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
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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 =
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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
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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
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