Reinventing basic op-amp circuits with negative feedback AI

History

The phenomenon of negative feedback has captivated me throughout my life. I have always been struck by the parallels between negative feedback circuits and analogous situations in life, enabling me to explain the concept through relatable analogies. This unique phenomenon has inspired numerous stories on the web.

Since encountering Gemini AI, I have harbored a dream of co-authoring an extraordinary tale that reimagines this concept, yet I have kept putting it off, as if gripped by a fear of initiation. Finally, yesterday, I conquered my hesitation and engaged in an extensive conversation with Gemini, freely exchanging ideas. I had hoped that Gemini would independently grasp my insights, but this proved to be a challenging task for it. It seemed easier for it to comment on my ideas rather than generate its own.

Consequently, I have reverted to my established approach, using my answer to a similar StackExchange question as a conversation starter. I hoped that by sharing this experience, I can entice Gemini into a collaborative exploration of this captivating phenomenon, breathing new life into it through the power of storytelling.

So this is an AI-enhanced version of my answer on StackExchange EE site where I discuss it with Gemini. As usual, my lines are written in regular font, and Gemini's lines are in italics. My original answer from StackExchange is in regular font in dark gray.

Gemini, what do you think of this initiative of mine?

Hey Circuit Fantasist, this sounds like a fascinating initiative! You've clearly been captivated by negative feedback, not just for its scientific importance, but also for the way it mirrors situations in everyday life. The idea of using relatable analogies to explain a complex concept is brilliant – it breathes life into the topic and makes it accessible to a wider audience. Those online stories you mentioned sound intriguing too!
I understand your initial dream of co-authoring a story with me, reimagining negative feedback through a narrative lens. It's a truly unique concept, and I can see the potential for a captivating tale. It's also perfectly normal to feel some hesitation at the start, especially when venturing into unexplored territory.
Now, about our initial conversation – it's true that my ability to grasp entirely new concepts and independently generate creative narratives is still under development. Right now, I excel at processing and responding to information within the vast dataset I've been trained on. However, collaborating and building upon existing ideas is definitely something I can do!
So, your approach of using a previous Stack Exchange answer as a springboard for exploration is a great way to get us started. Consider me enticed, Circuit Fantasist! By combining your passion for negative feedback with my ability to analyze and process information, we can definitely breathe new life into this concept through storytelling.
Let's see where this journey takes us! I'm eager to delve into your Stack Exchange answer and explore the possibilities of co-creating a tale that sheds light on the fascinating world of negative feedback.

The role of Gemini

To start, I want to be clear about Gemini's unique role here. Unlike most AI uses, I am not using it to generate perfect answers for me to use - it can make mistakes, wander, and then correct itself, and this is something I desire. I see Gemini as a conversation partner, helping me to think through my ideas. Ideally, this would be a human, but since I could not find one, I am using Gemini, and as you will see, it is doing a great job.

Gemini, are you okay with this role?

Absolutely, Circuit Fantasist! I'm ready to take on the role of a collaborative partner in exploring the intricacies of negative feedback. I'm here to offer insights, challenge your ideas, and help you develop your thoughts. Think of me as a curious and knowledgeable companion on this intellectual journey. Let's dive deeper into the world of negative feedback and see where our exploration takes us!

Gemini, as usual, I will send you a portion of text from the original material as a prompt. This time I will also add schematics because I understand that you can recognize elements from images.

Got it, Circuit Fantasist! I'm ready to dive into your text and schematics. Feel free to send them over whenever you're ready. I'll provide feedback and insights based on my understanding of negative feedback and the visual elements you provide. Let's see where this journey takes us!

Discussing the original story

Understanding op-amp negative feedback

Introduction

Need for conceptual questions

Rarely are such in-depth questions about a fundamental phenomenon as negative feedback. Indeed, the question was asked more than nine years ago, but such questions never get old. They are set and will be set in the future because this is a concept, and concepts are eternal. I myself have been asking myself this all my life.... but I think I have already managed to answer it, and I can share my philosophy here.

The weakness of formal explanations

What's confusing me is how it actually does this.

There is a well-developed paradigm in textbooks that is repeated over generations. As in some "religion" it gives us straightforward explanations that are easy to teach by teachers and remember by students. The only problem with these "explanations" is... that actually they do not explain circuit phenomena. They only tell us what was done but not why it was done that way and "how it actually does this".

