Impedance Matching (L-Section)

A series inductor and shunt capacitor transform a 200 Ω load into a 50 Ω input at one frequency.

Circuit operation

The 50 Ω line feeds a series 13.7832 µH inductor and a shunt 1.37832 nF capacitor across RL = 200 Ω. These values provide a resistive 50 Ω input at 1 MHz.

Expected behavior

$$Q=\sqrt{R_L/R_s-1}=\sqrt3$$ $$\begin{gathered}X_L=Q R_s\\|X_C|=R_L/Q\end{gathered}$$

At the design frequency, sending-end voltage is about 1 V peak and load voltage about 2 V peak. The voltage increase preserves power: 1²/50 = 2²/200. Reactive currents circulate internally; this is not power gain. The match is frequency dependent.

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 transient runs for 10 µs with a maximum step of 5 ns. Compare sending and receiving waveforms with time-axis cursors. The table uses the same probe order.

Try a change

Set V1 to 2 MHz; the L section no longer presents a purely resistive 50 Ω input and output amplitude falls. 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.