Question

An inverting scaling amplifier has three input voltages Va, Vb and Vc. Find it output voltage?

(a) VO= – {[(RF/Ra)×Va] +[(RF/Rb)×Vb]+[(RF/Rc)×Vc]}

(b) VO= – [(RF/Ra)+(RF/Rb)+(RF/Rc)]×[( Va +Vb+Vc)].

(c) VO = – {[(Ra/RF)×Va] +[(Rb/RF)×Vb]+[(Rc/RF)×Vc]}

(d) None of the mentioned

I had been asked this question in an online interview.

My doubt stems from Summing, Scaling & Averaging Amplifier in portion Operational Amplifier Applications of Linear Integrated Circuits

Answer 1

For an inverting scaling amplifier with three input voltages VaV_aVa​, VbV_bVb​, and VcV_cVc​, the output voltage VoV_oVo​ can be derived using the basic principles of summing amplifiers with scaling factors for each input.

In a typical inverting summing amplifier with scaling factors, the output voltage VoV_oVo​ is given by the formula:

Vo=−(RFRa)Va−(RFRb)Vb−(RFRc)VcV_o = - \left( \frac{R_F}{R_a} \right) V_a - \left( \frac{R_F}{R_b} \right) V_b - \left( \frac{R_F}{R_c} \right) V_cVo​=−(Ra​RF​​)Va​−(Rb​RF​​)Vb​−(Rc​RF​​)Vc​

Where:

• RFR_FRF​ is the feedback resistor,
• RaR_aRa​, RbR_bRb​, and RcR_cRc​ are the resistances associated with each of the inputs VaV_aVa​, VbV_bVb​, and VcV_cVc​, respectively.

Thus, the correct expression for the output voltage is:

Vo=−[(RFRa)Va+(RFRb)Vb+(RFRc)Vc]V_o = - \left[ \left( \frac{R_F}{R_a} \right) V_a + \left( \frac{R_F}{R_b} \right) V_b + \left( \frac{R_F}{R_c} \right) V_c \right]Vo​=−[(Ra​RF​​)Va​+(Rb​RF​​)Vb​+(Rc​RF​​)Vc​]

This corresponds to option (a):

(a) Vo=−[(RFRa)Va+(RFRb)Vb+(RFRc)Vc]V_o = - \left[ \left( \frac{R_F}{R_a} \right) V_a + \left( \frac{R_F}{R_b} \right) V_b + \left( \frac{R_F}{R_c} \right) V_c \right]Vo​=−[(Ra​RF​​)Va​+(Rb​RF​​)Vb​+(Rc​RF​​)Vc​].

Therefore, the correct answer is (a).