 Hello everyone. In today's session, we are going to see summing, scaling and averaging amplifier. At the end of this session, students will be able to describe and analyze some linear applications of operational amplifier in inverting and in non-inverting configurations. These are the contents of my today's presentation, inverting configuration and non-inverting configuration. Now, let us see the inverting circuit configuration, non-inverting circuit configuration and differential circuit configuration of operational amplifier can be used to implement applications such as semi-amplifier, scaling amplifier and averaging amplifier. Now, let us go for the inverting circuit configuration of operational amplifier. The figure shows the circuit diagram for inverting amplifier with multiple input voltages. VA, VB and VC are input voltages applied to inverting input of operational amplifier through resistor RA, RB and RC. Current resulting due to VA, VB and VC are IA, IB and IC respectively towards the node VA2. Non-inverting input of operational amplifier is connected to ground through resistor ROM. ROM stands for offset minimizing resistor. It is used to minimize output offset voltage due to input bias current. The value of offset minimizing resistor ROM is parallel equivalent resistance of all resistors connected to other input that is inverting input of operational amplifier. Those are input resistors RA, RB and RC and feedback resistor RF. So, output is taken across load resistor RL. RF is feedback resistor and RF, RB and RC are input resistors. So, to cancel out output offset voltage, the resistor ROM is used. Non-inverting input of operational amplifier is connected to ground. So, the voltage at non-inverting input V1 is equal to 0. OFM always tries to equalize the voltage at non-inverting and inverting. As the voltage at non-inverting V1 is zero-hold, the voltage at inverting input that is VA2 is also zero-hold. It acts as a virtual ground by the concept of virtual ground, virtually grounded. Inverting input is virtually grounded. So, output voltage of this circuit is maybe summing some of the inputs or scaling of the input or averaging of the input voltages. Let us see first a summing amplifier. This circuit can work as a summing amplifier, scaling amplifier and averaging amplifier depending on the relation between feedback resistor and feedback resistor RF and input resistor RA, RB and RC. The equation for output voltage indicates the operation of this circuit. So, working of this inverting amplifier with multiple inputs in this circuit three inputs are there can be verified by getting the equation for output voltage. Use KCL at node V2 current flowing towards at node V2 is equal to IA plus IB plus IC equal to current flowing away from the node V2 that is current flowing through feedback resistor RF that is IF. Since the input resistance of operational amplifier and open loop gain A of operational amplifier are very large ideally infinity. So, the input bias current IB is zero, approximately zero and the voltage at non-inverting input V1 is equal to the voltage at inverting input that is equal to zero volts. So, since inverting input of operational amplifier acts as a virtual ground by the concept of virtual ground. Therefore, the currents can be expressed in terms of voltage and resistance. The input currents the voltage VA upon RA plus VB upon RB plus VC upon RC is equal to minus Vo upon RF as voltage at inverting input V2 is zero. So, output voltage of the circuit is simplified to minus into bracket RF of upon RA into VA plus RF upon RB into VB plus RF upon RC into VC. If in this circuit registers RA equal to RB equal to RC equal to R then the equation for output voltage becomes Vo equal to minus RF upon R into bracket VA plus VB plus VC. This equation indicates that output voltage is gain times negative sum of all input voltages VA, VB and VC. The gain of this circuit is RF upon R. Hence, this circuit operates as summing amplifier. If the gain of this amplifier that is RF upon RF, RF upon R is set to 1 then the output voltage equation becomes Vo equal to minus into bracket VA plus VB plus VC. So, the circuit acts as an adder circuit in which output voltage is the addition of three input voltages. Now let us see how this same circuit can work as a scaling amplifier. If each input voltage is amplified by different factor or weighted differently at the output then the circuit works as a scaling amplifier. This condition can be achieved by selecting RA, RB and RC input registers of different value. So, the equation for output voltage of this circuit that is inverting amplifier Vo is equal to minus RF upon RA into VA plus RF upon RB into VB plus RF upon RC into VC where the ratio of feedback register to input register RF upon RA is not equal to RF upon RB not equal to RF upon RC. So, the circuit works as a scaling amplifier because each input is amplified by a different factor. So, each input is weighted differently at the output. Same inverting amplifier with multiple inputs can work as a averaging amplifier in which the output voltage is average of all input voltages. For this use all input registers RA, RB and RC of same value that is RA equal to RB equal to RC equal to R and the gain by which each input voltage is amplified must be equal to 1 over number of inputs. So, gain of this circuit is equal to RF upon R that is equal to 1 upon N where N stands for number of inputs. So, in this circuit number of inputs are 3 N equal to 3. So, output voltage is minus value of RF upon R is equal to 1 upon 3. So, minus into bracket VA plus VB plus VC divided by 3. So, this equation indicates that output voltage is average of all 3 input voltage with opposite side. So, output is of opposite polarity with respect to input. So, in this way the circuit works as averaging amplifier. Now, let us go for the second circuit configuration of operational amplifier that is a non-enrouting configuration. The non-enrouting configuration of operational amplifier can be implemented as semi or averaging amplifier by selecting a proper value for feedback resistor RF and input resistor R1. VA, VB and VC are 3 input voltages are applied to non-enrouting input of operational amplifier using same resistor same value of resistors R and the V1 is a voltage at non-enrouting input and V2 is a voltage at inverting input. The voltage at inverting input is approximately 0 volt since inverting input is at virtual ground. So, value of V2 is 0 volt. So, voltage at non-enrouting input V1 can be obtained using superposition theorem. So, it is a non-enrouting amplifier with multiple inputs. Multiple inputs are applied at non-enrouting input. So, using superposition theorem considering only one input voltage at one time and assuming other input voltage is 0. So, voltage at V1 is equal to R by 2 upon R plus R by 2 into VA plus this circuit works as a semi or averaging amplifier. V1 is equal to R by 2 upon R plus R by 2 into VA plus R by 2 upon R plus R by 2 into VVB plus R by 2 upon R plus R by 2 into VC. So, voltage V1 at non-enrouting input is equal to VA plus VV plus VC divided by 3. So, that is hence the output voltage is given by V1 equal to the gain of non-enrouting amplifier 1 plus RF upon R1 into V1. So, voltage at non-enrouting input. So, output final output voltage is equal to 1 plus RF upon R1 multiplied by VA plus VV plus VC upon 3. So, the above equation shows that output voltage is equal to gain times the average of all input voltages gain is equal to 1 plus RF upon R1. Thus, it operates as a averaging amplifier. Hence, the output voltage if gain is set to 1 the output voltage is equal to VA if gain is set to 3 output voltage is equal to VA plus VB plus VC. Now, student can pause video here and think over the question what are the two basic differences between inverting and non-inverting averaging amplifier. In inverting averaging amplifier output voltage is average of all input voltages with opposite sign. So, output is opposite polarity with respect to input there is a sign or phase reversal. In non-enverting averaging amplifier the voltage at non-enverting input is average of all input voltages VA, VB and VC. This is the reprocess. Thank you.