Click here for the full Guide to Practical Operational Amplifiers.
The summing circuit allows you to add two or more voltages together. To solve for the output, consider each inverting input on its own using the concept of superposition. The result is in an output term for each input where the input has the same inverting gain term as in the equation for an inverting amplifier (refer to part 1 of this post).
The above figure shows this circuit with the noninverting input node (V_{+}) of the op amp connected to ground. How would the output of this circuit be affected if a voltage was applied to the noninverting input? Using superposition, you would add that voltage as a noninverting gain term (refer to part 1 of this post) where the input resistance (R_{I}) is all of the input resistances (R_{1}, R_{2}, … R_{n}) in parallel.
The differencing circuit allows you to subtract one voltage from another. It is particularly useful when your application calls for converting a differential analog signal to a single ended signal. Superposition is once again used to solve for the output. The gain term for the V_{IN} input is the inverting term from equation for an inverting amplifier. To calculate the output term for the V_{IN+} input, consider R_{3} and R_{4} as a voltage divider. Then, the gain term from the equation for a noninverting amplifier can be used for the noninverting input (V_{+}).
This circuit and the resulting equation can be simplified by making the following restrictions on resistor values.
Then, the output of the circuit becomes the difference of the inputs multiplied by a gain that is the ratio of R_{2} to R_{1}. Here, gain or attenuation of the difference can be achieved.
The analog filters section is included to provide baseline knowledge for the nonideal op amp operation discussions later on. Only basic equations for the first order op amp filters are shown as the full details of analog filter design and characterization are out of scope for this guide. More information on analog filter design can be found readily available both online and in print. Maxim Integrated tutorials 733 and 1795 are good starting points.
The High Pass Filter (HPF) blocks DC signals and amplifies AC signals. It also functions as a differentiator where the output approximates the derivative of the input. The first order, high pass, op amp filter is shown here along with its frequency response.
The Low Pass Filter (LPF) limits the bandwidth of the signal by allowing DC and nearDC signals to pass while attenuating high frequency signals. It also can be used to perform the integral of the input signal. This makes it a useful mathematical function that can convert a square wave to a triangle wave, acceleration to velocity, velocity to position, etc. Low Pass Filters are also used to perform antialiasing functions. The first order, low pass, op amp filter is shown here along with its frequency response.
This demonstration sets up a first order, active, low pass filter where V_{IN} is a 100Hz sinusoidal input of 500mV_{PP}. The feedback resistor (R_{F}) is set to 69.8kΩ, and the input resistor (R_{I}) is set to 6.98kΩ. The capacitor has a value of 1000pF.
Based on the above LPF equations, the transfer function is:
At 100Hz the gain is:
Using the above LPF equations, the 3dB corner frequency is:
To run the demonstration…
vout_pp: PP(v(vout))=4.98976 FROM 0 TO 0.1 gain: vout_pp/vin_pp=9.97952
The simulated gain very closely matches our calculated gain.
vout_pp: PP(v(vout))=3.60998 FROM 0 TO 0.1 gain: vout_pp/vin_pp=7.21996
The gain at the 3dB corner frequency can be calculated as 7.07. The simulated gain at this corner frequency closely matches the expected value.
V_{initial} [V]  V_{on} [V]  T_{delay} [s]  T_{rise} [s]  T_{fall} [s]  T_{on} [s]  T_{period} [s] 

0.25  0.25  0  0.01u  0.01u  219u  439u 
Click here for the full Guide to Practical Operational Amplifiers.
The voltage follower circuit is used to buffer a signal for the next stage or to drive an output. A pure voltage follower is not commonly implemented because other components can be added for additional functionality (such as gain, filtering, etc.). Note that the voltage follower uses negative feedback and has unity gain.
With the voltage follower, the output equals the input.
The output of the comparator is a Boolean value based on the input compared to a threshold voltage. Depending on the input value, the output will be one of the two supply rails. Practical implementation of the comparator circuit is usually not this simple. To help prevent noise on the input from causing the output to “bounce”, a feedback network with hysteresis is typically implemented. This will be discussed in a future post.
