# What approach should be used when solving a circuit?

Boltzman Oscillation
Summary
I want to know what methods are typically made in analyzing a method.
I am close to graduating as an EE major but I have never been able to organize a step by step method on analyzing a circuit. It seems to me that every time I am trying to analize a circuit I end up with a bunch of equations and nothing more. I know that I should:

1. Know what im solving for (Vout, Vin, Pout) and find equations in relation to that.
2. Use KVL, KCL, and Ohms law.
3. Note the number of unknowns in my equation and try to find that same number of equations.

Now using these three rules then I should be able to find anything I want in a circuit but usually I dont. Let us say I need to find Vout for a circuit. I usually find an equation, any one, that has Vout in it. I then find other equations using KVL and KCL but only enough to match the number of unknowns. I then end up with a bunch of equations where I cannot single out Vout to the left side of the equations like so:

$$V_{out} == right side$$

What should I be doing to actually get a good final equation?

Delta2

Gold Member
2021 Award
What should I be doing to actually get a good final equation?
It's going to depend on the circuit but one important step you left out is to simplify the circuit before you start doing loop equations or node equations.

Also, focus on a step by step approach, not trying for a final equation all at once.

Thevinin and Norton are your friends.

hutchphd and DaveE
Gold Member
I agree with phinds - simpify the circuit first, and follow a step-by-step approach.

To be more explicit, instead of focusing so much on the one quantity you want (##V_{out}##), notice that you need to setup equations that can be solved for all of the currents/voltages in the circuit. There are a couple of standard approaches: nodal analysis and mesh analysis. I'm guessing whichever book you used for basic circuit theory covered this - have you re-read the relevant sections of your circuit book(s)?

The idea is that you follow a systematic procedure and end up with a system of linear equations ##\mathbf{A x} = \mathbf{b}##. Then you basically just solve for the unknown voltages and/or current contained in the vector ##\mathbf{x}##. There are situations where forming one or more of the equations takes extra work, but it is still a systematic procedure. There are a number of textbooks that describe these things better than I ever could, so again I recommend looking at your books. If you end up with specific questions please feel free to post and I'm sure folks here will be happy to help.

jason

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Boltzman Oscillation
I agree with phinds - simpify the circuit first, and follow a step-by-step approach.

To be more explicit, instead of focusing so much on the one quantity you want (##V_{out}##), notice that you need to setup equations that can be solved for all of the currents/voltages in the circuit. There are a couple of standard approaches: nodal analysis and mesh analysis. I'm guessing whichever book you used for basic circuit theory covered this - have you re-read the relevant sections of your circuit book(s)?

The idea is that you follow a systematic procedure and end up with a system of linear equations ##\mathbf{A x} = \mathbf{b}##. Then you basically just solve for the unknown voltages and/or current contained in the vector ##\mathbf{x}##. There are situations where forming one or more of the equations takes extra work, but it is still a systematic procedure. There are a number of textbooks that describe these things better than I ever could, so again I recommend looking at your books. If you end up with specific questions please feel free to post and I'm sure folks here will be happy to help.

jason

So you are saying that I should be using either nodal or mesh analysis? I find nodal/mesh to be difficult to do when I am given a component such as a BJT. If I try nodal then I have to find a way to transform my voltage sources to current sources which I can if I have a handy resistor in series to it but that is almost never the case. Mesh analysis requires there to be only voltage sources (the way I've learned it) but once again, the BJT is modeled by a dependent current source that needs to be converted into a voltage source; I figured I could just use ##r_{\pi}## to convert it since it is in parallel with the current source.

LvW
So you are saying that I should be using either nodal or mesh analysis? I find nodal/mesh to be difficult to do when I am given a component such as a BJT.
.............
Here is a "trick" which can help to simplify BJT amplifier analyses:
For DC operating point calculations you, normally, are assuming a fixed DC voltage between base and emitter of VBE=0.7 volts (or any similar value).
For calculation purposes, you can replace the base-emitter path with a DC voltage source of the same value - and make use of the superposition theorem. Thus, you are splitting the calculation into two separate parts which reduces the number of equations which have to be combined.
This procedure is allowed because of the existence of the substitution theorem.

jasonRF
In the text " The Art of Electronics" by Horowitz and Hill there is little formal network theory and need for solving large systems of equations. They believe that their approach gives a better understanding of the choices and compromises that engineers face in circuit design.

