Skip to content

Open-Circuit Time-Constant Method

An approximate high-frequency circuit method that opens all but one capacitor, finds each selected capacitor's seen resistance with independent sources zeroed, sums the RiCi terms, and inverts the sum for a first-order corner estimate.

Version
v1 · 2026-09-28 · History
Domain-specific #
11110
Domain group
Applied Sciences & Engineering
Origin domain
Engineering & Design (beyond software)
Subdomains
Analog Electronic Circuit Analysis, Electrical Engineering → Engineering & Design (beyond software)
Aliases
OCTC method, Open-circuit time constants, Method of open-circuit time constants

Core Idea

The open-circuit time-constant method extracts the coefficient linear in frequency from a capacitive small-signal network without solving the full transfer function. For each capacitor Ci, independent sources are set to zero, every other capacitor is opened, and a test source finds the resistance Ri seen at the selected capacitor's terminals. The sum of RiCi terms is the first-order denominator time coefficient.

Its reciprocal gives a rapid high-frequency corner or dominant-pole estimate and the individual terms reveal which nodes most limit bandwidth. The estimate is approximate: nearby zeros, complex poles, and higher-order interactions can make the -3 dB interpretation poor. Under the stated real-pole/no-zero condition, the reciprocal sum is conservative, but final designs still require full analysis or simulation.

Structural Signature

Sig role-phrases:

  • Linearized small-signal circuit — Supplies the lumped LTI network and declared high-frequency approximation. It is required model. Counterfactual: Nonlinear or time-varying behavior is outside the transfer-function method.
  • Capacitor set — Identifies reactive elements whose high-frequency poles are being approximated. It is required elements. Counterfactual: Inductive or mixed-reactance cases require the broader TTC treatment.
  • Zeroed independent sources — Creates the resistance-measurement network while dependent sources remain active. It is required test condition. Counterfactual: Removing dependent sources or leaving independent excitation changes resistance.
  • One-capacitor-at-a-time open-circuit condition — Opens every other capacitor while testing the selected one. It is defining operation. Counterfactual: Shorting the others yields a different time-constant method.
  • Seen resistance and RiCi contribution — Quantify each capacitor's contribution to the first-order denominator coefficient. It is required calculation. Counterfactual: Using a nominal resistor rather than port resistance misses network interaction.
  • Sum and reciprocal estimate — Aggregate contributions into the approximate corner and diagnostic ranking. It is required output. Counterfactual: A single largest capacitor does not by itself give the method's estimate.

What It Is Not

  • OCT is not an exact solution for every pole and zero.
  • It is not the short-circuit time-constant method, which shorts other capacitors for a different frequency regime.
  • Independent sources are zeroed, but dependent sources must remain active when seen resistance is computed.
  • The resistance is the port resistance seen by the capacitor in the modified circuit, not simply the nearest labeled resistor.
  • Closest near-miss. The short-circuit time-constant method is the dual approximation commonly used for low-frequency coupling and bypass capacitors, with other capacitors shorted rather than opened.

Scope of Application

  • Amplifier bandwidth estimation. Parasitic and device capacitances are ranked by their contributions to high-frequency roll-off.
  • Design iteration. The largest RiCi term identifies a node where resistance or capacitance reduction may buy bandwidth.
  • Hand analysis. Complex small-signal networks receive a quick first-order check before full symbolic or numeric solution.
  • Model sanity checking. The summed coefficient can be compared with a transfer-function expansion or simulation result.

Clarity

A derivation should include the exact small-signal model, source-zeroing rules, dependent sources, capacitor list, open-circuit configuration for each test, port-resistance calculation, signs if controlled-source behavior permits unusual values, and the definition of corner being approximated. Mixing intrinsic and Miller-transformed capacitances can double-count effects.

Manages Complexity

The method decomposes one global transfer-function coefficient into local-looking RC contributions while each seen resistance still contains the rest of the active network. This makes sensitivity legible and avoids a high-order determinant. The compression forgets pole and zero locations beyond the first coefficient, so it is a design guide rather than a complete frequency response.

Abstract Reasoning

  1. Linearize the circuit and identify the capacitors relevant to high-frequency behavior.
  2. Set independent voltage sources to shorts and current sources to opens while retaining dependent sources.
  3. Select one capacitor, open every other capacitor, and find the resistance at its terminals using a test source when needed.
  4. Multiply that resistance by the selected capacitance and repeat for all capacitors.
  5. Sum the time constants and invert the sum for the first-order estimate.
  6. Inspect dominant terms, modify the design, and verify poles, zeros, and bandwidth with full analysis.

