Switched Gain Networks: Include Analog-Switch Resistance in Every Range

System boundary

A printed resistor network connected to external analog switches and a feedback amplifier. The calculations describe the stated linear circuit; semiconductor limits and transient stability remain part of the assembled electronics review.

Integration interfaces

Integration risks

Draw a circuit for each selected range

Start with the complete gain-selection schematic, including the switch's common terminal and every selected channel. Replace a conducting switch by its applicable on-resistance for the first static calculation. Leave unselected channels present as leakage and capacitive paths where relevant. A symbol labeled multiplexer does not tell the reviewer whether the switch carries feedback current or merely senses a high-impedance voltage.

For an inverting stage, mark the input resistance from the source to the summing node and the feedback resistance from output to summing node. A series switch in either branch changes a different part of the gain expression. Keep these two cases separate even when the same resistor array and switch package are used. Record the reference potential against which the input and output changes are defined.

Calculate the error of a switch in the feedback branch

With an ideal linear inverting amplifier, an input resistance Ri and a selected feedback resistance Rf followed by switch resistance Rs give gain magnitude equal to (Rf + Rs)/Ri. Compared with the intended Rf/Ri, the fractional gain increase is Rs/Rf. This simple expression identifies why the lowest feedback-resistance range may be most sensitive to the same switch.

For an illustrative Ri of 10 kilohms, compare feedback resistors of 10 and 100 kilohms with a 20 ohm series switch. Intended gain magnitudes one and ten become 1.002 and 10.002. The absolute gain increment is the same, but the relative errors are 0.20 percent and 0.020 percent respectively. These assumed numbers are a circuit example, not switch specifications or a manufactured network accuracy.

A switch in the input branch moves the error in the other direction

When the switch instead lies in series with Ri, gain is minus Rf divided by Ri plus Rs. Relative to the desired magnitude, the error is minus Rs divided by Ri plus Rs. Moving the switch is therefore not merely a wiring change that preserves the earlier correction. A channel with switches in both branches requires both contributions in the exact transfer function.

For Rf and Ri both 10 kilohms and Rs equal to 20 ohms, the gain magnitude is approximately 0.998004, about 0.1996 percent low. A drawing review should list the actual equation beside each state rather than applying an unsigned switch error to every range. Include any series source resistance inside the same input-path boundary when it is not negligible, keeping its contribution distinct from switch variation.

Use a gain-state table to expose the controlling range

A compact table should identify selected resistor values, switch location, applicable resistance limits and resulting gain interval. Evaluate corners that represent permitted operation, not a mixture of a typical resistance curve and a guaranteed resistor tolerance presented as one worst-case bound. If the switch data do not bound the required signal and temperature combination, that missing input must be resolved before allocating an accuracy guarantee.

The table below continues the assumed 20 ohm example. It is deliberately small enough that a reviewer can check the circuit by hand. For a larger array, generate the same table directly from the controlled schematic connectivity and compare it with measurements for each command code. A valid digital command does not prove the intended analog channel was selected.

Do not calibrate signal-dependent resistance as a constant

Switch on-resistance can vary with analog voltage, supply and temperature. Channel-to-channel matching and variation within one channel across signal voltage describe different effects. A calibration made at one input amplitude removes only the error represented at that operating point. It cannot remove a changing transfer slope by applying the same fixed multiplier to every signal.

Assume the feedback switch in the 10 kilohm range changes from 20 to 30 ohms between two conditions while the printed resistors stay fixed. The gain magnitude moves from 1.002 to 1.003. Even after correcting the first condition, the second retains approximately 0.0998 percent relative movement. That independently calculated example explains why tightening the printed ratio alone does not address the dominant mechanism. Measure a voltage sweep when resistance flatness is the concern.

Consider whether the switch needs to carry the gain-setting current

A topology placing selection switches in a high-impedance sensing path can reduce their resistive voltage-drop contribution. Whether it works depends on the actual amplifier architecture and on which feedback paths remain connected. Redraw and solve the proposed circuit rather than assuming that any switch moved near an amplifier input is now harmless. Bias current, leakage and parasitic capacitance still act at that node.

Increasing all network resistances reduces the relative contribution of a fixed series on-resistance but changes noise, loading and capacitance-related response. Choosing a lower-resistance switch can alter its capacitance and charge-injection behavior. Compare those costs against the error allocation. The useful output is a specific topology or component decision, not a general requirement to buy the smallest available on-resistance irrespective of the rest of the channel.

Keep static gain accuracy separate from range-change recovery

Inspect the temporary circuit during a gain change. Break-before-make selection can briefly open a feedback path in some configurations, while make-before-break can temporarily parallel two resistors. Neither timing label is universally correct. Determine whether each intermediate state keeps the amplifier controlled and whether the resulting output excursion stays within the permitted system behavior.

Record the command edge, output trajectory and time at which the new gain produces a valid reading. Charge injection, settling and overload recovery must not be interpreted as steady-state ratio error. Test transitions in both directions because the starting output and stored charge differ. Firmware should use a validity interval justified by the assembled response instead of assuming that the switch's logic propagation time is also the analog measurement recovery time.

Provide the network and switch requirements together

Send the state equations, selected resistor values, source impedance and switch data covering the actual signal range. Identify whether acceptance is based on isolated printed ratios or the complete switched channel. If an active trim includes one external switch, record that component and operating condition in the calibration boundary; replacing it may change the corrected gain without changing the ceramic network.

Verify the assembled channel at multiple amplitudes, both relevant polarities and the required thermal conditions. Retain the individual state results and transition records so a later discrepancy can be assigned to a resistor, a switch or acquisition timing. This approach turns the resistor-network quotation into a clear component requirement while keeping system-level gain accuracy with the electronics that actually determine it.