Analysis of the Effect of Source Capacitance and Inductance on $N$ -Path Mixers and Filters

Abstract

Switch-R-C passive N-path mixers and filters enable interference-robust radio receivers with a flexibly programmable center frequency defined by a digital multi-phase clock. The radio frequency (RF) range of these circuits is limited by parasitic shunt capacitances, which introduce signal loss and degrade noise figure. Moreover, the linear periodically time varying (LPTV) nature of switch-R-C circuits results in unwanted signal folding which needs to be suppressed by linear time-invariant (LTI) pre-filtering by passive LC filters. This paper analyzes the interaction between capacitive or inductive LTI pre-filtering and an N-path mixer or filter, leveraging an analysis technique based on the impulse response of the adjoint network. Previously reported results for an inductive source impedance are derived in a simpler fashion, while providing circuit intuition. Moreover, new results for N-path receivers with a shunt capacitor, and a combination of a series inductor and shunt capacitor are derived, as well as design criteria to minimize loss and frequency shifting in the peak response of these circuits.

High-linearity bottom-plate mixing technique with switch sharing for N-path filters/mixers

“…It is observed that both the gain and optimum S 11 dip are shifted towards lower frequencies due to the presence of s , in agreement with the analysis in [13,21]. This issue can be addressed by introducing complex feedback with resistors [3] or adding a series inductor [21]. The measured gain is about 16 dB and the −3dB,BPF is about 13 MHz ( −3dB,BB =6.5 MHz), while the filter roll-off from 20 to 200-MHz offset is about -32 dB (-34 dB from (6)) for the upper sideband, and -33 dB (-38 dB from (6)) for the lower sideband.…”

“…The receiver conversion gain obtained from the RLC model can be computed by using (6) and 7, while p of (6) becomes p (ω LO )||( ω s ) −1 now. It is observed that both the gain and optimum S 11 dip are shifted towards lower frequencies due to the presence of s , in agreement with the analysis in [13,21]. This issue can be addressed by introducing complex feedback with resistors [3] or adding a series inductor [21].…”

A Fully Passive RF Front End With 13-dB Gain Exploiting Implicit Capacitive Stacking in a Bottom-Plate N-Path Filter/Mixer

“…Similarly, the peak gain frequency will also shift to the left of LO due to parasitic capacitance. However the amount of frequency shift is governed by the transfer function and it is different from the S 11 shift [32]. Both shifts can be compensated using complex feedbacks [6], though not implemented here.…”

Analysis of nonidealities of N‐path circuits using impulse response

“…Now, the expression presented in (21) can be described as V out,X,0 (f ) can be solved by setting τ d to zero in Equation (25). By using (5) and (17), the frequency response of the filter is calculated by…”

“…This paper likewise 24,25 proposes a simple analytical method to calculate the frequency responses of N-path circuits by means of impulse response. However, this paper uses impulse response of circuit driven by delayed clock, and Pavan and Klumperink 24,25 use adjoint network and SFG to calculate the transfer function. The method may also be used for sample-and-hold circuit.…”