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12-Amethyst

## Electric Circuits 1 and II. Part 3D.

Final Part to the prerequisite studies for Laplace Transforms In Electric Circuits.

RLC Higher Order Circuits Continuing Notes And Solved Examples and Problems.

Section 1: Introduction To Operational Amplifier (Op Amp) circuits.

I. Several parts of chapters 2, and 3 from Coughlin and Driscoll Op Amp Textbook.
Providing notes and solved examples to build the knowledge before entering
Schaums topics on Opamps. Often using the examples from Coughlin and Driscoll
to assist elsewhere in Schaums Op Amp topics.

II. Schaums:

1. Amplifier model
2. Feedback in amplifier circuits
3. Operational amplifiers
4. Analysis of circuits containing ideal Op Amps
5. Inverting Op Amp
6. Summing circuit
7. Non-inverting circuits
8. Voltage follower
9. Differential and difference amplifiers
10. Circuits containing several Op Amps

Followed by a sample Op Amp circuit called Servo Amplifier to build interest in Op Amps from Coughlin and Driscoll's textbook.

Section 2: Operational Amplifier (Op Amp) circuits.

I. Schaums:

11. Integrator and differentiator circuits
12. Analog computers
13. Low-pass filter
14. Decibel (dB)
15. Real Op Amp
16. A simple Op Amp model
17. Comparator (Briefly)
18. Flash analog to digital converter not on notes rather an example related to
analog to digital converter was solved in Section 3.

Section 3: Fully solving partially solved examples, partially solved problems, and
supplementary problems.

Problems are related to Op Amp circuits.

Primarily the topics covered in Schaums.

Purpose is toget an understanding on how to approach solving Op Amp Active circuits. These are circuits with Op Amp and R L and C components.

There is a special topic covered from Chapter 7 of 4th edition of Hyat and Kemmerly the topic is on The Lossless LC Circuit from section 7-8. This topic is relevant to RLC studies.

Section 4:

1. Engineering Circuit Analysis Hyat and Kemmerly 4th Edition:
Section 13-8: A Technique For Synthesizing The Voltage Ratio H(s) = Vout / Vin.

2. Schaums: Magnitude scaling

3. Schaums: Frequency scaling

4. Schaums: Higher order active circuits

Relevant 'partially solved examples, problems and supplementary problems' were solved. Electric Circuits textbooks have additional problems which can be worked on as required.

This is the last part of the series of parts starting from Part 1A.

Apologies for any errors and omissions.

Regards,

Karl Bogha.

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1 ACCEPTED SOLUTION

Accepted Solutions
11-Garnet
(To:KarlBogha)

Thanks Karl,

I've sorted out the band pass filter, its sorted now. I'll have a look at the previous pdfs.

13 REPLIES 13
12-Amethyst
(To:KarlBogha)

Thanks.

N/A.
11-Garnet
(To:KarlBogha)

Hi mate,

Thanks for this!

I am looking to design a Butterworth high order(say 5th order) band pass filter. Where can I find a book pdf on this and also where do I find the previous parts of the pdf notes you provided?

12-Amethyst
(To:AS_9824434)

You may be able to get the previous files by clicking on my name below the file. That had in the past led to previous files uploaded by the party.  You can scroll down the Electrical Engineering group and find it there. It maybe a while to pick up all the files. Else if thats not suitable maybe checking my profile may lead to my uploads.

With regards to the 5th order band pass filter? I suggest you put up a question on the electrical engineering group.

I can lead you to a text book on Filter design on Amazon but I may not personally have used it.

Signals Processing textbook have the introduction to the material. B P Lathi has a good signal processing textbook. Its thick but detailed. I don't advice it if you're looking for something quick.

Regards,

Karl.

N/A.
11-Garnet
(To:KarlBogha)

Thanks Karl,

I've sorted out the band pass filter, its sorted now. I'll have a look at the previous pdfs.

20-Turquoise
(To:KarlBogha)

p.207, You must use V1(s)=1/s.

12-Amethyst
(To:ttokoro)

Hi,

I know the file  you are referring too, can you please give me the 'example number' or 'exercise number' you refer to on page 207. Since that pdf file, Electric Circuits II Part 3D, is not page numbered on the page itself, and your attached file is mcdx. That will help.

Regards,

Karl.

