Tutorial: Mechanic – electrician Topic: Electronics II. class Operational Amplifiers: Non-Inverting Amplifiers – Part 2 – Derivations Prepared by: Ing. Jaroslav Bernkopf Projekt Anglicky v odborných předmětech, CZ.1.07/1.3.09/ je spolufinancován Evropským sociálním fondem a státním rozpočtem České republiky.

Let‘s 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

Non-Inverting Amplifiers – Part 2 - Derivations Operational Amplifiers 3 V1 = +1 V V+ V- +1 V V R1 = 1 V I R1 = 1 mA

Can this current flow from the input V-? No, it can‘t, 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

The current of 1 mA will create a voltage drop across the resistor R2. We can calculate it using the Ohm‘s 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

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

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

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

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

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

V+ V- Non-Inverting Amplifiers – Part 2 - Derivations Operational Amplifiers V V1 = +1 V V R1 = 1 V I R1 = 1 mA I R2 = 1 mA V R2 = 10 V V2 = +11 V

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 = 47kΩ Voltage gain A v = 34 Use the conception shown in the figure below. V+ V-

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 kΩ. V+ V- R i = ∞ R in = ∞

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 = 47kΩ. V+ V- R in = 47k

Non-Inverting Amplifiers – Part 2 - Derivations Operational Amplifiers 15 The values of R1 and R2 are not given. Let‘s choose the resistance of R1 = 1kΩ. Then we will calculate the value of R2. V+ V- 1k

Non-Inverting Amplifiers – Part 2 - Derivations Operational Amplifiers 16 The resistance of R2 will be 33 kΩ. V+ V- R in = 47k 1k 33k

Non-Inverting Amplifiers – Part 2 - Derivations Operational Amplifiers 17  