Transmission-Line Low-Pass Filter

Short sections of alternating high and low impedance approximate a series-inductor, shunt-capacitor low-pass network.

Circuit operation

T1 and T3 are short 200 Ω sections, predominantly inductive. T2 is a 12.5 Ω section, predominantly capacitive. The 50 Ω source and load terminate this three-section distributed filter.

Expected behavior

$$L_{eq}\approx Z_{high}T_D$$ $$C_{eq}\approx T_D/Z_{low}$$

The first-order equivalents are two 318 nH series inductors and a 255 pF shunt capacitor, targeting a 25 MHz Butterworth corner. Finite section lengths shift the actual corner. The low-frequency load approaches 1 V for a 2 V source. Attenuation increases above the first corner, but distributed filters have higher-frequency passbands: inspect the full sweep rather than assuming indefinite lumped-filter rolloff.

Reading the results

The first voltage probe is green and the second is red. Current probes start with blue. The schematic opens fitted to its extents. The logarithmic Bode chart shows voltage magnitude in dBV and phase in degrees. The saved AC sweep spans 1–200 MHz with 150 points per decade. Deep notches may fall between frequency samples; increase sweep density to locate a minimum precisely.

Try a change

Double all three delays; the entire frequency response shifts down by a factor of two. Restore the saved values after comparison.

Model limits

Each line is ideal and lossless: Z0 and TD are independent of frequency. Conductor and dielectric loss, dispersion, radiation, connectors, and breakdown are omitted. Line length is represented by propagation delay; the drawing is not a physical length scale. These examples describe differential line voltage relative to the shared return conductor.

References: Single-stub matching, distributed filter principles.