CHAPTER 5 Conclusion
5.2 Future Works
This dissertation reports new methodologies of making the synthetic waveguide.
The proposed synthetic waveguides have two distinct features. First, well-controlled guiding properties can be easily established and applied to the design of microwave circuits. Second, high level of integration can be achieved for the circuit or system implementations. Such high level of integration using the proposed synthetic waveguides leads to the development of the high performance system-on-chip (SOC) and system-in-package (SIP) as illustrated in Fig. 5.1, which shows that compacted, high-performance RF module and system can be systematically realized by the synthetic waveguide.
Fig. 5.1 High-performance RF system incorporating synthetic waveguide.
Integration of active and passive components
Planar and/or Quasi-planar Transmission Lines:
Microstrip, Coplanar-waveguide
Metallic Waveguides:
Rectangular Waveguide
Single integrating technology: Synthetic Waveguides
High-performance RF Module or System
Σ
Integration of low-loss components: filters, resonators
Appendix I
Simplified Waveguide Models for Synthetic Rectangular Waveguide (SRW)
The Cartesian system is applied through the Appendix I. The guide wave is represented using time-harmonic waves,e(jωt−γz), with time and distance variations.
The propagation constant (γ) is defined by α-jβ. We will assume that there is no net charge density in the dielectric and that any conduction currents are included by allowing permittivity and therefore k2 =ω2µεto be complex. The µ (ε) is the product between µ0(ε0) and µr(εr). The wave equations, which reduce to the Helmholtz equations for phasor fields, are
⎪⎩
The three-dimensional ∇2 may be broken into two parts:
2
With the assumed propagation functione γ−zin the axial direction,
2E
The foregoing wave equations may then be written
⎪⎩
The curl equations with the assumed functionse(jωt−γz)are written below for fields in the dielectric system, assumed here to be linear, homogeneous, and isotropic:
X
For propagating waves, it is convenient to use the substitution γ=jβ where β is real if there is no attenuation. Rewriting the above with this substitution,
Hz
Boundary Conditions:
The transverse electric waves have zero Ez and nonzero Hz. The wave equations are expressed in Cartesian coordinates:
Hz
Solution by the separation of variables techniques gives
yy
The forms of transverse electric field in TEnp mode are
yy
Corresponding transverse magnetic field components are
yy
Since the proposed SRW is realizable by multi-layered integrated circuit processes, the lateral dimensions (along x-axis) of the SRW are typically much larger
b
than the thickness of the substrate along the y-axis. Consequently, the lowest order TE modes are TE10, and TE20, etc. On the other words, the ky is assumed to be zero.
Therefore, the field components in the transverse and longitudinal directions for the TEn0 modes in SRW are
Boundary Conditions:
0
The transverse magnetic waves have zero Hz and nonzero Ez. The wave equations are expressed in rectangular coordinates:
Ez
Solution by the separation of variables techniques gives
yy
The forms of transverse electric field in TEnp mode are
yy
Corresponding transverse magnetic field components are
yy
Since the proposed SRW is realizable by multi-layered integrated circuit processes, the lateral dimensions (along x-axis) of the SRW are typically much larger than the thickness of the substrate along the y-axis. Consequently, the lowest order TM modes are TM00, and TM10, etc. On the other words, the ky is assumed to be zero. Therefore,
in SRW are
Appendix II
Volume Estimation for Transmission-Line Based Bandpass Filter incorporating Multi-layer Complementary Conducting Strip Transmission Line (CCS TL)
As shown in the Figure 3.11, the complete bandpass filter (BPF) including the parallel resonators and J-inverters can be realized using complementary conducting strip transmission line (CCS TL). Moreover, the placement of the CCS TL is mainly controlled by the period (P) of the unit cell and its connection with the adjacent cells.
Following the design procedure reported in the Section 3.2.2, the required electrical parameters including the characteristic impedances and electrical lengths for the TL-based BPF are given. Since the CCS TL can provide much more design solutions to meet the specified guiding characteristics of the TLs in BPF. For simplicity, the period of all the unit cells is identical. Therefore, the volume estimation of TL-based BPF using CCS TL is initially given by
h N P
Lt⋅ ⋅ − ⋅
= (2 1)
Vtotal (II.1)
where Vtotal, Lt, N and h are followed by the same definitions reported in the Section 3.4. If N equals to one, on the other word, the BPF is realized by conventional double-side print-circuit-board (PCB) with one signal layer and the total area of the BPF is proportional to the product of the period of the unit cell (P) and the total lengths (Lt) required by the filter design parameters.
Furthermore, applying the multi-layer complementary conducting strip transmission line (CCS TL), which provides more than one signal layer to realize the TL-based BPF, the required volume of the TL-BPF can be expressed by the following
equation:
h N N
P
Lt⋅ ⋅ − ⋅
= (2 1)
Vtotal (II.2)
Notably (II.2) reveals an intrinsic assumption that the area of each signal layer is fully occupied by the signal trace of the meandered CCS TL. After some algebraic manipulation, a estimate of volume for TL-based BPF incorporating multi-layer CCS
TL is give by:
N h P
Lt ⋅ ⋅ − ⋅
= 1)
2 (
Vtotal (II.3)
Appendix III
Equivalent Transmission-Line Model for Spiral Inductor
In this appendix, the mathematic derivations for representing the lumped inductor model using equivalent transmission line parameters are illustrated. What follows is the comparison of one-port input impedances between two models. One is the generic lumped spiral inductor model and the other one is the generalized transmission-line model. During the derivations, the definitions of voltage-drop and current-flow in two models are identical.
(a)
(b)
Fig. III.1 Equivalent model for representing spiral inductor: (a) generic lumped model, (b) transmission-line model
The two-port transmission matrix of the transmission line can be expressed in terms of transmission line parameters.
Cp
Notably, the characteristic impedance (Z0) and propagation constant (γ) are all complex number for representing the losses of the transmission line. Next, the input admittance of the transmission line with short termination is proportional to the ratio between D and B and can be expressed in the following equation.
Then, the input admittance of transmission line with short termination can be directly mapped to those of the lumped model as shown in Fig. III.1. Therefore, the elements in the lumped model can be expressed in terms of the equivalent transmission lime parameters including the physical length, the characteristic
l
assumeing γl <<
⎥⎦
impedance and propagation constant of the transmission line.
Notably, by doing the Taylor’s series expansion, the product of γlis assumed to be less than one for simplifying the mathematic expressions during the derivations.
This assumption also limits the usage of derivations.
Rp
Rs
Cs
Ls
Cp
γl0 2Z
Z0
γl V1
I1
+
-
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