2. Op-Amp Characteristics

2.1 What an op-amp is, in one breath

A high-gain ($10^5$ to $10^7$ open-loop), DC-coupled, differential amplifier in a single integrated circuit. Two input pins ($V_+$, the non-inverting input; $V_-$, the inverting input), one output pin, two power supply pins (typically $\pm 15$ V or $\pm 5$ V or single $+5$ V or $+3.3$ V), and sometimes a couple of offset-null pins.

Symbol:

       V+ ──┐\
            │ \
            │  ●── V_out
            │ /
       V- ──┘/

The triangle points from the inputs to the output. The non-inverting input is conventionally drawn on top with a "$+$"; the inverting input on the bottom with a "$-$". The plus and minus do not refer to power supplies but to the polarity of the input's effect on the output: a rise in $V_+$ raises the output, a rise in $V_-$ lowers it.

2.2 The ideal op-amp, a useful fiction

The "ideal" op-amp is a teaching device. It has:

• Infinite open-loop voltage gain. A vanishing input-difference produces a finite output.
• Infinite input impedance. No current draws into either input.
• Zero output impedance. The output is a perfect voltage source, can drive any load.
• Infinite bandwidth. Same gain at DC, at 1 kHz, at 1 GHz.
• Zero offset voltage. With both inputs at the same potential, the output is exactly zero.
• Infinite CMRR and PSRR. Common-mode and supply disturbances do nothing.
• Output that swings rail to rail and back instantly.

Real op-amps approximate these to varying degrees. The miracle of negative feedback is that, when the open-loop gain is huge, almost all the imperfections vanish in the closed-loop circuit. A 0.1% gain accuracy, a megohm input impedance, a thousand-ohm output impedance: with feedback you do not see them. That is the whole reason to wrap feedback around the op-amp.

2.3 The 741 op-amp's internal block diagram

                                  +V_CC
       ┌─────────────────────────────────────┐
       │                                      │
    [PNP diff pair]                        [Output
   V+ ───┐ (Q1, Q2)                        push-pull
   V- ───┘  │                              class AB
       │    │  ↑ tail current source       Q14, Q20]──── V_out
       │    │                                  ↑
       │   [NPN active load mirror]            │
       │    │                              [Driver
       │    │                              Q16, Q17]
       │   [Common-emitter gain stage]         ↑
       │   Q17 with Miller compensation cap    │
       │   30 pF from input to output    ──────┘
       │                                       │
       └─────────────────────────────────────┘
                                  -V_EE

Reading top-to-bottom, the four blocks are:

1. Input differential stage. A PNP diff pair with active-load current mirror. This is where CMRR is set and bias currents come from.
2. Voltage-gain stage. A common-emitter Q17 driven by the diff pair, loaded by an active current source. This is where most of the gain comes from. A 30 pF Miller compensation capacitor wraps from the base of Q17 to its collector.
3. Class-AB output stage. Two complementary transistors (Q14 NPN, Q20 PNP) push and pull. Both are biased with a small idle current to avoid crossover distortion.
4. Bias network. A widlar current mirror generates the tail current and various bias currents from the supply.

The 30 pF Miller cap is the "internal compensation" that makes the 741 unconditionally stable for any closed-loop gain $\geq 1$. It rolls off the open-loop gain at 6 dB/octave starting around 10 Hz so that the gain has dropped to 1 well before the higher-frequency poles of the chip cause too much phase shift to oscillate. The price: a slow op-amp, with $f_T \approx 1$ MHz and a slew rate of only 0.5 V/µs.

The 741 dates to 1968 (Fairchild µA741, designed by Dave Fullagar) and is still in production from a dozen manufacturers in 2025. It is the canonical example, the part you reach for when you want to teach somebody op-amps. Modern designs that need real performance use better parts, but the 741 is the textbook reference.

2.4 Datasheet specifications, one by one

These are the parameters every op-amp datasheet lists. Memorize them; you will read them every day if you do analog design.

• Open-loop voltage gain $A_{OL}$. Typically $10^5$ to $10^7$ at DC. Falls off above the open-loop bandwidth (a few Hz to a few kHz, depending on the part).

• Input bias current $I_B$. Tiny DC current that has to flow into each input to bias the input transistor. For the 741: 80 nA. For a JFET input like the TL072: 30 pA. For a CMOS input like the LMC6041: a few fA. Bias current matters because it flows through your feedback network and creates an offset voltage.

• Input offset voltage $V_{OS}$. The small DC voltage you would have to apply between the inputs to make the output exactly zero. Caused by mismatch between the input transistors. For the 741: typically 2 mV. For a precision part like the OP07: 30 µV. For a chopper-stabilized part like the LTC2050 or MAX44245: 1 µV or less.