Note that while this is a noninverting configuration, an inverting configuration could also be designed.
where, V_{CC} equals the op amp’s positive supply voltage and V_{EE} equals the op amp’s negative supply voltage.
The inverting and noninverting amplifiers are the building blocks of most op amp circuits. You should memorize their transfer functions. The arithmetic op amp circuits in the next post will be characterized by using these transfer functions and applying the concept of superposition.
The inverting amplifier will buffer a signal with gain or attenuation, and the output of the circuit will have a 180° phase shift. In simpler terms, gain (greater than one, unity, or less than one) can be applied, and the output will be inverted.
The advantage of the inverting configuration is that the common mode voltage is constant, and the input is protected by the resistance of the input resistor. Gain will simply be the negate of the ratio of the resistor in the feedback path (R_{F}) over the input resistor (R_{I}) and can be from zero to infinity.
This demonstration sets up an inverting op amp circuit where V_{IN} is a 1kHz sinusoidal input of 2mV_{PP}. The feedback resistor (R_{F}) is set to 750kΩ, and the input resistor (R_{I}) is set to 6.98kΩ.
Based on the inverting amplifier equation above, the gain of this circuit can be calculated as:
To run the demonstration…
In a new window, you should see text similar to the following:
vout_pp: PP(v(vout))=0.214267 FROM 0 TO 0.01 gain: vout_pp/vin_pp=107.134
LTSpice® calculates the gain as the peaktopeak output voltage divided by the peaktopeak input voltage. The simulated gain very closely matches our result from equation . However, LTSpice® calculates a positive number because the peaktopeak calculation produces an absolute value.
At what point does the output start to clip? What happens to the gain when the output is clipped? This demonstrates the nonideal, finite gain of the op amp as limited by the supply voltage.
The noninverting amplifier will buffer a signal with gain. With the noninverting topology, attenuation is not possible – gain is always at least one. The advantage of the noninverting amplifier is that the signal is not inverted and the input is directly into the op amp. The latter is beneficial since the input impedance into the op amp is high.
Click here for the full Guide to Practical Operational Amplifiers.
The ideal op amp follows some basic “golden rules”. Ideal op amps have infinite openloop gain. No current flows into the inputs, and the positive input terminal has the same voltage as the negative input terminal.
Practical op amps are real world devices primarily based on transistors but also have other internal circuitry. For example, the below figure shows a diagram of what is inside each op amp in the MC3317X series.
These nonideal op amps have input currents and offsets, input and output impedance, limited gain, and other nonideal properties. The next figure and the resulting equations describes the practical op amp model taking these effects into account.
This table compares these parameters with their ideal value. There will be upcoming posts covering nonideal effects such as temperature, noise, slew rate, and stability.
Parameter Name  Symbol  Ideal Value 

Input Current  I_{IN}  0 Amps 
Input Offset Current  I_{IO}  0 Amps 
Input Offset Voltage  V_{IO}  0 Volts 
Input Impedance  Z_{IN}  ∞ Ω 
Output Impedance  Z_{OUT}  0 Ω 
Gain  A_{VOL}  ∞ 
Bandwidth  BW  ∞ Hz 
The guide will be presented here in the form of multiple blog posts and will cover everything from reading a datasheet and common circuits all the way through nonideal effects such as stability, noise considerations, and input offsets. Throughout this guide the MC33172 op amp will be used as the example. Where appropriate, LTSpice circuit files will be provided that simulate the concepts presented in this guide.
There are literally hundreds of Op Amps to select from. There is no one right answer, and it is based on the circuit application.
Some considerations (not in any particular order):
The challenge is finding the op amp that meets the requirements of the design, including those that you do not even know yet. How are you going to do it? A parametric search is often a good starting point. Many vendors have parametric search functions on their website; or, you can use a third party parametric search provider that aggregates multiple manufacturers (such as findchips.com).
