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.
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.
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¶
- Linearize the circuit and identify the capacitors relevant to high-frequency behavior.
- Set independent voltage sources to shorts and current sources to opens while retaining dependent sources.
- Select one capacitor, open every other capacitor, and find the resistance at its terminals using a test source when needed.
- Multiply that resistance by the selected capacitance and repeat for all capacitors.
- Sum the time constants and invert the sum for the first-order estimate.
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.
Relationships to Other Abstractions¶
Current abstraction Open-Circuit Time-Constant Method Domain-specific
Parents (1) — more general patterns this builds on
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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
- Open-Circuit Time-Constant Method → Approximation → Representation → Abstraction
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
- Switching circuit theory — 0.85
- Correlated Double Sampling — 0.85
- Electrical Capacitance Tomography — 0.85
- Modified Ashworth scale — 0.84
- Integrated Injection Logic — 0.84
Computed from structural-signature embeddings · 2026-10-08