2. Signal characteristics and channel requirements

A data acquisition channel budget is only meaningful when it is derived from the physical signal it must capture. Before selecting an ADC, programming a gain stage, or sizing a settling time, the designer must translate sensor behavior into a small set of per-channel specifications: bandwidth, amplitude range, source impedance, and the electrical nature of the sensor itself. This section shows how to perform that translation systematically, using a representative industrial measurement case to keep the reasoning concrete.

From physical quantity to electrical signal

Every channel begins with a transducer that converts a physical variable into an electrical one. The first decision is therefore to classify the sensor output type, because it determines the front-end topology more than any other factor. The common categories are:

• Voltage-output sensors — thermocouples (µV-level, floating, high source impedance), piezoelectric accelerometers (AC-coupled, charge output requiring a charge amplifier or IEPE conditioning), and integrated sensors with buffered 0–5 V or 0–10 V outputs.
• Current-output sensors — 4–20 mA transmitters, where the current loop is immune to cable resistance and the receiver uses a precision shunt to convert current to voltage.
• Resistive sensors — RTDs, strain gauges, and potentiometers, which require excitation and are usually measured with a bridge or a ratiometric configuration.
• Capacitive and inductive sensors — proximity probes and displacement sensors, often with dedicated demodulators.

The sensor type fixes the excitation requirement, the common-mode voltage, whether the source is floating or ground-referenced, and whether isolation is mandatory. A thermocouple channel and a 4–20 mA channel may share the same ADC, but they cannot share the same front-end design.

Bandwidth: what the channel must pass

Signal bandwidth is not simply the sensor's rated frequency range. The correct requirement is the highest frequency component that must be preserved with acceptable amplitude and phase error, plus any components that must be rejected. For a vibration channel monitoring a 1.2 kHz bearing defect, the signal of interest may extend to 5 kHz, but the channel should be designed with margin — a common rule is to set the anti-alias filter corner at 2–5× the highest signal frequency and choose the sampling rate accordingly.

Two bandwidth figures matter and are often confused:

For a target signal bandwidth of 5 kHz, a practical choice is f_c = 10 kHz with a fourth-order Butterworth response, and f_s = 25.6 kSPS. The filter attenuation at f_s/2 = 12.8 kHz is then about 24 dB for a fourth-order response — adequate for a 12-bit system only if the out-of-band energy is modest, which is why the filter order is chosen from the expected interferer spectrum, not from habit.

Amplitude range and resolution

The amplitude requirement has two sides: the maximum signal the channel must handle without clipping, and the smallest change that must be resolved. Both must be expressed at the ADC input, after all gain and offset. For a 4–20 mA transmitter with a 250 Ω shunt, the full-scale voltage is 1–5 V, a 4 V span. If the ADC has a 0–5 V range and 16 bits, the LSB is 76 µV, corresponding to 0.3 µA of loop current — usually far more resolution than the transmitter's own accuracy justifies.

The more instructive case is a thermocouple. A type-K pair at 400 °C produces roughly 16.4 mV, with a Seebeck coefficient near 41 µV/°C. To resolve 0.1 °C, the channel needs about 4 µV of resolution at the input, plus cold-junction compensation. With a gain of 128 and a 2.5 V reference, a 24-bit delta-sigma ADC gives an LSB of about 0.15 µV at the input — comfortable margin. The same calculation with a 12-bit ADC and no gain yields an LSB of 610 µV, which cannot meet the requirement. This is the essence of the channel budget: resolution, gain, and reference are chosen together to place the required LSB below the sensor's meaningful resolution.

Source impedance and settling

Source impedance determines both noise pickup and settling behavior. A high-impedance source feeding a switched-capacitor or multiplexed ADC input forms an RC network with the sample capacitor; if the acquisition time is shorter than the required settling, the reading is corrupted by charge sharing from the previous channel. For a source resistance R_s and sample capacitor C_s, the settling time constant is τ = R_sC_s, and roughly 12τ is needed for 16-bit settling.

Consider a multiplexed 16-bit ADC with C_s = 10 pF and a 2 µs acquisition window. The maximum tolerable source resistance for 12τ settling is approximately R_s = 2 µs / (12 × 10 pF) ≈ 16.7 kΩ. A thermocouple with long lead wires can easily exceed this, so a buffer amplifier or a longer acquisition time is required. The same calculation explains why 4–20 mA channels with a 250 Ω shunt settle easily, while high-impedance piezoelectric channels need local charge amplification.

Putting the requirements together

The figure below shows how the four characteristics flow into a per-channel specification set. Each sensor type drives a distinct front-end path, and the resulting specifications — range, gain, filter corner, sample rate, and settling budget — are what the channel budget later consumes.

Documenting the result

The output of this analysis is a per-channel specification record that the budget stage can consume directly. A compact form is sufficient, provided it captures the numbers that later calculations depend on:

Channel: TC-03 (type-K, process heater outlet)
  Sensor type:        thermocouple, floating, ungrounded
  Signal bandwidth:   0–2 Hz (thermal), f_sig = 2 Hz
  Amplitude span:     -2.5 mV to +20 mV (0–500 °C)
  Source impedance:   ~200 Ω plus lead resistance
  Required LSB:       4 µV (0.1 °C)
  Front-end:          gain 128, 24-bit ΔΣ, f_s = 20 SPS
  Anti-alias:         internal sinc filter, f_c ≈ 10 Hz
  Isolation:          required (heater common-mode)
  Cold junction:      local RTD, ±0.5 °C

Two failure modes are worth anticipating at this stage. First, a channel specified from the sensor's nominal range alone will clip on transients — always add headroom of at least 20 % above the expected maximum. Second, a channel specified from the ADC's resolution alone will appear adequate on paper but fail in practice because source impedance and settling were never checked; the 16.7 kΩ limit derived above is a useful sanity check for any multiplexed design. When a channel fails validation, the first diagnostic step is to compare the measured noise floor against the budgeted LSB, and the second is to verify settling by injecting a full-scale step on the preceding channel and observing the residual at the channel under test.

With these per-channel specifications established, the next stage — allocating error and noise terms across the signal chain — becomes a matter of arithmetic rather than guesswork.