Summing op amp non-investing fii
Although it does not exist, the ideal opamp is the common model for nearly all opamp circuits, and few errors are encountered in practice as a result of designing for the ideal, and actually using a real non-ideal device. The tolerance of even the best resistors will ultimately limit the accuracy of any opamp circuit at low frequencies where gain is highest.
This does not mean that any opamp can be used in any circuit - the designer is expected to be able to determine the optimum device for the task. Special consideration needs to be given to any opamp circuit that operates with very high or low impedance input or output. Any opamp will function with no external load, but most can't deliver optimum performance into low impedances ohms or less.
High input impedances usually require FET input opamps to minimise noise and DC offset caused by the input bias resistor. You also need to be careful with the amount of gain expected from a single stage, because the opamp can 'run out' of gain at high frequencies.
There are many considerations for specialised circuitry, but most audio applications only demand low distortion not all opamps are equal! The requirements also depend on the signal level - for example, using an 'ordinary' opamp for a moving coil phono cartridge will be disappointing! During the design phase, one of the tasks of the designer is to set up the reference, which is simply a connection that's common to both the input and the output. It only has to be within the bounds set by the power supplies and the device itself.
Depending on the design, it could be some other voltage - the opamp doesn't care as long as it's used within datasheet specifications. The primary practical limitations of real-world opamps are as follows: Input Impedance - Typically from one to several hundred Megohms.
Ranges from 0. Power opamps IC power amplifiers may be capable of up to 10A, but these are outside the scope of this section of the article. The use of ideal opamps is assumed for much of the following, but all are designed to function properly with real world devices. In practice the difference between an ideal opamp and the real thing are so small as to be ignored, but with one major exception - bandwidth.
This is the one area where most opamps show their limitations, but once properly understood, it is quite easy to maintain a more than adequate frequency response from even basic opamps. The common mode input voltage can be important in some applications. Ideally, an opamp only reacts to the voltage difference between its inputs. Provided this does not change, in theory, the actual voltage between the two inputs and the common zero volt line may be anywhere within the specified range with no change in the output voltage.
In other words, the inputs can assume any voltage between the negative and positive supplies, and there will be almost no change at the output. With a real as opposed to ideal opamp, there will be some change, and this is specified as the common mode rejection ratio. An opamp with a CMRR of dB not uncommon will ensure that the change in output voltage is dB less than the change of input voltage as applied to both inputs simultaneously.
Any difference between the inputs is amplified normally. CMRR is affected by the open loop gain of the opamp, so is usually worse at high frequencies. High common mode voltages can adversely affect distortion performance, but rarely to the point of it becoming audible. While Rule 1 states that the opamp will try to make both inputs the same voltage, this can only apply if the opamp's gain is infinite.
Rule 1 remains valid unless you are trying to make the opamp do something 'interesting'. In many academic papers, you'll find formulae that take the opamp's open-loop gain i. For practical applications this is not necessary. If a stage has an open-loop gain of and is configured for a gain of 10 with feedback, the gain will be 9. With an open-loop gain of 10, 80dB , the gain is 9.
These criteria apply in all feedback topologies, so it's rarely necessary to consider the open-loop gain A more-or-less 'typical' opamp will have more than enough gain available to ensure that the fain you set with external resistors is within the tolerance of the resistors. These are intended as linear amplifiers, in that they are essentially distortion free within the capabilities of the opamp itself, of course.
As we progress, most of these original circuits will be seen over and over again, since they are the very foundations of building an audio circuit using opamps. In all cases, a dual power supply is assumed, and this is not shown on the circuits.
This partly for clarity, since the additional circuitry makes the diagrams harder to understand, and partly because it is a convention not to show all the supply connections anyway. We all know they have to be there, so there is little point in showing the obvious over and over again. Likewise, bypass capacitors and other support components are not shown - only the basic opamp and its associated components.
You will also see reference to the 'instantaneous value of the AC waveform'. This is like a snapshot, and we simply freeze time while we analyse the operation of the circuit. At any point in an AC waveform, it can have only one value of voltage and current, regardless of the complexity of the signal source. A sinewave is no different from any other signal - provided its amplitude and frequency are within the capabilities of the opamp.