Talking with the vendor directly is another option. Sometimes it is better to ask distributors rather than manufacturers. While a specific distributor may not carry every manufacturers’ line, manufacturers may frequently request information about the outcome of your part search and on the status of your project. There are lots of manufacturers of op amps. Be sure that the op amp you select can be purchased from an approved vendor.
The datasheet contains a lot of important information, and every vendor writes their specifications slightly different. It is critical to be able to understand a datasheet and get the information that you need with the correct interpretation. Ask the vendor for more information when needed – but make sure you document anything that is not explicitly on the datasheet, along with the source of the information.
Here are some things to consider and watch out for.
The front page of the op amp datasheet contains marketing material. This material shows a selected portion of the truth and generally represents best case scenarios. It should not be blindly trusted for design and calculation purposes. Know the specifics behind each parameter.
For example, consider the “excellent phase margin” statement from the front page of the MC33172 op amp datasheet as shown in the figure below. It states that the phase margin is 60°. However, if you look further into the datasheet, it is listed as 45° with a 100pF load and about 25° with a 200pF load.
All op amp datasheets will have a maximum ratings table. This table describes the stresses, that if exceeded, may damage the device. Both the operating and storage limits are listed. Never exceed the maximum ratings! If any of these limits are exceeded, the device functionality cannot be assumed and the reliability of the device may be compromised. The below table shows the maximum ratings of the MC33172.
The electrical characteristics section of the datasheet quantifies the expected electrical operation of the device. The actual values for each characteristic will be listed as a minimum, typical, or maximum value. In addition, many notes and operating conditions (such as temperature or frequency) will be specified that restrict the validity of the listed information.
What if the specified operating conditions do not match your design or implementation? You may need to interpolate the characteristics to match your operating conditions. Sometimes it is possible to do so from the electrical characteristics tables. Other times, you may need look at the graphs included in the datasheet or contact the manufacturer.
For example, in the DC Electrical Characteristics table below, the output voltage swing is listed for a specific supply voltage and load. If you are powering the op amp with a ±10V supply, you could reasonably conclude that the best case maximum output voltage range at room temperature would be about
In this case, if the design requires operating close to the supply rails, you may need to prove the design through prototyping or talk with the manufacturer to determine if the MC33172 would work.
When can you use the “typical” specifications for a design? In many circumstances, you cannot…
The typical specifications are not guaranteed, but are expected based on the model the manufacturer used for design and testing. They are useful for backofthenapkin calculations or where min/max values are not provided. For specifications that directly affect the output of the circuit stage in a calculable manner, typical specifications should not be used. These types of specifications include input offset voltage, input bias current, short circuit outputs, and power calculations.
Common Mode Rejection Ratio (CMRR), Power Supply Rejection Ratio (PSRR), phase margin, etc. might be able to use the typical value depending on the application. For specifications that are critical to the circuit’s operation, the min and/or max values should be used. If the min and/or max values are not obvious, it will be necessary to consult the datasheet graphs or confirm with the manufacturer. If they cannot or will not confirm a specification, you may need to select an alternate part.
When should you use information from a graph in the datasheet instead of from a table? Graphs are helpful for getting an idea of how a parameter changes over temperature, voltage, frequency, or some other variable parameter. Tables, on the other hand, generally contain a single value or limited range.
Let’s go back to the phase margin example. The front page lists 60° of phase margin. The AC electrical characteristics table lists
The related graph in the datasheet (below figure) relates both phase margin (φ_{m}) and percent overshoot to the load capacitance (C_{L}). Here you can determine phase margin (a predictor of circuit stability) for any load capacitance in your circuit. In this example, R_{L} and the other fixed parameters are included as an overlay.
Many classes of op amps have common pin connections for single, dual, and even quad packages. The pinout of the MC3317X for these packages is shown here.
