Superharmonic injection locked oscillators as low power frequency dividers

Abstract

I. AbstractSuperharmonic injection locking is investigated in a new theoretical approach. Low p o w er frequency dividers are designed using injection locked oscillators with cascode transistors. The Rockwell 0:5m CMOS process is used to design a 3mW injection locked frequency divider in the 1800M H z frequency range. A 200M H z maximum locking range is achieved in simulations. 2SC3302 TOSHIBA NPN transistors are also used to build a 1:75mW injection locked frequency divider in the 800M H z frequency range to verify the theory. II. IntroductionForced oscillations in nonlinear oscillators were rst analyzed by van der Pol [3] in a purely theoretical investigation. Adler [1] took an engineering approach and introduced the locking range gure of merit for an oscillator locked to the fundamental frequency of an incident signal. Others ([2],[4]) followed Adler's work and showed how a n oscillator can be locked to a harmonic of an incident signal in what is conventionally called subharmonic locking.In this work we show how an oscillator can be locked to an incident signal whose fundamental frequency equals a harmonic of the oscillator frequency in superharmonic locking, so that the oscillation frequency is an integer fraction of the fundamental frequency of the incident signal. We present a new method to calculate the locking range of an injection locked oscillator both for sub-and superharmonic locking. We also present a n o v el oscillator which is locked to half of the incident signal frequency. III. Injection LockingAn LC oscillator can be modeled as a non-linear system f(x), followed by a frequency selective system (e.g., RLC tank), H(!), in a positive feedback loop. The nonlinear system includes all nonlinear elements plus any nonlinear amplitude limiting mechanism. The same model can be used for an injection locked oscillator with an external input (i.e., incident signal) as shown in g. 1. To i n v estigate the locking phenomenon in an injection locked oscillator, dene the input, output, intermediate signal, and H(!) as:where, i (t) is the incident signal, o (t) is the output signal, is the phase dierence between the two signals, ! r and Q are the resonant frequency and quality factor of the RLC tank respectively. The output of the nonlinear element, u(t), may h a v e all the harmonics and intermodulation terms of i (t) and o (t), and can be written as: (5) is an intermodulation coecient dened as:whereWe assume that all components of u(t) far from the resonant frequency of the tank are ltered out and the output

A 5 GHz, 1 mW CMOS voltage controlled differential injection locked frequency divider

“…As expected, changing the control voltage only changes the operation frequencies and not the locking range. It is important to observe that, unlike the single-ended ILFD reported in [3], the locking range in a DILFD is phase limited and monotonically increases with incident amplitudes even as large as 810mV. This difference can be attributed to the fact that the voltage gain of M3 in Fig.…”

“…When the incident frequency ILS a harmonic of the oscillation frequency (superharmonic injection locking), frequency division is performed [3]. The oscillation conditions of unity loop gain and zero excess phase should be satisfied in an injection locked frequency divider.…”

“…The oscillation conditions of unity loop gain and zero excess phase should be satisfied in an injection locked frequency divider. The frequency of operation (locking range) of an ILFD can be limited by failure of either the phase or gain condition [3]. Fig.…”

“…The authors are with the Center for Integrated Systems, Stanford University, Stanford, CA 94305. where wr is the free-running oscillation frequency, Aw is the freqJency offset from w,, V, is the incident amplitude, HO is the impedance of the LC tank at resonance, Q is the quality factor of the LC tank, and a 2 is the second-order coefficient of the nonlinearity in f(x) [3]. As (1) suggests, a larger results in a larger locking range for a given incident amplitude.…”

“…Due to the frequency limitations of CMOS technologies, or to reduce power consumption, off-chip frequency dividers are often usqd [l]. Since most wireless systems operate in a narrow frequency band, injection locked frequency dividers (ILFDs) [3], which are narrowbatnd in nature, can be used to trade off bandwidth for power and maximum frequency of operation. Thus higher integration and lower power operation can be achieved.…”