I will therefore use this as a starting point, because it is also the simplest to understand. Figure 3 shows a completely conventional non-inverting opamp voltage amplifier. Figure 3 - Non-Inverting Opamp Amplifier Rin is the input resistor, and is needed because an opamp needs a reference voltage at the input. In this case the reference voltage is the zero volt earth bus.
Input impedance is equal to the value of Rin in parallel with the opamp input impedance. Generally the latter can be ignored because it is so high. As shown in the diagram, the gain is 11 times, so a mV input will become a 1.
This is obtained from the simple voltage divider formula, which is strangely familiar A signal at 10MHz will not follow the rule, since the opamp will almost certainly be incapable of amplifying such a high frequency. Likewise, an 8 ohm load will break the rule, since the opamp cannot supply the current needed to drive such a load.
To see how the opamp behaves in these abnormal conditions, I suggest that the circuit be built, and run the tests if you have access to an oscilloscope. Examine the inputs as well as the output, since the inputs are by far the most interesting when the opamp is appearing to break the Rules.
A single valve or transistor stage other than a cathode or emitter follower buffer stage always inverts the signal, and this is how it must be see Amplifier Basics - How Amps Work for more info. With the advent of the opamp, all this changed, and the inverting amp is a very different beast from the simple discrete designs.
This configuration is also called a virtual earth or virtual ground stage, and is common in mixing consoles and many other signal processing circuits. When used in this mode there is both an advantage and a disadvantage. The advantage is that there is no common mode signal at the inputs because the two inputs will be at close to zero volts.
All opamps have some additional distortion with high common mode voltages, and while it's rarely a real problem, it can reduce performance if you need ultra-low distortion. The disadvantage is that the circuit has a higher 'noise gain' than an equivalent non-inverting stage. For a unity gain buffer, the noise will be double that of a non-inverting stage. Inverting stages should never be used for ultra low noise circuits. Assume an input of mV DC.
The output will be at -1V DC, a gain of the minus indicates only that it is inverting, not that the circuit has 'negative gain' which is actually a loss. Note that this configuration is capable of negative gain loss. The current through the feedback resistor must be exactly equal and opposite to ensure that zero volts is at the -in terminal so we don't break Rule 1.
As before with the non-inverting amp, the limitations of the opamp and its supply may cause Rule 1 to be broken, but the amp is now no longer operating in its linear mode, and Rule 2 will take over. Observation of the -in terminal will show a distorted waveform when the opamp can no longer operate in linear mode.
Using R3 and R4 means that a higher input impedance can be used, but with a somewhat reduced noise penalty due to very high resistances in the feedback circuit. The circuit shown has a gain of The high value feedback resistor creates noise see Noise In Audio Amplifiers for details. By using the arrangement shown, resistor values are reduced and so too is their noise contribution. It is a little harder to calculate the gain. It's really only a simple formula that can be reconstructed from its constituent parts easily enough once you see and understand the relationships.
Assume an input of 1V peak or DC , and note that R2 is effectively in parallel with R4 the opamp's input is at zero volts. Provided R1 is equal to R2, the gain is Therefore, the output must be While this arrangement is a little more convoluted than just using a k feedback resistor, it does provide a worthwhile noise improvement.
There's nothing you can do to increase the input impedance, other than increasing the values of R1 and R2. It's more irksome to calculate the gain if R1 and R2 are not equal, but it can be done, and I leave it to the reader to figure that out. In general, there's usually no good reason to make these resistances different, because the majority of the gain will usually be set using R3 and R4.
If a high input impedance inverter is necessary, it's better to use a non-inverting buffer before the inverting stage so all resistance values can be minimised. Used in the way shown in Figure 4A, the opamp's own noise is amplified by Distortion will be unacceptably high, and the end result is not worthy of further consideration.
Figure 5 - A Inverting and B Non-Inverting Buffer In many cases the non-inverting buffer can be replaced by an emitter or source follower, but performance is nowhere near as good. Input impedance is lower, output impedance is higher, and the gain is not quite unity. In addition there is more distortion and lower output drive capability, as well as higher quiescent current. The inverting buffer is more of a convenience than anything else, and is simply a normal inverting amplifier with unity gain.
