Op-amps in the real world

Textbook op-amps have infinite gain, bandwidth and input impedance. Real ones run out of gain at high frequency, slew, have offset and bias current, hiss, ring into capacitive loads, and can’t reach their supply rails. This tool takes a catalogue of sixteen real parts — from the 1968 LM741 and the ubiquitous LM358 through audio parts (NE5532, OPA2134, OPA1612), rail-to-rail CMOS (MCP6002, TLV9062), zero-drift precision (AD8628, ADA4528) and the 3 A OPA548 — and works out what each limitation costs in your circuit.

How to use it

Open the Catalogue to compare the parts; click a row for the details, its datasheet, and which figures are estimates.
In each calculator tab, pick an op-amp from the list (it fills in its datasheet figures, which you can then edit) or choose Custom and enter your own.
Bandwidth: enter Rf and Rg for an inverting or non-inverting stage; read the noise gain, the −3 dB bandwidth, the gain error at your frequency, and how splitting the gain into stages helps.
Slew rate: enter the output amplitude and frequency; watch the output turn from a sine into a triangle as you drag the frequency past the full-power bandwidth, and read the THD.
DC errors: enter the resistors, temperature range and full scale for a worst-case and typical output-offset budget, and try Set Rp = Rf‖Rg to see bias-current compensation work.
Noise: enter the source resistance, the resistors and the band; read the rms output noise, which source dominates, and which catalogue part is quietest from that source.
Stability: load an example (a follower into 1 nF, an isolation resistor, in-loop compensation, a photodiode amplifier) and change CL, Riso, Cf; the phase margin, Bode plot and step response update.
Input/output range: enter the supply, gain and input range to check common-mode and output-swing limits on a single supply.
Selector: enter your requirements; the matching parts are ranked, and the rejected ones say why.

The models

Catalogue. Typical figures at 25 °C from each maker’s datasheet (TI, Analog Devices, Microchip; the document is named on each part), with the maximum beside the typical for offset, drift, bias and offset current where it is given. Figures marked ≈ are estimates — read off a typical curve (1/f corners, output swing against load), or a usual value for that kind of part where the datasheet is silent (the open-loop output resistance, the phase margin used for the second pole). Check the current datasheet before committing a design.
Bandwidth. A single-pole op-amp, A(f) = A₀/(1 + jf/f_p) with f_p = GBW/A₀. The loop sees the noise gain 1 + Rf/Rg whatever the configuration, so the closed-loop bandwidth is GBW/(1 + Rf/Rg): a gain of −1 has half the bandwidth of a follower. The gain error at f is from G/(1 + NG/A(jf)). n identical stages in cascade have a bandwidth √(2^1/n − 1) times one stage’s.
Slew rate. The full-power bandwidth is SR/(2π·V_peak). The animation integrates dV/dt = clamp(ω_c·(V_in − V_out), ±SR), the small-signal pole and the slew limit together, and the THD comes from the first fifteen harmonics.
DC errors. V_out = NG·(V_os − I_b+·R_p) + I_b−·R_f with I_b± = I_b ± I_os/2. The worst case adds the magnitudes at their maximums; typical is the root-sum-square of typical values. A resistor R_p = R_f‖R_g at the + input cancels equal bias currents, leaving only I_os·R_f; FET and CMOS bias currents double every 10 °C. Put the total into the offset line of the ADC error budget.
Noise. The same model as the circuit simulator's noise analysis: 4kT·R for each resistor, e_n in series with the + input, i_n from each input to ground, each carried to the output by its own gain and added in power, at 27 °C by default. The densities follow e_n(f) = e_white·√(1 + f_corner/f), and the closed-loop pole GBW/NG rolls them off. The rms is a numerical integral over your band (×6.6 for peak-to-peak). The quietest op-amp for a source resistance R_s minimises √(e_n² + (i_n·R_s)² + 4kT·R_s); the noise figure is lowest near the optimum source resistance e_n/i_n (Motchenbacher & Connelly, Low-Noise Electronic System Design).
Stability. A two-pole op-amp — the dominant pole and a second pole placed to give the datasheet phase margin — with its open-loop output resistance R_o, driving R_iso and C_L, with R_f taken from the op-amp pin or from the load (in-loop compensation), C_f across the feedback, and C_in at the − input. The loop gain is solved by nodal analysis, the step response by trapezoidal integration. For a two-pole loop, phase margin maps to damping and overshoot exactly (45° ≈ 23%, 60° ≈ 9%). The transimpedance C_f for a maximally flat response solves 1/Q = ω₀·(R_f·C_f + 1/ω_T) with ω₀² = ω_T/(R_f·(C_in + C_f)) for Q = 0.707; Graeme’s 45° value is (1 + √(1 + 8π·R_f·C_in·GBW))/(4π·R_f·GBW) (TI SBOA055, Graeme, Photodiode Amplifiers).
Input/output range. The common-mode range and output headroom from the datasheet, with the headroom growing linearly with load current between the light-load figure and a loaded one. Parts that reverse phase (TL072, LM741) send the output to the wrong rail when the input leaves the range.
Selector. Hard limits remove parts (supply, GBW, slew, maximum offset, bias, noise, rail-to-rail, output current, price, minimum stable gain, phase reversal); what is left is ranked by noise from your source resistance, offset, speed, price, or supply current.

Further reading: TI’s Op Amps for Everyone (SLOD006), Analog Devices' tutorials MT-033 (gain and bandwidth), MT-037 (offset), MT-038 (bias current) and MT-048 (noise), and Tim Green’s Operational Amplifier Stability series.

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The models

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