 Hello everyone, welcome to lecture on voltage series feedback amplifier. At the end of this lecture, students will be able to identify voltage series feedback amplifier, also able to calculate different parameters of it. Now before starting with the actual session, let's pause the video and think about what is the open loop gain of opamp. The equation is nothing but A equals to V0 upon VID, where A is nothing but the open loop gain, V0 is nothing but the output voltage and VID is nothing but the difference input voltages applied at the pin number 2 and 3 of the opamp. Now let's see voltage series feedback amplifier. Figure 1 shows the voltage series feedback amplifiers. If you see there are two parts, first one is a nothing but the opamp which is denoted by A and second is nothing but the feedback circuit which is composed of RF and R1. It is also known as a non-inverting amplifier with the feedback. Why it is called non-inverting amplifier with the feedback? If you observe the figure, you can see that VIN is applied to the non-inverting terminal of the opamp and the feedback circuit is used. So that's why it is called as a non-inverting amplifier with the feedback. It is also called as a closed loop amplifier. Now if you see the feedback circuit is composed of the RF and R1. Input signal drives the non-inverting terminal of the opamp and fraction of output voltage is then again used as a input to the inverting terminal of the opamp. Now let's see the different parameters of opamp one by one. First it is nothing but the negative feedback. It is called as a negative feedback. Why it is called as a negative feedback? Because whatever the output voltage you are using as a input to the feedback circuit and an output of the feedback circuit is connected as a input to the inverting terminal of opamp. Due to this the overall input applied to the opamp degrades. So that's why the input voltage is less as compared to previous one. So that's why it is called negative feedback. If you apply the Kritschoff's voltage equation for input loop from figure 1 you will get the equation VID equals to VIN minus VF. So from this equation you can see that voltage that is feedback voltage VF you always oppose this input voltage. It is called as a negative feedback. Next parameter is nothing but the closed loop voltage gain that is AF. So to get equation for the AF you have equation for the feedback circuit that is nothing but the beta. Beta equals to VO VF upon VO which is nothing but the R1 upon R1 plus RF. So from that you can see that VO equals to A into VV1 minus V2 where A is nothing but the gain of the opamp in open loop and V1 and V2 are nothing but the two inputs of the opamp. So you have the equation for V1 and V2 that is VIN and VF. So you can write A into VIN minus beta V0. Beta V0 is nothing but the value for the VF. So from that you can write VO equals to 1 plus A beta equals to A into VIN. So from that you can get VO upon VIN equals to A divided by 1 plus A beta. So A beta product value is much more greater than 1. So what that 1 plus A beta becomes nearly equals to A beta. So VO upon VIN equals to A upon A beta. So A gate cancels so that becomes 1 upon beta. So from that you can write the equation for AF that is nothing but the gain of the closed loop opamp is equals to 1 plus RF upon R1 means that the closed loop gain is no longer depend on the gain of the opamp. It depends on the feedback of voltage divider circuit. Next parameter is a difference input voltage ideally 0. How you can say that the difference voltage ideally 0? So for that we know that the open loop gain of opamp is nothing but the A equals to VO upon VID. Since the value of A is much much larger ideally so that VID nearly equals to 0. So that becomes V1 nearly approximately equals to V2. So from that you can say that V1 equals to VIN, V2 is equals to VF that is a feedback output voltage equals to in the bracket R1 upon R1 plus RF into VO. Since V1 equals to V2 so you can write final equation for AF equals to VO upon VIN equals to 1 plus RF upon R1 means that voltage at a non-inverting terminal of the opamp is approximately equals to the voltage at the inverting terminal of the opamp in case when A is having value more larger. Next parameter is a input resistance with a feedback. Figure 2 shows the derivation of input resistance with feedback. In that figure you can see that RI is nothing but the input resistance of opamp in open loop condition and RIF is nothing but the input resistance of opamp with a feedback. So from that you can write the equation for RIF that is RIF equals to VIN minus IN. So for IN you can have the you can write a equation from the figure that IN is nothing but the VID divided by RIF. So putting the value of IN in the equation you will get the equation for RIF. So RIF equals to VIN upon VID upon RIF. So for VID you have equation that is V0 upon A and for VO you have the equation that A divided by 1 plus A beta into VIN. So therefore by putting all the values of VID and VO in the above equation you can write the equation for RIF equals to A RI into VIN divided by A VIN divided by 1 plus A beta. So by solving this or rearranging this equation you will get the final equation for RIF that is a input resistance with feedback equals to nothing but RIF into bracket 1 plus A beta means RI it is a 1 plus A beta times of the input resistance of a open loop opamp. Next parameter is a output resistance with feedback. So figure 3 shows the derivation of output resistance with feedback. So from figure you can write the equation for ROF that is an output resistance with feedback equals to VO upon IO where VO is nothing but the output voltage and IO is nothing but the current flowing through the RO. By applying the Kirchhoff's current equation at the output node you can write a equation IO equals to IO plus AB means that current flowing into the node equals to current flowing out of the node that is IO plus AB where IO is nothing but the current flowing through the RO resistor that is output resistor and IB is nothing but the current flowing through the feedback circuit. So you can write that RF plus RO1 that is a element of the feedback circuit in parallel with the RI that is input resistance having a value much more than the output resistance RO means that the current flowing through the RO that is a I is much more greater than current flowing through the feedback circuit that is a IB. Therefore you can write a final equation for IO above equation is I nearly equals to I. So by applying Kirchhoff's voltage equation at the output loop we can write VO minus RO IO minus A VID equals to 0 but VID equals nothing but the input difference voltage V1 minus V2 in this case V1 is connected to ground so that becomes 0. So minus beta VO is final value for the VID so VID equals to minus beta VO. So by rearranging the equation you can write the equation for IO. IO equals to VO minus A VID divided by RO. So therefore ROF is nothing but the VO upon IO equals to RO divided by 1 plus A beta is the final value of output resistance with feedback. Next parameter is a bandwidth with feedback. Bandwidth is nothing but the band of frequencies over which the gain remains constant. In case opamp 741C from this figure 4 you can see that the gain is remain constant from the 5 hertz to 1 megahertz. At 5 hertz the gain is nothing but the 2 lakhs and at 1 megahertz it's 1. So the gain bandwidth product if you see 5 into 1 2 lakhs gives 1 megahertz and at 1 megahertz frequency the gain is 1. So gain bandwidth product is going to be remain constant. Also for 741C opam I see it has two points one is a break frequency and second one is a unity gain bandwidth. Break frequency is nothing but the frequency at which the gain is going down 3 dB at maximum gain and unity gain bandwidth is nothing but the frequency at which you are having gain value is 1. Now for open loop opamp your UGB equals to A into FO where A is open loop voltage gain and FO is nothing but the break frequency. For closed loop opamp UGB is nothing but the AF into FF where AF is our closed loop voltage gain and FF is nothing but the bandwidth with feedback. So by using these two equation you can write AO into FO equals to AF into FF. So by rearrange these you can get FF equals to A into FO divided by AF. But for non-inverting amplifier with feedback AF is nothing but the A divided by 1 plus A beta. So by putting a value of AF you can write the final equation for FF equals to A into F0 divided by A divided by 1 plus A beta. By solving this you will get FF is nothing but equals to F0 into 1 plus A beta. These are the references. Thank you.