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An AC-coupled sensor channel can reproduce a fast edge accurately while misrepresenting the level that follows it. The coupling capacitor and printed bias resistor continuously restore the receiver toward its bias voltage, so a long pulse loses amplitude and its trailing edge can drive the input below that bias. Review the longest relevant pulse and its return interval before selecting the network from frequency response alone.
System boundary
Voltage-output sensor, series coupling capacitor, printed bias resistor and receiving input. Pulse preservation and reference restoration are joint interface functions.
Integration interfaces
| Interface | Required input | Thick film role | Validation owner |
|---|---|---|---|
| Source waveform | Amplitude, source resistance, offsets and pulse timing | Set the receiver-side bias impedance in the reviewed RC path | Sensor interface designer |
| Receiver operating range | Bias source, input impedance and clamps | Establish the intended DC return without consuming pulse accuracy | Analog designer |
| Measurement timing | Amplitude sampling instant and event history | Maintain the time constant used by the waveform model | Acquisition owner |
Integration risks
| Risk | Control or verification | Validation owner |
|---|---|---|
| A short-pulse demonstration is applied to long events | Specify and test maximum pulse width | Interface owner |
| Trailing undershoot is omitted from headroom | Calculate both polarities relative to actual bias | Analog designer |
| Every pulse is assumed to start from equilibrium | Evaluate actual sequence and startup states | System designer |
System integration decisions
- Define pulse amplitude and duration at the source, then calculate the receiver waveform around its bias.
- Include both pulse-top droop and the negative excursion after a positive pulse.
- Resolve the conflict between preserving long pulses and restoring the baseline quickly.
Identify a voltage-coupling circuit, not a charge amplifier
The circuit considered here has a voltage source feeding a series coupling capacitor and a receiver node connected through a bias resistor to a stable reference. The receiver input is assumed high impedance for the first calculation. The capacitor blocks a steady source offset while the resistor establishes the receiver's DC operating point.
This is different from a charge-sensitive amplifier whose resistor is in parallel with a feedback capacitor. That circuit converts input charge and resets an active feedback integrator. Here the input is an already defined voltage waveform and the resistor controls how that waveform returns toward receiver bias. State the actual topology and signal units so the two physically different interfaces are not described by the same generic pulse-recovery specification.
Use the resistance seen by the coupling capacitor
For an ideal source with series resistance Rs and a bias resistor Rb connected to an ideal reference, the time constant is tau = (Rs + Rb)C. C is coupling capacitance in farads, both resistances are in ohms and tau is in seconds. The immediate high-frequency voltage division is K = Rb/(Rs + Rb), before other bandwidth limits are included.
A finite receiver input resistance changes the effective load branch. A nonideal bias source can add its own dynamics. Include those elements explicitly rather than using the printed resistor value as the whole time constant. The capacitor's relevant value also belongs to its actual operating conditions. The first-order model assumes linear components, a stable reference and edges fast relative to tau but compatible with the receiving circuit.
Calculate the level immediately before the trailing edge
For an isolated positive rectangular source pulse of amplitude A and width T, starting from equilibrium, the receiver excursion above bias is K A exp(-t/tau) during the pulse. A is in volts; T and time t are in seconds. The fractional loss relative to the initial received amplitude is one minus exp(-T/tau). This is pulse-top droop, not a change in the source's actual physical level.
Assume Rs is negligible, Rb is 100 kilohms, C is 100 nF and A is 1 V. The time constant is 10 ms. After a 2 ms pulse, the received excursion has fallen to approximately 0.81873 V, an 18.127 percent loss from its initial level. A successful check with a much shorter pulse would not establish that this longer event is represented accurately.
Include the excursion on the opposite side of bias
At the end of the ideal positive pulse, the source falls by A and the receiver makes an immediate step of minus K A. Its excursion just after that edge is therefore minus K A times (one minus exp(-T/tau)). In the example, the receiver moves to approximately 181.27 mV below its bias. It then returns exponentially toward the bias reference.
