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The phase shifters based on the synchronization of an oscillator to the input signal enable low consumption, low cost, and small size. However, the difficulties for an accurate design, associated to the complexity of the operation regime, limit their application to communication systems. Here, a technique is presented for the nonlinear synthesis of oscillator-based phase shifters. The technique provides the circuit-element values for a specified phase shift. The tuning voltage required to maintain a constant phase-shift value along a certain frequency band is also determined. Using these techniques, an injection-locked voltage-controlled oscillator, covering the 1.17-1.3GHz band has been designed and manufactured. The validity of the design is verified through nonlinear simulations and measurements. These include the phase-noise variation along the phase-shift interval and the circuit response versus modulated inputs. Good agreement has been obtained between measurements and simulations.