Learning the Art of Electronics: signal attenuation (Figure IN.34)

[j_thornton]

Hi all,

On a whim, I decided to teach myself the basics of electronics and a couple of weeks in, I'm having a great time!

I bought The Art of Electronics and the accompanying lab book, Learning the Art of Electronics (LAE) which both seem awesome, but occasionally quite dense (um, don't take the bait, please...).

A few pages in we encounter Thevenin equivalent circuits, which make sense, but LAE has an unworked example which has me stumped and I'd love some help (see image below).

The example uses two voltage divider circuits (A and B) and is attempting to build intuition about the load of circuit B when driven by circuit A.



What R for a <10% droop (attenuation)?

I get the idea that we want a much larger resistance in circuit B so that the voltage droop on circuit A is small enough to ignore (less than 10%), but the example goes on to suggest that the figure we are looking for is 4K for resistor R. I don't get where this comes from, I'd have thought that circuit B has an effective resistance of 5K (two 10K resistors in a voltage divider), so we'd want an internal resistance of 500 ohms in circuit A leading to R being 1K. I think where I'm going wrong is a previous statement "To do that, we need to understand, first, the characteristic we call 'R in' (this rarely troubles anyone)". I think I may be that rare individual...

Apologies for the long post by way of introduction, hopefully I can pay back any help via this forum in future... :-)

[aneevuser]

Short of time but .. the Thevenin equivalent resistance of R3 and R4 is R3||R4 and your circuit A sees 20K to ground i.e. 10K in series with 10K - it sees that since the current supplied from A to B will flow through both to ground, assuming no load is connected to B.

So you want R3||R4 = 1/10 x 20K = 2K, and assuming that R3=R4 then we need R3=R4=4K.

[j_thornton]

That's awesome - thanks for the incredibly quick reply!

That's consistent with the text - I can now see that the "R in" for such a circuit is the resistance from the input to ground, so the two resistors in series as per your explanation.

I need to go and have a think about why, and what the implications are for examples where another divider 'C' is similarly attached to B, but I think I'll get there with help from your response, thanks again!

[aneevuser]

I need to go and have a think about why, and what the implications are for examples where another divider 'C' is similarly attached to B, but I think I'll get there with help from your response, thanks again!

If another divider is attached to B, then this will alter the input resistance of B, as seen from A, but the details will depend on how large the resistors are in the third divider.

If they are very large, then they will have little effect (that's the point of the 10X rule of thumb that AoE stresses), but if they are small, the change (which will be a decrease) in input impedance will be larger - that's because small resistors allow more current to flow to ground, and in that case, circuit A will have to supply more current for the same voltage => R=V/I decreases.

In general, you want to connect A with low output impedance to B with large input impedance, as that maximises the voltage seen by B (as you can see by considering a voltage divider with a small R at the top, and a big R at the bottom) and also minimises the current (and therefore the energy) that A must supply to B.

[j_thornton]

Ah, right, I think I've got it.

I think part of the difficulty is that I am *completely* new to electronics and the mental model I've built up is pretty shaky.
If you wouldn't mind indulging me a little, I'd love to sketch out what I think is happening and if you could confirm my thought processes, I think you might save me a lot of misguided stumbling.

The ground/earth symbol at the bottom of the diagram threw me I think. If I imagine it as a connection wire back to some earlier voltage source, I think things make a lot more sense to me.

So,


can be redrawn as,


In which case the input resistance of B (and C) as seen from A is 10K ohms  + (10K Ohms in parallel with 50K Ohms) which is less than 10% less than the 20K ohms resistance of B on it's own. Right?

I really can't thank you enough, I think this would have been a considerable blocker and I think (hope), I've developed a much clearer intuition for what's going on.

[rstofer]

First a hint:  Assume the power supply (In A to Gnd) has 0 Ohms.  Draw a short circuit from In A to ground when you start looking at the various resistors.

Second:  Prove It!  Make friends with LTspice and model the circuit with the values you derive.  Measure the currents through the various branches as well as the various voltages.  The best way to find out if you did the problem right is to Prove It!

https://www.electronics-tutorials.ws/dccircuits/kirchhoffs-current-law.html
https://www.electronics-tutorials.ws/dccircuits/kirchhoffs-voltage-law.html

It's probably premature to recommend you also make friends with Octave  (free) or MATLAB (costs money).  You can stuff the node equations or mesh equations into a matrix and, voila', instant results.  However, this takes time and effort outside of the immediate topic and may not be worth it at this point.

