Op-Amps#

The operational amplifier is the universal building block of analog design. An op-amp is a high-gain differential amplifier — it amplifies the difference between its two inputs. With external feedback components, it can be configured as virtually any linear analog function: amplifier, filter, integrator, comparator, buffer, summing circuit.

The power of the op-amp comes from a useful simplification: if the open-loop gain is “high enough,” the circuit behavior depends entirely on the feedback network, not the op-amp itself.

Ideal Assumptions#

The ideal op-amp model makes analysis tractable:

1. Infinite open-loop gain — The output does whatever it takes to make the differential input zero
2. Infinite input impedance — No current flows into the inputs
3. Zero output impedance — The output can drive any load without voltage drop
4. Infinite bandwidth — Gain doesn’t roll off with frequency
5. Zero input offset voltage — With both inputs at the same voltage, the output is exactly zero

These assumptions lead to two golden rules for negative feedback circuits:

• No current flows into the inputs (from assumption 2)
• The two inputs are at the same voltage (from assumption 1 + negative feedback)

Apply these two rules, and any op-amp feedback circuit can be analyzed with just KCL and Ohm’s law.

Why the Ideal Assumptions Fail#

Every real op-amp violates all five assumptions. The question is whether the violations matter for the application.

Finite open-loop gain (A_OL):

• Typical: 100 dB (100,000 V/V) at DC
• Drops at 20 dB/decade above the dominant pole (usually a few Hz to a few hundred Hz)
• At the gain-bandwidth product (GBW) frequency, A_OL = 1
• Closed-loop gain can’t exceed A_OL at any frequency. If a circuit needs gain of 100 at 1 MHz, the op-amp must have GBW > 100 MHz

Finite input impedance:

• Typically megaohms to teraohms for FET-input op-amps
• Typically hundreds of kilohms to megaohms for BJT-input op-amps
• Input bias current is the practical issue: BJT inputs draw nanoamps to microamps, FET inputs draw picoamps. This current flowing through feedback resistors creates offset voltages

Non-zero output impedance:

• Open-loop output impedance is tens to hundreds of ohms
• Feedback reduces effective output impedance by the loop gain factor
• At high frequencies where loop gain is low, output impedance rises. This matters when driving capacitive loads

Finite bandwidth and slew rate:

• Gain-bandwidth product (GBW) sets the maximum useful frequency for a given gain
• Slew rate limits how fast the output can change (typically 1-100 V/us for general-purpose op-amps). A slew-rate-limited output clips large fast signals into a triangle wave regardless of the feedback network

Input offset voltage:

• Typically 1-10 mV for general-purpose, sub-millivolt for precision types
• Appears as an equivalent DC voltage between the inputs
• Gets amplified by the noise gain of the circuit. A 5 mV offset in a gain-of-100 circuit produces 500 mV of output offset

Core Topologies#

Non-Inverting Amplifier#

• Input at the + terminal, feedback from output to - terminal through a voltage divider
• Gain: A_v = 1 + (R_f / R_in)
• Input impedance: very high (the op-amp’s own input impedance, multiplied by loop gain)
• Non-inverting (output in phase with input)
• Minimum gain is 1 (can’t be less)

Inverting Amplifier#

• Input through a resistor to the - terminal, feedback resistor from output to - terminal
• Gain: A_v = -(R_f / R_in)
• Input impedance: R_in (the input resistor — the virtual ground means the input sees R_in to ground)
• Inverting (180-degree phase shift)
• Can have gain less than 1 (attenuator)

Voltage Follower (Buffer)#

• Output connected directly to - input, signal applied to + input
• Gain: exactly 1
• Input impedance: extremely high
• Output impedance: extremely low
• The simplest and most useful op-amp circuit. Isolates a high-impedance source from a low-impedance load

Differential Amplifier#

• Amplifies the difference between two inputs while rejecting what’s common to both
• Depends critically on resistor matching. 1% resistor mismatch in a differential amp limits common-mode rejection to about 40 dB. For better CMRR, use instrumentation amplifiers (three op-amp topology)

Real-World Limitations Checklist#

When selecting an op-amp for a real application, these are the parameters that actually matter:

Tips#

• Add a small series resistor (10-100 Ω) at the op-amp output when driving capacitive loads or cables to prevent oscillation
• For single-supply AC circuits, set the DC bias point at mid-supply using a resistive divider with a bypass capacitor
• Always install 100 nF ceramic bypass capacitors on both power pins, as close to the IC as possible
• Use FET-input op-amps when driving from high-impedance sources to minimize bias current errors

Caveats#

• Phase margin and capacitive loads — Most op-amps are not stable with capacitive loads. Cables or long traces add capacitance that can cause oscillation. A small series output resistor (10-100 Ω) often provides a fix
• Rail-to-rail doesn’t mean rail-to-rail — “Rail-to-rail output” means the output can get close to the rails under light loads — typically within 50-200 mV. Under heavier loads, the headroom requirement increases
• Single-supply biasing — On a single supply, the inputs need to be biased above ground. AC-coupled circuits need a DC bias point at mid-supply. This is straightforward but easy to forget
• Noise gain vs. signal gain — The noise gain (which determines stability and bandwidth) is not always the same as the signal gain. For inverting amplifiers, noise gain is 1 + R_f/R_in, which is higher than the signal gain magnitude |R_f/R_in|
• Decoupling is not optional — Op-amp power pins need local bypass caps (100 nF ceramic minimum). Without them, the power supply rejection degrades and oscillation can occur
• Comparator use — An op-amp without negative feedback acts as a comparator, but usually a poor one — slow, no hysteresis, and the output doesn’t swing cleanly to the rails. Use a dedicated comparator for comparison tasks

In Practice#

• An op-amp circuit that oscillates or rings often has a capacitive load or missing bypass capacitors — check output wiring and add series resistance or decoupling
• Output clipping well before the supply rails indicates the op-amp lacks rail-to-rail capability or the load is too heavy
• Unexpected DC offset at the output suggests input offset voltage being amplified by the noise gain — verify offset specs match the application
• An op-amp used as a comparator that responds slowly or chatters has no hysteresis — switch to a dedicated comparator IC with built-in hysteresis