# Find v1 and v2 of a summing amplifier when it is in series with another Op-Amp

There is a summing amplifier with two AC power sources (v1+v2,) each connected to a different Ground. Each of these sources connect to a resistor (R1+R2,) and then to a summing point, which branches off.

One branch leads to the inverting (-) input of an Op-Amp (with the non-inverting (+) input connected to a 3rd Ground.) The other passes through a feedback resistor "Rf1" before connecting, along with the output of the Op-Amp, to point Vx.

The circuit then continues from point Vx (through a resistor Rc) to a second summing point, which also branches off. One of these branches leads to the inverting input of a second Op-Amp (with the non-inverting input connected to a 4th Ground,) and the other passes through a second feedback resistor (Rf2) to meet the output of the second Op-Amp at another point. This point then continues on to V0.

I know that R1 is 1.8kOhms, Rc is 2kOhms, and Rf2 is 6kOhms.

Supposedly the operation of this circuit is v0= 3v1 + 1.5v2, but I don't know what that means.

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• Draw your circuit. Jun 6 '16 at 17:09
• What have you figured out so far? Show us any work you've done already -- we're not going to just give you the answer.
– Null
Jun 6 '16 at 17:15

Supposedly the operation of this circuit is v0= 3v1 + 1.5v2, but I don't know what that means.

This means that you should be able to calculate the output voltage from the two input voltages using algebra, according to the given formula.

If you work out the circuit, you will find a formula that gives $v_o$ in terms of $v_1$, $v_2$, $R_1$, $R_2$, $R_{f1}$, and $R_{f2}$. Your job is to find values of the resistors that makes the constants in the formula come out to 3 and 1.5.

Hints: -

• You have the gain for the 2nd op-amp circuit because it's just the ratio of two resistors named in the text.
• Armed with that gain value, concentrate on V1 (i.e. forget V2 for now because V2 doesn't affect how V1 gets amplified.)
• So the overall gain for V1 is 3 and after you reduce that gain by the gain of the 2nd stage you are left with "what" gain for the first stage? This is easy and I can do it in my head!
• Once you have that 1st stage gain you can easily calculate R1.

For V2 repeat the process whilst ignoring V1 (you can because the summing node is a virtual earth).

• Gains multiply so you have -1 x -3 Jun 6 '16 at 19:34
• I don't use multisim, sorry. Jun 7 '16 at 11:00

It's a little hard to know where to start. You seem to have missed everything in the book prior to your problem.

First, "There is a summing amplifier with two AC power sources", Well, no. Those two voltage sources can be AC or DC.

Next, "Supposedly the operation of this circuit is v0= 3v1 + 1.5v2, but I don't know what that means." Umm, how to say this. Let's say that V1 is some voltage like 2 volts, and V2 is a different voltage, like 1 volt. Then the output is 3 times 2 volts (3 x V1) plus 1.5 times 1 volt (1.5 x V2). If you don't understand basic algebra you need to drop the course. Now.

Finally, you must have been exposed to the formula for gain in an inverting op amp. Since the second stage has an input resistor of 2k (Rc, right?) and a feedback resistor of 6k (Rfb2, right) it will have a gain of -3 (6 divided by 2, right?). This means that the first section has a gain of ((3 x V1) + (1.5 x V2)) divided by -3. Either you can do the arithmetic or you can't, and in either case there is no need for me to do it for you. Knowing the gain of the first stage and two of three resistors, you should be able to figure out the third.

• First off, you are not asked to find the values of V1 and V2. Second, knowing the overall gain of the circuit allows you to tease out the various component values, as I stated. The gain of a summing amp is controlled by the ratios of the component resistors. If you know the gain of an amp (and you should be able to figure it from my answer) and you know one of the resistors, simple arithmetic will give you the value of the other resistor. Come on, this was covered in your book. Jun 6 '16 at 18:33