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Equivalent network representation is derived for thickness vibration modes in piezoelectric plates with a linearly graded parameter. The network is composed of a transmission line of a finite length, which is linked to the electric excitation port via ideal transformers connected serially at both ends. The ratios of the two transformers are different from each other and frequency dependent. Two frequency-dependent capacitors of the same value but opposite sign appear at the electric port. The frequency characteristic of the input electric admittance of the resonator, which shows the unique feature of the graded piezoelectric plate, is demonstrated by the equivalent network analysis.