The authors develop models for active devices as BJTs and FETs. They avoid what they call unnecessary pedagogical approaches not used by practicing engineers. They look at circuit design as more of an art using a combination of basic laws, rules of thumbs, and a large bag of tricks. They do not get lost in math.

Check it out.

jasonRF
Gold Member
So you are saying that I should be using either nodal or mesh analysis? I find nodal/mesh to be difficult to do when I am given a component such as a BJT. If I try nodal then I have to find a way to transform my voltage sources to current sources which I can if I have a handy resistor in series to it but that is almost never the case. Mesh analysis requires there to be only voltage sources (the way I've learned it) but once again, the BJT is modeled by a dependent current source that needs to be converted into a voltage source; I figured I could just use ##r_{\pi}## to convert it since it is in parallel with the current source.
Well, you asked a very general question, and mesh and nodal analysis are two of several general methods. As you mentioned, you can use the fact that the controlled current source in the hybrid-pi model is parallel to ##r_0## (I believe ##r_\pi## is in the other leg) and transform it to a voltage source. Also, there might be a source transformation that applies to your pesky voltage sources that you might not be aware of. An example transformation is below (from Basic Circuit Theory by Desoer and Kuh):

without seeing a specific circuit we can only talk in generalities.

EDIT: also, from your post you mention needing a resistor in series to transform a voltage source to a current source. Just in case you don't know, Thevenin-Norton theorem applies for general impedances, not just resistances.

Jason

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Boltzman Oscillation
In the text " The Art of Electronics" by Horowitz and Hill there is little formal network theory and need for solving large systems of equations. They believe that their approach gives a better understanding of the choices and compromises that engineers face in circuit design.

The authors develop models for active devices as BJTs and FETs. They avoid what they call unnecessary pedagogical approaches not used by practicing engineers. They look at circuit design as more of an art using a combination of basic laws, rules of thumbs, and a large bag of tricks. They do not get lost in math.

Check it out.

I have the book but stopped reading because I the solution manual does not exist. How can I make sure I am doing the circuits correctly? If I just solve the problems on my own without being corrected then I might just end up practicing a bad habit. Should I just read it without doing the problems?

Gold Member
Why not run the circuit through a simulation software such as LTSpice?

Something else that helps me is trying to solve the circuit with multiple methods if it's practical enough. The answers should be the same if it's right.

Tom.G
I have the book but stopped reading because I the solution manual does not exist. How can I make sure I am doing the circuits correctly? If I just solve the problems on my own without being corrected then I might just end up practicing a bad habit. Should I just read it without doing the problems?
Do you have the accompanying "Student Manual for the Art of Electronics"? It has more worked examples and solutions to select problems.

Many problems in the book are design problems for which he gives the specs. Does your design meet the specs. Other problems are of the show variety or prove variety. He gives a lot of information and builds on it. Design a circuit to do this, using the information and considerations that were discussed previously maybe all the way back to the beginning of the book. He gives lots of examples to build on.

Don't just read, study the book. Understand the reasons for the discussions. There is a boat load of information in that book.

yungman
Since you are close to graduation, I am going to assume you are going to enter the job market soon, so instead of talking about "how" to make the equations to calculate Vout, KVL all that, I am going to talk about the more practical way in real life on the job after almost 30 years mostly design analog, RF, IC circuit.

First off, I don't recall even ONCE I wrote KVL type of thing, I don't think I ever even sat down and wrote these kind of stuff at the beginning of a project. Now don't mistaken that I don't think theory is important, it's very important particularly now a days in microwave that you need all the knowledge of electromagnetics, signal integrity, RF designs etc. that require a lot of theory. BUT, analyzing using KVL and writing those equations in the books is NOT one comes to my mind.

When I approach a new project say to amplify a signal.
1) I look at the input drive characteristics to my circuit ( drive capability, impedance, voltage range, speed etc.). Then I look at what am I suppose to do with it. Then I look at the output requirements ( voltage range, slew rate, current capability etc.)

2) After those are clear, I would immediately think of what type of circuit that can do the job. I would google and look at other examples that do the similar job. I would go from the easiest way...........Like using an opamp I can buy.

3) To see whether I can use an opamp, this is where a lot of time is spent going on Digikey, Mouser etc. type of distributors to look. It is a learning process how to look at requirements of choosing to find something that fits your needs. Then it's a long process to read the datasheets of different opamps. Look at input range, input current, frequency response, slew rate, output range, output drive etc. etc. To confirm it can do the job.

