Thick-Film Resistor Summing Amplifiers: Calculate Weights and Output Headroom

System boundary

Input sources, printed input/feedback resistors, reference, voltage-feedback amplifier and output receiver form one active summer; the printed network alone does not establish the system operating envelope.

Integration interfaces

Integration risks

Identify the active summing node and its reference

Connect each voltage source through its own input resistor to the inverting input, and connect the output back through a feedback resistor. The noninverting input is held at a defined reference. Under stable negative feedback and linear operation, the inverting node remains close to that reference. It is not a passive common node free to settle at the conductance-weighted mean of the inputs.

State whether the reference is ground or a buffered intermediate voltage on a single supply. The sources, reference and receiver must use a compatible return convention. A virtual reference describes an operating approximation, not a physical ground connection capable of absorbing unlimited external current. Verify the actual amplifier input range and startup behavior before applying the ideal node equation.

Calculate each signed input contribution

With a low-impedance reference voltage Vr and negligible input current, current conservation gives Vout = Vr minus the sum of Rf divided by Ri times the quantity Vi minus Vr. Here Rf is the feedback resistance, Ri is the effective series resistance of input branch i, and Vi is its source voltage, all defined against the same return. Resistances are in ohms and voltages in volts.

The formula applies to a settled linear amplifier with adequate loop gain. Each source deviation from Vr is inverted and scaled independently. Unlike a passive averaging node, the expression does not divide by the sum of input conductances. A true open input removes its current contribution without automatically renormalizing the remaining signal gains, although it can change noise gain and dynamic behavior.

Check simultaneous extremes before accepting the resistor values

For an illustrative grounded-reference circuit, choose Rf = 20 kilohms, R1 = 10 kilohms and R2 = 40 kilohms. The output is minus two times V1 minus one-half times V2. Let V1 range from minus 1 to plus 1 V and V2 from minus 3 to plus 3 V independently. The possible output therefore spans minus 3.5 to plus 3.5 V.

Testing the first input alone reaches only 2 V magnitude, and testing the second alone reaches only 1.5 V. Both individual tests could appear satisfactory for an amplifier whose actual loaded usable swing were limited to plus or minus 3.0 V. The combined extreme would not. The assumed swing is an example constraint, not a device specification; the selected amplifier, supply, load and temperature determine the real permitted envelope.

Include the resistance and current at each source

A source with a justified linear output resistance adds that value to the printed input resistor. In the example, adding 1 kilohm to the first branch changes its effective input resistance to 11 kilohms and its gain to approximately minus 1.818 rather than minus two. Tightening the printed 10-kilohm resistor tolerance cannot remove an unknown or varying source contribution.

Calculate source current from its voltage relative to the summing reference divided by the effective branch resistance. Check whether the source can supply and absorb that current over its normal and powered-down states. Nonlinear clamps and current limits require a state-specific model, not a fixed series resistance. The active node reduces direct input-to-input coupling while feedback remains effective, but it does not provide galvanic isolation.

Include reference movement and amplifier offsets

Expanding the node equation shows that a change in the common reference is multiplied by one plus the sum of Rf divided by the input resistances, if the source voltages remain fixed against the external return. In the example that factor is 3.5. A 10 mV reference shift would then cause a 35 mV output shift under the ideal model. Sources that move with the reference need their own correlated treatment.

Account for amplifier offset and input bias current using the actual device and connection model. Do not assume a compensation resistor automatically cancels every offset or temperature effect. Reference output impedance, bias-current mismatch and unequal source conditions can matter. Keep these additive errors distinct from the printed ratio errors so a trim operation is directed at the mechanism it can actually correct.

Evaluate noise gain separately from each signal weight

For a voltage-feedback amplifier with ideal low-impedance input sources and purely resistive branches, the noise gain is one plus Rf times the sum of the input conductances. It is 3.5 in the example, even though the individual signal gains have magnitudes two and one-half. Noise gain, feedback impedance and the amplifier's open-loop behavior matter to stability and bandwidth; the smallest signal weight is not the correct stability gain.

Include real source and input capacitances when examining frequency-dependent behavior. Disconnecting an input can change the feedback network seen by amplifier noise without producing the passive averaging behavior discussed elsewhere. Validate the actual allowed connection states. Do not transfer a simple voltage-feedback gain-bandwidth approximation to a current-feedback amplifier or interpret a DC ratio measurement as a dynamic stability test.

Specify the relationships the printed network must preserve

Provide the schematic, terminal identities and ratio directions, not only a list of nominal resistor values. The feedback element influences every input weight, so its variation creates correlated gain changes. Identify whether the customer requires each absolute resistance, relative weights, total output accuracy or a combination under specified temperatures and loading.

Keep fired ceramic thick-film construction distinct from other resistor technologies. Review geometry, termination, protective glass and trim access by drawing without assuming a universal matching or drift capability. A resistor network can implement the agreed relationships, but the active amplifier, reference and connected sources retain responsibility for headroom, power sequencing and dynamic operation.

Verify individual weights and the combined operating envelope

Hold the other sources at defined states and perturb one input at a time to measure its local output weight. Then apply permitted simultaneous corner combinations and representative dynamic signals. Record the actual source voltages, output load, reference and supplies so the measured gains can be compared with the same model boundary.

Look for clipping, delayed recovery, source current limiting and changes when an input is disconnected or unpowered. Preserve raw waveforms rather than reporting only a fitted gain. For a ChipSimple resistor-network enquiry, send the full active summer interface and error allocation. The design handoff should show where resistor precision is useful and where the system requires a different signal scale, reference or amplifier operating range.