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A printed resistor network can set an accurate gain while the amplifier fails to reproduce a fast, large output waveform. Small-signal bandwidth and DC gain do not establish the available rate of voltage change. Calculate the slope required by the actual signal amplitude, then verify the active circuit under its load before treating a distorted waveform as a resistor matching problem.
System boundary
Printed gain resistors, active amplifier stages, output load and required waveform. The passive ratio sets amplitude demand; active circuitry must meet slope and range limits.
Integration interfaces
| Interface | Required input | Thick film role | Validation owner |
|---|---|---|---|
| Gain allocation | Input waveform and individual stage ratios | Establish the specified passive gain relationships | Analog designer |
| Active response | Slew rate, supplies, headroom and temperature | Keep the requested gain within the reviewed active operating envelope | Amplifier owner |
| Output load | Capacitance, resistance and accepted waveform error | Support the controlled interface without implying passive-only speed | System integration engineer |
Integration risks
| Risk | Control or verification | Validation owner |
|---|---|---|
| Small-signal bandwidth is used as a full-amplitude guarantee | Calculate and test actual output slope demand | Analog designer |
| Peak and peak-to-peak amplitudes are mixed | Record one explicit waveform convention | Test engineer |
| Resistor trim hides an active dynamic failure | Keep gain and waveform acceptance separate | Module engineer |
System integration decisions
- Convert required input amplitude through the intended gain before checking output slope.
- Keep slew-rate demand, small-signal response and voltage headroom as independent constraints.
- Verify distortion at the real amplitude and loading rather than accepting a necessary slope inequality as a performance guarantee.
State the output waveform the network must support
Identify the input amplitude, signal gain, output offset and expected waveform. For a linear gain stage, the demanded output excursion is the input excursion multiplied by the signal gain. Use peak, peak-to-peak and RMS values consistently. A sine wave described as 10 V peak-to-peak has a 5 V peak excursion about its center, not a 10 V peak excursion.
The printed network defines passive gain relationships; the amplifier supplies the changing output voltage and current. Its relevant slew-rate specification belongs to the active device under stated conditions. Do not attribute that speed to the resistor array alone. If several stages share gain, inspect their individual output demands rather than assuming the final output is the only node that can become rate-limited.
Calculate the necessary slope for a sinusoidal output
For an output v(t) = Vc + A sin(2 pi f t), the maximum slope magnitude is 2 pi f A. Vc is the center voltage in volts, A is the peak excursion in volts, f is frequency in hertz and t is time in seconds. The derivative reaches its largest magnitude at the sine wave's zero crossings relative to Vc, not at its positive or negative peaks.
An amplifier needs an available slope greater than the demanded slope to avoid this particular limiting mechanism. Equality is a theoretical boundary, not a low-distortion design target. Positive-going and negative-going behavior can differ, and supply, temperature and load can change the usable response. Use the selected amplifier's applicable documentation and verified circuit behavior rather than a typical number detached from test conditions.
Show why a low-level sweep can pass while the full signal fails
Assume a gain of ten and an input sine wave of 1 V peak-to-peak at 100 kHz. The intended output is 10 V peak-to-peak, so its maximum required slope is approximately 3.142 V per microsecond. An illustrative amplifier limited to 1 V per microsecond cannot reproduce that demanded waveform without rate limitation, even if its small-signal gain appears adequate at 100 kHz.
Reduce the input to 0.1 V peak-to-peak with the same gain and frequency. The output demand becomes 1 V peak-to-peak and the required slope falls to approximately 0.3142 V per microsecond. A small-amplitude test can therefore look satisfactory while the full-amplitude test fails. These are hypothetical signal and speed values, not specifications for a selected amplifier or a ChipSimple module.
Convert a slope limit into an amplitude-dependent boundary
Rearranging the sine-wave slope requirement gives f no greater than SR divided by two pi A, where SR is the allowed slope magnitude in volts per second. With the illustrative 1 V per microsecond limit and 5 V peak excursion, this boundary is approximately 31.83 kHz. With a 0.5 V peak excursion, it becomes approximately 318.31 kHz.
