Frequency dividers are essential building blocks in wireless and wireline communications as well as radar systems for functions such as frequency synthesis, quadrature signal generation, MUX/DEMUX, and bandwidth compression. An injection-locked frequency divider (ILFD) enjoys lower power dissipation and better noise performance than common digital dividers. However, their application is hindered by the limited locking range and division ratios. This paper addresses the latter problem.A differential-LC oscillator has become a popular choice for ILFDs [1]. Such a differential-LC ILFD can be viewed as a special type of regenerative divider with a single-balanced mixer [2,3]. Frequency division happens when the second-harmonic current is injected into the tail node and switched by the nonlinear differential pair to generate the mixing products. Then all harmonics except the fundamental frequency component are filtered out by the LC tank. Because the mixing function of the cross-coupled differential pair has odd symmetry, it only generates oddorder mixing products, which correspond to even frequency-division ratios (2, 4, 6 ...). In order to support divide-by-(2n + 1) operation, it is necessary to change the topology of the built-in mixer. A straight-forward way is to use a single transistor, e.g., injection locking a Colpitts oscillator [1]. Due to the current-switching nature of MOSFET transistors, however, doing so results in small lock range. Using a single transistor also loses all the benefits of differential circuits. Injection-locked ring oscillators can also be used for divide-by-3 operation [4]. However, they do not provide filtering like a resonant oscillator, and hence tend to have large unwanted harmonic components, particularly at the injected signal frequency. They are also prone to lock at the wrong harmonics and their phase-noise performance is inferior to resonant ILFDs.To address these problems and preferably maintain the differential LC oscillator topology, we construct a cascode differential LC ILFD by adding another differential pair: M 3 and M 4 (Fig. 32.9.1). M 3 and M 4 convert the differential injection signal into a differential current, which mixes with the differential output voltage signal by M 1 and M 2 . Since M 1 and M 2 are no longer a differential pair, their even-order nonlinearity can generate the desired mixing product, which corresponds to an odd division ratio. A shunt-peaking inductor L 0 is also introduced to resonate with the parasitic capacitances at the 3rd harmonic [2]. It also provides a short-circuit current path for the fundamental component. Therefore, the upper half of the circuit (M 1 , M 2 , L 0 and the LC tank) works as a differential LC oscillator at the fundamental frequency, and the lower half (M 3 , M 4 , and L 0 ) as a tuned differential amplifier. So the differential topology is preserved, although mixing is accomplished in a single-ended fashion. Overall, we confine signals at different harmonics locally by circuit topology and filtering. A balun T 1 is us...