Branch Current Calculations

[NCUSAHobbiest]

Hey everyone!  I'm a new eevblog member (been watching Dave's videos for a while) and this is my first post.   Been studying an online course (for fun, I'm just a hobbyist) and working through the Network Analysis/Branch Current Method section.  While reading through the examples, the author builds a system of equations step-by-step, which I uderstand.

He skips the details of solving the equations, stating it is complicated, and just shows the resulting answers.  I'm an old guy pretty well versed in math/physics, so I decided to solve the equations myself.  I used a couple of different manual methods, where both my answers matched each other, but not the ones in the study guide.  Thinking I was rusty, I ran the equations through two linear algebra apps which matched my manual work.

So I'm confused as to how the author arrived at his answers.  I'm thinking perhaps I need to use my answers in another calculation, and am missing a step.  I want to understand this issue before I move ahead, and hope someone can help.

The circuit has two branches with three resistors creating two current loops and two DC voltage sources.  Sorry I don't have software to upload a diagram.  I can supply more details if needed.

The three equations used to solve for current are:

-1A + 1B - 1C = 0
4A + 2B +  0C = 28
0A + 2B + 1C = -7

A, B, and C are the three currents.  His answers are:

A = 5A
B = 4A
C = -1A

The answers I get are:
A = 7A
B = 0A
C = -7A

I know his answers are correct, just want to uderstand where I'm going wrong.

Thanks in advance for any help.

James

[Ratch]

Hey everyone!  I'm a new eevblog member (been watching Dave's videos for a while) and this is my first post.   Been studying an online course (for fun, I'm just a hobbyist) and working through the Network Analysis/Branch Current Method section.  While reading through the examples, the author builds a system of equations step-by-step, which I uderstand.

He skips the details of solving the equations, stating it is complicated, and just shows the resulting answers.  I'm an old guy pretty well versed in math/physics, so I decided to solve the equations myself.  I used a couple of different manual methods, where both my answers matched each other, but not the ones in the study guide.  Thinking I was rusty, I ran the equations through two linear algebra apps which matched my manual work.

So I'm confused as to how the author arrived at his answers.  I'm thinking perhaps I need to use my answers in another calculation, and am missing a step.  I want to understand this issue before I move ahead, and hope someone can help.

The circuit has two branches with three resistors creating two current loops and two DC voltage sources.  Sorry I don't have software to upload a diagram.  I can supply more details if needed.

The three equations used to solve for current are:

-1A + 1B - 1C = 0
4A + 2B +  0C = 28
0A + 2B + 1C = -7

A, B, and C are the three currents.  His answers are:

A = 5A
B = 4A
C = -1A

The answers I get are:
A = 7A
B = 0A
C = -7A

I know his answers are correct, just want to uderstand where I'm going wrong.

Thanks in advance for any help.

James

You should not use the letter "A" for both a variable and an abbreviation for amps.  That is confusing.  You have solved the three equation correctly, but I have no way of verifying if the equations are correct without seeing a circuit diagram.  Who and what is Dave and his videos?

Ratch

[rstofer]

I got your answer.  See attached wxMaxima code and results.

Unfortunately, without the schematic, I have no idea whether the results are correct.

[John B]

Were you given the equations or did you derive them yourself? I got your answers, but I think you need another relationship, with one of the equations having a non-zero value for A or C

[Brumby]

I got the same answers you did.

When in doubt, go back to the very simple checks.... substitute his values into the equations:

-1A + 1B - 1C = 0
-5   +  4  +  1  =  0     Correct
4A + 2B +  0C = 28
20  +  8  +  0  =  28     Correct
0A + 2B + 1C = -7
0   +  8  -  1  =  7        INCORRECT - the sign is wrong

So - if you got the sign correct on the RHS of the last equation, then the other guy got it wrong.

[Brumby]

Who and what is Dave and his videos?

You aren't serious, are you?

[Brumby]

I got your answer.  See attached wxMaxima code and results.

I just used pen and paper.  Solving some really simple simultaneous equations.  Only took me a minute.

[Ratch]

Who and what is Dave and his videos?

You aren't serious, are you?

