A study for designing an ESL-cancelling circuit for shunt capacitor filters based on the biot-savart law

In general, insertion loss of a shunt capacitor filter at higher frequencies than its resonant frequency is deteriorated by equivalent series inductance (ESL) of the shunt path. There are some reports on circuits to improve the deterioration by cancelling the ESL by mutual inductance between coupled loops. However, a theory-based design equation is not clearly shown in these reports. On the other hand, another report derived recently that mutual inductance between vertically-stacked coupled square loops can be expressed in a relatively simple equation by applying the Biot-Savart law. In this study, a design process based on the equation for an ESL-cancelling circuit using vertically-stacked coupled square loops is proposed. A test circuit for a 10-μF shunt capacitor filter including a 30-mm microstrip line in its shunt path, which is equivalent to ESL of 10.5 nH, is designed and fabricated with an FR4 substrate. The measured results showed 30-dB improvement of insertion loss at several ten MHz. Moreover, the results were comparable to, or even better than, those of the directly-connected shunt capacitor filter.