4) If you can find one that can do the job, consider yourself lucky. If not, you might have to go to transistor circuits. You need to come up with the rough design ( no KVL and all that). Then repeat step 3) above on finding the right transistors. If transistor doesn't work, you research another way until you find one.

5) After determine what to do, then you start drawing up the circuit, look at the DC bias ( still I never use KVL stuffs). Circuits are usually the easy and simple part, believe it or not, circuit in the books usually works. If you find yourself having to have fancy tricks in the circuit or very critical in resistor values and all, IT'S LIKELY A BAD DESIGN. almost all the end circuits are very simple just like in the text books. The simpler the better, too complicate, look inward that your design is NOT GOOD. If you need KVL to find answer, it's time to look at your design.

Circuit design is the easy part, in my experience, making the circuit stable and reliable, not susceptible to interference, not radiate noise to the surrounding is where you earn your keeps. this is the real life hard part. This is too long to talk and off the topic of this thread. There is a big difference between academic environment and real life on the job. I've seen people from prestige colleges with good grades didn't manage to transition from academic to real life.

It's too long to talk about this subject, I can only give you a specific example above how to approach a task from my experience.

Gold Member
I feel like I might be in similar shoes with OP if they are graduating soon. I'm not sure how jobs worked 30 years ago, but all 3 of my jobs (including an RF engineer position) within the last 2 years and a few months required the fundamentals including KCL and KVL. I would definitely say at the very least almost every interview was loaded with circuit analysis questions, and I have done a lot of interviews.

yungman
I feel like I might be in similar shoes with OP if they are graduating soon. I'm not sure how jobs worked 30 years ago, but all 3 of my jobs (including an RF engineer position) within the last 2 years and a few months required the fundamentals including KCL and KVL. I would definitely say at the very least almost every interview was loaded with circuit analysis questions, and I have done a lot of interviews.
I have my share of interviews not 30 years ago, more recently. They asked like what is the DC setup and all, but it is a lot more obvious that you don't have to get into KVL notes. It's like if they ask you a question of a BJT bias, you look at the voltage at the base, emitter is 0.7V below for NPN. You know emitter is low impedance, it's like a voltage source, you easily calculate the current if there's a resistor to the -V. Point is it's very simple, you don't need to set up equations.

KVL in school get into a lot of resistor divider network, looking at the voltage at a note, combination of current and voltage source. In real life circuit, you avoid design like this at all cost, you want it to be simple, one stage at a time. If you have to fix in all the stuffs at one time, that's bad design.

Particular in RF circuits, each stage is very small, one RFIC, one or two transistors. In is very simple, the difficult part is the impedance with distributed elements using stripline and all. Not the normal KVL stuffs.

My interviews on RF is more on Smith Charts matching impedance type of thing. Now, that's important. not KVL!!!

Gold Member
I would put a lot of money on it, that interviews for entry-level candidates are very different from people who have more than 10 years of experience. Almost all of my interviews did involve setting up equations and using fundamentals.

yungman
I would put a lot of money on it, that interviews for entry-level candidates are very different from people who have more than 10 years of experience. Almost all of my interviews did involve setting up equations and using fundamentals.
That I don't know, My entry level was back in the 70s and 80s, but still, the question is more giving you a practical circuit like an opamp with common mode voltage and tell you to give the voltage on each node. BUT, it should be very obvious with knowledge to use KVL. I had like transistor bias circuits and asked for DC. As I said, you know the circuit, pick what is the low impedance note and not resort to KVL type of calculation of loops and all that.

yungman
Let's put it this way. I was a manager of EE of like 12 years. If I ask the candidate about the voltage of a circuit like an opamp or transistor, if the candidate tries to write KVL, he/she will NOT hear from me again. If they don't have the common sense to answer the question, they DON'T have it.

If someone don't have the common sense and said to me " in the emitter if current the transistor is 10mA and the r'e is 2.6ohm, so I have to calculate this in the divider network. I don't need this kind of people anywhere close to my group. This is real life. And don't give me how in the physics why it's 2.6ohm. I'll walk the candidate out the door.

