 ### Network # Determine the unknown voltage in an ideal Op-Amp circuit

#### LynneMac

Jun 21, 2016
5
Hi Everyone I am struggling with a problem and wondered if somebody could give me a push in the right direction on how to solve it?

I need to determine the unknown voltage highlighted by a red circle, however I do not have any values on the resistors to apply Ohms law.

Any help is appreciated.

#### (*steve*)

##### ¡sǝpodᴉʇuɐ ǝɥʇ ɹɐǝɥd
Moderator
Jan 21, 2010
25,509
1) what is the name of this circuit?

2) can you write the equation for the gain at each input?

that should be a good start.

#### LynneMac

Jun 21, 2016
5
1) what is the name of this circuit?

2) can you write the equation for the gain at each input?

that should be a good start.

I believe this is an inverting op amp.

As far as the gain is concerned I am completely confused with the formula due to 1V and the unknown voltage going into parallel circuits. Could you give any further hints?

Thanks

#### davenn

Moderator
Sep 5, 2009
14,196
As far as the gain is concerned I am completely confused with the formula

write out the formula for gain

#### Herschel Peeler

Feb 21, 2016
401
Hi Everyone I am struggling with a problem and wondered if somebody could give me a push in the right direction on how to solve it?

I need to determine the unknown voltage highlighted by a red circle, however I do not have any values on the resistors to apply Ohms law.

Any help is appreciated.
l

500 mV
With no second input voltage and R = R the output would be -1 V.
To double the output voltage (and feedback current) you need to double the input current sum.
Don't imagine it to be so hard. See the simple lesson intended.

• LynneMac

#### LynneMac

Jun 21, 2016
5
l

500 mV
With no second input voltage and R = R the output would be -1 V.
To double the output voltage (and feedback current) you need to double the input current sum.
Don't imagine it to be so hard. See the simple lesson intended.
Any chance you could break this down using a formula so I can see how it works? Thanks

#### (*steve*)

##### ¡sǝpodᴉʇuɐ ǝɥʇ ɹɐǝɥd
Moderator
Jan 21, 2010
25,509
@Herschel Peeler PLEASE do not give answers. This forum is to help people, not to spoon feed them.

@LynneMac can you find op amp circuits with multiple inputs? This one has a name.

What is the gain at each input?

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#### Herschel Peeler

Feb 21, 2016
401
@Herschel Peeler PLEASE do not give answers. This forum is to help people, not to spoon feed them.

@LynneMac can you find op amp circuits with multiple inputs? This one has a name.

What is the gain at each input?

The lesson was not in finding a formula to solve the problem but in seeing the simple process of a solution. See the simple question. His approach was what was hindering him. hint ... Resistor values were not important since they were not included. Forget the math. Understanding how the circuit works gave the solution.

Last edited by a moderator:

#### Herschel Peeler

Feb 21, 2016
401
Any chance you could break this down using a formula so I can see how it works? Thanks

Formula? What formula? I guess I could come up with one but it would only be meaningful for this specific question and be of no use in the real world. Understand how the circuit works. See the simple question intended.

#### Herschel Peeler

Feb 21, 2016
401
Hi Everyone I am struggling with a problem and wondered if somebody could give me a push in the right direction on how to solve it?

I need to determine the unknown voltage highlighted by a red circle, however I do not have any values on the resistors to apply Ohms law.

Any help is appreciated.

Not much math required.
What is the circuit? Inverting summing circuit. Sums the incoming currents.
Realize ... Rf = Ri, Second Ri is 1/2 of Ri
Known input is 1 V. Output is 2 V. Since Rf = Ri gain is -1.
Input current know is 1V/Ri.
If that were the only input the output would be -1 V. Since the output is -2 V the other input current must be equal to the known. To get that with 1/2 R the input voltage must be 1/2, or 500 mV.
What formula?
Your "find the formula" approach was what made it appear more difficult than it really was.

#### (*steve*)

##### ¡sǝpodᴉʇuɐ ǝɥʇ ɹɐǝɥd
Moderator
Jan 21, 2010
25,509
are you trying to get banned @Herschel Peeler?

FFS, we want the OP to come up with this on his own, not be spoon fed the answer.

And the ratio of resistor values is critical, which is why they're given.

sheesh

Last edited:

#### Herschel Peeler

Feb 21, 2016
401
are you trying to get banned @Herschel Peeler?

FFS, we want the OP to come up with this on his own, not be spoon fed the answer.

And the ratio of resistor values is critical, which is why they're given.

sheesh

Banned for showing him how to solve the problem?
Fine, I will stay out of the homework stuff.

#### (*steve*)

##### ¡sǝpodᴉʇuɐ ǝɥʇ ɹɐǝɥd
Moderator
Jan 21, 2010
25,509
you appear to confuse "help" with "doing"

#### Harald Kapp

##### Moderator
Moderator
Nov 17, 2011
13,337
Fine, I will stay out of the homework stuff.
@Herschel Peeler : You're free to do as you like, it's your choice.

However, we don't want to disencourage you. Your help is welcome. All we ask is that you back off a bit within the homework section. In this section it is our policy to guide the op to find his own solution, not to give it to him. Only by understanding the problem and the way to solve it will the op be able to learn from the thread and to solve similar topics in the future by himself.
In this thread, for example, one way would have been to hint at V+ - V- = 0 V at the opamp's input and to solve the resulting node and loop equations. Another hint was given by Steve about the resistor ratio. Thus the op would be able to find the transfer function for other opamp based circuits by himself. Giving the equation for this particular circuit will allow him to compute the result, but he will be at a loss when the circuit changes.

