Divider Clamp Equilibrium: Check the Current Sign at the Allowed Rail Limit

System boundary

A fixed resistor-divider and positive-clamp topology connected to a rail between its nominal voltage and independently defined upper limit. The review supplies a quasi-static current-sign and equilibrium screen, not complete electrical protection or equipment-safety approval.

Integration interfaces

Integration risks

Define a fixed circuit and a permitted voltage interval

Identify every upper resistor, lower resistor, source, positive clamp and common return. Let the rail begin at its intended voltage V0, with an independently specified allowed upper value Vmax. That limit must come from the actual connected circuitry and required function; it cannot be inferred from the equilibrium the calculation happens to produce.

This model examines a slowly varying rail above V0 after the normal regulator has stopped sourcing. It does not assume that the regulator can sink current. Include a supported rail-load and sink characteristic over the full interval. Startup, negative clamps, source disconnection and independently switching supplies require their own circuit states.

Test whether each positive clamp is actually conducting

For one divider, the unconstrained output is Vs times Rb divided by (Rt plus Rb). In a constant-drop approximation, a positive clamp conducts only when that output exceeds the rail voltage Vr plus its assumed forward drop Vd. Otherwise the positive-clamp current is zero, not a negative current that can absorb injection from another channel.

During conduction, the upper-leg current divides between Rb and the clamp. Subtract the lower-leg current before assigning rail injection. The resulting piecewise expression is continuous at the ideal turn-off boundary. A real diode requires an appropriate current-voltage relation, especially when small currents make a fixed drop inaccurate.

Evaluate the current sign at the allowed upper boundary

Define g(Vr) as total positive injection minus the current absorbed by the rail loads and any qualified sink. For positive effective rail capacitance, g determines the direction of voltage movement in this reduced first-order model. Evaluate g at Vmax using the permitted source combination, not at an arbitrary convenient voltage.

With fixed positive resistances and constant clamp drops, each channel's injection is nonincreasing as Vr rises. If guaranteed absorption is constant or nondecreasing, g is also nonincreasing. Positive g at Vmax then means no equilibrium exists anywhere between V0 and Vmax. If g starts positive and becomes negative by Vmax, continuity gives an equilibrium inside that interval; strict decrease makes it unique.

If g is already nonpositive at V0, the normal regulator can maintain V0 by supplying the remaining load, provided that behaviour is valid. Do not continue a source-off equation below V0 and report its artificial lower root. Equality at Vmax leaves no current margin for omitted effects or parameter error.

Calculate a small outward current at the allowed boundary

Consider hypothetical identical channels with Vs of 48 V, Rt of 100 kilohms, Rb of 10 kilohms and Vd of 0.3 V. Let V0 be 3.3 V and the illustrative allowed boundary be 3.6 V. The unclamped output is approximately 4.364 V, so the clamp remains active throughout this interval. At Vmax, its node is 3.9 V: upper current is 441 microamperes, lower current is 390 microamperes, and injection is 51 microamperes per channel.

Assume a constant 20-microampere rail load and a qualified 80-microampere sink throughout the interval, giving 100 microamperes absorption. Two channels leave positive boundary current of two microamperes. Solving their active-branch equation gives Vr approximately 3.6091 V, beyond the stipulated boundary even though the excess is small. These values are arithmetic examples, not product limits or recommended protection components.

Derive a channel limit or a minimum sink requirement

For identical channels with positive worst supported boundary injection Imax and guaranteed boundary absorption Amin, the simplified count condition is N times Imax no greater than Amin. Its integer ceiling on simultaneous channels is the floor of Amin divided by Imax. This result applies to the declared boundary and model; it is not a general connector-channel rating.

The nominal example gives floor(100/51), or one channel. To support two nominal channels at the boundary with a 20-microampere minimum load, the additional sink must absorb at least 82 microamperes there. Exact equality places equilibrium at the boundary without margin. Verify sink availability across the relevant voltage range and its thermal and control limits; a rated maximum does not establish delivered absorption.

For unequal sources or resistor networks, sum their individual worst credible injections instead of multiplying an average. Check which combinations can coexist. An off channel must be re-evaluated when its source range changes, and a negative result from the unclipped expression cannot be credited as a protective sink.

Challenge nominal clearance with a justified parameter envelope

For the stated positive-current model, higher source voltage, smaller upper resistance, larger lower resistance and smaller clamp drop increase injection at a fixed rail voltage. Use bounds appropriate to the same temperature and operating state. Correlated parameters should retain their supported relationship; an impossible combination can be overly conservative, while using only typical values can be optimistic.

As a hypothetical corner, take Vs of 50 V, Rt of 95 kilohms, Rb of 10.5 kilohms and Vd of 0.25 V. At Vr of 3.6 V, the upper current is approximately 485.79 microamperes and lower current 366.67 microamperes. Injection becomes approximately 119.12 microamperes. The previously assumed 100-microampere absorption no longer supports even one channel at the boundary.

With the same 20-microampere minimum load, that corner requires at least approximately 99.12 microamperes of additional boundary absorption for one channel, before a design margin. A real diode's voltage-current envelope must replace the invented drop range. Preserve each corner calculation and whether its clamp is conducting; do not merely apply a percentage to the final nominal equilibrium.

Recognize when the monotone screen is not the applicable model

A sink that folds back, a load that disconnects as voltage rises or a regulator that injects reverse current can change g's shape or its circuit state. Hysteresis, multiple rails and diode self-heating can introduce additional state variables. Do not assume a unique stable equilibrium from one voltage evaluation when those effects are unresolved.

The boundary calculation also does not establish transient overshoot. Inductance, control delay, charge injection and fast input changes can violate the reduced quasi-static description. Rail capacitance affects the path in time but does not change the static root of the fixed-current model. Qualify dynamic behaviour separately within an authorized safe test plan, preserving any limited applicability of the steady-state screen.

Deliver a reproducible boundary-current admission record

For each allowed simultaneous state, retain source and parameter bounds, the conducting-channel set, V0, Vmax, per-channel current, guaranteed absorption and the resulting signed margin. Record any root calculation with its valid branch interval. A root found after a clamp turns off must be recomputed with that channel removed from the conducting set.

ChipSimple can review the drawing-defined resistor network and its interface requirements with the electronics team. The system owner must still establish device stress, resistor voltage and power, normal accuracy, recovery and equipment safety. This calculation contributes one precise decision: whether the specified current model admits a rail equilibrium inside the allowed voltage interval, or requires a different channel allocation, absorption path or model.