Aiming to realize series-fed antenna array with good return loss, low sidelobe level (SLL), and small gain variation over a wide bandwidth, this paper presents a unified synthesis method of designing series-fed networks (SFNs) under the equal/unequal distributions with the bandwidth enhancement. We find the return loss and current distribution bandwidths of SFN are dominated by its input reactance slope. The ratio of SFN main line impedance Z₀ and antenna impedance Z_L plays an important role in it. When the optimal Z₀/Z_L makes the input reactance slope equal to zero at the center frequency, the bandwidth of SFN can be highly extended by 2~4 times compared with non-optimal solutions. In this context, four classical types of SFNs are investigated and synthesized. The closed-form optimal formulas for these SFNs are further deduced under the specified element number N and current distributions I₁, I₂, …, and I_N. For experimental verification, an eight-element series-fed antenna array driven by the SFN with Dolph-Chebyshev current distribution is designed and fabricated based on proposed design method. By virtue of the improved SFN, the designed series-fed array exhibits enhanced impedance and radiation bandwidths as predicted. The measured results show designed array achieves impedance bandwidth of 52.2% (3.34-5.70 GHz) with S11 ≤ -10 dB and the radiation bandwidth with SLL ≤ -20 dB is 20.9% (3.85-4.75 GHz). The measured antenna gain is 11.3 dBi with a small variation of 1.3 dB and the efficiency of array is better than 82% over the operational bandwidth of 18.7% (3.88-4.68 GHz).