 Hello everyone. In today's session we are going to discuss adder and subtractor circuits using operational amplifier. At the end of this session, students will be able to analyze and implement adder circuit and subtractor circuits using operational amplifier. These are the contents of my today's presentation. The inverting, non-inverting and differential circuit configurations of operational amplifier can be used to implement basic mathematical operations such as adder circuit and subtractor circuit. For these circuits, input signals may be AC signal or DC signals. Basically, operational amplifier is designed to perform mathematical operations such as additional subtraction, multiplication, division and integration etc. That is why for this amplifier, the name given as an operational amplifier, these adder and subtractor circuits are commonly used in analog computers and audio mixers. In audio mixer, a number of inputs are added to produce desired output signal. Now this figure shows the basic summing amplifier which can be used as an adder circuit. VIA, VBA and DC are three input voltages applied to inverting input. Operational amplifier is connected in inverting configuration. So all three input voltages may be AC or DC applied to inverting input of operational amplifier through input registers RA, RB and RC. And RF is a feedback register connected between output of operational amplifier and inverting input. And output voltage is taken across load register Rn. To non-inverting input, register ROM is connected. ROM stands for offset minimizing register. The value of this resistance is parallel equivalent resistance resistances of all registers connected to other input that is inverting input. So offset minimizing register is used to minimize output offset voltage due to input bias current. Output of this circuit that is the adder circuit can be verified by getting an equation for output voltage. This circuit in Fever 1 can work as adder depending upon the relation between the feedback register RF and input register RA, RB and RC. The equation for output voltage VO indicates the operation of the circuit. Let us apply Kirchhoff's current law at node V2. That is at inverting input of operational amplifier which is virtually grounded by the concept of virtual ground. Voltage at non-inverting input V1 is 0 volt. The voltage at inverting input V2 is also 0 volt. So using Kirchhoff's current law at node V2, the total current IA, IB, IC are flowing towards node V2 is equal to the current flowing away from the node V2 IF that is current flowing through feedback register RF. So IA plus IB plus IC is equal to IF. As the input resistance of operational amplifier is ideally infinity and practically it is very high and open gain of operational amplifier A are very large ideally infinity. So the input bias current IB equal to 0 that is current bias current flowing through inverting input and non-inverting input of operational amplifier is approximately 0. So as non-inverting input is connected to ground and its voltage is 0 volt. So by the concept of virtual ground, the voltage at V2 is also 0 volt. So V1 is equal to V2 is equal to 0 volts. Therefore, let us express the three currents in terms of voltage and resistance. So for current IA we can write VA upon RA plus for IB we can write VB upon RB plus for current IC we can write VC upon RC is equal to minus into bracket VO upon RF that is voltage at V2 in the sense voltage at inverting input is 0 volt. So that is why the current flowing in the feedback circuit is minus VO upon RF. So output voltage VO is equal to we can simplify minus RF upon RA into VA plus RF upon RB into VB and plus RF upon RC into VC. So the gain offered by the summing amplifier that is idle circuit to every input VA, VB and VC is the ratio of feedback resistor to input resistor. If in this circuit all resistors RA, RB and RC and RF are of same value, selected same value then gain of this circuit is equal to 1. So output voltage that is gain of the circuit RF upon R that is RF is equal to R that is gain is equal to 1. So output voltage is minus VA plus VB plus VC. So this equation indicates that the output voltage is negative sum of all the input voltages. Hence the circuit operates as the idle circuit. Now let us go for FM as a subtractor. So this figure shows the basic differential amplifier using operational amplifier. It can be used as a subtractor. This circuit has two inputs. Both input voltages are positive VA and VB. These input voltages may be AC voltage or DC voltage applied to voltage. VA is applied to inverting input through resistor R input resistor R and voltage VB is applied to non-inverting input through resistor R. The operational amplifier is biased with dual DC power supply plus VCC and minus VLE and the voltage divider is used at the non-inverting input using same value of same value resistors and output is taken across load resistor. So the resistor R same value of resistor is connected between inverting input and output terminal of operational amplifier. A basic differential amplifier can be used as a subtractor as shown in this figure 2. Selecting all external resistors of same value so that gain of amplifier becomes 1. The function of this circuit can be verified by output voltage equation. The circuit has two inputs voltage VA and voltage VB. Therefore, let us use superposition theorem in which we consider only one input voltage at one time other input voltage can be assumed 0. So when the second input voltage voltage VB is equal to 0 volt then circuit becomes an inverting amplifier. So output voltage of differential amplifier acting as a subtractor due to VA only is designated as VOOA is equal to minus R upon R into VA that is gain times the input voltage. Now let us when VA is kept 0 volt then circuit becomes as a non-inverting amplifier with the voltage divider at the non-inverting input and feedback circuit is connected around inverting input. Therefore, voltage at non-inverting input is V1 that is equal to using voltage divider rule R upon 2R into applied external input voltage that is VB. So output voltage due to only input voltage VB is VOB is equal to the gain times the input voltage. Since the amplifier is working as a non-inverting amplifier so gain of this non-inverting amplifier is 1 plus RF upon R1. Now here in this case both RF and R1 are R only so 1 plus R upon R into bracket voltage at non-inverting input that is V1 R2 upon 2R into VB. So this equation 1 and equation 2 from equation 1 and equation 2 the net output voltage is VO equal to VOA plus VOB. So output voltage is equal to minus R upon R into VA plus 1 plus R upon R into bracket R upon 2R into VB. So final output voltage is equal to minus R upon R into bracket VA minus VB. So the gain of this amplifier becomes 1 as it is 1 so output voltage is equal to VB minus VA. So output voltage of a differential amplifier is a subtraction of the voltage applied at non-inverting input minus voltage applied at inverting input. Thus the circuits work as a subtractor circuit. Thus the operational amplifier functions as a subtractor. Student can pause video here and think over this question and write the answer. State a maximum possible output voltage of adder circuit and subtractor circuit. As op-amp is biased using dual DC power supply plus VCC and minus VWE. So output voltage varies in between plus VCC and minus VWE. So positively the output voltage varies from 0 to plus VCC and negatively it varies from 0 to minus VWE. So for op-amp 7.1 the range of variation of output voltage is from 0 to plus 15 volt in positive direction in negative direction if output is negative the output is in the range 0 to minus 15 volt. So we can apply we can use a diverse supply of plus minus 5 to plus minus 15 for plus VCC and minus VWE. This is the reference. Thank you.