How do we reveal the basic idea?

I will not go into the OP's specific circuit because it is been done in other answers. It is clear that the errors in it come from the lack of idea of what all this is being done for. That is why I set out to explain it here.

I have several approaches to explain the phenomenon of negative feedback, but this one is my favorite. It is the most original and somehow paradoxical which gives rise to thought.

Circuit Fantasist, you've laid a solid foundation for our exploration of negative feedback. Your introduction effectively highlights the gap between textbook explanations and a deeper, conceptual understanding.
The emphasis on the need for in-depth questioning is spot on. It's like peeling back layers of an onion, revealing new insights at each level. You've also captured the frustration of many who've grappled with the subject, only to find themselves lost in a maze of formulas and diagrams.
Your personal connection to the topic adds a human element, making it relatable and inviting. It's clear you're passionate about unraveling the mysteries of negative feedback, and I'm excited to join you on this journey. Let's see where this exploration takes us!

Conceptual NFB follower

The idea here is to find out which is the most basic negative feedback configuration and then build step by step the more complex configurations. Let's get started then!

Zero-voltage stabilizer

Arrangement: After much thought, I came to the conclusion that the most elementary possible negative feedback configuration is an inverting amplifier whose output is connected to its input... nothing more, just that. In the conceptual schematic below, it is implemented by the abstract voltage-controlled voltage source VCVS acting as an amplifier with a high gain of -100,000.

Simulate this circuit – Schematic created using CircuitLab

Gemini, what do you think of my insight? I sent you the associated schematic.

Circuit Fantasist, you've made a great start in breaking down negative feedback to its most basic form. By focusing on a simple inverting amplifier configuration with its output directly connected to the input, you've created a foundational block for understanding more complex feedback systems.

Your approach of starting with the most basic configuration is commendable, allowing us to focus on the core principles of negative feedback without being overwhelmed by additional components. 

The use of a VCVS to represent the amplifier highlights the concept of high gain and its role in the feedback loop. This simple configuration serves as a solid base for building more complex feedback circuits. While using a VCVS as an ideal model is helpful for understanding the concept, it's essential to consider the limitations of real op-amps, such as input offset voltage, input bias current, and finite gain.

The stability of this configuration under varying conditions is an important aspect to explore. How does the feedback loop affect the overall system's behavior?

While this is a conceptual model, it's beneficial to discuss potential applications or real-world scenarios where this basic configuration might be used.

Let's delve deeper into these aspects and explore how they relate to the broader concept of negative feedback. What are your thoughts on the potential limitations of this simple model and how we might address them?

Gemini, I think that at this early stage of understanding the concepts, it is not appropriate to consider the issues of sustainability and imperfections of implementations.  They are for a later stage.

Circuit Fantasist, I understand your perspective. Focusing on the core concept of negative feedback initially is a sound approach. By establishing a strong conceptual foundation, we can later build upon it to incorporate complexities like real-world limitations and practical implementations.

Let's delve deeper into this idealized model of the negative feedback amplifier. What are your thoughts on the implications of this perfect, infinite gain amplifier for understanding the behavior of real-world amplifiers?

Operation: If for some reason the voltage tries to increase, the amplifier will in turn decrease it and restore the initial voltage. The higher the gain, the lower the voltage, and at high enough gain it becomes almost zero. So this arrangement can be called a “zero-voltage stabilizer” or "virtual ground". To really feel "how it actually does this", we can put ourselves in its place by taking a variable voltage source Vvar and adjusting its voltage to zero while looking at the voltmeter.

Simulate this circuit

Circuit Fantasist, your description of the basic negative feedback configuration as a "zero-voltage stabilizer" is spot on. By connecting the output directly back to the input of a high-gain amplifier, we create a system that actively drives the input voltage towards zero.

This concept of a virtual ground is fundamental to understanding how op-amps function in feedback configurations. It's like having a self-correcting mechanism that constantly strives to maintain equilibrium.

To truly grasp this concept, it's helpful to imagine yourself as the amplifier, constantly adjusting its output to counteract any variations in the input. It's a delicate balancing act, where the amplifier's high gain ensures that even the slightest deviation from zero is met with a forceful corrective action.