Gold Member
I have the book but stopped reading because I the solution manual does not exist. How can I make sure I am doing the circuits correctly? If I just solve the problems on my own without being corrected then I might just end up practicing a bad habit. Should I just read it without doing the problems?
If you want to be successful in a EE design position, you need to learn ASAP how to check your work and know if you are correct without help. Your coworkers are not being paid to solve the same problem as you, they have their own work to do. In fact, in may jobs, there isn't anyone that knows how to check your work. Yet, the final product does have to work, managers are not very tolerant of repeated inefficiencies or failures.

yungman
yungman
If you want to be successful in a EE design position, you need to learn ASAP how to check your work and know if you are correct without help. Your coworkers are not being paid to solve the same problem as you, they have their own work to do. In fact, in may jobs, there isn't anyone that knows how to check your work. Yet, the final product does have to work, managers are not very tolerant of repeated inefficiencies or failures.
It's the result. I don't want to hear reasons why, I just want it to work................AND don't make me having to worry about it.

Bottom line, I don't give a crap why it doesn't work, make it work. You can use voodoo, just make it work.

DaveE
Gold Member
Many EE programs don't really address your question. Yes KVL, KCL, Thevenin, etc. are necessary tools, and you will use them sometimes. However in practice much of EE design work is actually more like familiarization with common problems and solutions; pattern matching and modeling with similar solved problems. We don't "reinvent the wheel" very often, we are paid to get a good solution as quickly as possible. Sometimes that requires creativity and new designs, but it is usually just understanding what is already been done by others and modifying it to suit your needs. The crucial step is that you have to be able to really understand other's designs so you know how to use or modify them.

I'm pretty out of touch with entry level positions these days. But, in the past, most of these skills are learned in entry level position where you are learning from more experience engineers "on the job".

yungman
Many EE programs don't really address your question. Yes KVL, KCL, Thevenin, etc. are necessary tools, and you will use them sometimes. However in practice much of EE design work is actually more like familiarization with common problems and solutions; pattern matching and modeling with similar solved problems. We don't "reinvent the wheel" very often, we are paid to get a good solution as quickly as possible. Sometimes that requires creativity and new designs, but it is usually just understanding what is already been done by others and modifying it to suit your needs. The crucial step is that you have to be able to really understand other's designs so you know how to use or modify them.

I'm pretty out of touch with entry level positions these days. But, in the past, most of these skills are learned in entry level position where you are learning from more experience engineers "on the job".
That's what the newly graduates don't get, that's the reason I am so harsh in this. I have seen people from UC Berkley and Standford that I would fire if they were in my group. The last thing I want to hear is WHY it doesn't work. MAKE IT WORK.

You talk to me about KVL, I'll walk you out the door.

Gold Member
It's the result. I don't want to hear reasons why, I just want it to work................AND don't make me having to worry about it.

Bottom line, I don't give a crap why it doesn't work, make it work. You can use voodoo, just make it work.
Absolutely. But, I also need you to give me confidence that it will work tomorrow, too. Or that if there is a problem no one will die or go bankrupt as a result. "Working" has a complex definition.

Building trust is also necessary. Mistake can be more significant to your career than they initially may appear. OTOH, it would (probably) build trust if you came to me and said "I found a problem with my design, these are the ramifications, and this is how I will fix it." No one's perfect after all.

yungman
Absolutely. But, I also need you to give me confidence that it will work tomorrow, too. Or that if there is a problem no one will die or go bankrupt as a result. "Working" has a complex definition.

Building trust is also necessary. Mistake can be more significant to your career than they initially may appear. OTOH, it would (probably) build trust if you came to me and said "I found a problem with my design, these are the ramifications, and this is how I will fix it." No one's perfect after all.
That's later on, I am talking about the interview. It won't pass my interview................

I would test them with more common sense questions. I have my sets of question.....not including KVL. I have to write up my questions that I actually gave to the jr engineers I interview. I actually don't talk to them until I see the test results. If they fail, I just politely talk a little and walk them out. When they cannot answer, I would talk to them and ask " what would you do if this .....or that". I want to see how they face a problem. It's the thinking process I am looking for.

My question is only in AA level, you'd be surprised how many so called "degreed engineers" failed to answer the questions for like a two years Heald college stuffs.

Gold Member
This seems to infer that the people who couldn't answer your questions could answer it using KVL or KCL. My guess would be that if they couldn't answer your questions, then they probably couldn't do it with KVL or KCL neither.

My interviews were loaded with circuit problems. Similarly: They might start me off in an empty room with a 30 minute exam on paper before talking to me; they'd have my work in their hands during they actual interviewing portion where you talk to a person. They would definitely ask for the current and voltages at intermediate nodes as well, and I saw it come into play in my positions.

