= Threshold-reset margin for a periodic RC pulse train
The <threshold-reset margin for a periodic RC pulse train> is the separation between the reset threshold of an <electronic comparator> and the largest baseline that the periodic <RC low-pass filter> may leave between pulses. A positive margin excludes <missing comparator reset in an RC pulse train> in the ideal threshold model; its size measures tolerance to additional <electric potential difference> errors.
Let $V_0>0$ be the input high level, $T$ the high duration, $D$ the quiet duration and $\tau>0$ the <time constant>. From the periodic solution in <missing comparator reset in an RC pulse train>, write
$$
V_b=V_0\frac{\beta(1-\alpha)}{1-\alpha\beta},\qquad
\alpha=e^{-T/\tau},\quad\beta=e^{-D/\tau},\qquad
m=V_{\rm th}-V_b.
$$
This defines a margin in volts, rather than in units of <standard deviation>. If a nominal baseline $\bar V_b$ has a known absolute error bound $b_b$ and the reset threshold $\bar V_{\rm th}$ has bound $b_{\rm th}$, a sufficient worst-case condition is
$$
m_{\rm guaranteed}=\bar V_{\rm th}-\bar V_b-b_{\rm th}-b_b>0.
$$
These are simultaneous bounds on the actual baseline and threshold. Adding their <standard uncertainties> would not by itself provide a deterministic guarantee; a probabilistic statement requires a specified joint <probability distribution>.<Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement Results by Barry N. Taylor and Chris E. Kuyatt>[§§6.2–6.3, distributional conditions for interpreting uncertainty intervals]{ref}
For an original example, let $V_0=2\,\mathrm V$, $\tau=2\,\mathrm{\mu s}$ and $T=D=\tau\log2$. Then $\alpha=\beta=1/2$, $V_b=2/3\,\mathrm V$ and the peak is $4/3\,\mathrm V$. A threshold of $0.800\,\mathrm V$ gives $m=0.133333\ldots\,\mathrm V$. Bounds $b_b=0.040\,\mathrm V$ and $b_{\rm th}=0.020\,\mathrm V$ leave $m_{\rm guaranteed}=0.073333\ldots\,\mathrm V$. Raising the baseline bound to $0.120\,\mathrm V$ would remove this guarantee even though the nominal waveform still crosses the threshold.
A positive minimum separation does not specify the <reset dwell time below threshold in an RC pulse train>. A real <electronic comparator> needs enough time to switch, and the peak must separately exceed the acceptance threshold. For a <Schmitt trigger>, use the lower switching threshold in $m$, while checking the upper one against the peak.
A focused bench test records the <pulse generator> output, <capacitor> output and <electronic comparator> output on an <oscilloscope>, then varies $D$ near the predicted boundary. Compare the measured minimum with the reset threshold and record the low interval as well as the minimum. The underlying <exponential decay> can be checked by the natural-response experiment in the MIT laboratory; the margin calculation above is an original application of that model.<Laboratory 11: Sinusoidal Steady State Response of RC and RL Circuits by MIT OpenCourseWare>[Printed p. 1, capacitor response after switching and time-constant measurement]{ref}
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