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Operational amplifiers (wiki)

last updated: 2022-11-18

Quick links

Introduction
Op-amp
Comparator
Op-amp circuits with feedback (basic circuits, [wiki](https://en.wikipedia.org/wiki/Operationalamplifierapplications)
Interesting links

For students:

Beginning with this chapter we will come across many "Just do it" tasks. These tasks have to be carried out and have to be documented thoroughly!
Your marks will depend on the documentation!

To better understand parts of this module, first work through the module electronics fundamentals ELEFU.

Introduction

Song of this chapter: Imran Khan > Unforgettable > Amplifier

An operational amplifier (opamp or op-amp) is a very versatile building block used in analog circuits. The op-amp is a differential amplifier build with transistors and resistors in an integrated circuit. Op-amps are among the most widely used electronic devices because their characteristics (gain, impedances, bandwidth, ...) can be changed with external components. An advantage is that their characteristics change only slightly with temperature or internal component tolerance.

With op-amps we can build many different things like:

amplifier (differential, inverting and non-inverting),
buffer,
voltage comparators (e.g. used in Flash ADCs),
voltage and current regulators,
differentiators and integrators,
analog calculators,
precision rectifiers,
precision peak detectors,
active filters,
Schmitt trigger,
oscillators and waveform generators,
ADC's and DAC's

and so on.

Op-amps had their origins in analog calculators or analog computers!

Here a picture of an analog computing machine at the Lewis Flight Propulsion Laboratory circa 1949 (NASA):

We will not study op-amps in depth, but only so far that we can use them. In this module we need op-amps mainly to amplify voltages from analog sensors, so that microcontroller can work with the data.

Op-amp (wiki)

The op-amp is a voltage amplifier with a differential input (output is single-ended) and a a very high open loop gain (about 100000), meaning the differential input voltage is amplified by a factor 10⁵-10⁶.

The differential input is calculated with: U_in = U_in2 - U_in1.

Op-amps are differential amplifiers with a high gain and a high input impedance.

Differential amplifiers means we have two inputs, and amplify the difference between the inputs. The input impedance (impedance is the AC equivalent of the resistance, used for DC) is very high, meaning the op-amp has very little impact on whatever is connected to its inputs, because the current drain is negligible.

The output impedance is low (like the inner resistance of a battery), and the op-amp is able to supply a significant current (e.g. 20 mA) to its load.

The energy for the op-amp is provided mostly from a bipolar voltage power supply, from ±2 V to ± 18V (often ± 15V or ± 12V). Op-amps with unipolar power supply are more rarely used.

Without power (U_CC- and U_CC+) the op-amp will not function, so don't forget to connect these pins.

A very old and known general-purpose op-amp is the 741. Here we see the circuit:

source: https://en.wikipedia.org/wiki/Operational_amplifier, Daniel Braun license: https://creativecommons.org/licenses/by-sa/3.0/deed.en

There exist many modern and slightly changed (improved) versions of this chip (often cheaper and better than the original). Here some versions (always check the data sheet; thanks to Peter J. Vis):

LM741CN (bipolar),
CA3140E (MOSFET),
TL031CP (EJFET, low power, low offset),
TL051CP (EJFET, low offset),
TL061CN (JFET, low power),
TL071CP (JFET, low noise),
TL081CN (JFET),
LF351N or LF356N (JFET),
MC3317N,
MCP601 or MCP603 (low voltage 2.7-6 V),
OPA602 (high speed and precision).

Here is the DIL or DIP package for all these op-amps:

"Just do it" OA1:

We will use an TL081 op-amp. Research the "open loop voltage gain", also called "large signal voltage gain" in the data sheet. Express the gain in V/V (not dB).
Calculate the maximum differential input voltage for the TL081 if a bipolar voltage of ± 15V is used.

Op-amp symbol

We need five terminals to connect the bipolar voltage, the differential input and the output. Mostly the first symbol without the terminals for power is used, because of it's simplicity. The actual symbol (third symbol, DIN EN 60617) is seldom used in schematics. Without power (U_CC- and U_CC+) the op-amp will not function, so don't forget to connect pin 4 and 7 even when the first symbol is used in your circuit!

