrip line are width of strip (W), dielectric substrate of thickness H1, H2 and H3. The permittivity of dielectric substrate is ε1, ε2, and ε3. The formulation to compute line capacitance is discussed in [8-11]. The per unit length capacitance is computed from following relation.

Fig.1 Multilayer Microstrip Line

1C=L2εoQ2n=1∞ρs2βn,yGβn,y                      (1)

where Gβn,y  is Fourier transform of Green’s function, ρs is Fourier transform of charge distribution present on the conductor strip, Q is total charge present on strip. The characteristic impedance is computed from following relation.

Zo=1cCdCair                                                          (2)

III. OPEN-END MICROSTRIP LINE DISCONTINUITY

The equivalent circuit model for open-end microstrip line discontinuity is shown in Fig.2. This circuit model consists of parallel combination of a Capacitor (C1) and a series LC2R resonating circuit. The closed form expression for capacitance, inductance and resistance are calculated in terms of physical parameters of microstrip line, i.e., width of strip conductor and thickness of dielectric substrate [5]. The characteristic impedance of multilayer microstrip line is computed from the static spectral domain analysis method [8-10] discussed in section-II.

Fig.2 Oen-End Microstrip line Discontinuity and Equivalent Circuit Model

C1=1Zo1.125tanh1.358Wh-0.315  pF                  (3a)

C2=1Zo6.832tanh0.0109Wh+0.91  pF                  (3b)

L=Zo0.008285tanh0.5665Wh+0.0103  nH                      (3c)

R=Zo1.024tanh2.025Wh  ohm                                               (3d)

The reflection coefficient of open-end discontinuity is computed from following relation-

Γ=Yo-YinYo+Yin                                              (4)

Where Yin is input admittance of the equivalent circuit and Yo is characteristic admittance of the microstrip line. The input admittance of the circuit is computed by following expression [5]-

Yin=jωC1+1R+iωL+1jωC2                (5)

IV. NUMERICAL RESULT AND DISCUSSION

The characteristic impedance for microstrip line for different strip width W=0.15mm to W=0.4mm are computed using spectral domain analysis method. The results for characteristic impedance are given in Table-I. Open-end microstrip line discontinuity is taken on two-layer dielectric substrates. We have taken first layer of silicon (Si) dielectric substrate εr1 = 11.9 with thickness H1 = 0.4mm. On silicon substrate, a thin silicon dioxide dielectric substrate layer εr2 = 3.9 and thickness H2 = 3μm has been taken. The normalized capacitance, inductance and resistance are computed for different strip width ranging from 0.15mm to 0.4mm and dielectric substrate thickness H1 = 400μm and H2 = 3μm. Fig. 3(a) shows the variation of normalized capacitance (C1/εo) and (C2/εo) with width of microstrip line.

Table-I

Fig. 3(a) Normalized Capacitance C1 and C2

Fig. 3(b) Normalized Inductance

The shunt capacitance increases as the width of microstrip line increases. The minimum and maximum value of normalized C1 is 3.28×10-4 and 1.63×10-3 for W=0.15mm and W=0.4mm respectively. Similarly, this value for normalized C2 is 1.52×10-3 and 2.41×10-3. The normalized inductance and resistance of equivalent circuit are plotted in Fig. 3(b) and Fig. 3(c) respectively. The inductance decrease as the width of strip increases but resistance increase as width of strip increases. This shows the that wider strip has more loss.

Fig. 3(c) Normalized Resistance

Fig. 4(a) and Fig. 4(b) shows the variation of normalized conductance and normalized susceptance with frequency. As the operating frequency increases, more field is radiated from the edges of the open-end discontinuity. The frequency dependent circuit model also demonstrates this. As the frequency increases the power loss, radiation loss and surface wave loss increases. Furthermore, the magnitude and the phase angle of reflection coefficient are plotted in Fig. 5(a) and Fig. 5(b) respectively with four microstrip line width, W=0.2mm, 0.25mm, 0.3mm and 0.350m.  As the frequency increases, the reflection coefficient decreases.

Fig. 4(a) Normalized Conductance

Fig. 4(b) Normalized Susceptance

Fig. 5(a) Reflection Coefficient (Mag.)

Fig. 5(b) Reflection Coefficient (Phase, deg.)

Conclusion

In this paper, lumped circuit model of open-end microstrip line discontinuity on multilayer semiconductor substrate has been present. The lumped circuit model can be used to analyze and compute the reflection coefficient for microwave component and circuit design.

References

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Copyright

Copyright © 2025 Dr. Paramjeet Singh, Dr. Y. K. Awasthi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.