Unified Frequency-Domain Analysis of Switched-Series-$RC$ Passive Mixers and Samplers

Abstract

A wide variety of voltage mixers and samplers are implemented with similar circuits employing switches, resistors, and capacitors. Restrictions on duty cycle, bandwidth, or output frequency are commonly used to obtain an analytical expression for the response of these circuits. This paper derives unified expressions without these restrictions. To this end, the circuits are decomposed into a polyphase multipath combination of single-ended or differential switched-series-kernels. Linear periodically timevariant network theory is used to find the harmonic transfer functions of the kernels and the effect of polyphase multipath combining. From the resulting transfer functions, the conversion gain, output noise, and noise figure can be calculated for arbitrary duty cycle, bandwidth, and output frequency. Applied to a circuit, the equations provide a mathematical basis for a clear distinction between a "mixing" and a "sampling" operating region while also covering the design space "in between." Circuit simulations and a comparison with mixers published in literature are performed to support the analysis.

Wake-up Receiver Based Ultra-Low-Power WBAN

“…which corresponds with the result in [53]. It is interesting to note that the input impedance is a function of the source impedance.…”

“…The model is valid for both voltage domain and current domain mixers. This is different from the analysis presented in [53] in which an infinite load impedance is assumed and the transducer power gain is not analyzed. The presented model is used to design a passive mixer with maximal transducer power gain.…”

“…The fundamental limit on the noise factor of the presented 4-phase passive mixer is set by the noise factor of the first network, which reduces as the number of mixer phases increases [53]. Note that there is a 3dB difference in minimal noise figure, because here we use the output SNR of one differential output phase, whereas [53] uses the combined SNR of all the output phases.…”

A 4-Element Phased-Array System With Simultaneous Spatial- and Frequency-Domain Filtering at the Antenna Inputs

“…The network of conducting. From the LPTV network analysis, extensively discussed in [16,22], the output spectrum on the baseband capacitors in state "k" can be shown have a general form:…”

“…4a can be simplified to the one in Fig. 4c and it can be analyzed with the LPTV approach presented in [16,22], with two changes: 1) R S is 4 times lower (more bandwidth); 2) the source signal contains a weighted sum of 4 antenna signals components with time shifts…”