I normally applied for design positions; also normally in R&D groups. My past jobs I was in one large company that I don't think a lot of people have heard of although they've seen their products in the news very often. That job was basically all Kirchhoff's circuit laws. The other two are the Behamoths of their industry. KCL and KVL isn't an everyday thing for those two roles, but specifications are so tight, that we're looking for every knob we can turn in order to succeed.

Gold Member
My interview questions for analog design were always very simple schematics with "canonical" behavior. Like step response of an LC tank with Q=∞. I'll draw a current mirror, you explain it. Frequency response of a dominant pole compensated op-amp (integrator, or amp, whatever). Draw a flyback DC-DC converter and explain how it works. etc.

If they really understand the basics, then I want to know about the more complex stuff that they have knowledge of, a school project or such. If you don't know the simple stuff, I won't teach it. But if you do know that stuff, and you've shown me that you did sometime else worthwhile, then I'll probably assume that you can teach yourself the details you need. After all, no one would come in already knowing exactly what they'll be doing in the future.

BTW, it was astounding to me how many EEs can't deal with the step response of an LC circuit. There isn't a physics student out there that can't describe the motion of a weight hanging on a spring when you pull it down and let it go, yet most EEs can't do the same with the circuit version. Then sometimes you get a ringer, that just writes down the whole answer, frequency, amplitude, characteristic impedance and all, because they've used it before.

yungman
I gave very simple test. But you'd be surprised how many people failed.

Just very simple question like these. fill out the DC voltages and currents, then draw the output waveform respect to the given input waveform.

If anyone needs KVL, there's the door. Of cause, they can use calculator.

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yungman
I want to get off the interview and want to advice EE students. Study hard on Electromagnetics. It is HARD, but it is getting more and more important in the new age of RF and mixed signals. Learn how to do pcb layout ( IC layout also if applies). The topic of Signal Integrity is VERY VERY important. I don't mean learning any layout software, I mean the concept of layout, what is important, how to control the ground current return paths, component placements and trace layout. I layout all my own boards as I worked in mixed high speed and digital circuits. You cannot rely on pcb designers to do that for you. PCB layout is where the battle win or lose.

Even if you are not going into RF design, it is very important to know signal Integrity which needs the knowledge of electromagnetics. EMI emission and susceptibility is very important when RF coexist with low noise and digital circuits together. Learn how to layout for signal integrity. Study on closed loop stability, Bode Plot. These are where the rubber hit the road. Circuit design is very simple in general, it's how to make it not sing and don't make other circuits sing is where you earn your keeps in the job. People learn to draw ground return in schematic with just a triangular symbol, that little triangle is more than half the battle in EE. Circuit design is very simple, you take care of the grounding, stability, signal integrity, circuit is really as simple as you see in text books most of the time......except RF, then it's a different world. The world of dancing on the Smith Chart. That's where layout is even more important when you start using stripline and microstrip as distribute components.

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LvW
I would test them with more common sense questions. I have my sets of question.....not including KVL.

Concerning "common sense question": When you ask "tell me how the collector current of a BJT is controlled", I think that AT LEAST 50% of the beginners will answer "base current" because the only equation they remember is Ic=B*Ib (and because many books are wrong in this respect).
But they will fail completely when you ask them to explain this phenomenon.

LvW
By the way - the late great Barrie Gilbert wrote:
"...every time I undertake a new ....project I start out with just four basic truths

* Like elements match well
* V=I*R
* dV/dT=I/C
* Ic=Is*exp(Vbe/Vt) for bipolar out of saturation (Ids=K(Vgs-Vth)² for MOS in saturation).

yungman
By the way - the late great Barrie Gilbert wrote:
"...every time I undertake a new ....project I start out with just four basic truths

* Like elements match well
* V=I*R
* dV/dT=I/C
* Ic=Is*exp(Vbe/Vt) for bipolar out of saturation (Ids=K(Vgs-Vth)² for MOS in saturation).
I kind of regret I did not stay longer in the IC designer job. In my days, we mainly did custom bipolar IC, plenty familiar with Ic=Is*exp(Vbe/Vt), I never even worked with (Ids=K(Vgs-Vth)².

Yes, "Like elements match well" is VERY important in IC design. absolute resistor value inside IC was like 30% those days, but if you put two resistors side by side, they match very well, it's all about layout in the IC, the direction, the transistor geometry/orientation....... That's the reason I advice people to learn layout, be it pcb or IC. Layout is EVERYTHING. It all start with component placements. Good component placement make the ground and power plane easy and complete. Also making trace connection simple.

