Op Amp Fundamentals and Principles

Key Takeaways

• Learn the basic function of op amps

• Learn about op amp internals and how they work

• Applications and uses for op amps

Op amp schematic diagram with inputs, power rials, and output

An op amp, short for operational amplifier, is a high gain amplifier circuit with a differential input. Op amps are some of the most fundamental pieces of circuitry used for linear, nonlinear, and frequency dependent mathematical operations in circuits. 

Using feedback, the op amp becomes even more versatile, with applications in everything from scientific, consumer, and industrial devices. There are many resources describing op amps and their functions. We’ll be covering op amp functional basics and then delving into the applications of op amps.

Basic Op Amp Operation

Inverting op amp configuration with negative feedback

All op amps have especially useful features such as incredibly high input impedance and low output impedance, with little-to-no current draw into their terminals. Op amps without feedback in an open-loop configuration seem rather simple. However, feedback in a closed-loop configuration allows for a variety of applications, which we’ll be discussing. 

Open Loop Operation

Without any additional circuitry, an op amp simply outputs the difference between the positive and negative inputs. In other words:

 V_OUT = A_OL (V₊ - V_-)

A_OL is the open loop gain. The open loop gain in ideal op amps is infinity, whereas real op amps have an open loop gain of at least three or more orders of magnitude larger than the differential voltage. The open loop gain value is not always well controlled in op amp fabrication, so utilizing an op amp in a closed loop configuration is more useful. 

Closed Loop Operation

Op amps really shine when implemented with a feedback network, creating a desired predictable operation. With negative feedback, the gain and frequency response are determined more so by the feedback network rather than the op amp architecture itself.

Ultimately, with negative feedback, op amps function to minimize the differential input voltage between their terminals. In other words, when implemented in a circuit, they most often operate in a way that will cause their negative and positive differential inputs to be the same.

In the image above, we have a basic inverting op amp with negative feedback. The op amp will have the same voltage at both of its terminals—in this case, 0V (the positive terminal) is connected to ground. Using Kirchoff’s current laws, we can say that:

 V_IN / R ₁ = -V_OUT / R _f or  V_OUT / V_IN = A_ClosedLoop = -R _f / R₁

Op Amp Non-Idealities

Ideal operational amplifiers only exist in theory. Although op amp designs are constantly improving, real op amps suffer from a variety of non-idealities you should keep in mind when designing:

• Real op amps have a finite loop gain that rolls off with frequency. In other words, as frequency increases, the open loop gain decreases. The unity gain-bandwidth product is the frequency at which the finite loop gain becomes unity. This makes op amps behave similarly to first order low-pass filters near their GBWP. For high frequency applications, a current feedback op amp can be used. 

• Op amps usually have low (but non-zero) output impedances. Having a low output impedance is useful for when a low-impedance load is used. Using a low-impedance load reduces the open-loop gain and may also result in more quiescent current in the output stage, dissipating more power.

• Real op amps also have finite input impedances—both a differential input impedance between the two inputs and a common-mode input impedance, which is the input impedance relative to ground. 

• Real op amps require input bias current that, when coupled with a high output impedance load, can result in voltage drops. 

• Input offset voltage is the voltage required to set the output voltage to zero. In other words,  V_OUT = 0 =A_OL (V₊ - V_- + V_{Input - Offset}). This, in theory, should be zero so that when both inputs have the same value, the output is driven to zero. In reality, it is a small nonzero value that occurs from the differential input stage.

• Op amps may have a common-mode gain, where common-mode voltages may be slightly amplified due to the differential stage of an op amp. The common-mode rejection ratio (CMRR) quantifies this phenomenon. 

• Regardless of the power supply, ideal op amps are independent of fluctuations. In reality, the power supply rejection ratio measures how op amps reject changes in supply voltages.

• Other non-idealities may occur from temperature effects, drift, distortion, noise, and stability issues. 

