Low-Pass Filter (RL)

Take the output across a resistor in a series RL circuit to form a low-pass filter.

Schematic and stimulus

V1 on the left supplies an AC analysis magnitude of 1 V and phase of 0°. L1 (10 mH) is in series along the top; R1 (100 Ω) returns the output to ground.

Vin is green, Vout is red and Iin is blue. Current is positive from the source into the network.

Expected response

With $s=j2\pi f$ and $H=V_{\mathrm{out}}/V_{\mathrm{in}}$:

$$H(s)=\frac{R}{R+sL}$$

The output is taken across R1. At cutoff, its magnitude is $1/\sqrt{2}$ of the input: 0.7071 V, or −3.0103 dB, with −45° phase. Low-frequency magnitude approaches 0 dB and rolls off at about −20 dB per decade above cutoff.

$$f_c=\frac{R}{2\pi L}=1591.5\,\mathrm{Hz}$$

Read the Bode chart

The saved AC sweep runs from 100 Hz to 10 kHz, with 100 points per decade. Voltage magnitude and phase are shown separately. Current is hidden from the default chart to keep the voltage-gain scale readable; enable Iin in the chart series controls and expand the magnitude-axis range to plot it. Open Table for all 201 frequency samples and the same probe order. Because the input is 1 V, output voltage in dBV has the same numeric value as voltage gain in dB. Current magnitude is in dBA referenced to 1 A, so it is not a voltage gain.

$$G_{\mathrm{dB}}=20\log_{10}|H|,\qquad \phi=\arg(H)$$

AC sweep computes a sinusoidal steady state at every frequency; it does not show startup. AC analysis magnitude and AC analysis phase control this sweep. The source's Frequency and Peak voltage properties apply to transient simulation instead.

Try two changes

1. Change L1 → Inductance from 10m to 20m. Run again: cutoff halves to 795.77 Hz. Restore 10m.
2. Change R1 → Resistance from 100 to 200. Run again: cutoff doubles to 3.1831 kHz. Restore 100.

Click Run simulation after each change. Keep V1's AC analysis magnitude at 1 and phase at 0, then restore all component values above to return to the saved response.

Model limits

The source, resistor, capacitor and inductor models are ideal. Probes draw no current. Source impedance, component tolerance, parasitic resistance/capacitance and external loading are omitted; these can shift cutoff and reduce rejection.