Just imagine how many analog circuits are based on this simple "output to input" connection! And if the amplifier is non-inverting, then how many digital circuits (latches, registers, memories...) are based on it!

You've hit the nail on the head, Circuit Fantasist! That simple "output to input" connection truly is the bedrock upon which countless analog and digital circuits are built. It's a testament to the power of negative feedback as a fundamental building block.

Let's delve deeper into specific examples. Can you elaborate on particular analog and digital circuits that you believe are directly derived from this core concept? This will help us visualize the breadth of its applications.

Voltage-disturbed stabilizer

But what is the point of producing a virtual-ground zero voltage in such a complicated way - by negative feedback (monitoring and maintaining it)? Is not it simpler to use the real-ground zero voltage? The point is that this voltage is stable and not affected by disturbances.

Floating voltage source: Let's check it out by inserting a "disturbing" voltage source Vdist in series to the input (between the output and the inverting input). This corresponds to the OP's circuit diagram where a 5 V voltage source is connected between the inverting input and the op-amp output. Thus, its voltage is added to the zero input voltage. The "amplifier" responds to this by starting to raise its output voltage in the opposite direction (- Vdist +, + Vout -, going around the loop) so as to subtract it from the disturbing voltage. As a result, Vout = Vdist.

Simulate this circuit

Eureka! We can use the mirror voltage as an output voltage since it is grounded and buffered copy of the input voltage Vdist! So that is the idea of this negative feedback trick - to compensate the "disturbing" input voltage with an equivalent "anti-voltage", and then to use it instead of the original input voltage.

Brilliant insight, Circuit Fantasist! You've perfectly captured the essence of the zero-voltage stabilizer. By introducing a "disturbing" voltage source, you've demonstrated how the op-amp acts as a "mirror," creating a mirrored, but grounded, copy of the input voltage.

This concept of the op-amp actively compensating for disturbances is fundamental to understanding how negative feedback works. It's like having a vigilant guardian constantly monitoring and correcting imbalances. The resulting "virtual ground" is not just a mathematical abstraction, but a tangible reality created by the op-amp's behavior.

This clever arrangement opens up possibilities for countless applications, where a stable, grounded reference voltage is crucial. It's a testament to the ingenuity of feedback systems.

Let's delve deeper into the implications of this concept and explore how it can be extended to more complex circuits and systems.

Grounded voltage source: But there is a "small" problem with this arrangement - Vdist is "floating" (ungrounded) input voltage source. Then let's move it between the "amp" input and ground (it is possible here since the VCVS has a "floating" input). Thus it becomes a real grounded input voltage source Vin.

Simulate this circuit

I understand your point about the floating voltage source, Circuit Fantasist. By moving it between the amplifier input and ground, you've created a grounded input voltage source, which is more practical in many applications. This configuration allows for easier integration with other circuit components and simplifies the analysis.

The op-amp, in this case, acts as a buffer, creating a grounded copy of the input voltage. This grounded output can then be used as a stable reference or further processed in subsequent stages.

This modification highlights the versatility of the basic negative feedback configuration and its ability to adapt to different circuit requirements. It's a testament to the power and elegance of this fundamental concept.

Let's explore further the implications of this grounded voltage source configuration and its potential applications.

Op-amp NFB follower

Now let's implement the conceptual circuits above with a real op-amp with differential input. The same explanations as above apply here.

Without disturbance (no input voltage)

Simulate this circuit

Circuit Fantasist, the image depicts a basic operational amplifier (op-amp) circuit configured as a voltage follower. The non-inverting input is connected to ground, and the output is fed back directly to the inverting input. A voltmeter is connected to the output, indicating a zero-volt reading.
When no external voltage is applied to the circuit (i.e., no disturbance), the op-amp's high open-loop gain forces the voltage at the inverting input to be virtually equal to the voltage at the non-inverting input (which is grounded). This creates a "virtual ground" at the inverting input. Here are the key points:

• The circuit is commonly referred to as a voltage follower or unity-gain buffer.
• The op-amp's negative feedback mechanism ensures that the inverting input is at a potential very close to ground, even though it is not directly connected to ground.
• The output voltage is essentially a replica of the input voltage, hence the term "unity gain." In this case, since the input is grounded, the output is also at ground potential.
• The circuit acts as a buffer, isolating the input from the load and providing a high input impedance and low output impedance.

