Mixers are essential functional blocks in most radio frequency (RF)
communication systems. They are also considerable noise contributors
to the systems. Hence firm understanding of noise generation mechanism
in mixers and accurate and effective prediction of noise are important
tasks for the mixer design and optimization. However, mixer noise problems
are complicated due to frequency translations in mixing process, time
variance of elements and cyclostationary noise sources originating from
periodic operating point change, and high frequency effects in the presence
of capacitors.
General simulation methodologies for mixer noise evaluation have been
devised in last ten years. Although the the simulation methodologies
are accurate in general, they are very time consuming as they require
multiple simulation runs to numerically calculate the noise for a given
topology of mixers. In addition, only relying on simulators hardly provides
design insight into noise generation mechanism during the circuit operation
and effective design optimization can hardly be achieved.
In this work, we rigorously analyze the cyclostationary noise in the
presence of an IF capacitor in commonly used switching mixers to achieve
further design insight into them. Our analysis is based on a combination
of analytical and numerical approaches. A state equation describing
the mixer dynamics is first obtained, from which a deterministic differential
equation for RF-IF signals and an SDE for noise are found. The deterministic
and stochastic differential equations are used to evaluate the conversion
gain and the noise power spectral density (PSD) at the IF port of the
mixer, respectively. A careful study of the state equation reveals the
existence of three different noise generation regimes and provides criteria
to distinguish each one.
Numerical analysis yields a periodic PSD in time-domain. The dynamics
of mixer noise generation is better understood with the help of the
time-varying PSD, which facilitates a comparison between stationary
and cyclostationary noise calculations. The numerical analysis agrees
with the analytical study in terms of design insights. The dependence
of the PSD on the IF capacitance and switching modes provides further
insight to mixer design by identifying an optimum IF capacitance and
an optimum operation mode of the mixer for minimum noise figure and
maximum conversion gain.
The thorough experimental verification of the theory has been done.
The complete account of theory and experiment is to be submitted for
publication.
