All-polymer, semi-transparent, three-layer-dielectric (3L) organic field effect transistors (OFETs) are fabricated on polyethylene terephthalate plastic substrate, using high-throughput printing techniques. Analog small-signal characteristics of the 3L OFET are presented and are compared against the previous version of this technology, which was based on a single-layer dielectric and a metal gate electrode. The 3L transistor withstands 50 V, can continuously drive 50 μA/mm, reaches an excellent intrinsic-gain (Av0) of 43 dB, an equivalent mobility of 0.85 cm2/V, and a transit frequency (fT) of 68 kHz, well suited for applications such as driving printed piezoelectric loudspeakers and flexible audio systems. The effects of the relaxor-ferroelectric high-k layer in the 3L stack on the gate capacitance, gm, and Av0 are measured in the frequency domain. In addition, it is observed that PEDOT:PSS makes a better interface with polymer dielectric comparing to copper particle ink. Five-hour small- and large-signal bias stress tests are performed. A novel direct Av0 measurement technique, and an improved transconductance extraction method are also presented.