An extended transmission-line model is presented for an inset-fed rectangular microstrip patch antenna. The transmission-line model agrees to the cos4 impedance variation for inset-fed microstrip antennas with an addition of a corrective extended feed length upto the inner radiating edge. Verification of the model's complex reflection coefficient is concluded with good agreements with measured results. Further extension of the transmission-line model with for or more thin shorting post connected to multiple varactor diodes have been conducted. Fourty two test cases across five independent antenna designs have been worked upon. Results obtained using the transmission-line model are compared with those obtained with a 3D full-wave solver and measurements. In 69% of the test cases, the transmission-line models have less than 3% deviation to the measured or simulated results. 41% of them have less than 1% deviation. For the first two antennas, both simulated and measured results were compared with the transmission-line model. For the rest of three, results from the transmission-line model were compared to the simulated ones.