The magnetically-insulated induction voltage adder (MIVA) is a pulsed-power accelerator widely used in the X-ray flash radiography and -ray radiation simulation. The operating impedance of magnetically-insulated transmission line (MITL) on the secondary side of MIVA will produce significant influence on the power coupling between the pulsed-power driving source and the terminal load. Therefore, optimizing the secondary impedance of MIVA to maximize the electrical-power or radiated output of load is critical for the design of MIVA facility. According to whether the MITL operating impedance is smaller than the load impedance, MIVAs can be divided into two different types, i.e., the impedance-matched case and impedance undermatched case. For the impedance-matched MIVA, because the MITL of MIVA operates at the minimal current point or self-limited flow, the output of MIVA just depends on the MITL operating impedance and is independent of load. Correspondingly, the circuit analysis is relatively easy. However, for MIVA with impedance undermatched load, the analysis method is more complicated. Based on the classical Creedon theory of the magnetic insulation equilibrium and the sheath electron re-trapping theory, a circuit method is established for MIVA with impedance under-matched load. The analysis process consists of two steps. Firstly, the working point of the forward magnetic insulation wave is solved by the minimal current theory on the assumption that the MIVA is terminated by impedance-matched load. Then, the actual operating point after the re-trapping wave has passed is solved, in which the characteristic impedance of the re-trapping wave is treated as a vacuum impedance. And the relationship between the output parameters of MIVA, e.g., the output voltage, the cathode and anode current, and the electrical power, and the undermatched extent of load is obtained numerically. Based on the analysis method, a method to optimize the secondary impedance of MIVA with ten-stage cavities stacked in series to drive X-ray radiographic diodes is developed. This optimization method aims at maximizing the radiated X-ray dose rate of the diode loads on the assumption that only the cathode current is available for the X-ray radiographic diode. The optimization secondary impedance, Zop*, varying with the scaling factor, , is achieved, where is the power exponent between the dose rate and the diode voltage (Ḋ Ud). is usually determined by the diode type, geometrical structure, and operating characteristics. It is found that the optimization secondary impedance Zop* decays exponentially with the increase of value , i.e., the increase of the diode-voltage-dependent degree of the radiated X-ray dose rate. And the larger the load impedance, the larger the value of Zop* is. The circuit analysis method and the impedance optimization method developed in this paper are specially useful for the applications of MIVA in the flash radiographic fields.