# Operational Amplifier multiplier

I have a question involving a couple problems in the following PDF: http://www.engr.colostate.edu/ECE103/FA13/homeworks/Homework6%20FA2013.pdf

For convenience, I'll also post them below.

As far as I understood, an inverting op amp would take the input voltage and multiply it by -(Ro/R1). So for instance, in #1 the output voltage would be 2 volts, correct?

However, what is the input voltage I am to multiply by in the case of #2, where the positive terminal is linked to a 5 volt power supply? Is it still 10 volts (v1) or is it now 5 volts (or something else)?

Problems:

• I like how they arbitrarily decided that dots indicating connections are optional... Nov 4, 2013 at 3:35
• Op amps multiply the difference between their two inputs. That's why an infinite-gain op amp acts as a comparator. Nov 4, 2013 at 3:41
• But isn't the difference between the two inputs supposed to be negligible? I apologize for my ignorance in this subject. I'm just trying to understand how to solve these problems. Nov 4, 2013 at 3:42
• The op amp will attempt to make it negligible. Current will flow, and voltages will result. Nov 4, 2013 at 3:46
• David, you were asking where to start. Start with ideal OpAmp assumptions and Kirchhoff Current Law (KCL). The rest is algebra. Keep in mind that this board is not here to do your homework. So far, you haven't demonstrated any effort to speak of. You were only asking questions. Nov 4, 2013 at 4:31

For the first case, you are right. It's an inversor amplifier.

The second exercise has a differential amplifier. In mostly books, it has the next output:

$$v_{o}=v_{2}-v_{1}$$

However, it's a special case assuming equal resistors.

If you perform nodal analysis in your exercise, you will get:

$$v_{o}=\frac{[(200+100) \Omega]V_{2}-(200 \Omega)V_{1}}{100 \Omega}$$

• So it should be 5 volts, correct? Nov 4, 2013 at 4:07
• How did you do that nodal analysis? Nov 4, 2013 at 4:11
• Remember it's a new configuration. I prefer to analyse the circuit. In the standard differential amplifier, all resistors are the same. This case is different.
– Chuz
Nov 4, 2013 at 4:11
• Oh I get it. So the output voltage of the op-amp is +5, but Vo must be -5 volts in order to equal zero at the reference node. Nov 4, 2013 at 4:13
• @David what equation are you using to get $v_{o}=+5V$?
– Chuz
Nov 4, 2013 at 4:16