The search for a cost feasible, optimal design of LLC converter for wide input voltage range conditions is inhibited by errors in steady state values of peak gain, tank current, tank voltage, active power etc., due to various approximations in the analysis. This leads to erroneous selection of circuit parameters. The present work provides an exact, approximation free time domain mathematical model of LLC converter operating in transformer secondary current discontinuous mode (DCM) below resonance in boost mode. The proposed approach defines voltage gain as a function of relative switching frequency $\omega$ and td, which represents the rectifier diode to switch conduction ratio for DCM operation. Existing works have defined voltage gain as an explicit function of quality factor (Q) and $\omega$. The current approach leads to accurate derivation of converter voltage gain, tank RMS current, tank capacitor voltage, zero voltage switching (ZVS) angle etc. Analytical expressions are validated with simulation studies using PSIM for various inductor ratio values. A final design is verified on an experimental prototype of 320W output LLC converter designed for an input range of 20–40V for solar PV applications.