One-dimensional ternary photonic crystals with dielectric and piezoelectric layers offer intriguing properties and potential applications in the terahertz (THz) region. In the first plan, a piezoelectric layer is placed between two different dielectric layers, resulting in a structure with a controllable band gap through the application of an external electric field. In the second plan, a ternary photonic crystal is proposed, consisting of dielectric layers and a piezoelectric defect layer. This structure introduces a narrow bandpass region that can be finely adjusted using both the external electric field and the incident angle. The bandpass region is characterized by a Gaussian shape, centered around a frequency of approximately 50 THz, with a full width at half maximum (FWHM) of around 50 GHz. The proposed photonic crystal exhibits versatile tunability as a narrow bandpass filter in the THz range. The utilization of an external electric field facilitates the development of optical crystal applications, making it easier to manipulate and control the properties of the photonic crystal.