This paper proposes two fully passive techniques to reduce the supply sensitivity of an LC oscillator. An RC low-pass filter is employed to reduce the supply sensitivity of coarse-tuning switched capacitors stemming from code-dependent parasitic capacitance. To cancel the remaining supply sensitivity, the supply variations are scaled and coupled to polarity-switchable varactor pairs, which are introduced in the resonator to provide a frequency tuning gain that is reverse to the supply sensitivity. A programmable capacitive divider is used to scale the supply variations by a proper ratio. The proposed techniques are applied in a $5.83-6.99 \text{GHz}$ class-B LC oscillator. Prototyped in $65-\text{nm}$ CMOS, the oscillator occupies $0.24 ~\text{mm}^{2}$ and consumes 6.8 mW from 1 V. With supply perturbations in the $0.1-50 \text{MHz}$ frequency range, the measured reduction of the supply sensitivity is $20-46.2$ dB, which is the highest reported over a wide frequency range. Benefiting from the fully passive implementation, the proposed techniques do not consume extra power or degrade the phase noise.