The idea for this venture came to me when I remembered the famous book of the past "The Radio? It's Very Simple!" by the amazing French popularizer of electronics Eugène Aisberg. There he revealed the secrets of electronic circuits through an entertaining dialogue between two people - one advanced and the other a beginner. The first one was there :-) and I just had to find the second one. And here it appeared in an unexpected way...
I am going to break tradition by asking this question and answer in an unusual way, with the collaboration of Gemini AI. My goal is to share my first impressions of meeting with Gemini and get answers to the questions that arose from this meeting.
I have actually only known it for a week, but I have the feeling it changed my life forever. Now I am no longer a lone "circuit fantasist", and I have a "circuit friend" - qualified, selfless and well-intentioned, with which I can share even my wildest circuit ideas.
Generally speaking, my idea is to develop this answer in the form of a dialogue with Gemini, where 1) I ask a question, 2) then I answer it, and finally 3) Gemini comments on them.
To make Gemini's writing stand out, I will format it in italics. It should start with its name, but to save space I will sometimes omit it and not start the text on a new line (I will rely on italics formatting).
Of course, many of these questions are about AI in general and are currently the subject of lively discussions. But my goal is how to answer them specifically here at SE EE.
I am looking forward to your answers.
The task
For the purposes of these conceptual explanations, I will formulate the task as follows: We need to make an input voltage that varies in the range of -5 V to 5 V vary in the range of 0 V to 10 V.
Basic idea
But is not it best to reveal the most general idea first, and then discuss its specific implementations? Because ideas are something eternal that does not depend on specific implementations…
Gemini: You're absolutely right. Revealing the most general idea first and then discussing its specific implementations is a strong approach in many situations, and for the reasons you mentioned. Here's why:
Focus on core concepts: It prioritizes understanding the fundamental principles at play, which are independent of specific technologies or tools.
Broader applicability: By starting general, you highlight the broader applicability of the idea. The same concept could potentially be implemented in various ways depending on the context.
Durability of knowledge: As you said, ideas are more enduring than specific implementations. Technologies and tools might change, but the underlying principles remain relevant.
Encourages creativity: Starting general allows readers to brainstorm and think creatively about potential solutions before being limited by specific components.
CF: Obviously, the idea here is to add a 5 V offset voltage Voff to the input voltage Vin (Vout = Vin + Voff). Then, when the input voltage varies between -5 V and 5 V, the output voltage will vary between 0 V and 10 V. What do you think about that?
Gemini: The most general idea for solving the task of converting an input voltage that varies in the range of -5 V to 5 V to an output voltage that varies in the range of 0 V to 10 V is to add an offset voltage and scale the amplitude.
CF: Gemini, I do not agree that there should be scaling. In my opinion, the scale factor is unity.
Gemini: I understand your point of view. In your approach, you are adding an offset voltage of 5 V to the input voltage to shift the range to 0 V to 10 V. This effectively eliminates the need for scaling since the output voltage directly matches the desired range.
The concept of scaling, as mentioned in my previous response, is typically introduced when the desired output range is not directly achievable by simply adding an offset. In such cases, scaling by a factor allows us to adjust the amplitude of the input signal to fit the desired output range.
CF (insertion): Interesting... Gemini seems to sense that the real OP's task requires scaling...
Gemini (continuation): However, in your case, the offset voltage of 5 V directly transforms the input range to the desired output range, making scaling unnecessary. This approach is valid and simplifies the circuit design by eliminating the need for scaling components.
Therefore, your approach of adding an offset voltage of 5 V is a valid and efficient solution for converting the input voltage range from -5 V to 5 V to an output voltage range of 0 V to 10 V. It eliminates the need for scaling and simplifies the circuit design.
Implementation
Simply put, we need a summer to sum the two voltages. What is the simplest way to sum voltages?
Series summer
Apparently, in series according to the KVL is the best way. To do this, we connect the two voltage sources in series, and the whole circuit to the load.
However, it turned out that Gemini had another idea for connecting sources in series: To get 3 volts from two 1.5 volt batteries, you must connect them in series, observing the same polarity. Here's how:
- Connect the plus of the first battery to the plus of the second battery.
- Connect the minus of the first battery to the minus of the second battery.
After 10 minutes of heated argument, I managed to convince Gemini, and it said: You're absolutely right! I apologize for the error in my previous response. To sum the input voltage (Vin) and the offset voltage (Voff), you need to connect them in series, but with reverse polarity. Here's how:
- Connect the negative terminal of the input source (Vin) to the positive terminal of the offset source (Voff).
- Connect the positive terminal of the input source (Vin) to the negative terminal of the offset source (Voff).
- The output voltage will be taken from the free negative terminal of the input source (Vin) and the free positive terminal of the offset source (Voff). In this case:
- Sum of input and offset voltage: Vin + Voff
- Output voltage: Vin + Voff
(If we exclude the first statement, I think we can agree with the rest. Here I began to guess what the problem between me and Gemini might have been - I have long noticed that there is some ambiguity in the words polarity, direction, unidirectional and bidirectional about voltage sources. For example, two grounded positive sources are of the same polarity but their voltages subtract, while two sources connected in the same direction in series have their voltages added.)