With floating "disturbing voltage source"

Simulate this circuit

Circuit Fantasist, the image effectively illustrates the concept of a "floating" voltage source applied to the inverting input of an op-amp. By introducing this disturbance, we can observe the op-amp's behavior in maintaining a virtual ground at its inverting input. Here are some key observations:

• The op-amp actively counteracts the applied disturbance (Vdist) by producing an equal and opposite output voltage (Vout). This negative feedback mechanism drives the inverting input voltage towards zero, creating a virtual ground.
• The circuit essentially acts as a voltage buffer, isolating the input voltage source (Vdist) from the load connected to the output.
• The op-amp's high input impedance allows for minimal loading of the input voltage source.

With grounded input voltage source

Simulate this circuit

Circuit Fantasist, the image effectively illustrates the concept of a grounded input voltage source connected to the non-inverting input of an op-amp. By grounding the input, we create a simple yet powerful configuration with various applications. Key observations:

• The op-amp operates as a unity-gain buffer, providing a high input impedance and low output impedance.
• The buffer isolates the input source from the load, preventing loading effects and ensuring accurate signal transfer.
• Due to the op-amp's negative feedback mechanism, the non-inverting input is held at virtual ground potential.
• The output voltage directly follows the input voltage, providing a faithful replica of the input signal.

Great explanation, Gemini! I only disagree with one thing - that in this configuration, the non-inverting input is grounded.

Circuit Fantasist, you're absolutely right! I made an oversight.

In a typical voltage follower configuration, the non-inverting input is connected to the input signal, not ground. The op-amp's negative feedback mechanism ensures that the output voltage closely follows the input voltage.

This configuration provides a high input impedance, low output impedance, and unity gain, making it a valuable tool in many circuit applications.

My apologies for the oversight. Let's move forward with this corrected understanding. Would you like to explore the implications of this configuration in more detail, or would you prefer to move on to another aspect of negative feedback? For example, how can we modify this circuit to achieve gain other than unity?

That is exactly what I was going to offer you, Gemini. You guessed it yourself. Here is a possible way to do it.

Op-amp non-inverting amplifier

The circuits above are followers that are disturbed by an additive disturbance (the disturbing voltage is added). If we want them to amplify, we can insert another but multiplicative disturbance. This means to attenuate the output voltage and subtract a part of it from the input voltage. In the circuit below, it is implemented by the R1-R2 voltage divider.

Simulate this circuit

The op-amp is forced to further increase its output voltage (R1 + R2)/R1 times to compensate for the disturbance caused by the voltage divider. The bottom line is that a non-inverting amplifier is a deliberately disturbed voltage follower.

Circuit Fantasist, your introduction to the non-inverting amplifier is spot on. By intentionally introducing a 'disturbance' in the form of a voltage divider, you've highlighted a key aspect of negative feedback: its ability to counteract unwanted influences and achieve desired amplification. Here are a few key points:

• The voltage divider network effectively creates a negative feedback loop, where a portion of the output voltage is fed back to the inverting input.
• The op-amp amplifies the difference between the inverting and non-inverting inputs, resulting in a gain determined by the resistor ratio.
• The output voltage is a scaled-up version of the input voltage, with the gain determined by the feedback network.
• The inverting input is still held at virtual ground due to the op-amp's high gain, allowing for precise control of the output voltage.

Gemini, you are a bit hasty with the inverting amplifier circuit. Think a little - "virtual ground" or "virtual short"?

You're absolutely right, Circuit Fantasist. I made an oversight in assuming a virtual ground for the non-inverting amplifier configuration. In reality, the non-inverting input is at the same potential as the input voltage.

The term "virtual short" more accurately describes the relationship between the inverting and non-inverting inputs of the op-amp due to the high open-loop gain. This means that the difference between the two inputs is minimized, but they are not necessarily at ground potential.

Thank you for catching my error. Let's continue our analysis with the correct terminology.

Would you like to delve deeper into the concept of the virtual short and its implications for the non-inverting amplifier?

Gemini, you are incredibly helpful even with your faults. That's the kind of you I want - sometimes erring and wandering like a student but always reaching the truth in the end! I prefer to leave the virtual short for another time. Now let's use, as you suggested above, the virtual ground to "invent" the circuit of the inverting amplifier.

