Differential Amplifier Calculator

The calculator computes differential gain (Ad), common-mode gain (Acm), Common-Mode Rejection Ratio (CMRR in dB), output voltage (Vout), input and output voltage ranges relative to supply rails, and resistor matching error impact on CMRR. It also estimates worst-case CMRR degradation due to resistor tolerance.

Use it during analog front-end design—especially for sensor interfaces (e.g., strain gauges, thermocouples), instrumentation amplifiers, and ADC driver stages. It helps verify gain accuracy, assess noise rejection, ensure output stays within supply rails, and select appropriate resistor tolerances before PCB layout.

R₁ is the input resistor connected to each op-amp input (typically equal on both sides), and R₂ is the feedback resistor from output to the inverting input. For ideal matching, R₁ = R₃ and R₂ = R₄ in the full 4-resistor topology; this calculator assumes that symmetry and derives performance from R₁/R₂ ratio.

Even small mismatches between R₁/R₃ or R₂/R₄ degrade CMRR significantly—e.g., 1% tolerance can limit practical CMRR to ~40 dB, far below an op-amp’s intrinsic capability. This calculator quantifies that degradation so you can decide whether to use matched resistor networks, trimming, or integrated instrumentation amps.

R₁ commonly ranges from 1 kΩ to 100 kΩ; R₂ is chosen to set gain (e.g., R₂/R₁ = 10 for ×10 differential gain). Values >100 kΩ increase noise and susceptibility to leakage; <1 kΩ may overload driving sources. Always verify current draw against op-amp output capability and thermal noise requirements.

V_s defines the op-amp’s output swing limits (accounting for headroom). The calculator checks whether Vout falls within the linear output range (e.g., V_s − 1.5 V for a typical rail-to-rail op-amp) and flags saturation risk. It also informs input common-mode range constraints.

First, verify input common-mode voltage is within the op-amp’s specified range. Then reduce gain (lower R₂/R₁ ratio), attenuate inputs, or choose a higher supply voltage. Alternatively, consider an instrumentation amplifier with better common-mode handling or rail-to-rail output capability.

No—it models only the classic 4-resistor differential amplifier (in-amp topology without internal gain stage). For non-inverting amps, use a separate op-amp gain calculator. To adapt for single-ended input, set one input (e.g., V₂) to a stable reference (like V_REF) and interpret Vout as referenced to that node.

CMRR = |A_d/A_cm|, where A_cm is derived from resistor mismatch: A_cm ≈ 2·(ΔR/R) for small mismatches. For industrial sensors, ≥60 dB is typical; precision metrology often requires ≥80–100 dB—achievable only with 0.01% resistors or monolithic solutions.

No—this calculator assumes ideal op-amp behavior (infinite gain, zero offset, infinite bandwidth). Real-world effects like input offset (which adds error proportional to gain) and GBW limitations (causing gain roll-off at high frequencies) must be evaluated separately using datasheet specs and SPICE simulation.