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We investigate all-optical format conversions by using cascaded second-order nonlinearities in periodically poled lithium niobate (PPLN) waveguides. Analytical solutions under non-depletion approximation with clear physical insights are derived, showing operation principles of various PPLN-based format conversions. We propose and theoretically demonstrate all-optical 40 Gb/s nonreturn-to-zero (NRZ) to carrier-suppressed return-to-zero (CSRZ), nonreturn-to-zero differential phase-shift keying (NRZ-DPSK) to return-to-zero differential phase-shift keying (RZ-DPSK), and NRZ-DPSK to carrier-suppressed return-to-zero differential phase-shift keying (CSRZ-DPSK) format conversions based on cascaded sum- and difference-frequency generation (cSFG/DFG). Tunable all-optical 20 Gb/s NRZ to return-to-zero (RZ) format conversion based on cascaded second-harmonic generation and difference-frequency generation (cSHG/DFG) is successfully confirmed in the experiment by setting NRZ signal at SHG quasi-phase matching (QPM) wavelength. Moreover, we experimentally report for the first time, PPLN-based all-optical 40 Gb/s NRZ-to-CSRZ, NRZ-to-RZ, and NRZ-DPSK-to-RZ-DPSK format conversions.