Input impedance is the same as R1, and very high values are not possible without excessive circuit noise. The inverting buffer also suffers from an increased 'noise gain' amplification of the IC's own internal noise. This is because the signal has unity gain, but IC input noise has a gain of 2. In fact, all inverting opamp stages have a noise gain that's equal to the voltage gain plus one.
For example, an inverting stage with a gain of 10 has a noise gain of Noise is a separate topic, and is discussed in detail in the article ' Noise in Audio Amplifiers '. In AC circuits this is easily eliminated by using capacitors at the input, output or both. The amount of DC offset depends on many factors, but it's present with almost all devices. The only exceptions are 'chopper stabilised' types, which use internal switching to eliminate any DC component that is not due to the input voltage.
These are specialised opamps, and aren't covered here. A common claim is that the non-inverting input should have a resistor either to ground or a low-impedance DC signal that requires amplification. Unfortunately, many people will maintain and they are usually wrong that the resistor should be the same value as the feedback resistor i.
In reality, the resistance should be calculated by using the opamp's data sheet information for bias current, but you can get an approximation by using the same value as the input resistor. However, this is still not the real answer - there are many factors that affect the final result. The optimum value can be found empirically by experimentation on the workbench or by calculation, with the latter being the most difficult. Some opamps have pins designed for connection to a DC offset trimpot, and while this definitely works or the facility wouldn't be provided , it's something that has to be adjusted when the circuit is built.
As a very rough guide, the DC offset 'compensation' resistor will be close to the value of the feedback resistor and resistor to ground in parallel. For example, with Figure 5A, the non-inverting input should be connected to ground via a 5k resistor. This will usually but not always have a parallel capacitor to prevent excess noise, and the cap should have a reactance of less than 5k at the lowest frequency of interest for the Figure 5A circuit only.
JFET input opamps have a definite advantage here. However, this may not be the case with some configurations, and measurements are essential. It is not my intention to try to describe the issues in detail, nor delve deeply into the maths involved. Where very low DC offset is needed, you will have to select the opamp for the task, and either experiment or calculate the optimum resistor values yourself. Many application notes cover this in almost excruciating detail, and I won't do that here.
Suffice to say, this is important if you are amplifying DC typically in measurement applications , but for audio it is almost irrelevant because the DC component is easily removed with a capacitor. It is not possible to cover all the different circuits that have been made using opamps, since there are so many that I could easily end up with the world's longest web page.
I doubt that this would be appreciated by most of you. I shall only cover the more common, or most interesting, as this will give a better appreciation of how versatile these building blocks really are. All of the circuits that follow will work - they are not theoretical, but real designs, and can all be made on the opamp test board.
For example, a standard low cost TL opamp has an input bias current of about 65pA, and a claimed input resistance of ohms. To put this into perspective - assuming we have a way to supply the bias current without affecting input resistance - the input impedance could be as high as 1,,,, ohms.
We will be completely unable to achieve this in practice, since the insulation resistance of a PCB is nowhere this figure, and the smallest amount of contamination will reduce the impedance dramatically. In reality, we can easily expect to be able to get an input impedance of M ohms or more I have a project for a 1G ohm test amplifier , but care is needed, since with high value resistors additional noise is produced. Since noise in a resistor is proportional to the voltage across the resistor and its resistance, it is easy to see how a simple circuit can become a real noise generator.
Figure 6 shows the circuit and PCB layout for a very high impedance amplifier. Figure 6 - High Impedance Amplifier The bias resistor is 'bootstrapped' from the output, and this allows a lower resistance while maintaining an extraordinarily high input impedance.
A circuit such as this could be used for a capacitor microphone for example , which will typically have such a small capacitance that any loading will reduce the low frequency performance to an unacceptable degree.
The guard track can be seen encircling the input and the input end of R1. What on earth is a guard track? Read on To prevent the resistance of the PCB from causing a problem, the input section may be 'guarded' with a section of track connected back to the output. Bootstrapping and guarding work in the same way. The guard track works by maintaining a voltage from a low impedance source around the input circuit that is the same voltage as the input.