Comparator (wiki)

An op-amp without feedback and external components can not be used as an amplifier. Even with a small voltage, the output voltage will be equal to or greater than the supply voltage. Such a situation is called the saturation of the amplifier.

But a comparator needs this behaviour!

Without feedback (open loop) an op-amp acts as a comparator.

If we hold the inverting input to ground (0 V) the voltage U_in applied to the positive input will saturate the op-amp and the the output will be maximum positive. With a negative U_in the output will be maximum negative.

"Just do it" OA2:

Let's test the comparator by building a battery driven polarity tester with an TL081. The test voltage is applied between U_in- connected to GND (pin 2) and U_in+ (pin 3). In which supply voltage range this op-amp can work (check the data sheet). How can we get the bipolar supply voltage with two 9 V batteries? Draw the battery circuit (Tip: Check the Ohm chapter in ELEFU).
We need two resistors (R₁, R₂) for the LED's. Calculate their values, if the current should not exceed 2 mA and document the calculations. Now test the polarity tester circuit. Use for this an 1.5 V AA battery connected between U_in- (GND) and U_in+ in two ways. Measure and document the voltages on all your batteries and the output voltages for a positive and a negative input voltage.
What is the maximum voltage that can be applied to both inputs (data sheet)?
The maximum output current can't be found in the data sheet, but the data sheet mentions that the output has a short-circuit protection. So let's measure the shorted output current. Calculate the internal output resistance from your measurement.
Do you remember the parallel comparator (Flash) ADC in our last chapter of MICSY? There were 7 comparators engaged.
Enhance the circuit from above to toggle at 3 V instead of 0 V (GND). Calculate the resistances from the needed voltage divider. Draw the circuit and test it.

Op-amp circuits with feedback (basic circuits, wiki)

The operational amplifier has a - and a + input called the inverting (-) and non-inverting input. To key to using op-amps as amplifiers is to feed the output back to the input. To use the op-amp as amplifier the feedback will normally go to the inverting input to reduce the input voltage an with this the overall gain (a part of the output voltage is subtracted from the input voltage an so reduces the input voltage). A positive feedback to the non-inverting input enforces the difference and can be used to get a faster comparator.

Inverting amplifier

For an inverting op-amp we feed the output back to the inverting input through R₂ and apply the input signal through R₁ to the inverting input. The non-inverting input is connected to ground.

As the input voltage between the two inputs is very small (near 0 V) and the positive input is tied to ground we get a virtual ground (0 V) on the negative input. U_out lies over R₂ to virtual ground and U_in lies over R₁ to virtual ground. With the high impedance of the op-amp the current into the op-amp is near 0 A, so the only current flows through the two resistors. With Kirchhoff's second (voltage) law we get: U_in·R₂ = -U_out·R₁ respectively the gain G_U = -R₂/R₁.

"Just do it" OA3:

Calculate the gain from the circuit above.
Here a simple circuit to amplify the signal from an electret microphone. It uses an op-amp working with unipolar 5 V. Explain the circuit in detail (what are the different components doing?) and calculate the gain. Build the circuit on a breadboard and document the input and output (speech with no saturation) with the two channels of an oscilloscope. If you don't have a MAX 4167 you can use an MCP 607 or an OPA 2336.

Non-inverting amplifier

To get a non-inverting amplifier we have to feed the input voltage to the non-inverting input. With the same thinking as above we get: U_in·R₁ = U_out·(R₂ + R₁). So the gain of the non-inverting op-amp is always greater than one. With two similar resistors we get a gain of two.

"Just do it" OA4:

Build a non-inverting op-amp with a TL081. The gain should be 3.3. What resistances will you choose (note calculations) and justify the choice. Apply a sine wave with U_ss= 2 V and document the result with an oscilloscope screen.