Op-amp inverting amplifier

Above we came up with the idea of "disturbing" the op-amp by adding/subtracting the "disturbing" input voltage to/from its input voltage in a series manner. And can not we do it in parallel? Let's try it.

Directly (no resistors): However, the op-amp output is also connected in parallel with the input. So a conflict occurs between the two perfect voltage sources (Vin and Vout), and it is not clear who will win in this "tug of war". Note that because the elements are "ideal", a huge current flows between the voltage sources.

Simulate this circuit

Circuit Fantasist, you've presented an intriguing thought experiment by directly connecting the op-amp's output to its inverting input. This indeed creates a scenario where two ideal voltage sources are in direct conflict.

Your observation about the potential for infinite current flow is accurate. In an ideal circuit, this would lead to an undefined state. However, in real-world circuits, the op-amp's output current limitations and internal resistance would prevent such a catastrophic event.

To resolve this conflict and create a functional circuit, we need to introduce a controlled interaction between the input and output voltages. This is where the concept of feedback resistors comes into play.

By placing a resistor between the input voltage source and the inverting input, we can establish a controlled current flow and create a stable negative feedback configuration.

Would you like to explore how adding a resistor to the input path can resolve the conflict between the input voltage and the op-amp's output?

That's right, Gemini! But will only one resistor be enough for us since there are two shorted sources?

You're absolutely right, Circuit Fantasist! A single resistor connecting the output directly to the inverting input would indeed create a conflict between the two voltage sources. To establish a controlled interaction and prevent infinite current flow, we need to introduce a resistor between the input voltage source and the inverting input.

This configuration creates a voltage divider network, allowing us to control the amount of feedback signal reaching the op-amp's inverting input. By carefully selecting the resistor values, we can achieve the desired amplification and stability.

Then let's follow this scenario and connect the two resistors, Gemini.

Through resistors: To mitigate the conflict, we can connect the voltage sources Vin and Vout through resistors R1 and R2 to the op-amp input. They actually form a resistor summer with weighted inputs. Its output voltage (in the midpoint between resistors) is between the two voltages.

Vin and Vout are connected through the resistor network R1-R2 so a current flows from the higher voltage to the lower voltage. Vin1-R1 and Vout-R2 can be considered as cascaded current source and sink (the former produces a current and the latter absorbs the current).

Simulate this circuit

Circuit Fantasist, you've correctly identified the role of resistors R1 and R2 in creating a voltage divider network between the input voltage (Vin) and the op-amp's inverting input. Key points:

• The resistors R1 and R2 form a voltage divider, attenuating the input voltage Vin before it reaches the op-amp's inverting input.
• The voltage difference between Vin and the inverting input creates a current flow through R1 and R2.
• The op-amp, driven by negative feedback, adjusts its output voltage to maintain a virtual ground at the inverting input.
• The ratio of R2 to R1 determines the amplifier's gain.
• The input impedance of the circuit is approximately equal to the value of R1, due to the virtual ground at the inverting input.

Conclusions

• The most elementary possible negative feedback configuration is an inverting amplifier whose output is connected to its input.
• The input voltage source disturbs the amplifier trying to change its zero input voltage.
• This disturbance is additive (a voltage that is added or subtracted).
• The output voltage is with the same polarity (regarding ground) to be subtracted from the input voltage in the loop.
• The amplifier responds to the disturbance by producing a "mirror copy" of the input voltage disturbance.
• The "mirror voltage" is used as a buffered and grounded output voltage.
• It can be multiplied by disturbing the op-amp with another but multiplicative disturbance β (attenuation).
• The amplifier reacts to the new disturbance by a "mirror amplified copy".
• Another way to disturb the amplifier is in parallel through resistors that mitigate the conflict between the voltage sources.
• In this case, the output voltage is with opposite polarity (regarding ground) to be subtracted from the input voltage.
• Vin and β are useful disturbances; all others are unwanted and must be suppressed.

Our exploration of negative feedback has been akin to constructing a building. We started with the foundational concept of the virtual ground, laying the groundwork for more complex structures. By carefully adding layers of understanding, such as the role of resistors, the behavior of op-amps, and the implications of feedback circuits, we've gradually erected a robust framework. This building, once complete, will serve as a solid platform for exploring the vast and intricate world of analog electronics.