The "speed" of an operational amplifier (op amp) refers to its frequency response and slew rate. The models presented here apply to the voltage-feedback family of op amps. These two parameters are related to some degree. Figure 1 shows a two-stage op amp model, simplified for AC analysis.

Figure 1: AC model of op amp
(Click on image to enlarge)

.The input is a transconductance stage. For a voltage input, it produces a current output. The output stage is best modeled as an integrator with the compensation capacitor as the integration element. Analysis yields a transfer function of:

At frequencies above the first pole in the op amp response, this function has the same slope as was demonstrated in Part 13 of this series. The gain decreases by a factor of 10 for every decade increase of frequency. Unity gain frequency is found by setting the gain expression equal to one:

The unity gain frequency is determined by the transconductance of the input stage and the compensation capacitor. These two parameters are not published separately. The point of interest is the unity gain frequency.

Another indicator of op amp speed is the small-signal slew rate. This parameter is tied to the frequency corner where the closed-loop gain meets the amplifier open-loop gain curve. This point is shown in Figure 2.

Figure 2: Corner frequency as function of closed loop gain
(Click on image to enlarge)

The small-signal slew is described by the exponential function:

This function is solved for the time to reach a voltage level as:

Small-signal slew rate is the time for V_out to slew from 10 to 90 percent of final value. Using these ratio values for V_out/V_final, the rise-time reduces to:

From Part 13, recall that:

Therefore, slew rate is a function of the closed-loop gain as:

Small-signal slew rate is determined by the unity gain bandwidth of the op amp and the closed-loop gain of the circuit. As the closed-loop gain increases, the slew rate decreases.

The large-signal slew rate is a non-linear function of the op amp. In this case, "large signal" input signal which is one which large enough so that one side of the input stage is turned fully off and the other side is fully on.

Figure 3: Large-signal slew rate model
(Click on image to enlarge)

The differential input stage transistors share a common current source. As seen in Figure 3, with the positive input turned off and the negative input turned full on, all of the input stage current is driven into the second stage integrator.

Some op amps have protection circuits at the input that do not allow the input devices to be turned full on and off. The differential voltage necessary for this maximum slew rate action can vary over a range of three or four volts depending on the characteristics of the input devices and the circuit topology.

A special note from author Bill Klein:

Thanks for reading this column. After more than 16 years with Texas Instruments and Burr Brown (prior to its acquisition by TI), I will soon be retiring. As they say, analog engineers never really go away; they just go on to teach! I'll be doing a lot of that in the next phase of my career when I start teaching analog theory and practice at a community college in the Phoenix, Arizona, area.

While this may be my last article for TI, my colleagues there will continue to provide relevant and timely information about the analog signal chain, so stay tuned for their material. Remember that in this increasingly digital environment, the real world is analog!

About the author



William P. (Bill) Klein is a Senior Applications Engineer with the High Performance Analog group at Texas Instruments. Bill joined TI through its acquisition of Burr-Brown in August 2000. His experience as an analog circuit designer covers over 40 years in fields ranging from mineral exploration to medical nuclear imaging. One current role Bill has is hosting the Analog e-LAB Web Cast, presenting real world solutions to real world problems in analog circuit design. In addition to a BSEE from Arizona State University and registration as a Professional Engineer in the State of Arizona, he has authored numerous magazine articles, application notes and conference papers.

Previous installments of this series:

• "SIGNAL CHAIN BASICS (Part 19): Exploring and understanding linear voltage regulators", www.planetanalog.com/features/showArticle.jhtml;?articleID=209900450, click here
• "SIGNAL CHAIN BASICS (Part 18): The op amp as integrator", www.planetanalog.com/features/showArticle.jhtml;?articleID=209101070, click here
• "SIGNAL CHAIN BASICS (Part 17): Hysteresis--Understanding more about the analog voltage comparator", www.planetanalog.com/features/showArticle.jhtml;?articleID=208802817, click here
• "SIGNAL CHAIN BASICS (Part 16): Understanding the analog voltage comparator", www.planetanalog.com/features/showArticle.jhtml;?articleID=208403856, click here
• "SIGNAL CHAIN BASICS (Part 15): Analog/digital converter—dynamic parameters", www.planetanalog.com/features/showArticle.jhtml;?articleID=208401183, click here
• "SIGNAL CHAIN BASICS (Part 14): Analog/digital converter—static parameters", www.planetanalog.com/features/showArticle.jhtml;?articleID=207800114, click here
• "SIGNAL CHAIN BASICS (Part 13): Putting the Bode plot to use", www.planetanalog.com/features/showArticle.jhtml;?articleID=207403561, click here
• "SIGNAL CHAIN BASICS (Part 12): The Bode plot, an essential ac-parameter display tool", www.planetanalog.com/features/showArticle.jhtml;?articleID=207403561, click here
• "SIGNAL CHAIN BASICS (Part 11): Introducing voltage- and power-conditioning circuits", www.planetanalog.com/features/showArticle.jhtml;?articleID=207001505, click here
• "SIGNAL CHAIN BASICS (Part 10): Exploring the Delta-Sigma Converter", www.planetanalog.com/features/showArticle.jhtml;?articleID=206903892, click here
• "SIGNAL CHAIN BASICS (Part 9): SAR Converter Operation Explored", www.planetanalog.com/features/showArticle.jhtml;?articleID=206901015, click here
• "SIGNAL CHAIN BASICS (Part 8): Flash- and Pipeline-Converter Operation Explored", www.planetanalog.com/features/showArticle.jhtml;?articleID=206504089, click here
• "SIGNAL CHAIN BASICS (Part 7): Op Amp Performance Specification--Bias Current", www.planetanalog.com/features/showArticle.jhtml;?articleID=206101908, click here
• "SIGNAL CHAIN BASICS (Part 6): Op Amp Input Voltage Offset", www.planetanalog.com/features/showArticle.jhtml;?articleID=205901111, click here
• "SIGNAL CHAIN BASICS (Part 5): Introduction to the Instrumentation Amplifier", www.planetanalog.com/features/showArticle.jhtml;?articleID=205208593, click here
• "SIGNAL CHAIN BASICS (Part 4): Introduction to analog/digital converter (ADC) types", www.planetanalog.com/features/showArticle.jhtml;?articleID=204803631, click here
• "SIGNAL CHAIN BASICS (Part 3): Analog and the digital world", www.planetanalog.com/features/showArticle.jhtml;?articleID=204400376, click here
• "SIGNAL CHAIN BASICS (Part 2): Op Amp--Basic operations", www.planetanalog.com/features/showArticle.jhtml;?articleID=203101699, click here
• "SIGNAL CHAIN BASICS: Operational Amplifier--The Basic Building Block", www.planetanalog.com/features/showArticle.jhtml;?articleID=202801320, click here