Neither frequency is a guaranteed useful bandwidth. Linear amplitude error, phase error, distortion and output headroom still impose their own limits. The comparison simply identifies a large-signal demand that a small-signal frequency response does not express. When the customer requires a distortion limit, verify that limit with margin below the rate-limiting boundary rather than converting the equality directly into a product claim.
Use edge slope for pulses and ramps
A pulse or ramp should be assessed from its required voltage change and edge time, not assigned the sine-wave formula automatically. An illustrative 4 V transition completed as a linear ramp in 2 microseconds requires a slope of 2 V per microsecond. The same nominal repetition frequency could accompany much slower or faster edges and therefore very different amplifier demands.
A rectangular waveform with mathematically instantaneous edges demands unlimited bandwidth and slope, so the specification needs a finite rise or fall criterion. State where the edge timing is measured and which overshoot and settling are permitted. For a triangular waveform, the slopes are set by amplitude and the actual ramp durations. Preserve that waveform definition when comparing simulations, generator settings and measured output.
Distinguish rate limitation from other waveform errors
Change amplitude and frequency independently while observing the waveform. The way the error moves helps identify the controlling mechanism, although it does not replace the amplifier model or a complete measurement. Avoid trimming a resistor ratio to compensate for an amplitude-dependent dynamic error that will return at another operating point.
| Observation | Requirement to investigate | Why gain trim alone is insufficient |
|---|---|---|
| Large waveform develops nearly linear slopes | Available voltage slew versus demanded slope | A correct DC ratio does not increase active-device speed |
| Small and large signals both lose high-frequency amplitude | Closed-loop frequency response and loading | Bandwidth may limit before slew rate |
| Waveform flattens near a voltage boundary | Input, internal-node and output headroom | Changing gain may conceal but not remove the range conflict |
| Fast edges ring under a capacitive load | Loop stability and output interface | A DC calibration cannot establish phase margin |
| Only one edge direction is slow | Directional slew and current behavior | A single symmetric speed value can hide the limit |
Verify the real load and measurement chain
The output may need to charge a capacitance as well as change voltage. For an ideal capacitance, the required current is C times the voltage slope. An assumed 2 nF load at 3 V per microsecond requires 6 mA of capacitive current before any resistive load current is added. This current calculation is not a complete output-stage model, but it exposes a demand that can matter to the loaded waveform.
Use measurement bandwidth and probes appropriate to the signal without creating a significant extra load. Verify the generator's delivered amplitude and distortion at the stage input. Capture both output edge directions and relevant temperatures or supply states. Distortion analysis should identify the tested amplitude, frequency, load and bandwidth; a smooth-looking trace alone is not an adequate substitute for a numerical requirement.
Specify gain accuracy together with the signal envelope
For a ChipSimple gain-network enquiry, provide the resistor schematic, amplifier selection, stage gains and the maximum required waveforms at each relevant node. Include output center voltage, supply limits, load impedance and any capacitor. This allows the passive ratio requirement to be reviewed without confusing it with the active circuit's speed or range.
After any gain change, recalculate output amplitude and slope demand before repeating the operating-envelope tests. Keep DC calibration, internal headroom, small-signal response and full-amplitude distortion as separate acceptance records. The useful deliverable is an accurately scaled signal that remains valid where the customer uses it, not an exact resistor ratio accompanied by an untested assumption that the amplifier can follow every requested waveform.
Provide the full-amplitude signal envelope
Send the waveform and load that must remain accurate after gain scaling.
- Resistor topology, amplifier, individual stage gains and supply conditions.
- Input and output amplitude conventions, center voltage, frequencies and edge times.
- Resistive/capacitive loading, distortion limits and required settling.
- DC gain, small-signal response and full-amplitude waveform measurements.
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