[j_thornton]

Cheers rstofer!

I'm familiar with KVL and KCL, but I'm sure of the finer points evade me at these early stages.

Thanks for the LTspice suggestion - an emulator would be a fantastic learning aid (looking ahead, components for the labs in Learning the Art of Electronics look reasonably cheap, but buying an oscilloscope and signal generator this early in my journey seems a little foolish...).
Unfortunately the analog.com site looks like it's down at the moment, so I'll have to try another day... (boo hiss!). [update: analog's site doesn't like being browsed through a VPN - it works fine if VPN switched off.]

I've messed with Octave a little bit in the past, so although I've forgotten most of what I learned, I should be able to start using that once I get past the initial hurdle with basic comprehension.

Loving the quality of reply in this forum. Gold dust!

[aneevuser]

In which case the input resistance of B (and C) as seen from A is 10K ohms  + (10K Ohms in parallel with 50K Ohms) which is less than 10% less than the 20K ohms resistance of B on it's own. Right?

Sorry, busy at the moment, but if I've understood what you wrote correctly, then you are right. I'll return to it at a later time.

However, given what you wrote re: being new to electronics, can I suggest that you make sure that you are confident with basic circuit theory before you continue. For example, do you:

a) understand what a voltage is, and how it relates to energy? Do you know the relationship between charge, time and current?
b) know what a voltage and current source are, and how to draw their I-V curves? What does a current source look like to a voltage source, and vice versa?
c) know KCL and KVL, and can compute circuit voltages and currents using them?
d) know Ohm's law, and can compute power dissipated in a resistor?

et al. If not, then you will quickly run into insuperable difficulties working through AoE or LtAoE. If you are, fine: but if not, I'd suggest that you maybe look at the appropriate bits of the Khan Academy, or a textbook, and solving some problems on paper (and making them up and measuring them with meters, of course).

And on a more contentious note: I personally don't think that AoE is a great book to learn from - many do, but IMHO, you'd be better off getting a book that takes a more methodical approach to circuit analysis first of all, and returning to AoE later (or maybe dipping into it from time to time).

[j_thornton]

aneevuser, I'm mostly ok with the topics you listed (didn't have a clue last week, but this week I do... :-) )

"What does a current source look like to a voltage source, and vice versa?" doesn't make sense to me, but I'm sure it will do soon.

I'm also skimming a Coursera course (pretty good, but fairly error strewn) from Georgia Tech and the MIT online Circuits and Electronics course, so mostly I'm able to find what I need to get going. I think doing some practical work will be essential to put things in some kind of context - as you allude to, the Art of Electronics book can be a little difficult to follow without any prior knowledge, although I'm already drawn in by it's tone - my kind of writing overall!

[rstofer]

Have you thought about the Electrical Engineering Course at Khan Academy

https://www.khanacademy.org/science/electrical-engineering

Or perhaps the Real Analog course at Digilent:

https://learn.digilentinc.com/classroom/realanalog/

I'm going to plug the Digilent Analog Discovery 2 as the single best tool you can have on your bench in terms of learning.  It's less than the cost of a decent scope, has a dual channel scope, a dual channel arbitrary waveform generator, dual power supplies (more current if you use a wall wart to feed the AD2), 16 channels of digital IO including protocol debugging.  It might not make sense today but as soon as you hit AC circuits,  you will find the AD2 indispensable  for Bode' Plots and other experiments.  The Real Analog course uses the AD2 for the lab exercises.  Not required but, in my view, recommended. 

It won't have come up yet but differential inputs to a scope is a handy feature for certain measurements.  The AD2 has differential inputs.

https://store.digilentinc.com/analog-discovery-2-100msps-usb-oscilloscope-logic-analyzer-and-variable-power-supply/

And get a good DMM if you don't already have one.  Stay away from mains and the Aneng 8008 is a pretty nice meter.  Dave did a review...  Despite having a bunch of high dollar meters, the 8008 is the one I reach for.