I know, sometimes it is hard to restrain oneself, especially when the answer seems to be so obvious to the experienced eye. But keep in mind we all had to learn sometime and 'learning by doing' is still one of the most efficient methods (in my opinion).

Regards,
Harald

• (*steve*) and davenn

#### Herschel Peeler

Feb 21, 2016
401
@Herschel Peeler : You're free to do as you like, it's your choice.

However, we don't want to disencourage you. Your help is welcome. All we ask is that you back off a bit within the homework section. In this section it is our policy to guide the op to find his own solution, not to give it to him. Only by understanding the problem and the way to solve it will the op be able to learn from the thread and to solve similar topics in the future by himself.
In this thread, for example, one way would have been to hint at V+ - V- = 0 V at the opamp's input and to solve the resulting node and loop equations. Another hint was given by Steve about the resistor ratio. Thus the op would be able to find the transfer function for other opamp based circuits by himself. Giving the equation for this particular circuit will allow him to compute the result, but he will be at a loss when the circuit changes.

I know, sometimes it is hard to restrain oneself, especially when the answer seems to be so obvious to the experienced eye. But keep in mind we all had to learn sometime and 'learning by doing' is still one of the most efficient methods (in my opinion).

Regards,
Harald

Okay. Backing off.
In the case at hand his problem was not seeing a probes to find the answer, not just not having the answer. Show him what a process is like. You could ask him questions for a week going back and forth and get nowhere.
.

#### (*steve*)

##### ¡sǝpodᴉʇuɐ ǝɥʇ ɹɐǝɥd
Moderator
Jan 21, 2010
25,509
The point of this area is to help people with their homework. We have no desire to cater for those who get an assignment, have no idea what it means (due, perhaps, to not doing any study) and come here for the answer.

The initial question looked good. It was an ask for a push in the right direction.

My initial questions were an attempt to elicit something like "inverting", "non-inverting", or perhaps the name for this particular form.

Each of these have a method of determining the gain. The gain is used to determine the output for a given input.

The OP may have asked how to do this with two inputs. We would suggest they do the calculation for both as if each one was the only input (yielding 2 formulae).

Presumably, at this point the OP may have asked how that is done if the resistor values are unknown. We would have simply suggested the resistor "values" as they are given should be put into the formula to see what comes out. This on its own is a valuable lesson.

Having this, the OP might have found that the output didn't match what they should get given the known input. We would have sent the OP away googling (or looking in their text or notes) for an op-amp circuit with multiple inputs. Presumably they would find one (and its name).

The next step is for them to determine the relationship between the input voltages and the output voltage in this configuration.

This would lead pretty quickly to a formula involving a single unknown, the value of which was the answer to the assignment question.

At the end, the OP would have the answer, but more importantly have the understanding to answer the question.

And THAT is the aim of this area of Electronics Point. If the person didn't leave enough time for that, it's hardly our problem.

• Harald Kapp

#### Laplace

Apr 4, 2010
1,252
As far as the gain is concerned I am completely confused with the formula due to 1V and the unknown voltage going into parallel circuits. Could you give any further hints?
Whenever an op-amp circuit operation is not intuitively obvious (quite often, for me) and writing the gain equation is not a clear path, it is best to write the node equations for the circuit. In this case a single node equation for the '-' input to the op-amp consisting of 3 terms because the '-' input is connected to 3 adjacent node voltages via 3 resistors. As always, the node equation is formed over the summation of all adjacent nodes as (Vnode-Vadjacent)/(Resistance to adjacent node) and all set equal to zero.

But in this case we know that Vnode (at the '-' input) is the same as the voltage at the '+' input (ground) = 0 because of the negative feedback and the infinite open-loop gain of the op-amp. And the other adjacent node voltages are all specified (-2, +1, V). So the node equation for the '-' input looks like: Multiply each side of the equation by R, and the specific value for R becomes irrelevant. Then solve for V. You might ask why develop the node equation for such a simple circuit? For more complicated circuits, like active filters, node equations are the only path to a solution so one should practice getting the method right on the simple circuits.

• Harald Kapp

#### Herschel Peeler

Feb 21, 2016
401
Whenever an op-amp circuit operation is not intuitively obvious (quite often, for me) and writing the gain equation is not a clear path, it is best to write the node equations for the circuit. In this case a single node equation for the '-' input to the op-amp consisting of 3 terms because the '-' input is connected to 3 adjacent node voltages via 3 resistors. As always, the node equation is formed over the summation of all adjacent nodes as (Vnode-Vadjacent)/(Resistance to adjacent node) and all set equal to zero.

But in this case we know that Vnode (at the '-' input) is the same as the voltage at the '+' input (ground) = 0 because of the negative feedback and the infinite open-loop gain of the op-amp. And the other adjacent node voltages are all specified (-2, +1, V). So the node equation for the '-' input looks like:
View attachment 27513
Multiply each side of the equation by R, and the specific value for R becomes irrelevant. Then solve for V. You might ask why develop the node equation for such a simple circuit? For more complicated circuits, like active filters, node equations are the only path to a solution so one should practice getting the method right on the simple circuits.

I guess that is what he was looking for.

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