Electronic Circuits Formula Sheet

This formula sheet collects common first-pass relationships for electronic devices and analog circuits. It is useful for hand checks, design reviews, simulation sanity checks, and test planning. Detailed electronic design still requires datasheet limits, layout review, tolerances, thermal analysis, EMC review, manufacturing constraints, and fault testing.

State whether values are DC, RMS, peak, peak-to-peak, small-signal, large-signal, nominal, worst-case, or measured.

Ohm’s law and power

Ohm’s law:

Power:

Equivalent forms:

Energy over time:

Always check resistor voltage rating, power rating, temperature rise, tolerance, and pulse-energy rating.

Kirchhoff laws

Kirchhoff current law at a node:

Kirchhoff voltage law around a loop:

These laws are the basis of nodal analysis, mesh analysis, bias calculation, and circuit simulation. In high-speed circuits, parasitic inductance, capacitance, and transmission-line effects must be included in the model.

Voltage divider

For two resistors in series:

The Thevenin resistance seen from the divider output is:

If a load R_L is attached, replace R_2 with:

A voltage divider is not a voltage regulator unless load current is small and well controlled.

Impedance

Resistor:

Capacitor:

Inductor:

Angular frequency:

Admittance:

Use impedance for AC and transient checks. Component parasitics can dominate at high frequency.

RC and RL time constants

RC time constant:

Capacitor charging:

RL time constant:

Inductor current change:

After about five time constants, a first-order system is usually near final value for many practical checks.

Low-pass filter

First-order RC low-pass cutoff:

Magnitude response:

For a first-order filter, the roll-off beyond cutoff is approximately:

Filter checks should include source impedance, load impedance, tolerance, phase shift, noise, and required attenuation.

Op-amp gains

Ideal inverting amplifier:

Ideal non-inverting amplifier:

Voltage follower:

Open-loop relation:

Real designs must check input common-mode range, output swing, offset, bias current, noise, slew rate, gain-bandwidth product, capacitive-load stability, and output current.

Op-amp bandwidth and slew rate

Approximate closed-loop bandwidth for a single-pole op-amp:

Sine-wave slew-rate requirement:

If slew-rate limit is exceeded, the waveform distorts even when small-signal bandwidth appears sufficient.

Diode checks

Shockley diode equation:

Thermal voltage:

At room temperature, V_T is approximately:

First-pass silicon diode forward drop is often approximated near:

This approximation is current- and temperature-dependent. Check reverse voltage, leakage, surge current, recovery time, capacitance, and power dissipation.

Zener and clamp power

Zener or clamp power:

Series resistor for a simple shunt reference:

Worst-case power should be checked at maximum input voltage and minimum load current.

Clamp circuits also need pulse-energy and thermal checks. A device that survives DC power may fail under surge energy.

Signal-to-noise ratio

Power SNR:

Decibels:

For equal-impedance voltage ratios:

Thermal noise voltage of a resistor over bandwidth B:

Noise depends on bandwidth, source impedance, temperature, device noise, layout, shielding, and measurement point.

ADC range and quantization

Ideal ADC step size:

Ideal quantization noise RMS:

Ideal full-scale sine-wave ADC SNR:

Use these equations only as ideal checks. Real ADCs include offset, gain error, differential nonlinearity, integral nonlinearity, jitter, reference noise, input bandwidth, and distortion.

Switching converter screening

Inductor voltage relation:

Capacitor current relation:

Switch conduction loss:

First-pass switching loss:

Flyback stored energy per cycle:

Power transferred in discontinuous conduction mode:

Switching converters need worst-case input, load, temperature, startup, transient, short-circuit, insulation, and EMI checks.

Junction temperature

Steady junction temperature estimate:

With case temperature known:

Power derating margin:

Thermal resistance depends on board layout, copper area, airflow, vias, enclosure, neighboring components, and transient duration.

H-bridge and inverter checks

Motor or load power:

Bridge device conduction loss, approximate:

where n is the number of conducting devices in the current path.

Dead-time and shoot-through must be controlled. Inductive loads require freewheel paths, clamp ratings, current sensing, and transient protection.

Error and tolerance budget

Worst-case sum:

Root-sum-square estimate for independent errors:

Relative error:

Use worst-case analysis for guaranteed limits and RSS only when independence and distribution assumptions are justified.

Practical checklist

Use these formulas with a short electronic design checklist:

1. Define supply range, signal range, bandwidth, load, temperature, and fault cases.
2. Check DC bias, AC response, noise, tolerance, and loading.
3. Check op-amp limits, diode stress, switch stress, and regulator stability.
4. Check junction temperature, derating, startup, transients, and short-circuit behaviour.
5. Review layout for return paths, decoupling, high di/dt loops, EMI, and creepage.
6. Validate with measurements across voltage, load, temperature, tolerance, and fault conditions.

The formulas are first-pass engineering tools. Real electronic performance is often decided by layout, parasitics, thermal path, component variation, and how the circuit fails outside nominal conditions.