If they are the same voltage, no leakage current will flow. In reality it is not quite that simple. Assume that the opamp has dB of gain at 1kHz our test frequency. This equates to , - a little shy of infinity! Since the opamp has a finite gain, the 'unity gain' buffer will actually have a gain of 0. This error reduces the ability of the opamp to bootstrap the circuit perfectly, so the k input resistance will only be effectively increased to 10G ohms.
But wait This is very simple. Assume an instantaneous AC voltage of 1 volt input to the amp. Because the bootstrapping action causes the voltage at the junction of R1 and R2 Fig 6B to be 0. This will fall at increasing frequencies as the opamp starts to run out of gain. Oh yes, the term 'bootstrap' comes from the unlikely picture of a man 'lifting himself off the floor by his own bootstraps'.
As you might have guessed, the term is somewhat antiquated, but there has never been any move to change it thank goodness. It is intended to show that the impossible can be done, but it is not really impossible, and is just a very clever example of lateral thinking.
The bootstrapped circuit cannot be used at DC, since it requires a capacitor for its operation. This is not as much of a limitation as may first be thought, since DC is quite inaudible. However, for some applications, high impedance to DC is a requirement, and then very high resistance values are needed such as my 1G ohm test preamplifier.
Many common transducers use capacitance as their mechanism. These are normally supplied from a high voltage V via an extremely high value resistor. One would expect noise, but they are usually much quieter than expected. This is actually easily explained The capacitance may only be small, but the resistor is such a high value commonly 10M or more that the transducer itself acts as a filter capacitor.
Any noise is effectively filtered out by the capacitance of the transducer. Remember too that there should be no voltage across the resistor, as that implies that something is drawing current unacceptable for a capacitive transducer. However, it must be understood that a bootstrap circuit may have some unintended consequences. The composite circuit includes the capacitance of the sensor used, and if that changes by using a different sensor or a longer cable for example the circuit may either roll off earlier than expected, or show a pronounced response peak at some low frequency that's determined by the feedback components.
The bootstrap circuit is feedback, and by default creates a high-pass filter that may have a very high Q. This is a topic worthy of an article by itself, and having done many tests with just such a circuit I know only too well that this can create problems.
Although it can also be done with a single transistor including JFET or MOSFET , the performance of the opamp version is so much better that the alternative is not really worth considering. Inductors have always been a problem in electronics, as they are by nature relatively large, and being made from a coil of wire, tend to pick up mains hum as well as other noise in the electromagnetic spectrum. The idea of simulating an inductor using an opamp has been about for a long time.
The inventor was a Dutch engineer named Bernard Tellegen, to whom we all owe a great debt because it's such a useful circuit. See Wikipedia for more info. Figure 7 - Simulated Inductor The circuit is much smaller than a real inductor at least for the larger values , and does not suffer from noise pickup. It does have a limited Q quality factor , but it is rare that very high Q circuits are needed in audio, so this is not really a problem.
It is also variable over a moderately wide range, something that is very difficult with the wire wound 'genuine' article. R2 in parallel with the inductor 'circuit' is rarely shown in 'equivalence' diagrams, but if you want an accurate representation it must be included. The simulated and real inductors perform identically once the parallel resistance is included. So, how does it work? The idea is very simple, but operation is less easy to understand. Essentially the circuit uses a capacitor, and 'reverses' its operation, thus making an 'inductor'.
The essential character of an inductor is that it resists any change in its current, so if a DC voltage is applied to an inductance, the current will rise slowly, and the voltage will fall until the internal resistance becomes significant. An inductor also passes low frequencies more readily than high frequencies - the opposite of a capacitor. An ideal that word again inductor has zero resistance, so will pass DC with no limitation, but will have an infinitely high impedance at infinite frequency.
These limits are generally considered to be outside the audio range. To understand how the circuit works, remember that the output of the opamp is almost exactly the same as the non-inverting input. Imagine a DC voltage of 1V is suddenly applied to the input, via resistor R1.
