Trimmed Gain Verification: Separate Source Amplitude Error from Channel Gain Error

System boundary

The source, channel input boundary, trimmed analog network and output receiver form the verification chain. This page establishes measured transfer rather than hardware-to-calibration identity or instrument certification.

Integration interfaces

Integration risks

Locate the gain input before connecting instruments

Mark where the gain requirement starts: at an external connector, after a protection resistor, or directly at the amplifier inputs. Different boundaries include different losses. For a differential channel, define input as the positive-terminal voltage minus the negative-terminal voltage, while separately recording their common-mode level. Measuring one lead relative to the bench ground does not necessarily measure the differential stimulus.

Keep the actual output load attached if it belongs to the gain specification. Record supply, reference voltage, thermal state and settling condition. A measurement made with a convenient unloaded output may not represent the installed channel. The purpose of this exercise is to identify a transfer error, not to modify trim until an unspecified bench arrangement produces the expected number.

Read the generator's load convention correctly

A generator may display the amplitude expected into a selected load rather than its internal source voltage. For some instruments, choosing a high-impedance display setting changes the amplitude interpretation without changing the physical output resistance. Verify the behaviour of the exact generator. Do not infer that selecting a load in a menu installs a resistor in the external circuit.

As a simple circuit example, an internal 1 V Thevenin source with 50 ohms series resistance delivers 0.5 V to a 50-ohm load, but nearly 1 V to a sufficiently high-impedance input. A channel with gain ten would produce 5 V or nearly 10 V respectively if it remained linear. Calculating against the same assumed 1 V input would assign different apparent gains even though the channel gain did not change.

Use differences to separate gain from a fixed offset

For a linear transfer Vout equals G times Vin plus b, two settled input-output pairs give gain as the output change divided by the measured input change. This removes a constant offset b from the slope. It does not remove a drifting offset, nonlinearity, clipping or a change in source loading between measurements. Keep the two points within the declared operating range and preserve their actual terminal voltages.

Suppose measured inputs are 0.100 V and 0.300 V, with outputs 1.015 V and 3.019 V. The difference ratio is 2.004 divided by 0.200, giving gain 10.02. The inferred intercept is 0.013 V. Dividing the first output by its input alone gives 10.15 and mixes offset into gain. These hypothetical values illustrate interpretation, not a calibration result for a supplied product.

Use the same amplitude definition on both sides

For an alternating signal, distinguish peak, peak-to-peak and root-mean-square amplitude. Their conversion depends on waveform shape. A sinusoidal conversion is not valid for a clipped waveform, a pulse train or a signal with a substantial offset included in the root-mean-square calculation. Retain frequency and bandwidth because a channel can have a correct low-frequency gain but a different gain at the verification frequency.

For transient measurements, define whether the requirement concerns the settled plateau, peak overshoot or a frequency-domain transfer. Do not divide the largest output sample by an unrelated input peak from another time. If two instruments acquire sequentially, establish that the source is stable over the interval; otherwise synchronized acquisition or a monitored source reference is needed.

Budget the two instrument channels

If the input measurement has fractional gain error ein and the output measurement has error eout, the measured channel gain is multiplied by one plus eout divided by one plus ein. For small errors the residual is approximately eout minus ein. Ratiometric calculation can reject a truly common error, but it does not cancel errors of unrelated ranges, probes or instruments.

For example, a positive 0.2 percent output-channel error and a negative 0.1 percent input-channel error multiply the reported ratio by 1.002 divided by 0.999, approximately 1.003003. The gain result is biased high by about 0.3003 percent. Include noise and the uncertainty of the input difference, especially when the two verification points are close together. A larger valid input span usually makes fixed voltage errors less dominant, but it must not introduce nonlinearity or saturation.

Locate the first transfer that disagrees

Record the programmed source setting, actual channel input, channel output and calculated slope together. This makes it possible to distinguish a source problem from an analog transfer problem before changing resistor values. Repeat one comparison with a controlled load change only when that change is within the permitted interface conditions.

Do not trim away an error outside the network

Changing a gain-setting resistor to compensate for an incorrect stimulus can create a real error when the channel returns to its intended source. Likewise, trimming against a loaded probe condition can bind the circuit to the test instrument. Confirm the source and measurement chain before assigning any residual slope error to the printed network.

If a trim adjustment is justified, record the measured transfer before and after it using the same valid boundary. Keep the hardware calibration identity and stored coefficients linked to the assembled channel through the separate calibration-control workflow. The present verification establishes the measured gain; it does not establish that a coefficient file belongs to the correct serial-numbered assembly.

Deliver the raw pairs as well as the fitted gain

The handoff should contain raw input-output pairs, amplitude definition, source termination, measurement ranges, timing, common-mode voltage, output load and the error allocation. Include fit residuals or additional points where linearity matters. A single rounded gain number cannot reveal whether the apparent pass depended on offset cancellation or one favourable input point.

Recheck the interface after changing a generator, harness, receiver, probe or channel configuration. A repeatable test can still be consistently wrong if its stimulus convention is wrong. Keeping actual terminal measurements with the resistor-network acceptance record makes verification portable between engineering, production and customer integration.