What circuit checks are included?

The template includes nodal voltage solving, branch currents with a KCL consistency check, and RC low-pass magnitude and phase calculations.

Can I use this for different component values?

Yes. Update resistor, capacitor, and source values. The transfer function and derived frequency metrics update automatically.

Electrical Engineering Template

Problem statement and knowns/unknowns

The first half solves a nodal network and checks Kirchhoff current balance. The second half builds a first-order low-pass transfer function and plots frequency response metrics.

Solve node voltage and branch currents from resistor values and source voltage.
Compute and validate KCL residual (`kcl_error`).
Calculate corner frequency and inspect gain/phase trends.

Recommended workflow

Start with the nodal rows and ensure `kcl_error` is near zero. Then replace `R` and `C` for your filter stage and inspect `fc`, `HdB`, and `phase` behavior over your frequency band.

Assumptions, validity limits, and unit discipline

Nodal rows assume a linear resistive DC network with consistent current direction sign conventions.
The RC transfer function is a first-order small-signal model; parasitics and loading from following stages are not included by default.
Keep units consistent: `R` in ohms, `C` in farads, `f` in Hz, and use `w=2*pi*f` when comparing rad/s formulas.

Derivation and governing equations

H(s) = 1 / (1 + sRC)
fc = 1 / (2*pi*R*C)
|H(jw)| = 1 / sqrt(1 + (wRC)^2)

FAQ

Can this be extended to active filters?

Yes. Use the same structure and replace the transfer function with your active stage equation.

Does this support symbolic manipulation?

Yes. Keep rows symbolic as long as possible and evaluate numerically only when needed.

Worked example (interpreted)

Step 1: The nodal solve gives Vn=3.103 V and branch currents I1=4.044 mA, I2=3.103 mA, I3=0.940 mA.

Step 2: kcl_error evaluates to approximately zero, confirming current conservation with the chosen sign convention.

Step 3: The unloaded corner is fc=723.43 Hz, with about -0.043 dB at 0.1fc and -20.04 dB at 10fc.

Interpretation: this is the expected first-order low-pass shape; use the loaded variant rows before trusting bandwidth in cascaded stages.

When this model is invalid

Condition	Why invalid	Use instead
Output stage loading is non-negligible	Unloaded transfer function overestimates bandwidth.	Use `Rload`, `Req_loaded`, `fc_loaded` rows.
High-frequency parasitics dominate	Single-pole RC model omits ESR/ESL and layout effects.	Use measured/identified higher-order transfer model.
Large-signal nonlinear operation	Linear small-signal assumptions break near clipping/saturation.	Piecewise or nonlinear circuit simulation.

How to validate your worksheet

kcl_error_mag should be near zero.
gain_low_dB should stay near 0 dB and gain_high_dB near -20 dB/dec trend.
loaded_fc_ratio far from 1 indicates you must use loaded design equations.

Domain-specific variants in this template

The loaded RC branch models finite output loading so cutoff shift is explicit, not hidden in assumptions.

Practice problems (with answer outlines)

Practice 1

Change resistor network values and verify kcl_error remains near zero.

Outline: Solve Vn, compute branch currents, then evaluate KCL residual magnitude.

Practice 2

Assess how a smaller Rload changes cutoff frequency.

Outline: Use parallel equivalent resistance and compare loaded/unloaded cutoff ratio.

References and standards

Sedra/Smith, Microelectronic Circuits (small-signal circuit fundamentals). Publisher page.
IEEE Std 181-2011 (pulse and transition terminology for waveform interpretation). IEEE standard.
Horowitz & Hill, The Art of Electronics (practical RC/filter behavior). Reference site.