Simplified Unified Analysis of Switched-RC Passive Mixers, Samplers, and $N$ -Path Filters Using the Adjoint Network

Abstract

Abstract-Recent innovations in software defined CMOS radio transceiver architectures heavily rely on high linearity switched-RC sampler and passive-mixer circuits, driven by digitally programmable multi-phase clocks. Although seemingly simple circuits, the frequency domain analysis of these Linear Periodically Time Variant (LPTV) circuits is often deceptively complex. This paper uses the properties of sampled LPTV systems and the adjoint (inter-reciprocal) network to greatly simplify the analysis of the switched-RC circuit. We first derive the transfer function of the equivalent linear time-invariant filter relating the input to the voltage sampled on the capacitor in the switched-RC kernel. We show how a leakage resistor across the capacitor can easily be addressed using our technique. A signal-flow graph is then developed for the complete continuous-time voltage waveform across the capacitor, and simplified for various operating regions. We finally derive the noise properties of the kernel. The results we derive have largely been reported in prior works, but the use of the adjoint network simplifies the derivation, while also providing circuit insight.

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

“…In this section we will analyze the transfer function of the Npath filter/mixer circuit with the proposed implicit capacitive stacking with two main aims: 1) verify the in-band achievable 6 dB voltage gain; and 2) find the frequency dependence of the conversion gain, especially the selectivity of the N-path filtering. We will use a recently introduced simplified analysis for N-path filters/mixers using the adjoint network [28].…”

Analysis of nonidealities of N‐path circuits using impulse response

“…As shown in Figure 14A, charge sharing of Npath filter with parallel capacitor will be taken place by sharing transfer functions of X(τ d ), X(0), X(0), … at T S /N − τ d , T S /2+T S /N − τ d , T S +T S /N − τ d , …, respectively. Using (24) and substituting X(τ d ) with C p v 0 T S =N −τ d ð Þ , the resulting impulse response is simplified as…”

“…Further, analysis was performed on noise behavior and driving port impedance of the circuit with and without load resistance. Using sampled LPTV network analysis, a relatively simple analysis was proposed in SFG calculations of switched‐RC N‐path filters . Therefore, with impulse response of the RC circuit using adjoint network analysis, the behavior of the N‐path filter is modeled in an SFG diagram.…”

“…Using sampled LPTV network analysis, 23 a relatively simple analysis was proposed in SFG calculations of switched-RC N-path filters. 24 Therefore, with impulse response of the RC circuit using adjoint network analysis, the behavior of the N-path filter is modeled in an SFG diagram. However, the presented SFG is specified for a simple ideal N-path filter.…”

A Unified Analysis of the Signal Transfer Characteristics of a Single-Path FET-R-C Circuit

“…13 [35, Fig. 17], which is equivalent to the ones presented in [37], [44]. The upper half is for V on = F [v on (t)] generation and the lower half is for…”