本研究以差動橋式T線圈與相位轉換器為基本組件，將鼠競耦合器的傳輸線用差動橋式T線圈取代，使其可具有寬頻、雙頻、微小化與不等功率輸出的特性。並以積體被動元件製程與0.18 μm CMOS製程實現微型化寬頻鼠競耦合器、雙頻鼠競耦合器與雙頻不等功率分配鼠競耦合器，以展現所達到的電路效能。
首先，使用差動橋式T線圈與相位反轉器實現2.5GHz微型化寬頻鼠競耦合器，因為使用了上述兩個組件，所以使電路面積大幅縮小，實際電路面積為1.13 × 1.19 mm2，電氣尺寸在中心頻率2.5GHz下為0.0190  0.02750，也因為使用了相位反轉器來增加頻寬，反射損耗大於15dB的比例頻寬為69.2%。
其次，沿用微型化寬頻鼠競耦合器的架構，以雙頻差動橋式T線圈取代原本的差動橋式T線圈，達成雙頻操作的效果，並分別使用積體被動元件製程與0.18 μm CMOS製程實現。以積體被動元件製程實現的2.45/5.5GHz雙頻鼠競耦合器，實際電路面積為2.73 × 4.17 mm2，電氣尺寸於2.45GHz為0.0223λ0 × 0.0341λ0，於5.5GHz為0.0501λ0 × 0.0765λ0，反射損耗大於10dB之比例頻寬，在2.45GHz與5.5GHz分別為81.2%與27.3%。而以0.18μm CMOS製程所實現的10/24GHz雙頻鼠競耦合器，實際電路面積為0.871 × 1.18 mm2，電氣尺寸於10GHz為0.029λ0 × 0.0393λ0，於24GHz為0.0697λ0 × 0.0944λ0，反射損耗大於10dB的比例頻寬，在10GHz與24GHz分別為99.8%與30.38%。
最後，藉由改變雙頻差動橋式T線圈的等效阻抗，實現於2.45GHz有3dB功率分配比，於5.5GHz有0dB功率分配比之鼠競耦合器，電路面積為3.1  4.4 mm2，電氣尺寸於2.45GHz為0.0697λ0 × 0.0944λ0，於5.5GHz為0.0697λ0 × 0.0944λ0，以輸出振幅誤差在±0.5dB來計算頻寬，在2.45GHz與5.5GHz兩頻段分別為42%與7.5%。本研究也探討了使用雙頻差動橋式T線圈實現雙頻不等功率分配鼠競耦合器之設計限制，包括兩中心頻率下的功率分配比與頻率比，做為判定可實現規格範圍的依據。

In this paper, differential bridge-T coils and phase inverter are employed as basic building blocks to realize rat-race couplers with features, like wide bandwidth, dual-band operation, miniaturization and unequal power division ratios. To demonstrate the performance achieved, several design examples are implemented in the integrated passive device (IPD) and 0.18-μm CMOS technology, including wideband rat-race coupler, dual-band rat-race coupler, and dual-band rat-race coupler with unequal power division ratios.
First, by using differential bridge-T coils and phase inverter, a 2.5 GHz miniaturized wideband rat-race coupler is implemented in IPD. The circuit size is only 1.13 × 1.19 mm2 and the corresponding electrical size is 0.0190  0.02750 at 2.5 GHz. The 15-dB return loss bandwidth is 69.2%. It outperforms the conventional rat-race coupler in terms of circuit size and operation bandwidth.
Secondly, by using the same structure of the proposed miniaturized wideband rat-race coupler while replacing the original differential bridge-T coils by dual-band differential bridge-T coils, miniaturized dual-band rat-race couplers are achieved. A 2.45/5.5 GHz dual-band rat-race coupler is realized in IPD, and the circuit size is only 2.73 × 4.17 mm2. The corresponding electrical size is 0.0223λ0 × 0.0341λ0 at 2.45GHz, and it is 0.0501λ0 × 0.0765λ0 at 5.5 GHz. Its 10-dB return loss bandwidth is 81.2% at 2.45 GHz while it is 27.3% at 5.5 GHz. In addition, a 10/24 GHz dual-band rat-race coupler is impemented in 0.18-μm CMOS technology, the circuit size is only 0.871 × 1.18 mm2. The corresponding electrical size is 0.029λ0 × 0.0393λ0 at 10 GHz and it is 0.0697λ0 × 0.0944λ0 at 24 GHz. The 10-dB return loss bandwidth is 99.8% at 10 GHz while it is 30.38% at 24 GHz.
Finally, by varying the equivalent characteristic impedances of the dual-band differential bridge-T coil at the two bands, miniaturized dual-band rat-race coupler that is capable of achieving different power division ratios over the two bands can also be achieved. As an example, a proposed dual-band rat-race coupler having 3dB power division ratio at 2.45 GHz and 0dB power division ratio at 5.5 GHz is realized in IPD. The circuit size is only 3.1  4.4 mm2. The corresponding electrical size is 0.0697λ0 × 0.0944λ0 at 2.45 GHz and it is 0.0697λ0 × 0.0944λ0 at 5.5 GHz. The bandwidth of ±0.5dB amplitude error is 42% at 2.45 GHz and it is 7.5% at 5.5 GHz. Also, the design limitations, of using dual-band differential bridge-T coils for dual-band rat-race coupler designs, including the power division ratio and frequency ratio of the two center frequencies, are thoroughly investigated.

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