Correct.  I have no idea who Dave is and what his videos are.

Ratch

[rstofer]

I got your answer.  See attached wxMaxima code and results.

I just used pen and paper.  Solving some really simple simultaneous equations.  Only took me a minute.

I was watching TV and didn't have a way to use paper and pen.  I was done in one commercial break!

My real purpose in solving the problem is to increase my use and knowledge of wxMaxima even though I copied and pasted from a previous problem (code reuse!).  I need to up my game so I can show my grandson how to use it for his college classes, he will need it. 

The problem itself, lacking a schematic, wasn't really worth solving.

[Zero999]

Who and what is Dave and his videos?

You aren't serious, are you?

The fact he's never heard of Dave and is unaware of his videos doesn't surprise me. He probably found the forum via Google, without having any idea the rest of the site or video blog exists.

Who and what is Dave and his videos?

You aren't serious, are you?

Correct.  I have no idea who Dave is and what his videos are.

Ratch

See links below. They're also at the bottom of the main forum page but aren't obvious.
https://www.youtube.com/user/EEVblog
http://www.eevblog.com/

[MrAl]

Hey everyone!  I'm a new eevblog member (been watching Dave's videos for a while) and this is my first post.   Been studying an online course (for fun, I'm just a hobbyist) and working through the Network Analysis/Branch Current Method section.  While reading through the examples, the author builds a system of equations step-by-step, which I uderstand.

He skips the details of solving the equations, stating it is complicated, and just shows the resulting answers.  I'm an old guy pretty well versed in math/physics, so I decided to solve the equations myself.  I used a couple of different manual methods, where both my answers matched each other, but not the ones in the study guide.  Thinking I was rusty, I ran the equations through two linear algebra apps which matched my manual work.

So I'm confused as to how the author arrived at his answers.  I'm thinking perhaps I need to use my answers in another calculation, and am missing a step.  I want to understand this issue before I move ahead, and hope someone can help.

The circuit has two branches with three resistors creating two current loops and two DC voltage sources.  Sorry I don't have software to upload a diagram.  I can supply more details if needed.

The three equations used to solve for current are:

-1A + 1B - 1C = 0
4A + 2B +  0C = 28
0A + 2B + 1C = -7

A, B, and C are the three currents.  His answers are:

A = 5A
B = 4A
C = -1A

The answers I get are:
A = 7A
B = 0A
C = -7A

I know his answers are correct, just want to uderstand where I'm going wrong.

Thanks in advance for any help.

James

Hi,

There is no way around it.  Iff you want to be sure you MUST post the circuit or a link to it.  That's the ONLY way we can verify the work.

If you cant post a picture then you can use a text schematic posted within code tags for example:

Code: [Select]


        +----E2-----------+
        |                 |
   +----+---R1---+---R2---+----+---Vo1
   |    |        |        |   
   E1   R3       R4       R3   
   |    |        |        |   
   +----+--------+--------+----+---GND


E1 positive on top
E2 positive on right

[v1=E2+E1,v3=(E1*(R2+R1)*R4+E2*R1*R4)/((R2+R1)*R4+R1*R2)]





[Brumby]

Hi,

There is no way around it.  Iff you want to be sure you MUST post the circuit or a link to it.  That's the ONLY way we can verify the work.

The question of whether the OP got things right or not from the information supplied has been given.  Several of us have done the exercise and agree with the OPs results.  If that information has been presented correctly, then what's in the book is wrong.  The issue the OP had - whether the process they used was correct - has been resolved.

If, however, you want to work out where the error has specifically occurred by your own derivation, then yes - a diagram would be helpful.

[Brumby]

Who and what is Dave and his videos?

You aren't serious, are you?

The fact he's never heard of Dave and is unaware of his videos doesn't surprise me. He probably found the forum via Google, without having any idea the rest of the site or video blog exists.

Then I owe Ratch an apology.

I predicated my response on the basis that Ratch had been a member for several months and had a reasonable number of posts to their name.  It did not occur to me that during that time, Ratch had not come across any references to Dave or his videos through general exposure on the forum.  This was further supported in my thinking by his very detailed responses in that time - even to the point of labouring on minutiae - there would have been some attention given to the macro world of the EEVblog.

