 Hello everyone. In today's session, we are going to learn about V2I i.e. voltage to current and I2V current to voltage converters using operational amplifiers. At the end of this session, students will be able to explain and analyze voltage to current i.e. V2I and current to voltage I2V converters implemented using operational amplifiers. These are the contents of my today's presentation. The voltage to current converter provides output current that is directly proportional to input voltage. Input voltage is converted into proportional output current. So V2I converter that is voltage to current converter can be used in applications such as low AC and DC voltmeters to convert voltage into current and light emitting diode that is LEDs tester and GENER diode testers. To find matching light emitting diodes of equal brightness, this V2I converter can be used. The current to voltage converter that is I2V converter is a special case of inverting amplifier in which input current is converted into output proportional voltage. So I2V converter is commonly used with digital to analog converters whose output is always current. So output of digital to analog converter that is current is converted into a proportional voltage. So at the output of DAC I2V converter is used as well as I2V converter is used in sensing the current from photo detectors such as solar cells, photo diodes, photo cells which is proportional to light intensity. Now let us see the first version of voltage to current converter with floating load that is V2I converter with floating load. So figure shows the circuit diagram for V2I converter with floating load in which load resistor RL is connected in feedback loop of operational amplifier. It is connected in between output terminal and inverting input of operational amplifier in place of feedback resistor RF. The input voltage to be converted into proportional output current is applied to non-inverting input of operational amplifier. So op-amp is working in non-inverting mode and the feedback voltage the voltage appearing across R1 that is feedback voltage that is proportional to output current is applied at inverting input. Whatever current flowing through inverting input of operational amplifier that is a bias current it is approximately 0. So output current flowing through load resistor RL almost all output current flows through R1 and produces a voltage. So voltage producing produced across R1 that is applied to inverting input of operational amplifier that is a feedback voltage. The load resistor RL is floating means it is not connected to ground and input voltage applied at non-inverting input terminal that is the feedback voltage R1 is applied to inverting input terminal. So we can verify the working of this circuit by getting the equation for output that is output current. So let us write Kirchhoff's voltage equation for input loop of this circuit. So VIN is equal to VID plus VF where VIN is applied input voltage and VID is a differential input voltage of operational amplifier and VF is a feedback voltage but VID is approximately 0 volts since the gain of operational amplifier that is basic gain of operational amplifier A is very large ideally infinity. So it tends to infinity means input voltage tends to differential input voltage tends to 0. So therefore VIN is equal to VF. So voltage applied at non-inverting input appears across the feedback resistor R1 input resistor R1 VF. So VIN is equal to R1 into IO that is output current. So IO equal to VIN upon R1. So this equation shows that input voltage VIN is converted into proportional output current. So that is given by VIN upon R1. This means that input voltage VIN appears across resistor R1. If in place of resistor R1 if we are using a precision resistor the output current will be precisely fixed. Now let us go for the second version of V2I converter that is the voltage to current current converter with grounded load. So this figure shows circuit diagram for V2I converter with grounded load. In this the input voltage to be converted into output current is applied to non-inverting input. Opium is working in non-inverting mode and feedback circuit is designed around inverting input. So in place of RF and R1 same value of resistor R is used and operational amplifier is biased with dual DC power supply plus VCC and minus VW and load connected at the output is connected to ground. It is grounded. So one terminal of load is connected to the output terminal through resistor R and another terminal is connected to ground. So input voltage VIN is applied through resistor R. So identical resistors are used and the current resulting due to input voltage is I1 and current resulting due to output of this circuit PO is I2 and the current flowing through load is IL is a summation of I1 and I2 and input bias current of operational amplifier is approximately zero IB is zero as input resistance of op-amp is very high very large ideally infinity. So to verify the working of this circuit we can get the equation for output voltage. So let us analyze this circuit. Load current is controlled by the input voltage. Let us find voltage V1 at non-inverting input terminal then establishing the relation between V1 and load current or the input voltage VIN and the load current IL. So use KCL at node V1 so that is I1 plus I2 is equal to IL. So let us express I1 in terms of potential difference in resistance VIN minus V1 upon R plus VO minus V1 upon R that is equal to IL. So VIN plus VO after simplification VIN plus VO minus 2VN 2VN is equal to IL into R. Therefore V1 is equal to VN plus VO minus ILR divided by 2. Since operational amplifier is working in non-inverting mode the gain of this circuit voltage gain of this circuit is 1 plus RF upon R1 that is here 1 plus R upon R so that is equal to 2. So then output voltage VO is equal to again times the input voltage so that is equal to 2VN V1. So this is equal to 2 to gate cancels so VIN plus VO minus IL into R. So after simplification VIN is equal to IL into R so output load current IL is equal to VIN upon R. This means that the load current depends upon the input voltage VIN and resistance R. Now let us go for I to V converter that is current to voltage converter. This figure shows the circuit diagram for current to voltage converter. It is a special case of inverting amplifier. So in place of VIN and R1 a current source can be shown so that is IN. So IN is the input current resulting due to input voltage that is applied to inverting input and current flowing through inverting input and non-inverting input. So those are bias currents IB1 and IB2 are approximately 0. So the input current is applied to inverting input and current flowing through inverting input is approximately 0 because the input resistance of the amplifier is very large ideally infinity. So all input current flows through feedback resistor RF. RF is connected in between inverting and output terminal of operational amplifier. Operational amplifier is biased with dual DC power supply plus VCCS and minus VW and load resistor IL is connected at the output. So the proportional voltage corresponding to the input current will appear across load resistor IL so that is across RF. The non-inverting input plus input is connected to ground so voltage V1 is 0. So therefore voltage V2 is also 0 because differential input voltage tends to 0 as the basic gain of op-amp tends to infinity. So let us consider ideal voltage gain of inverting amplifier. So a ratio of output voltage to input voltage V1 upon VIN is equal to minus RF upon R1. So that is equal to VA equal to minus for VIN upon R1 into RF. Since V1 is equal to 0 volts therefore V2 is also 0 volts. This is by the concept of virtual ground. Op-amp always tries to equalize voltage at non-inverting and inverting. So non-inverting is 0 volts so inverting is also 0. So inverting input of operational amplifier is acting as a virtual ground. So VIN upon R1 is equal to IN. So output voltage is equal to the input current minus IN into RF. So output voltage is directly proportional to the input current IN as feedback resistor RF is fixed constant. So output voltage becomes proportional to the input current IN. In other words the circuit converts the input current into a proportional voltage. Now a student can pause video here and think over this question and try to write the answer. Identify and justify the type of feedback used in V2i converter with floating load. The current series negative feedback is used since the current flowing through resistor R1 that is proportional to output current that is current flowing through feedback resistor RF. So voltage produced across R1 is feedback voltage it is applied to inverting input of operational amplifier and this feedback voltage depends upon output current. So this feedback voltage it is in series with the input differential voltage or difference voltage VID. So feedback voltage across R1 is coming in series with differential input voltage VID as well as the input voltage applied at non-inverting input. Therefore it is also called as current series negative feedback amplifier. So current series negative feedback amplifier is a voltage to current converter with floating load. This is the reference. Thank you.