ETA:  You can download the Digilent Waveforms software for free.  The Demos aren't all that useful...  Nevertheless, look at the list of tools!

[j_thornton]

Have you thought about the Electrical Engineering Course at Khan Academy?

Hadn't done, but great suggestions - I now know what I'm doing today...

With regards to the Digilent Analog Discovery 2, I did have a quick look into options.
It's really hard to know what's going to be useful in the future, so thanks very much for the guidance. I think my options are to go for a couple of dedicated benchtop devices (for the sake of argument a Rigol 4 channel oscilloscope and separate waveform generator) this would set me back something like £550 which is a little more than I wanted to spend this early. I did look at USB multi-purpose devices, and I'm torn. I don't want to have to replace a 'learning' device in a couple of years if I can help it, but maybe this is the best approach as I'll have much more domain knowledge  and will be better able to judge what I need (although several reviews suggest that the Rigol instruments, while not up to high end use, are sufficient for a lifetime of casual tinkering).

In the longer term, I'm really motivated to complete the labs in LtAoE, but agree with the feedback that I might need a primer.
it's off to Khan Academy for me. Hopefully I'll be able to ask smarter questions in a couple of weeks!

[j_thornton]

Now look what you've got me into... :-)
https://store.digilentinc.com/analog-discovery-studio-a-portable-circuits-laboratory-for-every-student/

[j_thornton]

Yup, looks like if I double the kind of total budget I had in mind, Digilent will supply me with a powered breadboard with oscilloscope and function generator functionality and take care of most of the equipment requirements for the AoE lab work...

https://www.mouser.ie/ProductDetail/Digilent/471-031?qs=sGAEpiMZZMuxMqKG3cH2FMognVumOSX4UVpcKtWxXzxolurarRdjUQ%3D%3D

Sheesh.

Does anyone have any experience with these bad boys? Would this seem like a reasonable convenience/time/money trade off for a keen beginner?http://

[j_thornton]

rstofer:

Second:  Prove It!  Make friends with LTspice and model the circuit with the values you derive.

Bit of a learning curve and not very pretty on a Mac, but looks good.
I've entered the circuit and run a simulation and get the expected voltages and currents. I guess what's missing is the intuition.
Without help from this forum, I'd have had no idea what 'R in" meant (I now see it's the resistance looking from the source towards the connected dividers, but I think that the book just assumes this is obvious (and even states it as such) - wasn't obvious to me...).

I did a pick and mix from a couple of tutorials to come up with the simulation, but if anyone's following along I found this the most useful (in that nothing else made sense to me at all...). https://www.woolseyworkshop.com/2019/10/04/getting-started-with-ltspice-for-mac/

[rstofer]

Now look what you've got me into... :-)
https://store.digilentinc.com/analog-discovery-studio-a-portable-circuits-laboratory-for-every-student/

It's a little rich for my blood considering that I already have a bench full of equipment plus the AD2 and the Digital Discovery.  If my grandson were doing EE instead of ME, he would have one.

I have attached a couple of plots from the Waveform software.  Both are based on an identical circuit with a 10k Ohm resistor in series with a 0.1 ufd capacitor.  Same exact circuit, two different views...

The first, "ForcedRCresponse.png" is called a forced response because the circuit is getting hit with a signal.  We are looking at the capacitor voltage as a function of time so we're viewing it in what is called the 'time domain'.  We can see the characteristic exponential rise and decay in the capacitor   You will run across the equation:

Vout = Vin * (1-e^(-t/Tau))   -- the charging equation

where Tau, the time constant is R in Ohms times C in farads or, in this case.  10⁴ Ohms * 0.1 * 10^-6 Farads or 0.001 seconds (1 millisecond).  Note that the capacitor is over 99.7% charged in 6 time constants, that is, t/Tau = 6.  This is a very important plot when you get to AC circuits.

The second plot is the very same circuit viewed as a function of frequency - we're looking at a plot (Bode' Plot) of the output attenuation and phase shift versus frequency so we're viewing the circuit in the 'frequency domain'.  There's a cursor at approximately the -3dB point and about 45 degrees of phase shift.  This will come up when you get to low pass filters.  That -3dB point is often called the breakpoint and will seem terribly important when you get to AC circuits.

