13.3.2 The ideal operational amplifier

Operational Amplifiers (Op-Amps) and Amplification

An amplifier is a device designed to increase the strength of an analogue signal's input. Amplifiers are widely used in electronics to boost signals for various applications, from audio to instrumentation.

• The output of an amplifier is a larger version of the input signal, which means it follows the same pattern or waveform as the input but with greater amplitude.
• Output voltage $(V_{out})$ represents the amplified signal, while input voltage $(V_{in})$ is the original signal.

What is an Operational Amplifier?

An operational amplifier (op-amp) is an essential electronic component that provides amplification of signals. It has two inputs:

1. Inverting input $( V_{-} )$ – often marked with a minus sign $(-)$
2. Non-inverting input $( V_{+} )$ – marked with a plus sign $(+)$ The symbol for an op-amp typically shows these two inputs and an output $( V_{out} )$.

• Op-amps are versatile and can be set up in different ways to achieve various levels and types of amplification.
• A key measure of amplification in op-amps is the gain (A), defined as the ratio of output voltage to input voltage:

$$A = \frac{V_{out}}{V_{in}}$$

Types of Gain in an Op-Amp

1. Open-loop Gain $(A_{OL})$:

• In this mode, there is no feedback in the circuit; signals are not fed back from the output to the input.
• This produces very high gain, as there is nothing limiting the amplification.

2. Closed-loop Gain $(A_{CL})$:

• In this configuration, part of the output is fed back to the input.
• This feedback can control and stabilise the gain, making it more useful in practical applications.

Op-Amp Transfer Function and Ideal Characteristics

An operational amplifier amplifies the difference between the two input voltages ($V_{+}$ ) and $( V_{-} )$, described by the equation:

$$V_{out} = A_{OL} (V_{+} - V_{-})$$

where $A_{OL}$ is the open-loop gain.

An ideal operational amplifier is assumed to have the following characteristics:

• Infinite open-loop gain $(A_{OL})$, allowing it to generate any necessary finite gain in a closed-loop setup.
• Infinite input resistance between the $V_{+} \ and\ V_{-}$ inputs, meaning no current is drawn from the input sources.
• Infinite bandwidth, enabling the op-amp to amplify signals at any frequency.
• Zero output resistance, ensuring the output current remains unaffected by changes in the output load.

Saturation in Operational Amplifiers

An op-amp cannot produce an output voltage exceeding its supply voltage. If the input voltage difference attempts to generate an output voltage larger than the supply, the op-amp reaches saturation. In this state:

• If $V_{out}$ attempts to exceed the positive supply $( V_{S+})$, it remains at $V_{S+}$.
• If $V_{out}$ attempts to go below the negative supply $( V_{S-})$, it remains at $V_{S-}$. This behaviour can be visualised on a graph showing how $V_{out}$ changes with $(V_{+} - V_{-})$.

Comparator Circuits Using Op-Amps

In comparator circuits, an op-amp in an open-loop configuration can compare two input voltages:

• If $V_{+} > V_{-}$, the output $V_{out}$ reaches the positive supply voltage (e.g., +$10$ V).
• If $V_{+} < V_{-}$, the output $V_{out}$ reaches the negative supply voltage (e.g., $-10$ V).
• If $V_{+} = V_{-}$, the output is theoretically $0$ V, but this scenario is rare and usually results in an undefined output.