If the receiver bias is 1.2 V, that initial post-pulse voltage is approximately 1.01873 V. With a lower bias or a larger pulse it might approach an input clamp or the end of the linear range. Once protection conducts, the simple linear waveform is no longer sufficient. Check both positive and negative excursions, including the real source baseline shifts, rather than using the pulse amplitude alone to establish headroom.
Expose the conflict between droop and recovery
To limit isolated pulse-top loss to a fraction d, the required time constant is at least minus T divided by ln(1 minus d). For a 2 ms pulse with a two-percent droop allowance, tau must be at least approximately 99.0 ms. At that limiting value, a 1 V received initial step leaves an approximately 20 mV negative excursion after the pulse.
To reduce that 20 mV residual to 1 mV takes tau times ln(20), approximately 296.6 ms for this example. If the next event must arrive after only a short idle interval, the two requirements may not coexist in a simple passive coupling network. A baseline-restoration circuit, a different measurement method or DC coupling may be needed. Increasing the resistor without examining the recovery requirement only moves the problem.
Assign the observed waveform error to the right decision
Use pulse duration, source impedance and receiver bias as independent test variables. A frequency-sweep corner is useful, but the customer often needs a guaranteed waveform interval rather than a nominal cutoff. The following distinctions prevent a resistor tolerance change from being used to compensate for an unsuitable signal architecture.
| Observation | Likely model feature to test | Action |
|---|---|---|
| Initial amplitude too low but normalized droop correct | Source-to-load resistance division | Review Rs, receiver loading and Rb |
| Long pulse falls toward bias | Coupling time constant too short for pulse width | Calculate the required droop window |
| Negative tail reaches an input limit | Trailing-edge excursion and bias headroom | Reallocate bias or coupling architecture |
| Baseline not restored before the next event | Time constant too long for idle interval | Evaluate actual event sequence or restoration |
| Waveform becomes asymmetric near a limit | Clamping or another nonlinear path | Replace the linear model with the real circuit behavior |
Test the real pulse sequence and startup offset
The isolated-pulse result assumes the capacitor begins in equilibrium. In a repeated or irregular sequence, its initial voltage depends on preceding events. Add the signed responses of the actual input transitions while the system remains linear. A duty-cycle change can move the apparent baseline even when the pulse amplitudes are unchanged. Do not reset the model artificially to zero before every event.
A source offset change at power-up also passes through the coupling capacitor as a transient. The capacitor blocks the eventual DC level, not the initial transition. Include the order in which source, reference and receiver power become valid. Specify when acquired data become usable after startup, reconnecting a cable or changing a measurement range; that delay is an interface requirement, not an undocumented software convenience.
Record the pulse-preservation envelope with the network
Measure source and receiver waveforms simultaneously using connections that do not add a significant parallel resistance. Record bias voltage, source resistance, pulse width, repetition pattern and the time used to judge amplitude. Compare initial received amplitude, end-of-pulse amplitude and recovery separately. An AC-coupled oscilloscope input can introduce another high-pass response, so use an appropriate measurement configuration.
For a ChipSimple resistor-network enquiry, provide the capacitor and receiver circuit alongside the printed bias-resistor requirement. State the longest pulse to preserve, allowable droop, shortest return interval and accepted voltage range around bias. The resulting drawing should support an explicit waveform envelope. It should not promise preservation of arbitrary DC or long-duration signals through a circuit deliberately designed to remove them.
Define the AC-coupled waveform requirement
Provide the source pulse history and the receiver voltage window, not only the nominal cutoff frequency.
- Complete coupling circuit, resistor and capacitor values, source and receiver impedances.
- Pulse amplitude, duration, shortest intervals, duty changes and startup offset.
- Bias voltage, input limits, permitted top droop and residual baseline.
- Raw source/receiver waveforms with measurement coupling and loading recorded.
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