Lately I have been designing very high end hifi power amps as hobby, I looked at the service manuals of some pcb of the amps, I saw traces running all over the place, long and thin. Their layout really sucks. A good layout makes a complicate circuit look like very simple, very few traces and traces are short. Long trace forms large current loops...........like a loop antenna for UHF, ready and willing to receive EM noise. Also emitting noise to the surrounding.

yungman
Concerning "common sense question": When you ask "tell me how the collector current of a BJT is controlled", I think that AT LEAST 50% of the beginners will answer "base current" because the only equation they remember is Ic=B*Ib (and because many books are wrong in this respect).
But they will fail completely when you ask them to explain this phenomenon.

I would make them design so Ib is not even important and not even worry about it. Like when designing a circuit, make sure resistance of the bias network for the base is not too high that it will affect the voltage at the base. Then I don't even worry about Ib, hfe all that, that I can assume base current is 0, hfe is high.

If base current is an issue cannot be ignore, it's time to think MOSFET or jFET. That's the reason I am against thinking KVL. You use common sense to eliminate complication. If base current effect cannot be eliminate, change transistor!!! If someone stuck with trying to KVL to design, that's bad. Yes, there are cases Ib is a big issue, like transimpedance amps that measure current into pA. there's no way to avoid Ib......more the drift of Ib. You go to MOSFET, no KVL is going to make the day with BJT, go MOSFET........with new sets of problem!!!

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Gold Member
Quite honestly I think you'd be pointing me to the door and I'd probably be fine with that, but I'm curious why you're so against KVL or why it wouldn't work well? I think it would. I personally would not be discouraging recent grads from using it in interviews; I'd actually encourage it and would prefer if my coworkers could solve problems using the fundamentals.

Averagesupernova
yungman
Quite honestly I think you'd be pointing me to the door and I'd probably be fine with that, but I'm curious why you're so against KVL or why it wouldn't work well? I think it would. I personally would not be discouraging recent grads from using it in interviews; I'd actually encourage it and would prefer if my coworkers could solve problems using the fundamentals.
You look at my questions and comments? How you can using common sense to simplify the problem?

The idea is using common sense, simplify, knowing what is important, how to eliminate unnecessary complication. It's the real world in the job. I don't care how you do it, just get there, fast, reliable.

I've seen people from UC Berkley and Standford, they just so hung up with useless things, I would fired them if they were under me. RESULTS.

That's the problem, so many people studied and get good in all the formulas, but they don't have what it takes to design, getting the job done. That's the one I want to eliminate. Believe me, there are plenty of those people. Some people just don't have it, I just want to find people that have it.

You said you are into RF, I would test you in a totally different things. Smith Charts impedance matching, how to design distribution elements.

I think today, it's the job seeker's market, they let you pass with simple questions. I was applying for jobs in 2002, the deepest of depression in hightech. You better believe I got test on Smith Charts impedance matching on the spot. What is KVL?

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yungman
Quite honestly I think you'd be pointing me to the door and I'd probably be fine with that, but I'm curious why you're so against KVL or why it wouldn't work well? I think it would. I personally would not be discouraging recent grads from using it in interviews; I'd actually encourage it and would prefer if my coworkers could solve problems using the fundamentals.
Ha ha, I hope if you work on my two questions in post 25, you don't ask me about what's the beta of the transistors and doing KVL. I would hope you would ask me to lower the 20K and 10K voltage divider resistors to get better consistence.

These are REAL circuits in projects, not some made up stuffs.

Gold Member
Ha ha, I hope if you work on my two questions in post 25, you don't ask me about what's the beta of the transistors and doing KVL. I would hope you would ask me to lower the 20K and 10K voltage divider resistors to get better consistence.

These are REAL circuits in projects, not some made up stuffs.
Well I might be one you'd show the door too. And knowing what I know, I wouldn't be sorry about it. I'd likely ask the beta to determine if it's necessary to improve the voltage divider bias as you describe. Your management style would attract fly by the seat of their pants type folks in my opinion. Lowering the voltage divider resistance also draws more power. Would you show me the door if I asked if this circuit went into a product that is powered by battery? Concerned about battery life and all. You want an engineer who is actually able to make the best set of compromises or one that simply gives you answers that make you feel good?

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Tom.G and Joshy