Passive Frequency Shifting of N-Path Filters Through Rotary Clocking: Analysis and Design

$N$
-path switched-
$RC$
circuits have been extensively investigated as a promising solution for realizing various novel functionalities, including on-chip tunable high-
$Q$
filters, true time delays operating beyond the delay-bandwidth product, and non-reciprocal components. The clock frequency typically sets important parameters of the functionality, such as the frequency of the filter, the amount of achievable delay etc. The ability to tune the clock frequency through a wideband synthesizer enhances the reconfigurability of
$N$
-path switched-
$RC$
circuits, but the presence of multiple independent
$N$
-path circuits on a chip results in the need for multiple independent wideband synthesizers. Here, we introduce a novel concept of rotary clocking in
$N$
-path circuits which enables us to passively frequency shift any
$N$
-path filter by either rotating clockwise or anti-clockwise the clocks exciting the switches of each of the paths. The effect of rotary clocking is analyzed using linear periodically-time-variant (LPTV) circuit theory, and has been verified through simulations and measurements. The effects of quantization due to finite clock phases, and the resultant spurs produced by this method, are also analyzed and compared with measurement results. Measurement results are presented for a two-port
$N$
-path filter implemented in a 65-nm CMOS 0.1-1 GHz highly-reconfigurable self-interference canceling receiver. The two-port filter achieves a maximum frequency shift of
$f_{s}/8$
in the steps of
$f_{s}/160$
and also has a phase control covering all of 360° in steps of 45°.