It is commonly practiced in millimeter-wave and terahertz cascode amplifiers to enhance the power gain by shorting the base-impedance in the common-base transistor. However, it is found that the merit of high output power is not achieved simultaneously under the zero base-impedance scenarios. This paper theoretically analyzes the optimum designs by varying the base-impedances for power gain and output power level enhancement. In addition, numerically results are given to prove that non-zero base-impedances are key parameters towards gain and output power enhancements. Thus, each stages of the power amplifier must contain different and optimized base-impedances, based on their power gain and output power targets. To validate the design theory, a 220 GHz power amplifier is designed and fabricated in a 0.13- $\mu \text{m}$ SiGe technology. The measurement reveals that the amplifier achieves operation bandwidth of 185 to 240 GHz, power gain of 25 dB, and output $P_{\mathrm {1dB}}/P_{\mathrm {SAT}}$ of 7.3/9.5 dBm. It consumes 310~324 mW dc power and occupies a core area of 0.09 mm2.