| Radio-frequency low pass filter is an indispensable part of cryogenic microwave circuits and superconducting qubit readout circuits.It is typically placed on input and output paths to protect sensitive devices from stray radiation on coaxial lines.A popular way to solve this problem is to use metal powder(copper powder,aluminum powder,silver powder,etc.)filter,using the skin effect of high frequency signal in the powder to achieve the effect of attenuation.The main structure is a mixture of metal powder and epoxy resin material as a matrix wrapped transmission line.Such filters are very effective at attenuating high-frequency(terahertz and far infrared)radiation signals,but at low frequencies(<10 GHz)passband usually introduces several dB of undesired insertion losses.Here we describe a design method of microwave low-pass filter based on superconducting artificial transmission line structure.By using the cut-off characteristics of artificial transmission line,a low-pass filter with a cut-off frequency of 30 GHz,minimal insertion loss in the passband and the attenuation of the stopband up to 200 GHz is lower than that of the-25 dB is realized.There are four key design points.(1)The superconducting Ti/TiN metal film with a kinetic inductance of 15 pH/sq is used as the inductance material,and the lossless metal film(such as aluminum)is used as the capacitance material.By designing the unit inductance Lu and the unit capacitance Cu,the cut-off frequency of the filter is fc=1/(π(?))≈30 GHz and the characteristic impedance is Z0=(?)=50 Ohm.(2)The low superconducting transition temperature(Tc≈700 mK)of superconducting Ti/TiN is used to attenuate high frequency microwave photons.According to BCS theory,when the input microwave frequency is greater than the superconducting energy gap frequency(≈50 GHz),the Cooper pair will be excited into quasiparticle,and the feed-line will change from inductive state to resistive state,serving as a lossy transmission line to attenuate the high-frequency signal.(3)The cavity resonant peak can be effectively suppressed by adding microwave absorbing material under the substrate to absorb electromagnetic energy near the cavity wall.(4)The capacitance unit of artificial transmission line is designed as aperiodic structure,and a series of transmission zeros formed by aperiodic capacitance are used to suppress the stray passband at high frequency.Detailed design methods and electromagnetic simulations based on real material parameters will be described in follow-up chapters.Our design features low frequency(<10 GHz)insertion loss close to 0,cut-off frequency easy to control,steep band edge,compact size,easy to manufacture,easy to cascade with other superconducting integrated circuits,etc.In addition,the method of fast calibration of characteristic impedance of transmission line is studied by using time domain reflectometry experiment data.The characteristic impedance of transmission line can be determined by fitting experimental data in simulation and mathematical modeling.It can also determine the position of the reflection point in the circuit,quantify the degree of impedance mismatch according to the reflection amount,and get important parameter such as attenuation in the test line and the length of the transmission line. |
