S5-4.1 The Operational Amplifier

What this is and why it exists

Designing an amplifier from individual transistors means choosing a bias point, working out a small-signal model, and living with the spread between parts.

The operational amplifier removes almost all of that. It has so much gain that the feedback network around it, and not the device, decides what the circuit does. You design with resistors instead of with transistors.

The vocabulary

• Open loop gain — the gain of the device with no feedback. It is very large and poorly controlled.
• Virtual short — the ideal result that feedback drives the two inputs to the same voltage.
• Inverting amplifier — input applied through a resistor to the inverting terminal. The output has the opposite sign.
• Non-inverting amplifier — input applied to the non-inverting terminal. The output has the same sign.
• Voltage follower — a non-inverting amplifier with a gain of one.
• Input offset voltage — the small input needed to make the output zero.
• Input bias current — the small current the inputs actually draw.
• Slew rate — the fastest the output can change, in volts per microsecond.
• CMRR — common mode rejection ratio. How well the device ignores a signal present on both inputs.
• PSRR — power supply rejection ratio. How well it ignores movement on its supply rails.

The mental model

Two ideal rules solve most circuits in one line.

The first is that no current flows into either input. The second is that feedback drives the two inputs to the same voltage. The second rule holds only under two conditions. There must be negative feedback, and the output must not have hit a supply rail.

Apply the rules to the inverting configuration. The non-inverting input sits at zero, so the inverting input is driven to zero as well. All the input current therefore flows through the feedback resistor. The gain is the ratio of the two resistors, with a sign change. Apply them to the non-inverting configuration and the gain is one plus the ratio. Both results should come out instantly.

The voltage follower is the extreme case, with a gain of exactly one. That sounds pointless until you need it. Its input draws almost no current and its output can drive a load, so it stops one stage from loading the next. It is the most used circuit in this topic.

Every parameter below is one specific way a real device breaks one of the two rules. Learn each as a named failure rather than as a number.

Input offset voltage says the device does not output zero for zero input. It is small, and it dominates when the signal you are amplifying is also small. Input bias and offset currents say the inputs do draw a little current. That matters most with large resistors, which is exactly when a designer assumes it will not.

Slew rate is the one that surprises people. It is a large-signal limit, so no small-signal analysis will ever reveal it. A circuit can be perfectly linear on paper and still turn a fast sine wave into a triangle. The output physically cannot change any faster.

The two rejection figures say how well the device ignores what it should ignore. Common mode rejection covers a signal appearing on both inputs at once. Power supply rejection covers movement on the supply rails. They are the numbers to look at when a circuit works on the bench and fails inside a noisy cabinet.

The habit worth building is to solve every circuit twice. Once with the ideal rules, and once with the assumptions removed. The difference between the two answers is what the specification sheet has been telling you.

What you should now be able to explain or do

State the two ideal rules and the condition under which the second holds. Derive the gain of the inverting and non-inverting configurations without hesitating. Say why a voltage follower is useful despite its gain of one. Name the parameter each of offset voltage, bias current, slew rate and the two rejection ratios breaks. Explain why slew rate cannot be found by small-signal analysis.

Check yourself