Knowledge Transfer

OCT transfers among lumped capacitive LTI circuits when its one-at-a-time open-circuit and source rules remain valid. Inductor-capacitor networks require the broader time- and transfer-constant framework, and low-frequency coupling analysis often uses the short-circuit counterpart. Calling any reciprocal RC estimate OCT omits its network procedure.

Examples

Canonical

For each of two shunt capacitors, the other is opened, a test source finds its port resistance, and the two RC products are summed to estimate 1/(R1C1+R2C2).

Mapped back: aggregate → sum RC; condition → other capacitor open; estimate → reciprocal; measurement → test-source resistance; model → small-signal RC network.

Applied / In Practice

A designer ranks RiCi terms, changes the largest contributing node resistance or capacitance, and then verifies the revised bandwidth with full transfer analysis.

Mapped back: boundary → verify exact response; diagnostic → largest time constant; intervention → change R or C.

Structural Tensions

T1 — Rapid Design Insight versus Limited Spectral Fidelity. The sum exposes dominant contributors without solving all poles, but nearby zeros and complex poles can invalidate corner interpretation.

Diagnostic: What pole-zero structure was discarded by the first-order approximation?

T2 — Isolated Port Calculation versus Coupled Circuit Behavior. One-at-a-time resistance tests are simple even though the summed coefficient reflects the full network through dependent sources.

Diagnostic: Were source-zeroing and dependent-source effects handled correctly?

Structural–Framed Character

Open-Circuit Time-Constant Method is strongly structural within an approximate model. Circuit topology, port resistance, capacitance, and transfer coefficients determine the calculation. The designer chooses the small-signal model and acceptable error, so usefulness is context-sensitive even when arithmetic is exact.

Structural Core vs. Domain Accent

The skeleton is decomposing a first-order system coefficient into elementwise sensitivity terms. Analog circuit analysis supplies capacitors, source suppression, port resistance, poles, zeros, transfer functions, and bandwidth. Removing those yields generic first-order approximation.

This entry is a kind of Approximation.

  • Approved root. No reviewed parent entails this capacitor-specific open-circuit approximation.

  • Related — approximation, decomposition, and sensitivity. They characterize the method without asserted parent edges.

Relationships to Other Abstractions

Local relationship map for Open-Circuit Time-Constant MethodParents appear above the current abstraction, mutual partners to the right, and children below. Node labels state whether each abstraction is prime or domain-specific; colors identify relation types.Open-CircuitTime-Constant MethodDOMAINPrime abstraction: Approximation — is a kind ofApproximationPRIME

Current abstraction Open-Circuit Time-Constant Method Domain-specific

Parents (1) — more general patterns this builds on

  • Open-Circuit Time-Constant Method is a kind of Approximation Prime

    The Open-Circuit Time-Constant Method is an Approximation that estimates a circuit's high-frequency corner from a summed first-order resistance–capacitance surrogate.

Hierarchy path (1) — routes to 1 parentless root

Neighborhood in Abstraction Space

Open-Circuit Time-Constant Method sits in a moderately populated region (60th percentile for distinctiveness): it has near-neighbors but no dense thicket of look-alikes.

Family — Biomedical Signal Sensing & Recording (20 abstractions)

Nearest neighbors

Computed from structural-signature embeddings · 2026-10-08

Not to Be Confused With

  • Short-circuit time-constant method. Tell: Shorts other capacitors and is commonly used for low-frequency poles from coupling and bypass capacitors.
  • Dominant-pole approximation. Tell: Is a broader approximation that need not be calculated through open-circuit element tests.
  • Exact pole calculation. Tell: Solves the complete characteristic equation rather than retaining only the first denominator coefficient.
  • Miller approximation. Tell: Transforms bridging impedance effects and can be used before OCT, but is not the same procedure.

References

  • Frozen Wikipedia discovery revision: https://en.wikipedia.org/wiki/Open-circuit_time_constant_method (revision 1309767261).
  • Preserved source candidate: https://books.google.com/books?id=1Tyzjmf0DI8C&pg=PA8
  • Preserved source candidate: https://authors.library.caltech.edu/71086/1/FinalDraft.pdf
  • Preserved source candidate: http://authors.library.caltech.edu/20383/1/Hajimiri2010p11511Ieee_T_Circuits-I.pdf
  • Preserved source candidate: http://worldcat.org/isbn/0-471-32168-0
  • Preserved source candidate: https://books.google.com/books?id=TjFkX93jyRAC&q=+%22open+circuit+time+constant+method%22&pg=PA148

The frozen Wikipedia revision is discovery provenance. The retained source set was reviewed for identity, formal or operational relation, and scope. The encyclopedia's structural synthesis is bounded to those claims; a thin authority surface is recorded as a nonblocking source-strengthening repair rather than concealed.