Module-1 (Sub Code: MPYC-205 Sub: ELECTRONICS) Applied Physics 2 years M.Sc Syllabus: Operational amplifiers: The differential amplifiers, integral amplifier, rejection of common mode signals. The operational amplifier input and output impedances, application of operational amplifiers, unit gain bffuer, summing, integrating and differentiating amplifiers, comparators and logarithmic amplifiers Content ➢ ➢ ➢ ➢ ➢ ➢ The ideal Op-Amp, Differential Amplifier CMRR, Inverting and non-inverting configurations, Difference amplifier, Application of Op-Amp (Instrumentation amplifier, Summing amplifier, ➢ Integrator and Differentiator).
Operational Amplifiers Operational amplifiers are direct coupled high gain amplifiers. Figure 2.1 a basic OPAMP Figure 2.2 opamp with dual supply Ideal characteristics of op-amp as under• Infinite input impedance, (no current flows inside the op-amp). • Zero output impedance (due to output as a ideal voltage source) • Zero common-mode gain or, equivalently, infinite common-mode rejection (for any common inputs applied 𝑣𝐼𝑑 = 𝑣2 − 𝑣1 = 0, 𝑣𝑜 = 𝐴𝑣𝐼𝑑 = 0) • Infinite open-loop gain A (direct coupled with low signals) • Infinite bandwidth (can amplify signal of all frequencies) Theory of OPAMP An amplifier has an input port and an output port. (A port consists of two terminals, one of which is usually connected to the ground node.) In a linear amplifier, the output signal = A input signal, where A is the amplification factor or “gain.” Depending on the nature of the input and output signals, we can have four types of amplifier gain: voltage gain (voltage out / voltage in), current gain (current out / current in), transresistance (voltage out / current in) and
transconductance (current out / voltage in). Since most op-amps are used as voltage-tovoltage amplifiers, we will limit the discussion here to this type of amplifier. The circuit model of an amplifier is shown in Figure 1 (center dashed box, with an input port and an output port). The input port plays a passive role, producing no voltage of its own, and is modeled by a resistive element Ri called the input resistance. The output port is modeled by a dependent voltage source AVi in series with the output resistance Ro, where Vi is the potential difference between the input port terminals. Figure 1 shows a complete amplifier circuit, which consists of an input voltage source Vs in series with the source resistance Rs, and an output “load” resistance RL. From this figure, it can be seen that we have voltagedivider circuits at both the input port and the output port of the amplifier. This requires us to re-calculate Vi and Vo whenever a different source and/or load is used: Ri Vi = Rs + Ri Vs RL AVi Vo = Ro + RL SOURCE _ INPUT PORT Vi VS Ro + Ri (2) + OUTPUT PORT RS (1) AVi Vo AMPLIFIER RL _ LOAD Figure 1: Circuit model of an amplifier circuit. Figure 2.3 Equivalent circuit of the ideal op amp Differential inputs of Opamp are given as-- 𝑣𝐼𝑑 = 𝑣2 − 𝑣1 Common inputs of an OPamp is given as- 𝑣𝐼𝑐𝑚 = V1 in terms of VId & VIcm 1 (𝑣2 2 𝑣1 = 𝑣𝐼𝑑 − 𝑣𝐼𝑐𝑚 ⁄2 + 𝑣1 )
𝑣2 = 𝑣𝐼𝑑 + 𝑣𝐼𝑐𝑚 ⁄2 V2 in terms of VId & VIcm Inverting configuration • • • • • Input is given at inverting terminal of opamp Feedback resistor is connected between output and inverting terminal This is said to give a negative feedback from output. Open-loop gain of opamp is reduced by this feedback. Resulting gain is called closed-loop gain of opamp Figure 2.4 inverting configuration of opamp For a finite output can be written in terms if open-loop gain 𝑣2 − 𝑣1 = 𝑣2 = 𝑣1 𝑣𝑜 𝐴 = 0, for 𝐴 = ∞ called as virtual short-circuit Since V2 = 0, V1 = V2 = 0 called as virtual ground Although terminal 1 is not connected to ground it is virtually ground due to short circuit effect. For the input voltage vI 𝑣𝐼 − 𝑣1 𝑖1 = 𝑅1 𝑣𝐼 𝑖1 = 𝑅1 For output 𝑣𝑜 = 𝑣1 − 𝑖1 𝑅2 𝑣𝑜 = 0 − 𝑖1 𝑅2 𝑣𝑜 = − 𝑣𝐼 𝑅 𝑅1 2 For closed loop gain G can be written by 𝐺= For a finite open loop gain 𝑣𝑜 𝑅2 =− 𝑣𝐼 𝑅1