Need basic circuit help

[Blue Calx]

So I'm trying to teach myself basic electronics without a real textbook or teacher. I've got several resources at my disposal: Articles and video lectures I find on the net, circuit modeling software, and a book on guitar amp construction with an intro chapter on basic electronics theory.

This is where I'm stuck, since the book claims to be for the beginner, but seems to offer examples with lots of gaps in the reasoning. When introducing new ideas, the author just spits out formulas for certain example circuits without proving it component by component, or sometimes even without sufficiently defining some of the terms being used. I'm the kind of person who wants to verify that what I'm reading is true, so I end up making little examples for myself to make sure I understand what's going on... and it's been working - I can fill in some of the gaps. But I've hit a wall at what I feel is a pretty basic concept (don't laugh).

The voltage divider. I understand how this simple example works:


The author of my book uses the terms "input voltage" and "output voltage," with input coming from the 10V battery and output being the voltage across R2. He spits out the formula: Vout = R2/(R1+R2) * Vin (which I verify component by component to make sure I get it), and all is well.

But then later in the intro chapter, the author brings up this next situation, and simply regurgitates the same formula without any further explanation:


When I try to verify component-by-component, I get stuck. My calculations do not measure what my software simulator seems to indicate. The values for Voltage and Current in R1 and R2 have changed in my software (understandably, since they are now part of a larger network), but I cannot account for this change. How do I approach analyzing this circuit component-by-component?

Any web searches for this situation have returned only the simple case of the original voltage divider I posted above. Can anyone suggest an approach to this?

[tone4days]

combine R3 and R4 into a single, 350 ohm resistor that is in parallel with R2 ... so the combined resistance of R2 (200 Ohms) with 350 Ohms is 127 ohms

that combined resistance is the value of resistance in series with R1 - so you can do the voltage divider deal again


help?

[garublador]

Any web searches for this situation have returned only the simple case of the original voltage divider I posted above. Can anyone suggest an approach to this?

Simplify your drawing so it looks like the simple case.

[Blue Calx]

combine R3 and R4 into a single, 350 ohm resistor that is in parallel with R2 ... so the combined resistance of R2 (200 Ohms) with 350 Ohms is 127 ohms

that combined resistance is the value of resistance in series with R1

Simplify your drawing so it looks like the simple case.

AH! So it can be combined into one single voltage divider. I guess you can tell I'm new at this, since I had tried every way I thought possible to combine these by series/parallel, etc.

As these circuits get more complex, can I do more of this same thing to simplify them?

Thank you both!

[tone4days]

As these circuits get more complex, can I do more of this same thing to simplify them?

Thank you both!

youre welcome

and yes, in fact, it is pretty much the only thing you CAN do to analyse them

[Blue Calx]

youre welcome

and yes, in fact, it is pretty much the only thing you CAN do to analyse them

Let me just make sure my approach to calculation is appropriate:

First, I simplify the circuit
Next, I find total current
Then I use total current to find individual values at individual components.

[GuitarStv]

So I'm trying to teach myself basic electronics without a real textbook or teacher. I've got several resources at my disposal: Articles and video lectures I find on the net, circuit modeling software, and a book on guitar amp construction with an intro chapter on basic electronics theory.

This is where I'm stuck, since the book claims to be for the beginner, but seems to offer examples with lots of gaps in the reasoning. When introducing new ideas, the author just spits out formulas for certain example circuits without proving it component by component, or sometimes even without sufficiently defining some of the terms being used. I'm the kind of person who wants to verify that what I'm reading is true, so I end up making little examples for myself to make sure I understand what's going on... and it's been working - I can fill in some of the gaps. But I've hit a wall at what I feel is a pretty basic concept (don't laugh).

The voltage divider. I understand how this simple example works:


The author of my book uses the terms "input voltage" and "output voltage," with input coming from the 10V battery and output being the voltage across R2. He spits out the formula: Vout = R2/(R1+R2) * Vin (which I verify component by component to make sure I get it), and all is well.

But then later in the intro chapter, the author brings up this next situation, and simply regurgitates the same formula without any further explanation:


When I try to verify component-by-component, I get stuck. My calculations do not measure what my software simulator seems to indicate. The values for Voltage and Current in R1 and R2 have changed in my software (understandably, since they are now part of a larger network), but I cannot account for this change. How do I approach analyzing this circuit component-by-component?

Any web searches for this situation have returned only the simple case of the original voltage divider I posted above. Can anyone suggest an approach to this?

You will find that circuits are a lot easier to understand if you break them down and redraw them. In your second equation you have four resistors. R3 and R4 are in series with each other. R2 is in parallel with (R3 + R4). R1 is in series with the rest.

So let's break it down each step:

R3 and R4 are in series with each other:
R3 + R4 = 50 + 300 = 350

R2 is in parallel with R3 and R4:
1/R234 = 1/R2 + 1/R34
1/R234 = 1/200 + 1/350
1/R234 = 11/1400
R234 = 127.27

R1 is in series with everything else:
R1234 = R1 + R234 = 100 + 127.27 = 227.27


Is that what you were looking for?

[GuitarStv]

Let me just make sure my approach to calculation is appropriate:

First, I simplify the circuit
Next, I find total current
Then I use total current to find individual values at individual components.