However, I made an assumption - and we all know how they often turn out.

[Ratch]

OK, I looked at some of Dave's videos.  He has good info on hardware, but some of his theory is just plain wrong.  As an example, his video #748 titled "How Transistors Work" contain lots of errors.  He states that a BJT is a current controlled device, and a FET is a voltage controlled device.  The fact is, a BJT, FET, and vacuum tube are all transconductance devices, i.e., voltage controls current.  I know that is not what a lot of books and magazines aver, but I can back up what I stated. First, I would like to hear some arguments on why so many folks think that the base current controls the collector current of a BJT.

Ratch

[basinstreetdesign]

OK, Ratch's topic should have its own thread.

[retrolefty]

That topic was covered extensively just over the last month or so. 

[Zero999]

He states that a BJT is a current controlled device, and a FET is a voltage controlled device. The fact is, a BJT, FET, and vacuum tube are all transconductance devices, i.e., voltage controls current.

In reality it's not that simple.

First, I would like to hear some arguments on why so many folks think that the base current controls the collector current of a BJT.

See the thread linked below.
https://www.eevblog.com/forum/beginners/current-controlled-device-vs-voltage-controlled/

I can think of situations where it's better to think of I_B controlling I_C, as well as V_BE controlling I_C, but that's a debate for the other thread.

[MrAl]

OK, I looked at some of Dave's videos.  He has good info on hardware, but some of his theory is just plain wrong.  As an example, his video #748 titled "How Transistors Work" contain lots of errors.  He states that a BJT is a current controlled device, and a FET is a voltage controlled device.  The fact is, a BJT, FET, and vacuum tube are all transconductance devices, i.e., voltage controls current.  I know that is not what a lot of books and magazines aver, but I can back up what I stated. First, I would like to hear some arguments on why so many folks think that the base current controls the collector current of a BJT.

Ratch

Hi,

This has been covered in this forum in a long thread.

The better picture is that the transistor is a voltage controlled device in the STATIC sense only, and since that is usually the de facto standard for determining the basic control scheme it is usually acceptable.  When we look at an actual application however we see that there is always a transfer of energy taking place which means current is also involved.

To give an analogy to this way of thinking the water faucet idea is brought up.
When we turn the faucet on, the water flows.  We then turn the faucet to the flow of water we desire.  We then have the right flow of water so we can say that we 'controlled' the flow of water.  So the flow of water has been controlled, and we can say that the flow is controlled by the position of the handle (distance).  We can state this two ways:
1.  The position controls the water flow.
2.  Once we change the position, the water flow is right.

One is a static condition where we assume all the work necessary to achieve the proper outcome has been done, while the other is a dynamic statement about what work has to be done to get the necessary outcome.

So in one case it appears that NO work has to be done in order to get the necessary outcome, while in the other case it is clear that we need to do work to get the proper control.

The static case is often sufficient, but in the case of the transistor it's only in the basic physics sense that voltage control is the basic control scheme.  In the electrical sense we can either use voltage control or current control, so stating that voltage control is in effect IN ALL CASES can not be right.  In the article maybe a side note would have been a good idea, but in the statement of rejection of such an article a side note should ALSO be included, such as the likes of something like: "current control is also widely used" as a minimum.  Stating that it is just plain wrong is just wrong also.

If you still dont agree, ask yourself why anyone would EVER want to use current control if voltage control is the only true standard, and how it could have been used for so many years for so many applications and is still in use today.
In fact, you not only have to ask yourself that question you also have to be able to answer it yourself too.

[Ratch]

Mr. Al,

All I am stating is that in the active region, a BJT is controlled by the voltage on its base-emitter terminals.  This is true whether the BJT is handling AC or DC, or operating statically or dynamically, whatever that means.  I never said that circuits should be designed using BJTs as voltage controlled devices. Voltage control of a BJT is too nonlinear for that.  When you drive a BJT with a current source, you are not using a BJT alone.  You are incorporating the resistance of the current source into a circuit.  You will find within the circuit a BJT whose base-emitter voltage, at the same collector current, is the same as if it were breadboarded with a voltage source.  When some folks hook up a current source to a BJT base, and notice the current amplification, they rush to judgement and proclaim that the transistor is a current amplifier.  But, what they really have is a current amplifying circuit.  The BJT within is doing the same thing it will do alone.  The base current is waste current that is an indicator of the collector current, but it does not control the collector current.  The physics of the BJT show and prove that.

