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**640 251 Instrumentation for Scientists**

Lecture 9 Operational Amplifier Circuits Inverting Amplifier Non-Inverting Amplifier Instrumentation Amplifier Electro-Cardiogram Amplifier Geoff Taylor & Paul Main

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**Operational Amplifiers (1)**

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**Ideal Operational Amplifiers (2)**

To simplify design calculations, the following characteristics are assumed for an ideal operational amplifier (abbreviated op. amp.): Open-loop gain = infinity Input impedance Rd = infinity Output impedance Ro = 0 Bandwidth = infinity (infinite frequency response) vo = 0 when V1 = V2 (no offset voltage)

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**Ideal Operational Amplifiers (3)**

Rule 1. When the op amp is in the linear range the two inputs are at the same voltage. Rule 2. No current flows into either terminal of the op amp.

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Inverting Amplifier Inverting Amplifier Vo = - (Rf / Ri) Vi

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**Non Inverting Amplifier**

Vo = Vi . (Rf + Ri)/(Ri)

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**Differential Amplifier**

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**Instrumentation Amplifier**

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**Instrumentation Amplifier Analysis 1**

First Stage: In this example R2=R3=10K Using Superposition Step 1: Set V2 = 0 => V+ = V1(R2+R1)/R1 = 11 V1 V- = –V1(R3/R1+R2) = -10 V1 Step 2: Set V1 = 0 => V+ = –V2(R2/R1+R3)= -10 V2 V- = V2(R2+R1)/R1 = 11 V2 Common Mode Transfer Function: Set V1 = V2. V+ = 11V1 – 10 V2 = V1 V- = 11V2 – 10 V1 = V2 Differential Transfer Function: V+ - V- = 21 (V1 – V2)

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**Instrumentation Amplifier Analysis 2**

Second Stage – Differential Amplifier VOut = (V+ - V-) Rf/Ri VOut = 10 (V+ - V-) = 210 (V1 – V2) Providing both V1 & V2 remain within the linear input & output range of the op amp. (typically a volt less than +15V V power supply range)

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**Instrumentation Amplifier Features**

The instrumentation amplifier is unique because it can reject a signal such as 50-Hz mains noise that is common to both inputs. The input impedance is 2 x input impedance of the op amp. For a FET input op amp – input resistance is close to infinity. The insulating gate oxide layer can be damaged by high voltages, so some protection may be required.

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**Instrumentation Amplifier CMRR**

The equation for the differential amplifier shows that if the two inputs are driven by the same voltage source (common-mode voltage = CMV = V1 = V2) then Vo = 0 If differential voltage gain (DG) is equal to Rf/Ri. In practice the instrumentation amplifier cannot perfectly reject the common-mode voltage. A quantitative measure of the ability of the differential amplifier to reject common-mode voltage is called the common-mode rejection ratio (CMRR). Typical Values are 100 to or 40dB to 80dB.

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**Instrumentation Amplifier CMRR**

Common Mode Rejection Ratio (CMRR) = Differential Mode Gain / Common Mode Gain Often expressed as a ratio or in dB

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**Electro Cardiogram Amplifier**

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