N/A.
20-Turquoise
(To:KarlBogha)

Example 8.15 (Active Circuit)

v1 = u(t) = 1 for t>0, but V1(s):=1/s instead of 1.

If you use 1, it means impulse response of the system.

12-Amethyst
(To:ttokoro)

On the unit step going with what I recollect without opening a textbook.

It's a magnitude 1 with no phase angle - flat. That is in time domain.

No frequency value for step function either.

So in frequency domain it should be 1 also - transform.

On the impulse function, that is sudden rise and fall, at a particular point in time, not continuous.

So in this case in example problem the step function was used.

Thats how I see it.

Your engineering textbook would give the correct Laplace transform for step function.

I hope that helped. I suggest you take it up with your local affiliate (lecturer/engineer).

Maybe resourceful.

N/A.
23-Emerald III
(To:KarlBogha)

In general, the Laplace transform of a constant a is:

Hence the Laplace transform of 1 is 1/s, as is the Laplace transform of the unit step function (because the Laplace transform uses the integral from 0 to infinity. Note that the unit step function is 1 over that same range) ,

The Laplace transform of the derivative of a function f(t) is.

( That is:  s times the Laplace transform of the function f(t) minus the function value at t=0 )

The derivative of the unit step function is the impulse, or delta function. The value of the unit step function at t=0 is 0 to 1, let's take 0. Then by the above rule the Laplace transform of the delta function must be s * 1/s = 1. Mathcad agrees:

Success!
Luc

12-Amethyst
(To:LucMeekes)
I am sorry that's not the way I see it. But if that's what your lecturer taught at your polytech or uni you should go by that at your locality. I like to see the citation on your engineering math textbook, seriously it may be of interest to some math majors and math graduates. Weldone on your effort on your behalf.

The message, data, and attached files are confidential to the intended recipient(s). If you are not the intended recipient(s) please notify the sender and erase all contents of the message, data, and attachments. Dissemination, copying and use of this message, data, and attachments are strictly prohibited.

N/A.
23-Emerald III
(To:KarlBogha)

I don't understand your reaction "I am sorry that's not the way I see it".

What I showed above is from Mathcad (11, with Maple as symbolic engine).

In Prime it looks like:

You want to see textbook contents regarding the matter, I see you like to refer to Schaum series on other topics. Here is the Schaum book on Laplace transforms (by Murray M. Spiegel) regarding the matter:

( F(t) is the time function, f(s) is its Laplace transform )

Of course you are entitled to your 'way of seeing things', but as far as I know there are no cultural differences or different scientific/technical/engineering views on the Laplace transform of a constant.

Please show me your textbook that says that the Laplace transform of 1 is anything other than 1/s.

Regarding the value of the unit step function at t=0.

Mathcad 11 numerical and symbolic results are:

The symbolic result appears to indicate that the value may be debatable.

Prime (7 and 8 ) settles for:

(May be the same in Mathcad 15, with Mupad as symbolic engine.).

Some textbook (from MIT):

Success!
Luc

24-Ruby IV
(To:KarlBogha)

There are two areas where hard differential equations come up. These are electrical circuits and chemical reactions.

12-Amethyst
(To:ValeryOchkov)

Valery,

You may be right there at a high level situation, personally I find them hard every which way they come.😄

Typically at the starting point they mechanical systems are used for constructing the differential equation, since here most of us are able to visualise the system. 🤔

Eventually from the simple stuff to the harder stuff requires in my experience a good grounding on the math and specific field of discipline. Here some do better than others. 🤒

I like to share my present interest with you. I had an interest in yacht and small boat design and construction. This was in the early 2000s. Had a book on yacht design or study on it, but it lacked the typical engineering approach. Years go by and I returned to it this time to make it a hobby and a personal interest subject. I have finished the 3rd chapter of the book the topic was Stability and Equilibrium. Fore me there were lots of points packed in 50 pages of this chapter. It has end of chapter problems to solve. So right now I am not at the differential equations or electrical side of things.  🚢🛳🚢😃

I do feel I need to add more work on the continuing electrical notes by going into Laplace and solving electric circuits using Laplace. But that may be a recognition thing on my part and I do keep away from that destroying ego. There are also the chapters continuing RLC, and the Bode plots. I leave that to others. Too much time, exhaustive, and may be one day in the future I may attempt but not any time soon.

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