本論文主要針對功率分配器與巴特勒矩陣，以頻寬不減損為前提實現微小化之設
計。傳統的功率分配器或直交分合波器等，均由多段λ/4傳輸線組成，面積都會受限於傳
輸線長度，頻率越低面積越大。一般縮小傳輸線長度的方法大致有兩種：其一為使用彎
折的方式，縮小幅度有限；其二為使用集總元件等效傳輸線，如傳統的T模型，但頻寬
會因此縮減。本論文提出利用修正T模型取代傳統T模型，使頻寬在不減損的情況下達到
縮小化的目的。在電路設計方面，使用平衡式電感與平行板電容的架構來實現，以利於
積體電路製成實現。
本研究以GaAs與Glass Integrated Passive Device (GIPD) 製程分別實現出中心頻率
2.5 GHz的威爾京生分波器與直交分合波器，面積分別為0.020λg × 0.034λg與0.021λg ×
0.022λg，遠小於傳統設計，而頻寬相對於理想電路並無減損。再利用直交分合波器與45
度等效傳輸線，在GIPD製程上設計中心頻率2.5 GHz之4 × 4巴特勒矩陣，面積為0.044λg
× 0.047λg，頻寬34%(反射損耗>10 dB)；在GaAs製程上設計中心頻率5.5 GHz之二階功率
分配器，面積為0.044λg × 0.078λg，頻寬129.1%(反射損耗 > 15 dB)。

In this thesis, compact Wilkinson power divider and Butler matrix are designed with no
bandwidth reduction. Traditional Wilkinson power divider and branch-line coupler are
composed of many quarter-wavelength transmission-line sections at a designated frequency.
However, at the lower frequencies of the microwave band, the sizes of conventional
Wilkinson power divider and branch-line coupler are too large for practical use.
Conventionally, there are two ways to reduce the size of transmission lines. The first one is
achieved by using the folded line configuration, but the resultant circuit area is still large. The
other is accomplished by adopting lumped-element components, such as using the T or π
equivalent model, may be employed to reduce the circuit size, however these equivalent
models are useful only in a narrow bandwidth around the center frequency. In order to expand
the applicable frequency range of the equivalent circuit, this thesis adopts the modified-T
model for the λ/4 lines, so that the very compact designs may be implemented with no
bandwidth reduction. The proposed circuit designs are accomplished by adopting balance
inductors and metal-insulator-metal (MIM) capacitors so these designs may be suitable for
MMIC applications.
This thesis presents a compact 2.5GHz Wilkinson power divider, which is fabricated by
GaAs, shows the circuit size of 0.020λg × 0.034λg, and a compact 2.5GHz branch-line coupler,
which is fabricated by Glass Integrated Passive Device (GIPD), shows the circuit size of
0.021λg × 0.022λg. The circuit size is really small compared with traditional ways, and these
deigns are no bandwidth reduction. In addition, a compact 2.5GHz 4 × 4 Butler matrix, which
is fabricated by GIPD, is presented. The circuit size is 0.044λg × 0.047λg and the bandwidth is
34% (|S11| > 10 dB). A compact two section Wilkinson power divider is also presented in
GaAs process. The circuit size is 0.044λg × 0.078λg and the bandwidth is 129.1% (|S11| > 15
dB).

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