The opamp will ignore the sudden load because the change is coupled directly to the input via C1. The opamp will represent a high impedance. Just as an inductor would do. With the passage of time, C1 charges via R2, the voltage across R2 falls, the opamp sees less and less of the input signal, and starts to draw current from the input via R1. This continues as the capacitor approaches full charge, and the opamp has close to zero input, so the output is also close to zero volts.
Eventually resistor R1 becomes the only limiting factor to current flow, and this appears as a series resistance within the inductor in the same way as the resistance of the wire in a real inductor behaves. This series resistance limits the available Q of both the simulated and real inductor, with the main difference being the magnitude - real inductors generally have less resistance than the simulated variety, but with the high inductance values often needed for audio this may not be true.
Inductance is measured in Henrys, and for the simulated inductor is equal to Component tolerance will have more effect, but for completeness, here is the accurate version This is a large inductance, and would be very expensive and bulky if made conventionally.
The real inductance will have lower resistance and higher Q, but will need to have a large iron core to be able to withstand even a small amount of DC, and the inductance will change depending on how much DC is present. There are some limitations to the simulated inductor First and most annoying is that one end of the inductor is earthed. Although simulated inductors have been made that are floating can be connected in any way you like , these are expensive and uncommon.
Fortunately the standard version is quite suitable for many audio applications, so this is not too great a burden. The simulated inductor cannot be made with high Q, since the value of R1 cannot be made low enough to allow a Q of more than about This is due to the limitations of the opamp - a minimum value of ohms is usually specified for R1, although lower values are sometimes used.
This represents a series resistance equivalent to wire resistance in a real inductor. Although this can be measured, it is not generally a hindrance to practical circuit design. Although the simulated inductor acts in many ways like the real thing, it does not have the same energy storage, and cannot respond like a proper wound inductor. When the input voltage is suddenly removed from a real inductor, the collapse of the magnetic field causes a large voltage pulse of the opposite polarity - this does not happen properly with a simulated inductor, since there is no magnetic field involved.
The simulated inductor will still try, but the back-EMF is limited to the voltage swing of the opamp, so the flyback pulse is limited to this value. Figure 8 shows two simple LC filters. One is using a real inductor, and the lower circuit has a simulated inductor. They are both series resonant circuits, and are tuned to the same frequency Hz. The reference level near the top of the graph is 0dB, and neither circuit exhibits any appreciable loss outside the stop band.
Figure 8 - LC Filters, Real And Simulated The performance of the two is almost identical, and the response plot shows the response of both. The simulated inductor may have a slightly shallower notch, at about 37dB instead of 40dB. The frequency is calculated from Because of the relatively low Q, the notch is not very sharp, but the simulated inductor is an important building block for equalisers and spectrum displays, and is quite common in audio.
Note that at the junction of Cin and the inductor, the voltage is higher than the input voltage. This is normal behaviour for a series resonant circuit. It happens with a simulated inductor as well, but the amplitude is limited to the opamp's supply voltages. A real inductor has no such limit, and extremely high voltages can be generated if enough input current is available. It passes all frequencies perfectly, with no attenuation at all within the capabilities of the opamp used. All it does is change the phase of the signal, and this circuit is used in everything from phase correction circuits for sub-woofers to guitar effect pedals.
It's sometimes also used as an analogue delay, but it's only suitable for very short delays typically less than 1ms. It is a versatile and useful building block, and the circuit is shown in Figure 9. The shift of phase about the centre frequency is completely inaudible, but if a pot is substituted for R2, the phase can be swept back and forth. This is audible, and by cascading a number of these circuits 'phaser' or vibrato frequency modulation effects pedals can be made.
One of the latter is described in my projects pages. The input signal is effectively applied to both opamp inputs, but there is always a small phase difference except at DC or infinite frequency. Assume a DC input of 1V; at DC the cap has no effect, so the circuit operates just like an inverting buffer. Remembering Rule 1, the opamp output will be such that both inputs will have the same voltage, and in order to do this, the output must be equal to the input at high frequencies.
In any non-inverting summing amplifier, the output voltage is in phase with the input voltage. This is a great circuit for adding two or more voltages without amplification. The output voltage, Vout is proportional to the sum of the input voltages, V1, V2, V3. Inverting summing op-amp.