• Input offset current $I_{OS}$. The difference between the two bias currents. Smaller than $I_B$ because the two input transistors track each other.

• CMRR. Decibels of rejection of common-mode signals. 80 dB to 130 dB.

• PSRR (Power Supply Rejection Ratio). Decibels of rejection of supply ripple. Equally important; supply noise that gets to the output looks just like a signal.

• Slew rate. The maximum rate at which the output can change. Typically expressed in V/µs. For the 741: 0.5 V/µs. For a high-speed part like the LT1226: 200 V/µs. Slew rate is set by the maximum current available to charge the Miller compensation cap; once you hit slew limit, the output cannot keep up with the input regardless of frequency.

• Gain-bandwidth product (GBW). The frequency at which the open-loop gain has fallen to 1. For a single-pole-rolloff op-amp, GBW also equals (closed-loop gain) × (closed-loop bandwidth). Set the closed-loop gain at 100 with a 1 MHz GBW op-amp and your bandwidth is 10 kHz, period.

• Input voltage range and output swing. Some op-amps have inputs that work down to or even below the negative rail ("rail-to-rail input"); some have outputs that swing within a millivolt of the rails ("rail-to-rail output"); some have both. The 741 does neither: its inputs must stay 2 V away from each rail and its output saturates 1.5 V from each rail.

• Noise. Voltage noise density (nV/√Hz) and current noise density (pA/√Hz). Matters for low-level signal acquisition; we will revisit it in Chapter 22.

2.5 A small zoo of real op-amps

A handful of part numbers covers most of analog design. Memorize at least these.

• µA741. The classic, 1968. General purpose, slow, robust, ubiquitous.
• LM358 / LM324 (dual / quad). Single-supply, low cost, the workhorse of cheap consumer electronics.
• TL072 / TL082 / TL074. JFET input, low noise, low bias current. The audio default.
• OPA2134 / OPA1612. Audiophile-grade audio op-amps. Low noise, low THD.
• LMV358 / LMV324. Rail-to-rail, low voltage (1.8 V minimum). Battery-powered devices.
• OP07 / OP27. Precision op-amps, 25 µV offset, low drift.
• LTC2050 / MAX44245. Chopper-stabilized, sub-µV offset. Precision instrumentation.
• ADA4528, AD8628. Zero-drift precision op-amps for thermocouples and bridge sensors.
• AD8253, INA821, LT1167. Instrumentation amplifiers (programmable-gain or external-gain-resistor); the standard for sensor signal conditioning.
• AD8429. Ultra-low-noise instrumentation amp; 1 nV/√Hz, used in sub-microvolt physics measurements.
• OPA627 / OPA827. High-precision JFET, the boutique audio choice.
• LM7171, LT1226. Fast voltage-feedback op-amps for video and high-speed applications.
• ADA4807, OPA855. GHz bandwidth current-feedback amplifiers for high-speed scopes and lab gear.
• LTC6655, ADR4525, REF5025. Not op-amps but related: ultra-precision voltage references with integrated buffers, sub-ppm temperature drift, used as ADC and DAC references. Critical for any precision system.

The point of memorizing parts is that picking the right op-amp is most of analog design. There is no single "best." There is a part with the right combination of noise, bandwidth, offset, supply voltage, package, and price for the job at hand.

2.6 Frequency compensation, briefly

Most modern op-amps include a Miller compensation capacitor on-die, designed to make the part unconditionally stable for unity gain or higher. The cap rolls off the open-loop gain at 20 dB/decade so that by the time the gain crosses 0 dB, the phase shift around the loop has not yet hit 180° (which would make oscillation possible).

For "decompensated" op-amps (no internal cap, or a smaller-than-standard cap), you must add external compensation tailored to your closed-loop gain. The reward for this complication is more bandwidth at higher gains: a part stable only at $A \geq 10$ can be 10x faster than the same silicon stable at $A = 1$.

2.7 Hardware-security implications of op-amp parameters

• Slew rate as a side channel. A glitch on the supply might briefly drive a precision op-amp into slew limit, where it stops being linear. An attacker knowing the slew rate can craft glitches that saturate sensors during sensitive measurements.
• Offset and bias drift under attack. Forced temperature transients (laser heating, freezing spray) shift offsets in op-amps used for tamper detection. Attackers exploit this to disable alarms.
• PSRR matters for supply-glitching. Op-amps with poor PSRR pass supply noise to their output, which can corrupt downstream comparisons or ADC inputs. A defender wants high PSRR specifically so a glitched supply does not rattle the analog rails.
• CMRR limits side-channel measurement. When you point an instrumentation amp at a power-line shunt, its CMRR sets the floor of what you can resolve through the noise on the rail. A 130 dB amp lets you see microvolts on a 1 V rail; an 80 dB amp does not.