Watch out for devices with a pinout that you don’t expect. It is advantageous to use common pinouts and footprints when selecting an op amp for a production design. An op amp may become obsolete or you may need to replace it for a different reason. It is easier to replace if the Printed Circuit Board (PCB) layout does not need to be changed. However, it can also be beneficial to select a different pinout or package for other layout reasons. Sometimes a different package (i.e. inputs and output on the same side of the package instead of the opposite side) is just what is needed to make a tricky layout work.
Many op amp datasheets include an application section. Be sure to familiarize yourself with this section when becoming acquainted with a new op amp. Many important details that cannot be captured as a specification are included. Some things that may be discussed are performance features, PCB layout guidelines, bypass capacitor requirements, diode input protection, common use cases for specialty op amps, stability, and phase reversal.
When comparing op amps from two different vendors be sure to read through the application information sections of both if available. Even if the op amps are “identical”, there may be subtleties in part operation that can be easily missed.
Some datasheets will include a section detailing recommend circuits for the selected op amp’s typical uses. For example, the MC33172 has multiple 5.0V supply amplifiers and a couple filter circuit schematics included in the datasheet. Having some circuits listed as a starting point may be nice, but do not use them without first understanding the design completely. Be sure to figure out all of the assumptions made by the datasheet author.
Make sure that you are really ordering the part you are trying to order. Many vendors use complicated part numbering schemes where RoHS compliance and even the shipping packaging (tape & reel vs. cut tape vs. tray) information is a component of the part number.
As an example, look at below table to see how small changes in the orderable part number of the MC3317X series of op amps affect the temperature range, device package, and shipping packaging.
Marking diagrams are extremely valuable when you are trying to find out what part is on a Printed Circuit Assembly (PCA). This is especially true now that part sizes are shrinking to the point that full part numbers cannot be printed on them. Often part numbers are abbreviated. Lot, manufacturing date, and leadfree status can also be shown.
Orientation information is also provided as part of the marking diagram. Many op amps (and other integrated circuits) indicate via a depression in the package or a printed marking which is pin number one. For hand assembly and for troubleshooting and testing purposes this is a valuable indicator that lets you quickly identify which pin is which.
Reference the below figure for the MC3317X op amp series marking diagram.
The package dimensions detail the physical size of the available package options. The physical dimensions will help you identify if the part will fit in a cramped layout, under a daughter card, or on the back side of the PCA for boards with components on both sides. It will also help identify if an alleged “drop in replacement” part is mechanically compatible.
Often a soldering footprint is included with or near the package dimensions. If a tested and approved footprint is not already available in your layout CAD software, the included footprint is a good starting point for a PCA engineer bringing in the new footprint or device. The below figure shows the SOIC8 package dimensions for the MC33172 as a representative sample of the type of information to expect.
Location  Texas 
Voltage Class  34.5 – 345 kV 
Facility Rating  560 MW 
Quantity of GSU Transformers  3 
Special Features 

To learn more about this project, click here.
Location  Texas 
Voltage Class  34.5 – 345 kV 
Facility Rating  300 MW 
Quantity of GSU Transformers  2 
To learn more about this project, click here.
Location  Nebraska 
Voltage Class  34.5 – 345 kV 
Facility Rating  250 MW 
Quantity of GSU Transformers  1 
Special Features  34.5 kV Shunt Capacitor Bank 
To learn more about this project, click here.
Location  Texas 
Voltage Class  34.5 – 345 kV 
Facility Rating  500 MW 
Quantity of GSU Transformers  3 
Special Features  34.5 kV Shunt Capacitor Banks 
It is a projectcentric GUI that allows the end user to:
The goal of this project was to:
Features & Design Techniques
Responsibilities & Scope
Screen Captures
]]>Given a specific MEMS accelerometer, this circuit was designed to meet the following requirements:
Features & Design Techniques
Hardware integrator to convert from acceleration to velocity
Band pass filtering
Dual vibration output (velocity and acceleration)
Specifications
Responsibilities & Scope
Project Photos
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