A Programmable Frequency Multiplier-by-29 Architecture for Millimeter Wave Applications

Simulation Method for Complex Multivalued Curves in Injection-Locked Oscillators

“…A multiharmonic input source (input pulse) will relax the frequencymultiplication requirements of the device nonlinearities. It is also possible to drive the circuit with a sinusoidal lowfrequency source and use a pulse-forming network to drive the oscillator circuit, such as the one in [5]- [6]. Here the pulseforming network will be implemented with a nonlinear transmission line (NLTL) [7]- [11].…”

“…A comparison of state-of-the-art phase-locked loops [5]- [6] indicates that a lower voltage-controlled oscillator (VCO), followed by a frequency multiplier, enables lower phase noise than a high frequency VCO. Since efficient multipliers are limited to low multiplication factors, the authors of [5]- [6] propose the use of high-order subharmonic injection locking of an oscillator at the desired carrier frequency. The high-order subharmonic synchronization is achieved by introducing the low-frequency sinusoidal input signal into a pulse-shaping circuit [5]- [6], based on a comparator and a delay element.…”

“…Since efficient multipliers are limited to low multiplication factors, the authors of [5]- [6] propose the use of high-order subharmonic injection locking of an oscillator at the desired carrier frequency. The high-order subharmonic synchronization is achieved by introducing the low-frequency sinusoidal input signal into a pulse-shaping circuit [5]- [6], based on a comparator and a delay element. This provides a square pulse that switches the high frequency oscillator on and off.…”

“…In [7], a similar approach is presented, using a nonlinear-transmission line (NLTL) for the pulse forming [8]- [11]. As in the case of [5]- [6], the intended application of this sub-synchronized operation is its use in low phase-noise local oscillators.…”

“…Due to the difficulties in the analysis of the high-order subharmonic injection-locked regime, approximate oscillator models are used in [5]- [6], [12]- [14], whereas the simulations in [7], [15] rely on the Poincaré-map technique [16]- [18]. This map is applied to the sequence of steady-state solutions obtained through time-domain integration of the differential algebraic equation system when varying a particular analysis parameter, such as the input power or frequency.…”