I threw in a bonus plot:  We're looking at the impedance of the RC circuit as a function of frequency.  There is a cursor where the capacitive reactance is equal to the series resistance.  Oddly, this is the same frequency as the -3dB breakpoint.  Again, you will be all over this stuff when you get to AC circuits and impedance vectors become important.

I can spend an entire day messing around with just two components.  I guess I'm easily amused by shiny objects!  The point is, the AD2 is an amazing piece of equipment, especially in a learning environment.  Oddly, my grandson has a "Circuits" course as part of his ME program.  I have no idea why it is included but the lab work is done using, you guessed it, AD2s.

I would seriously consider the Analog Discovery Studio if I didn't already have the AD2.  Heck, I might buy it anyway.  Experiments with transistor circuits would be my next topic.  I don't do a lot with small signal amplifiers but if I wanted to experiment, the Studio might be just about perfect.

Check out w2aew's videos on small signal amplifiers.  This one is very good:

[rstofer]

Do a bit of Google Foo on 'Thevenin Equivalent Circuits' and 'Norton Equivalent Circuits'.  These usually come up after Kirchhoff's Laws

https://www.electronics-tutorials.ws/dccircuits/dcp_7.html

That will take care of the voltage source equivalent circuits.

Norton's Theorem is the reverse, the equivalent circuit in terms of a current source and an equivalent parallel resistance.

https://www.electronics-tutorials.ws/dccircuits/dcp_8.html

That seems to be a pretty good tutorials site...

[rstofer]

I forgot to mention how nice the Waveform plots look on a 27" monitor.  It's also pretty easy to annotate the plots which provides some documentation of what is being displayed.  I don't always do that but it is pretty easy.

[rstofer]

While I'm on a roll, I might as well post the MATLAB solution to the charge/discharge of the circuit above (10k, 0.1 ufd)

Code: [Select]

V0 = 1; % assume a supply voltage
R = 10000; %10k Ohms
C = 0.1*10^-6; % 0.1 ufd
Tau = R*C;
t = linspace(0,8*Tau);
Vchg = V0 * (1 - exp((-t/Tau)));
Vdis = V0 * (exp((-t/Tau)));
plot(t, Vchg)
grid on
hold on
plot(t,Vdis)
ylabel("Voltage")
xlabel("Time - seconds")
%there is a known bug in 'legend', the [h,~] is a kludge to work around it
[h,~]=legend("Charge Voltage","Discharge Voltage");
figure(gcf) % or shg command - pull plot to top
for Tau = 0:6
    charge = V0 * (1 - exp((-Tau)));
    fprintf("Tau = %.0f Percent Charge = %0.f\n",Tau, 100*charge)
end
[/font]

This code should work in the free Octave program.  I didn't try it.  Note that the time axis is scaled by 10^-3 or milliseconds.

There are a lot of tools available today that would have made EE a lot more fun.  Doing this stuff with a slide rule was not as cool as it might seem.

[j_thornton]

Ha, I'm still on resistors, so although, looking ahead a few pages, I can see that I'm going to bump into some of the topics you mentioned, all meaningless at the moment!

I think crunch time for equipment will be fairly soon. I'm working through both textbook and workbook at the same time along with a bunch of online courses. The first lab is tantalisingly close. I can see that I'll need at least a power source, an oscilloscope and a signal generator. If I were to buy all of these separately, it'd be close to £1000, but for that I'd get decent lower end benchtop devices that would last me until I die or run out of enthusiasm. For half that, I could get the Discovery Studio which has the advantage of having a logic analyser and the nifty breadboard interface.

I'm definitely torn. I feel like the Studio might be a whole heap of fun for years to come, but it lacks the cred and, presumably robustness of dedicated equipment (and needs a laptop for readouts). Gosh, tricky!

On the reading material front, I'm now familiar with Thevenin, but haven't touched on Norton equivalent circuits yet. The other thing I *really* need to do is consider *why* I'm learning this. I'd definitely like to build a modular synth, but suspect I could do that by just soldering components together cookbook style. Part of me just wants to know what's going on under the hood, but that probably doesn't justify tooling up...

