 Hello, welcome to the session on precision rectifiers. Learning outcomes are at the end of session students will be able to explain the working of precision rectifiers and they can sketch the output waveforms for the rectifier circuit for given input signal. Contents are like this. So, what are the precision rectifiers and what is the need for this? As you know due to the voltage drop across the diode, we cannot get the characteristics of diode as ideal diode. The drop across conducting diode of 0.7 volt, but when we connect the diode in the feedback path of the opamp that is operational amplifier, we can get the diode as a ideal diode. So, these characteristics are called as super diode. So, where we get the rectification of the signals less than 0.7 volt which is not possible with the ideal diode. So, which will eliminates the error in the output signal. So, it can give you the rectification of the signal that is VD upon the voltage gain of the opamp that is in terms of lakhs that is VD upon AOL that is open loop gain. Even the signal is in the millivolt or microvolt we can rectify that signal. Therefore, this is called as precision rectifiers. So, there are two types of precision rectifier that is half wave and full wave based on the signal we are connecting to the inverting or non-inverting terminal we have the types as inverting half wave rectifier or non-inverting half wave rectifier. Figure shows the circuit diagram for precision rectifier that is half wave rectifier where the diode is connected in the feedback path and signal is applied to the non-inverting input of the opamp. So, it is called as non-inverting half wave rectifier. As you know you are connecting the signal to the non-inverting input when input voltage is greater than 0 that is positive half cycle then diode D1 gets conduct. When diode D1 get conducts we can say it is act as a short circuit. So, as input signal increases output signal will also increase. So, in this way we will get this transfer characteristics of the half wave rectifier. In the negative half cycle what happens diode will not conduct as negative signal is at the positive terminal of the opamp. So, diode D1 will be reverse biased and therefore, we will get 0 voltage at its output. So, what will be the equation and the waveforms for precision half wave rectifier during positive half cycle as D1 conducts we will get the signal same as the input signal and during negative half cycle D D1 not conducts therefore, you will get the 0 over here. So, this is the equation that is V out equal to plus V in and opamp is now acting as a unity gain buffer when negative half cycle is applied diode does not conduct and it acts as a ideal opamp switch therefore, output voltage will be 0. But here when you go for the higher frequencies sometimes it will not give you the precise rectification therefore, we will give one more diode connection in the same circuit. So, this is called as modified precision half wave rectifier where signal is connected to the inverting input of the opamp and non-inverting input terminal is grounded. So, you can assume now positive half cycle is there at the input signal D1 conducts, but diode D2 will not conduct because as you know this terminal is the inverting terminal and therefore, you will get the condition that is D1 is on, but D2 is totally off therefore, you will not receive any signal at the output of the opamp or output of the circuit. But in the other case where negative input is applied to the inverting input terminal at that time diode D1 will not conduct, but diode D2 conducts and therefore, you will receive the positive half cycle over here because as you know inverting input terminal will give you the phase shift in the signal. Therefore, you will get this positive half cycle for the negative half of the input signal. So, this is the waveform for the inverting precision half wave rectifier. Now the circuit for precision full wave rectifier is like this, input signal is connected to the inverting terminal of the opamp A1 and here both the diodes are connected. Now assume input signal is greater than 0 that is during positive half cycle. During positive half cycle diode D1 conducts, but D2 will not conduct. So, this complete part will be like a open circuit there will be no connection over here, but now you see this act as a short circuit. So, you will see here opamp A1 and A2 both are in the inverting amplifier configuration. So, at that time you can say both will give you the gain of minus 1. So, both are connected with the input signal. So, V out will be minus 1 into minus 1 into V in. So, output voltage is equal to plus V in over here. This is during positive half cycle. Now in the negative half cycle this will be the equivalent circuit. In the negative half cycle diode D1 will not conduct. So, it is like open circuit and diode D2 conducts. So, this path will be in the closed loop path. So, D1 is off, D2 is on. Now just see input signal is applied to the inverting input terminal and here current flowing through these three paths. So, we can apply case here to this node A because we are interested to find the voltage V at this terminal for the opamp A2 and that will decide the output voltage of this rectifier circuit. So, we can say I1 plus I2 plus I3 equal to 0. So, I1 will be V in minus 0 just apply the concept of virtual ground, non-inverting terminal is grounded. So, this terminal is also assumed to be at 0 volt. So, this is V in minus 0 divided by R. See V minus 0 divided by R as this terminal is 0 we can say this voltage is also 0. So, next is V minus 0 divided by 2R. Just see here in the previous case these two registers are connected in series when D1 is open circuit condition then we can say here these two will be forming the value of 2R. Therefore, if you find the equation for V it will be like this it is minus 2 by 3 times the value of input voltage. Therefore, this is the amplifier closed loop configuration. So, it is gain as you know 1 plus R by R1 that is 1 plus Rf is the feedback resistor R divided by R1 that is at the input terminal that is 2R. So, 1 plus R by 2R into V, but when you put the value of V. So, that will be 2R plus minus 2 by 3 times V in. So, here this comes 3 by 2 and this comes minus 2 by 3 that will get cancel out. So, output voltage is equal to negative of the input signal, but now see we are dealing with the negative cycle. Therefore, when input is negative over here this negative and this negative comes positive over here. Therefore, output voltage is positive for the negative half cycle. Thus we will get this waveform for the precision full wave rectifier that is in both the half cycles we will obtain the positive voltage over here, but if you change the directions of diode over here we will get the negative signal at the output. We can write and sketch the waveforms for the transfer characteristics of precision full wave rectifier. So, as we have seen the transfer characteristics for half wave rectifier thus pause this video and sketch the transfer characteristics for precision full wave rectifier. Yes and you will get the linear relationship between input and output voltage for positive as well as in the negative half cycle. Thus this will be the transfer characteristics for full wave rectifier circuit. These are the references. Thank you.