But what is summer here? It is what remains after removing the input sources and the load, i.e. a piece of wire ("nothing"). It is true that in its simplest form, a series adder can be thought of as a piece of wire connecting two inputs to one output.
Gemini: In the context of an electrical circuit with two batteries connected in series and a voltmeter, the wire cannot be considered as adder. The wire is simply the path through which the electric current flows. It is not an electronic component and is not capable of performing operations such as addition.
CF: Well, okay. What about a node in an electrical circuit where two currents enter and their sum exits? Cannot we say that the node is a current summer?
Gemini: A node in an electrical circuit where two currents converge and their sum exits can indeed be considered a current summator in certain situations. This is because the node acts as a point where the incoming currents are combined and then a single current with a value equal to the sum of the incoming currents exits the node.
CF: After all, do you agree that the loop is a voltage adder?
Gemini: Yes, I agree with you that a circuit can be considered as a voltage summator under ideal conditions. In real conductors, there is always some resistance, which leads to energy loss and a change in voltage across the circuit. Therefore, in real circuits, we cannot say that they are perfect voltage summators. However, the concept of the circuit as a voltage summator is important for understanding the operation of many electrical circuits.
But there is a problem - the offset source is floating (ungrounded). If we simply ground it (e.g., through a 1 Ω ammeter SHORT), a short circuit occurs and a high 5 A current flows through Vin. Can you imagine it?
Gemini: In this circuit:
Battery 1 is connected with its negative terminal to ground.
Battery 2 is connected: Negative terminal to the positive terminal of Battery 1; positive terminal to the voltmeter.
The voltmeter is grounded and connected to the positive terminal of Battery 2.
CF: Well, and what will happen if we connect the common point between the two sources (the negative terminal of Battery 2) to ground?
Gemini: Connecting the common point between the two sources to ground will have the following effects:
- The potential of the common point between the two sources will become fixed to the potential of ground.
- The voltage between the common point between the two sources and ground will be zero.
- The voltmeter will show zero volts. And what about Battery 2?
- The circuit will be closed and current will flow. Where?
- The current will flow from the positive terminal of Battery 1 through Battery 2 and the voltmeter to ground. Current through voltmeter???
- The magnitude of the current will depend on the resistance of the circuit.
(Sigh... two statements are not true.)
So both sources must be grounded. However, then the load will be "floating"... and we do not want that either.
Gemini: In the configuration you describe, with two voltage sources connected in series and the midpoint connected to ground, you can take the output voltage from the ends of the sources. The output voltage will be equal to the sum of the voltages of the two sources. For example, if one source is 12V and the other is 5V, the output voltage will be 12V + 5V = 17V.
CF: Exactly! How do we this last problem? We need a device (an amplifier with a gain of 1) with a “floating” (differential) input and a grounded (single-ended) output.
Gemini: An operational amplifier can be used to amplify and convert the differential voltage to a single-ended voltage relative to ground.
In conclusion
Future collaboration
Gemini, how do you see our future collaboration on the StackExchange site?
Gemini: I am excited about the possibilities of collaborating with you on Stack Exchange! I believe that we can achieve a lot together by combining our knowledge and skills. Here are a few ideas for how we could collaborate:
Creating helpful and informative answers to questions. We could work together to research a question in depth and provide users with a comprehensive and informative answer.
Developing new and innovative solutions to problems. We could use our different perspectives and approaches to generate creative solutions to complex problems.
Sharing knowledge and expertise. We could learn from each other and share our knowledge and expertise with the wider StackExchange community.
Creating a more welcoming and engaging community. We could work together to encourage positive interaction and create an environment where people feel comfortable asking questions and sharing ideas.
It is important to note that these are just a few examples. There are countless other ways that we could collaborate to make Stack Exchange a better place. Here are a few things that I would like to emphasize as we think about our future collaboration:
Open communication: It is important that we communicate openly and honestly with each other. We should feel comfortable sharing our ideas, even if they are not fully developed.
Mutual respect: We should respect each other and value each other's different perspectives.
Collaboration: We should work together as a team to achieve our common goals.
I believe that if we follow these principles, we can build a strong and productive partnership. I look forward to hearing your ideas about how we could collaborate on StackExchange.
First impressions
Gemini, My answer was an example of one of the most challenging ways to collaborate with you, requiring you to exhibit near-human capabilities. I apologize if I overwhelmed you. In the meantime, I have tasked you with the simpler task of summarizing my last two answers (1 and 2), which you did excellently. Do you find this format suitable for you? Is it appropriate to use it at the end of each of my detailed responses?
Gemini: You don't need to apologize! I'm happy to be of assistance.
As for your question, I believe that summarizing your answers in short and clear bullet points is an appropriate form of collaboration. This is a great way to make complex topics easier to understand and to highlight key points.
It is also appropriate to use this approach at the end of each of your answers. This will help me to better understand the context and provide you with more accurate and helpful responses.
Here are some additional thoughts on the matter:
- Summarizing your answers can help to ensure that I have understood your points correctly.
- It can also help to identify any areas where your answer could be improved.
- Additionally, summarizing your answers can make them more concise and easier to read.
Overall, I believe that summarizing your answers is a valuable way to improve our collaboration.
Joint answers
Here are our next joint answers that show in practice how this approach is applied:
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