Snmek 1

Anglicky v odbornch pedmtech"Support of teaching technical subjects in EnglishTutorial: Mechanic electrician

Topic: Electronics II. class Operational Amplifiers: Non-Inverting Amplifiers Part 2 DerivationsPrepared by: Ing. Jaroslav Bernkopf

Projekt Anglicky v odbornch pedmtech, CZ.1.07/1.3.09/04.0002je spolufinancovn Evropskm socilnm fondem a sttnm rozpotem esk republiky.

1Lets 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 - DerivationsOperational Amplifiers2Voltage Gain

V+V-+1 VV1 = +1 V

2Non-Inverting Amplifiers Part 2 - DerivationsOperational Amplifiers3Voltage Gain

V1 = +1 VV+V-+1 VVR1 = 1 VIR1 = 1 mA

3Can this current flow from the input V-?No, it cant, because as we know the input resistance of an op amp is infinitethe 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 - DerivationsOperational Amplifiers4Voltage Gain

V+V-+1 VV1 = +1 VVR1 = 1 VIR1 = 1 mAIR2 = 1 mA

4The current of 1 mA will create a voltage drop across the resistor R2.We can calculate it using the Ohms law:

VR2 = IR2 * R2VR2 = 1mA * 10kVR2 = 10 V

Non-Inverting Amplifiers Part 2 - DerivationsOperational Amplifiers5Voltage Gain

V+V-+1 VV1 = +1 VVR1 = 1 VIR1 = 1 mAIR2 = 1 mAVR2 = 10 V

5What 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 - DerivationsOperational Amplifiers6Voltage Gain

V+V-+1 VV1 = +1 VVR1 = 1 VIR1 = 1 mAIR2 = 1 mAVR2 = 10 V+-+-

6The 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 isV2 = VR1 + VR2V2 = 1 V + 10 V V2 = 11 V

The output voltage is positive and its value is +11 V.Non-Inverting Amplifiers Part 2 - DerivationsOperational Amplifiers7Voltage Gain

V+V-+1 VV1 = +1 VVR1 = 1 VIR1 = 1 mAIR2 = 1 mAVR2 = 10 V+-+-V2 = +11 V

7What is the voltage gain?

As you can see, the amplifier makes eleven volts out of one voltpositive output voltage out of positive input voltage

Its voltage gain must be +11.Non-Inverting Amplifiers Part 2 - DerivationsOperational Amplifiers8Voltage Gain

V+V-+1 VV1 = +1 VVR1 = 1 VIR1 = 1 mAIR2 = 1 mAVR2 = 10 V+-+-V2 = +11 V

8Look 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 - DerivationsOperational Amplifiers9Voltage Gain

V+V-+1 VV1 = +1 VVR1 = 1 VIR1 = 1 mAIR2 = 1 mAVR2 = 10 V+-+-V2 = +11 V

9Non-Inverting Amplifiers Part 2 - DerivationsOperational Amplifiers10Voltage Gain

V+V-+1 VV1 = +1 VVR1 = 1 VIR1 = 1 mAIR2 = 1 mAVR2 = 10 V+-+-V2 = +11 V

10

V+V-Non-Inverting Amplifiers Part 2 - DerivationsOperational Amplifiers11Voltage Gain+1 VV1 = +1 VVR1 = 1 VIR1 = 1 mAIR2 = 1 mAVR2 = 10 V+-+-V2 = +11 V

11Non-Inverting Amplifiers Part 2 - DerivationsOperational Amplifiers12TaskConstruct the first stage of a preamplifier for record players.

The preamplifier should have the following features:Input resistance Rin = 47kVoltage gain Av = 34

Use the conception shown in the figure below.

V+V-

12Non-Inverting Amplifiers Part 2 - DerivationsOperational Amplifiers13SolutionThe input resistance Rin of a non-inverting amplifier is infinite.

The desired input resistance Rin of the preamplifier is 47 k.

V+V-Ri = Rin =

13

Non-Inverting Amplifiers Part 2 - DerivationsOperational Amplifiers14SolutionWe must add another resistor R3 = 47k in parallel to achieve the desired input resistance Rin = 47k.

V+V-Rin = 47k

14

Non-Inverting Amplifiers Part 2 - DerivationsOperational Amplifiers15SolutionThe 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

15Non-Inverting Amplifiers Part 2 - DerivationsOperational Amplifiers16SolutionThe resistance of R2 will be 33 k.

V+V-Rin = 47k1k1k33k

16Non-Inverting Amplifiers Part 2 - DerivationsOperational Amplifiers17Referenceshttp://www.wikipedia.comhttp://www.thefreedictionary.com

17