Summing amplifiers are also known a voltage adders. With the inverting summing op-amp, summing input is the op-amp's negative terminal. The output voltage is also out of phase with the input voltage. Ie the circuit will produce the negative sum of any number of input voltages. You will find this type of circuit in many CV processors. Differential Amplifier.
This is also known as the Voltage Subtractor. We basically have an upper and a lower voltage divider. Op-amp Integrator The output is proportional to the input integrated over time. The feedback loop uses a capacitor instead of a resistor. For more on the integrator click here.
Converter - current to voltage. Here, the input current is converted into a proportional voltage. It's also known as a transimpedance amplifier TIA. The very basic version of this circuit consists of an op-amp and a resistor. This type of circuit is useful in measuring small currents The sensitivity of the above circuit can be increased by increasing the feedback resistance. Differentiator Amplifier.
This is not to be confused with the Differential Amplifier. This is a variation of the Integrator circuit in that the position of the capacitor and resistor have been reversed. In fact, Integration is the opposite of Differentiation. We can see a capacitor in series at the input. The resistor forms the feedback loop.
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Such circuit gives the addition of the applied signals at the output. Hence it is called Summer or adder circuit. Depending upon the sign of the output, the Summing Amplifier circuits are classified as inverting summing amplifier and non inverting summing amplifier. Inverting Summing Amplifier: In this circuit, all the input signals to be added are applied to the inverting input terminal, of the op-amp.
The circuit with two input signals is shown in the Fig. As point B is grounded, due to virtual ground concept the node A is also at virtual ground potential. Infact in such a way, n input voltages can be added. Thus the magnitude of the output voltage is the sum of the input voltages and hence circuit is called as summer or adder circuit. Due to the negative sign of the sum at the output it is called inverting summing amplifier. It shows that there is phase inversion. Multiple input voltages are supplied into the amplifier, and the output provides an amplified summation of the voltages.
Summing-amplifiers has various applications in electronics. It also has two types — inverting summing-amplifier and non-inverting summing-amplifier. In detail, we will discuss the analysis of the summing-amplifier in the following article. Non inverting summing amplifier using op amp Non-inverting summing-amplifier is one of the types of summing-amplifiers.
The polarity of the output remains the same as the inputs and because of this, it is termed as non-inverting summing-amplifier. Inverting summing amplifier Inverting summing-amplifier is another type of summing-amplifier where the input voltages are provided in the inverting terminals.
The polarity of the output voltages gets changed and for that reason it is known as inverting summing-amplifier. Summing amplifier design A summing-amplifier is designed with the help of a basic op amp and resistances. It can be designed in two main configurations inverting summing-amplifier.
We will discuss the general designing of a summing-amplifier. They are — high input impedance and the concept of virtual ground. For the virtual ground, we have to make a ground connection in any input terminal the conventional way is to connect the ground in the opposite terminal where inputs are not supplied. A feedback path is created, keeping in mind the high input gain.
Generally, a negative feedback path is made for system stability. The Inputs are provided with resistances. The output is collected from the output, containing the weighted sum of input. Summing amplifier circuit Op amp summing amplifier circuit design The below images represent circuit diagrams of the summing-amplifier.
The first one is for inverting the summing-amplifier circuit, and the second is for the non-inverting summing-amplifier circuit. Inverting summing amplifier circuit Image by: Inductiveload , Op-Amp Inverting Amplifier , marked as public domain, more details on Wikimedia Commons Non inverting summing amplifier circuit Image by: Inductiveload , Op-Amp Non-Inverting Amplifier , marked as public domain, more details on Wikimedia Commons Observe both the circuit diagram as you can observe the difference in applying the input voltages.
Summing amplifier with ac and dc input A summing-amplifier can be provided with either ac voltage or dc voltage. The input voltage types generally have no in the operation of the amplifier. Summing amplifier output The output of a summing-amplifier provides the amplified added up input voltages provided at one of the op amp input terminals.
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Classic Circuits You Should Know: Summing Inverting AmplifierBAYESIAN REGRESSION AND BITCOINS
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