[rstofer]

It's difficult to decide at what level you want to learn something.  A lot of electronics can be done with just a wee bit of DC theory and Ohm's Law.  Kirchhoff's Laws will probably get you through op amps and even discrete amplifiers.  You really don't have to understand this stuff at a very low level.

That said, I find it is just fun to know stuff.  The only reason I went to EE school was to learn about the electronics of Numerical Control circa 1969.  As an electrician, I was installing some gigantic machines and the part the impressed me was watching them operate as directed by a 1" punched paper tape.  Hundreds of cutting head horsepower machining huge planks of aluminum all driven by a paper tape.  Amazing!  I had to know how it worked!

These days I still spend most of my time on digital stuff.  I avoided analog because, way back when, the math was just too ugly to contemplate.  I could do it but I didn't want to do it.  I excelled in Slide Rule 101 but that just wasn't something that interested me.  Nevertheless, the 'beginner' stuff comes up from time to time and I usually spend a bit of time writing about the early classes.  I actually have fun playing with a simple resistor and capacitor. 

From what I read around here, 90% of the hobbyists are doing copy and paste projects.  There's nothing wrong with this, it's still electronics.  The other 10% (and that may be optimistic) actually want to understand the theory.  That's fine too!  Either approach works.

Clearly, a DMM is required.  Actually, 3 are required but you'll discover that when you get to transistor amplifiers.  You will want to measure Vce, Ic and Ib and it's more fun to do it with 3 meters.  That's why I always put in a plug for the Aneng 8008.  A really accurate meter that isn't terribly expensive.  Lacking a mA scale was a concern for Dave when he did the review.  OTOH, having a uA scale is a plus.  So, maybe this meter isn't the end-all of meters but it's a start and certainly good enough for most of what needs to be measured.  Dave sells a couple of higher performance meters (I have both) and you can always peruse the Test Equipment forum to see what is popular at various price points.

As soon as you get to AC circuits, you just about have to have a scope.  I have an old 350 MHz Tek 485 but I bought the Rigol DS1054Z a couple of years ago.  Nice scope!  The new Siglents are similarly priced.  When people talk about 4 channels, they are usually talking about digital decoding, not analog circuits.  Well, there are other ways to do decoding: a dedicated logic analyzer or the AD2 will work fine at reasonable speeds.  I wanted 4 channels but I don't use all 4 nearly as much as I thought I might.  Two channels are used all the time.

One way or another, test equipment tends to accumulate.

The AD2 also has two variable power supplies.  Both the voltage and current capabilities are limited even with a wall wart feeding the gadget.  It may be necessary to scale some kinds of exercises.  You probably won't be doing that 400V 200A circuit in the textbook.  Somehow those problems seem to gravitate toward higher voltages and multiple amps, what I call "neat numbers".  The real world is in the range +-15V and milliamps.

Look at the specs on the AD2 and the Studio and see how far you can get with your learning exercises.  Either may be more than adequate for the frequencies, voltages and currents.

I kind of knew you were working with resistors.  I just wanted to point out where you were heading.

It's true, a bench full of equipment has more cred than the AD2.  So, given that I have a bench full of equipment, why do I still reach for the AD2 for learning examples?  Probably the 27" screen and the ease of printing the plots to a color LaserJet.

So many choices...

[dkggpeters]

Second:  Prove It!  Make friends with LTspice and model the circuit with the values you derive.  Measure the currents through the various branches as well as the various voltages.  The best way to find out if you did the problem right is to Prove It!

^  This is so true.  Trying to learn electronics passively is really hard.  You will learn a lot quicker by proving things out and you will get a better understanding both from your failures and successes.

[rstofer]

Second:  Prove It!  Make friends with LTspice and model the circuit with the values you derive.  Measure the currents through the various branches as well as the various voltages.  The best way to find out if you did the problem right is to Prove It!

^  This is so true.  Trying to learn electronics passively is really hard.  You will learn a lot quicker by proving things out and you will get a better understanding both from your failures and successes.

It's even better if the circuit can be breadboarded.  Sometimes the problem needs to be scaled and sometimes the exact values aren't available but the parts on hand can be calculated and then verified with a DMM.  That's learning!

I don't really learn very well from books and lectures.  I'm more tactile, I have to do something with my hands.  In that theme even LTspice isn't as valuable as a real circuit.