Ratch

[Zero999]

Mr. Al,

All I am stating is that in the active region, a BJT is controlled by the voltage on its base-emitter terminals.  This is true whether the BJT is handling AC or DC, or operating statically or dynamically, whatever that means.  I never said that circuits should be designed using BJTs as voltage controlled devices. Voltage control of a BJT is too nonlinear for that.  When you drive a BJT with a current source, you are not using a BJT alone.  You are incorporating the resistance of the current source into a circuit.  You will find within the circuit a BJT whose base-emitter voltage, at the same collector current, is the same as if it were breadboarded with a voltage source.  When some folks hook up a current source to a BJT base, and notice the current amplification, they rush to judgement and proclaim that the transistor is a current amplifier.  But, what they really have is a current amplifying circuit.  The BJT within is doing the same thing it will do alone.  The base current is waste current that is an indicator of the collector current, but it does not control the collector current.  The physics of the BJT show and prove that.

Ratch

But the base current is dependant on V_BE, which can be predicted from I_B, using the diode equation.

It's important to take I_B into account. Anyone working with BJT input op-amps needs to beware of the input bias current. The fact that a BJT is not a perfect voltage controlled current source becomes evident when taking the amplifier's input impedance into consideration.

Calculate the input impedance seen by V2 in the emitter follower circuit attached below. If the BJT were perfect voltage controlled current source, then the input impedance would be very high but because of the base current, it's proportional to the load resistance and transistor's current gain. Now try replacing the BJT with a current controlled current source, equal to the BJT's beta, with a diode on the input and you'll find the input impedance is very similar to the BJT.



Saying a BJT is either voltage or current controlled, is a simplification. It may help for designing circuits but it's important to remember this.

[Ratch]

But the base current is dependant on V_BE, which can be predicted from I_B, using the diode equation.

The Schockley diode equation cannot be used discern the base current of a BJT in the active mode because most of the emitter current is diverted to the collector by the collector voltage and the geometry of the base slab.  What little current escapes from the emitter to collector path to the base terminal is considered waste current.  The ratio of the collector current to the waste current in the base circuit is called beta. 

It's important to take I_B into account. Anyone working with BJT input op-amps needs to beware of the input bias current. The fact that a BJT is not a perfect voltage controlled current source becomes evident when taking the amplifier's input impedance into consideration.

Yes, the waste current has to be known and dealt with.  If the waste current were zero, then, if we disregard secondary effects,  a BJT would be a perfect transconductance (voltage controls current) amplifying device with an input impedance of infinity.

Calculate the input impedance seen by V2 in the emitter follower circuit attached below. If the BJT were perfect voltage controlled current source, then the input impedance would be very high but because of the base current, it's proportional to the load resistance and transistor's current gain. Now try replacing the BJT with a current controlled current source, equal to the BJT's beta, with a diode on the input and you'll find the input impedance is very similar to the BJT.

Yes, it is handy that the waste current is somewhat proportional to the collector current.  But whichever way you use the transistor in a circuit, and operate it in its active region, the collector current of the BJT will be dependent on the Vbe voltage.

Saying a BJT is either voltage or current controlled, is a simplification. It may help for designing circuits but it's important to remember this.

A BJT is a voltage controlled or transconductance device.  That is a fact, period.  I can show and prove it by the physics of the  BJT if necessary.  One can easily incorporate it into a current amplifying circuit by driving it with a current source, or loading the base and emitter lines with lots of resistance. But, within the circuit, the BJT is still operating as a transconductance device.

Ratch

[Brumby]

This is somewhat removed from a simple algebra question.

[Ratch]

Brumby,

True, but it appears that the OP got his question answered.  The tangential discussion still remains interesting.

Ratch