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Slide 2 Tutorial: Mechanic electrician Topic: Electronics II. class Operational Amplifiers: Non-Inverting Amplifiers Part 2 Derivations Prepared by: Ing. Jaroslav Bernkopf Projekt Anglicky v odbornch pedmtech, CZ.1.07/1.3.09/04.0002 je spolufinancovn Evropskm socilnm fondem a sttnm rozpotem esk republiky. Slide 3 Lets apply a voltage V1 of +1 V to the input of the amplifier in the figure. The voltage difference between the inputs V+ and V- is zero. This implies that the voltage on the input V- is the same as the input voltage, i.e. +1 V. This voltage will cause a current to flow through the resistor R1. What will this current be? Non-Inverting Amplifiers Part 2 - Derivations Operational Amplifiers 2 V+ V- +1 V V1 = +1 V Slide 4 Non-Inverting Amplifiers Part 2 - Derivations Operational Amplifiers 3 V1 = +1 V V+ V- +1 V V R1 = 1 V I R1 = 1 mA Slide 5 Can this current flow from the input V-? No, it cant, because as we know the input resistance of an op amp is infinite the input current of an op amp is zero So the current of the resistor R1 has to flow through R2. Non-Inverting Amplifiers Part 2 - Derivations Operational Amplifiers 4 V+ V- +1 V V1 = +1 V V R1 = 1 V I R1 = 1 mA I R2 = 1 mA Slide 6 The current of 1 mA will create a voltage drop across the resistor R2. We can calculate it using the Ohms law: V R2 = I R2 * R2 V R2 = 1mA * 10k V R2 = 10 V Non-Inverting Amplifiers Part 2 - Derivations Operational Amplifiers 5 V+ V- +1 V V1 = +1 V V R1 = 1 V I R1 = 1 mA I R2 = 1 mA V R2 = 10 V Slide 7 What is the value and the polarity of the output voltage? The upper end of R1 is positive with respect to the ground. We can draw a small plus sign to the upper end of R1, a minus sign to its lower end. The current through R2 is the same as the current through R1: It flows from above to below. We can draw the same plus and minus signs to the ends of R2. Non-Inverting Amplifiers Part 2 - Derivations Operational Amplifiers 6 V+ V- +1 V V1 = +1 V V R1 = 1 V I R1 = 1 mA I R2 = 1 mA V R2 = 10 V + - + - Slide 8 The output voltage consists of the sum of two individual resistor voltage drops. These voltage drops are in series, like two batteries. Their voltages add together. The total output voltage V2 is V2 = V R1 + V R2 V2 = 1 V + 10 V V2 = 11 V The output voltage is positive and its value is +11 V. Non-Inverting Amplifiers Part 2 - Derivations Operational Amplifiers 7 V+ V- +1 V V1 = +1 V V R1 = 1 V I R1 = 1 mA I R2 = 1 mA V R2 = 10 V + - + - V2 = +11 V Slide 9 What is the voltage gain? As you can see, the amplifier makes eleven volts out of one volt positive output voltage out of positive input voltage Its voltage gain must be +11. Non-Inverting Amplifiers Part 2 - Derivations Operational Amplifiers 8 V+ V- +1 V V1 = +1 V V R1 = 1 V I R1 = 1 mA I R2 = 1 mA V R2 = 10 V + - + - V2 = +11 V Slide 10 Look at the voltages and at the values of the resistors: Do the values look so similar just by accident? No, it is no accident. Non-Inverting Amplifiers Part 2 - Derivations Operational Amplifiers 9 V+ V- +1 V V1 = +1 V V R1 = 1 V I R1 = 1 mA I R2 = 1 mA V R2 = 10 V + - + - V2 = +11 V Slide 11 Non-Inverting Amplifiers Part 2 - Derivations Operational Amplifiers 10 V+ V- +1 V V1 = +1 V V R1 = 1 V I R1 = 1 mA I R2 = 1 mA V R2 = 10 V + - + - V2 = +11 V Slide 12 V+ V- Non-Inverting Amplifiers Part 2 - Derivations Operational Amplifiers 11 +1 V V1 = +1 V V R1 = 1 V I R1 = 1 mA I R2 = 1 mA V R2 = 10 V + - + - V2 = +11 V Slide 13 Non-Inverting Amplifiers Part 2 - Derivations Operational Amplifiers 12 Construct the first stage of a preamplifier for record players. The preamplifier should have the following features: Input resistance R in = 47k Voltage gain A v = 34 Use the conception shown in the figure below. V+ V- Slide 14 Non-Inverting Amplifiers Part 2 - Derivations Operational Amplifiers 13 The input resistance R in of a non-inverting amplifier is infinite. The desired input resistance R in of the preamplifier is 47 k. V+ V- R i = R in = Slide 15 Non-Inverting Amplifiers Part 2 - Derivations Operational Amplifiers 14 We must add another resistor R3 = 47k in parallel to achieve the desired input resistance R in = 47k. V+ V- R in = 47k Slide 16 Non-Inverting Amplifiers Part 2 - Derivations Operational Amplifiers 15 The values of R1 and R2 are not given. Lets choose the resistance of R1 = 1k. Then we will calculate the value of R2. V+ V- 1k Slide 17 Non-Inverting Amplifiers Part 2 - Derivations Operational Amplifiers 16 The resistance of R2 will be 33 k. V+ V- R in = 47k 1k 33k Slide 18 Non-Inverting Amplifiers Part 2 - Derivations Operational Amplifiers 17 http://www.wikipedia.com http://www.wikipedia.com http://www.thefreedictionary.com http://www.thefreedictionary.com