  High quality factor coplanar resonators are critical elements in
superconducting quantum circuits. We describe the design, fabrication and
measurement of stepped impedance resonators (SIRs), which are more compact in
size than commonly used uniform impedance resonators (UIRs). With properly
chosen impedance ratio, SIRs can be 27% shorter than UIRs. As a result, the
area occupied by SIRs can be reduced. Two kinds of designs containing both SIRs
and UIRs are fabricated and measured. The power dependence of the extracted
internal quality factors (Qi) for all the resonators showed that SIRs and UIRs
have comparable performance with Qi around half-million under single-photon
level excitation. These results indicate that SIRs could be used in
superconducting quantum circuits. The reduced size of SIRs may also lead to
reduced overall circuit area and increased integration level.