Whoops, took too long typing up my response I see . . . remember that you will have to do your current calculations differently depending on series/parallel and you should be cool with that approach.

[tone4days]

You will find that circuits are a lot easier to understand if you break them down and redraw them. In your second equation you have four resistors. R3 and R4 are in series with each other. R2 is in parallel with (R3 + R4). R1 is in series with the rest.

So let's break it down each step:

R3 and R4 are in series with each other:
R3 + R4 = 50 + 300 = 350

R2 is in parallel with R3 and R4:
1/R234 = 1/R2 + 1/R34
1/R234 = 1/200 + 1/350
1/R234 = 2/550<-- brain cramp step? dontcha need to find a common denominator to add fractions? 1/200 + 1/350 = 7/1400 + 4/1400 = 11/1400 = 1/~127
R234 = 275

R1 is in series with everything else:
R1234 = R1 + R234 = 100 + 275 = 375


Is that what you were looking for?

or am i brain cramping?

[tone4days]

then he can voltage divide across R1 and R234 ... because they are in parallel, the voltage over R234 can then be divided between R3 and R4 by the same formula .. the current thru R2 is the voltage divided by R2

or am i in need of totally handing in my degree as 25 yrs is the shelf life?

[GuitarStv]

or am i brain cramping?

whoops! I'm going to blame that on it being an unusually warm Wednesday . . .

[Blue Calx]

Alright, so, thanks to you all, I have been able to calculate V and I for each resistor in the circuit (calculations match the software sim).

Just for reference, I'm getting
R1: V = 4.4v, I = .044A
R2: V = 5.6v, I = .028A
R3: V = .8v, I = .016A
R4: v = 4.8V, i = .016a

But that was just an example I threw together myself to try and work out what the author of my book was getting at. When I returned to the book, I was reminded of the whole reason I became confused in the first place:




The book seems to be treating the circuit as two separate voltage dividers that appear to not be affecting one another. I do not get the same numbers when I calculate using the author's method.

I don't intend to post pages of my book every 5 minutes and beg for help, but this is still part of the original confusion I thought I got over.

[tone4days]

i think you are over-thinking it, chris ...

the circuit network in question's input impedance forms a voltage divider with its source's output impedance and its output impedance forms a voltage divider as an input source with its follow-on network's input impedance

so only the network characteristics of network 1 interact directly with those of network 2 ... but those characteristics are influenced by the input characteristics of the source network, albeit indirectly

what numbers are you using ?

[Blue Calx]

I was just using the voltages and impedances from my original example.

Zsource = R1
Zin1 = R2
Zout = R3
Zin2 = R4

So, according to the numbers I got going component by component earlier,
equation 1.12 should read:

5.6v = 200/(100+200) * 4.4v ... but that's simply not true.

Likewise, when I consider Zout and Zin2.

[firebirdV]

This is how I would go about it (keep in mind that I actually hate circuits and this could be incorrect).

Just think of the second circuit as a voltage divider which leads into a second voltage divider. The second divider does not care about the existence of the first one, and as far as it is concerned, there is a perfect voltage source of 6.67V. Then just use the the voltage divider formula again to calculate V4.

Vout = R2/(R1+R2)*R4/(R3+R4)*Vin = 5.71V

[garublador]

I just think that picture from the book isn't very clear. Here's how I interpret it.

There is a voltge source with an output impedance Zsource. You plug in one module with an input impedance Zin 1 and calculate Vin 1 from Vout. Then you plug another module in with input impedance Zin 2. The output impedance that the second module sees is Zout. Zout is the combination of everything to its left and the Vout you use to get the Vin 2 is the same Vout you used to get Vin 1. Vin 1 will change, but you don't use it to get Vin 2.

I agree it's a very confusing way to show that.

[Blue Calx]

This is how I would go about it (keep in mind that I actually hate circuits and this could be incorrect).

Just think of the second circuit as a voltage divider which leads into a second voltage divider. The second divider does not care about the existence of the first one, and as far as it is concerned, there is a perfect voltage source of 6.67V. Then just use the the voltage divider formula again to calculate V4.

Vout = R2/(R1+R2)*R4/(R3+R4)*Vin = 5.71V

That's the way I originally interpreted it... but what happens in the simulator is that I get the perfect 6.67V out of the first divider when it is in isolation, but the instant I connect the second divider, ALL the values change, including Vout which then measures 4.8V instead of the 5.71V that you and I expected.

You guys, I really do appreciate your help. I've been stuck on these two pages for the past week, and I don't want to move on until I'm sure I get it. I hope there's no error in the book.

[Blue Calx]

Sorry if this is overkill, but I'm determined to get this. Hopefully this will make clear any flaws in my reasoning:

[garublador]

Sorry if this is overkill, but I'm determined to get this. Hopefully this will make clear any flaws in my reasoning:

You and the simulator are both right. That picture in the book is misleading. Does this explanation make more sense?

There is a voltage source with an output impedance Zsource. You plug in one module with an input impedance Zin 1 and calculate Vin 1 from Vout. Then you plug another module in with input impedance Zin 2. The output impedance that the second module sees is Zout. Zout is the combination of everything to its left and the Vout you use to get the Vin 2 is the same Vout you used to get Vin 1. Vin 1 will change, but you don't use it to get Vin 2.

[exnihilo]

I have no idea what I'm doing, but this fun.

cg