This research focuses on the load characteristics of piezoelectric transducers in the process of longitudinal vibration ultrasonic welding. We are primarily interested in the impedance characteristics of the piezoelectric transducer during loading, which is studied by leveraging the equivalent circuit theory of piezoelectric transducers. Specifically, we propose a cross-value mapping method. This method can well map the load change in ultrasonic welding to the impedance change, aiming to obtain an equivalent model of impedance and load. The least-squares strategy is used for parameter identification during data fitting. Extensive simulations and physical experiments are conducted to verify the proposed model. As a result, we can empirically find that the result from our model agrees with the impedance characteristics from the real-life data measured by the impedance meter, indicating its potential for real practice in controller research and transducer design.