This paper proposes an active-RC filter that achieves a wide pseudo-continuous bandwidth-tuning range and a wide gain range with fine steps using a novel switched resistor architecture. A channel-selection filter with the proposed resistor bank is designed for a multi-mode mobile-TV receiver with the 6th order Chebyshev-I topology. The bandwidth, 0.5-6MHz with 5% steps, supports multiple mobile-TV standards with sufficient margins for process and temperature variations. The filter also accomplishes a 30-dB variable gain range with 6-dB steps, and it relaxes the dynamic range requirement of a succeeding programmable gain amplifier. The power consumption of the filter, 3.4-5.0mW, is adjustable according to the bandwidth and the signal level. The filter was fabricated with on-chip bandwidth-calibration circuitry in 0.18-µm CMOS and occupied 0.81mm².