Bode & Nyquist Analyzer for RC, RL and RLC Filters

Design and analyze first- and second-order passive RC, RL and RLC filters. Set the target frequency and, for second order, the Q factor: the tool derives component values, selects preferred values and generates Bode and Nyquist plots from the same complex transfer function \(H(j\omega)\).

Filter configuration and design

Configuration

Design from specifications

Target frequency f_c [Hz]

Fixed component

Its value is read from the R, L or C fields below.

Preferred values for calculated components

The tool searches nearby combinations to reduce frequency and Q error.

Component values

Resistance R

Capacitance C

Use the tool either to design from frequency/Q or to enter an existing set of R, L and C values directly.

Ideal values

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Implemented values

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Achieved frequency

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Transfer function

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Frequency range and analysis

Automatic range

Two decades below to two decades above the characteristic frequency.

Start frequency [Hz]

Stop frequency [Hz]

Points per decade

Magnitude plot floor [dB]

Especially useful for the ideal notch, where magnitude reaches −∞ dB.

Frequency marker [Hz]

The marker can be moved without changing the filter.

Characteristic parameters

Order

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Characteristic frequency

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Time constant / Q

—

Damping ζ

—

Bandwidth / −3 dB points

—

Gain at f₀ / f_c

—

Numeric marker

Frequency

—

|H|

—

Magnitude [dB]

—

Phase

—

Re{H}

—

Im{H}

—

Bode plot

Magnitude

Phase

Logarithmic frequency scale. The vertical line marks the numeric marker frequency.

Nyquist plot

The orange branch follows positive frequencies in increasing order; the dashed branch shows negative-frequency symmetry. This is the locus of \(H(j\omega)\); the Nyquist stability criterion applies only when the analyzed transfer function is a loop gain.

Characteristic points

Point	Frequency	\|H\|	Magnitude [dB]	Phase	Re{H}	Im{H}

Equations

The calculation uses \(\omega=2\pi f\) and directly evaluates \(H(j\omega)\).

\[G_{dB}(f)=20\log_{10}|H(j\omega)|\]

\[\varphi(f)=\arg\{H(j\omega)\}\]

For second-order series RLC networks:

\[D(s)=LCs^2+RCs+1\]

\[f_0=\frac{1}{2\pi\sqrt{LC}},\qquad Q=\frac{1}{R}\sqrt{\frac{L}{C}},\qquad \zeta=\frac{1}{2Q}\]

The design section applies the same relations in reverse. For example, with C fixed:

\[L=\frac{1}{\omega_0^2C},\qquad R=\frac{1}{\omega_0CQ}\]

For band-pass and notch:

\[BW=f_2-f_1=\frac{R}{2\pi L}=\frac{f_0}{Q}\]

Model assumptions and limits

Components are ideal: capacitor ESR/ESL, inductor series resistance and parasitic capacitance, source resistance, load impedance and frequency dependence are not included. The design result is therefore a starting point; for hardware comparison use measured R, L and C values and include source, load and parasitics when they are significant.