"Just do it" OA5:

Let's measure the current drawn by our rover. For this we add a 200 mΩ resistor (shunt) into the ground line and measure the voltage corresponding to the current. Calculate the voltage to be expected (see ELEFU exercises for current drawn by the rover) and dimension an amplifier (½ MAX4167, MCP 607 or OPA 2336) to get a maximum voltage of about 2 V (abs. max. is 3.3 V) for the analog input of our ESP32. Document your calculations and draw the circuit.
Test the circuit on a breadboard with the help of multimeter and a power supply. Measure the current trough and the voltage on the shunt and the output voltage ehen using a 12 Ω resistor as rover. Document your measurements.
Test the circuit on a breadboard by adding the MH-ET LIVE D1 mini ESP32. Use ADC input pin 34 to read the shunt voltage and calculate the corresponding current. Write and document your program. Document the measured current with a screenshot of the serial monitor.
Add a voltage divider to your drawing. We use it to measure the overall battery voltage. Use the ADC input pin 35. Document your calculations. Extend your sketch and document the new output of your serial monitor (current and voltage).
If you have time and feel like it:
Built the circuit on a PCB and mount it to your rover. Add an LED or piezo speaker and modify your rover program to measure the voltage and signalise if the voltage drops under 5.4 V. Document everything.

Voltage follower

A very interesting circuit is the voltage follower. It is a non-inverting amplifier with R₂ = 0 and R₁ = ∞, witch gives us a gain of 1. The word amplifier is not really appropriate so voltage follower or buffer are better.

The voltage follower does not change the signal. It's advantage is the high input impedance and the low output impedance to isolate (buffer) a signal. The input signal will be unaffected by the circuit it is driving. We have already seen a good example in the chapter about DAC's. An R-2R ladder will function only if no current is drawn from the circuit. To use the output signal (get a current) we need to use a buffer circuit:

Summing amplifier

By adding resistances to the inverting input of an inverting amplifier we can create a summing amplifier. The currents are added in the node (junction) at the inverting input. Because there is practically no current entering the op-amp, the sum of the currents pass through R₂. If all resistors have the same value (R), we get: U_out = -R·((U_in1/R) + (U_in2/R)) respectively U_out = -(U_in1 + U_in2). With different values for the resistances we get a weighted sum. With three resistances we can add 3 voltages etc..

In our oscilloscope picture the output is already inverted!

An interesting option is to make the resistors adjustable.

Differential amplifier

With the differential amplifier we are able to calculate the difference between two voltages. Often we use R₁ = R₂ and R₃ = R₄ reducing the formula to: U_out = R₂/R₁·(U_in2 - U_in1). For good results the resistances must be very precise.

In our example all resistors are equal, so we get U_out = U_in2 - U_in1.

Inverting differentiator and integrator

Changing resistances with capacitors can build an inverting differentiator (left) or integrator circuit (right). They can be used as a low-pass electronic filter or a high-pass electronic filter. Other uses will be as controller in control and feedback systems (D and I controller).

In a practical application one encounters difficulties (drift of the voltage) with this simple circuits. They have to be enhanced with further components.

Active filters (wiki)

Filters are very important in electronics and are used in a variety of manners in circuits. In electronics fundamentals (ELEFU) we have seen how to build filters with a resistor and a capacitor. These passive filters are often simple, inexpensive and need no power supply. To build more complex filter (higher order) with passive components can get very challenging and expensive because of the needed inductances. Op-amps with especially their high input impedance (voltage follower) help to isolate the different stages of a filter and have a gain that helps to adjust the signal and to compensate the losses. A filter including active elements like op-amps is called an active filter. A drawback of active filters could be the limited bandwidth.

A popular and simple filter of the second order combining two first order RC filter is the Sallen-Key filter. Such a filter can easily be designed by an online tool like here.

"Just do it" OA6:

Determine the components for a Sallen-Key low-pass filter with a cutoff frequency of 3.4 kHz. C₂ should be 100 nF.
Build the filter with an TL081 and test the filter with an oscilloscope (Sine, U_in = 2V_ss). Document the screen for 1 kHz, 3.4 kHz and 10 kHz (input and output voltage on the same axes!).
What problems could be detected?

More applications of op-amps (wiki)

There are much more circuits that could be realised with op-amps. Examples are a Wien bridge oscillator, inductance gyrator, precision rectifier, logarithmic amplifier, exponential amplifier etc..

"Just do it" OA7:

To repeat and consolidate this chapter, read the article about the op-amps in the HackSpace Magazine (free pdf download) number 18 (page 74-79).

Interesting links

https://de.wikipedia.org/wiki/Operationsverst%C3%A4rker (wiki in German)
https://www.changpuak.ch/electronics/calc_08.php

Tutorials:Sensors, interfaces and bus systems (SENIN, BUSSY)