We originally develop a network analysis method to study the non-ideal superconducting resonator circuits. We model the resonator device by a 3-block serial network, consisting of input feedline, resonator-coupler and output feedline. We show that the resonance curve will be modified if non-negligible discontinuity (reflection) exists at input or output side of the resonator. The extracted resonance parameters (such as coupling quality factor Q c ) from only fitting the transmission deviate from their true values as originally defined in matched impedance conditions, and the deviation depends on a single parameter which includes all the non-ideal effects from the circuits. We prove that the internal quality factor Q i can be accurately extracted from the modified transmission curve by using a very simple graphical method. Our methods and results are quantitatively verified by both simulations and experiments on superconducting microstrip resonators. Comparing to the usual circuit analysis, our network analysis method is more intuitive and easier to understand. It can serve as a general tool to study the non-ideal superconducting resonator circuits.

中文翻译：

---

非理想超导谐振器电路的网络建模

我们最初开发了一种网络分析方法来研究非理想的超导谐振器电路。我们通过一个由输入馈线、谐振器耦合器和输出馈线组成的 3 块串行网络对谐振器设备进行建模。我们表明，如果谐振器的输入或输出侧存在不可忽略的不连续性（反射），则谐振曲线将被修改。从仅拟合传输中提取的谐振参数（例如耦合品质因数 Q c ）与匹配阻抗条件中最初定义的真实值有偏差，并且偏差取决于单个参数，其中包括来自电路的所有非理想效应. 我们证明可以通过使用非常简单的图形方法从修改后的透射曲线中准确提取内部品质因数 Q i 。我们的方法和结果通过超导微带谐振器的模拟和实验进行了定量验证。与通常的电路分析相比，我们的网络分析方法更直观、更容易理解。它可以作为研究非理想超导谐振电路的通用工具。