In this research treatise, a novel Calculus Based Unipolar Double Reference Single Carrier PWM (CB-UDR-SC PWM) is proposed for single phase T-Multilevel Inverter (T-MLI) for renewable energy applications. The main downsides of conventional two-level inverters are i) dv/dt of output voltage is high, ii) requirement of fast switching devices, iii) requirement of bulky filter, iv) Electromagnetic Interference is high, iv) temperature of switches is increases with high speed, v) not suitable for high power application and vi) high THD. Single switch with four diodes are used to design the auxiliary structure of T-MLI structure. Total 8 diodes (including anti-parallel diode of switch), five switches are used to design T-MLI for five-level. CB-UDR-SC PWM methodology is proposed by utilizing two modulation signals (derived from calculus) and single carrier. The technique is employed to investigate T-MLI circuitry is for the under-modulation index. The general idea of calculus based PWM is explained in detailed. SPARTAN 3E-XCS250E FPGA trainer kit is utilized to obtain PWM for the switches of T-MLI. Experimental and simulation results are provided which validates the concept and always shows a good agreement with theoretical approaches.