Other imperfections that occur in real op amps involve non-linear and power-related considerations:

• Saturation occurs when the output can only reach a couple volts (or in rail-to-rail op amps, millivolts) of the power supply.

• Slewing, where the op amp can only output signals that change at specific rates, usually specified in volts per microsecond (V/μs).

• Finite output current, usually around 25 mA for common 741 op amps.

• Finite output sink current, where an op amp can only sink so much current from another source.

• Especially at high frequencies, stray capacitance can occur between the input and output. 

• Trace inductance at the non-inverting input of high-speed op amps can cause oscillations. 

Op Amp Architecture

741 series op amp internal schematic with highlighted subcircuits. From Wikipedia.

There are a variety of off-the-shelf op amps available for most of your needs, including rail-to-rail, high precision, and low noise. That being said, having a general understanding of how basic op amps are constructed can be useful in debugging and further understanding circuits.

At their most basic level, op amps consist of a differential amplifier, a gain stage, and an output stage. Here, we’ll take a quick look at the internal circuits of the 741-type op amp, one of the most common and readily available op amp designs.

Individual stages include:

• Current mirror in red
• Differential amplifiers in blue
• Class A gain stage in magenta
• A voltage level shifter in green
• An output stage in cyan 

The differential amplifier amplifies the differential signal while rejecting the common mode signal. It has low noise and high input impedance, uses a cascade architecture, and is connected to an active load. This active load presents a high small-signal impedance without a large DC voltage drop. Q1 and Q2 are an emitter follower pair that have high input impedance. Q3 and Q4 are a common-base pair that drive active load Q7, which converts the differential signal to a single-tail going into the base of Q15.

The magenta class-A voltage amplifier, formed by Q15 and Q19 in a Darlington configuration, has a high voltage gain, as it uses Q13 as its collector load, creating even higher gain. Q20 has its base driven from Q15/Q19. Q16 is a level-shifter that drives that base of the output transistor Q14. In the case of excess current, Q22 sinks current and prevents it from reaching Q22.

The output amplifier in cyan, composed of Q14 and Q20, is a Class AB complementary-symmetry amplifier. Q16 (in green) provides the quiescent current and can be current limited by Q17. 

Op Amp Applications

Op amps are some of the most versatile circuit components. Anytime you want to perform a mathematical function with your analog signal, an op amp can likely serve this purpose, resulting in a wide arrange of circuit applications:

• Variable gain amplification can be achieved by modifying the resistor feedback network. This can be done with CMOS switches that toggle various combinations.

• Op amps can be used to form mixers and modulators by adding or subtracting signals with various frequencies. 

• Sample-and-hold circuits can be built around op amps for data collection. The circuit switches between sampling a signal value to holding it for a specific amount of time–useful for creating audio-to-digital converters.

• Op amps can be used in 4-20 mA receiver design to remove the offset voltage corresponding to live zero or 4 mA current.

• Op amps can be useful in constructing active filters such as pi filters. 

Op amps are used in a variety of devices and sensors as well. For example:

• Creating a differential pulse voltammetry circuit used for chemical analytical methods requires a potentiostat made of op amps. 

• Op amps can be used to collect current from electrochemical cells in a current measurement setup. 

• Voltage-controlled oscillators and  multivibrator circuits can be constructed out of op amps. Alternatively, with tuned-collector oscillators, tuned-base oscillators, Colpitts oscillators, and Hartley oscillators, op amps can be used to amplify and buffer the signal.

• Op amps with positive-feedback and hysteresis can be used to create Schmitt triggers, although they might be limited in frequency (depending on the application, a comparator might be better).

• Anti-aliasing filters usually use high order active filters with low noise amplification capabilities made out of op amps. 

• Various temperature sensors and other IC-based sensors have built-in op amps for ADC and amplification purposes.

Whatever circuit design you plan on using op amps for, it’s important to have a strong fundamental understanding of their functions. In order to create a schematic and layout your electronic design, you’ll need strong PCB design and analysis software to help you out. Consider Cadence’s suite of tools for your next project.